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  • 1.
    Anandan, Jeeva S.
    et al.
    Dept. of Physics and Astronomy, Univ. of South Carolina, USA .
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Pati, Arun K.
    Institute of Physics, Bhubaneswar, India.
    Ekert, Artur
    Centre for Quantum Computation, Univ. of Oxford, UK .
    Ericsson, Marie
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Oi, Daniel K.L.
    Centre for Quantum Computation, Univ. of Oxford, UK .
    Vedral, Vlatko
    Optics Section, Blackett Laboratory Imperial College, UK.
    Reply to Comment on `Geometric phases for mixed states in interferometry'2002In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 89, p. 268902-Article in journal (Other academic)
    Abstract [en]

    The only difference between Bhandari's viewpoint and ours [Phys. Rev. Lett. 85, 2845 (2000)] is that our phase is defined modulo 2π, whereas Bhandari argues that two phases that differ by 2π n, n integer, may be distinguished experimentally in a history-dependent manner. (Reply to the Comment in Phys. Rev. Lett. 89, 268901 (2001) by R. Bhandari.)

  • 2.
    Andersson, Ole
    et al.
    Dept. of Physics, Stockholm University, Sweden.
    Bengtsson, Ingemar
    Dept. of Physics, Stockholm University, Sweden.
    Ericsson, Marie
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry. Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy. Uppsala universitet.
    Geometric phases for mixed states of the Kitaev chain2016In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 374, no 2069, article id 20150231Article in journal (Refereed)
    Abstract [en]

    The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyze the intricate behaviour of Uhlmann’s geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyze the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation. 

  • 3.
    Azimi Mousolou, Vahid
    et al.
    School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
    Canali, Carlo M.
    School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Non-Abelian off-diagonal geometric phases in nano-engineered four-qubit systems2013In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 103, no 6, p. 60011-Article in journal (Refereed)
    Abstract [en]

    The concept of off-diagonal geometric phase (GP) has been introduced in order to recover interference information about the geometry of quantal evolution where the standard GPs are not well-defined. In this Letter, we propose a physical setting for realizing non-Abelian off- diagonal GPs. The proposed non-Abelian off-diagonal GPs can be implemented in a cyclic chain of four qubits with controllable nearest-neighbor interactions. Our proposal seems to be within reach in various nano-engineered systems and therefore opens up for first experimental test of the non-Abelian off-diagonal GP. 

  • 4.
    Azimi Mousolou, Vahid
    et al.
    School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
    Canali, Carlo M.
    School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    Non-Abelian quantum holonomy of hydrogen-like atoms2011In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 84, no 3, article id 032111Article in journal (Refereed)
    Abstract [en]

    We study the Uhlmann holonomy [Rep. Math. Phys. 24, 229 (1986)] of quantum states for hydrogen-like atoms, where the intrinsic spin and orbital angular momentum are coupled by the spin-orbit interaction and subject to a slowly varying magnetic field. We show that the holonomy for the orbital angular momentum and spin subsystems is non-Abelian, while the holonomy of the whole system is Abelian. Quantum entanglement in the states of the whole system is crucially related to the non-Abelian gauge structure of the subsystems. We analyze the phase of the Wilson loop variable associated with the Uhlmann holonomy, and find a relation between the phase of the whole system with corresponding marginal phases. Based on the result for the model system we provide evidence that the phase of the Wilson loop variable and the mixed-state geometric phase [Phys. Rev. Lett. 85, 2845 (2000)] are in general inequivalent.

  • 5.
    Azimi Mousolou, Vahid
    et al.
    Dept. of Mathematics, Faculty of Science, Univ. of Isfahan, Iran.
    Canali, Carlo M.
    School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Spin-electric Berry phase shift in triangular molecular magnets2016In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 94, no 23, article id 235423Article in journal (Refereed)
    Abstract [en]

    We propose a Berry phase effect on the chiral degrees of freedom of a triangular magnetic molecule. The phase is induced by adiabatically varying an external electric field in the plane of the molecule via a spin-electric coupling mechanism present in these frustrated magnetic molecules. The Berry phase effect depends on spin-orbit interaction splitting and on the electric dipole moment. By varying the amplitude of the applied electric field, the Berry phase difference between the two spin states can take any arbitrary value between zero and π, which can be measured as a phase shift between the two chiral states by using spin-echo techniques. Our result can be used to realize an electric-field-induced geometric phase-shift gate acting on a chiral qubit encoded in the ground-state manifold of the triangular magnetic molecule.

  • 6.
    Azimi Mousolou, Vahid
    et al.
    School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
    Canali, Carlo M.
    School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry. Centre for Quantum Technologies, NUS, Singapore.
    Unifying Geometric Entanglement and Geometric Phase in a Quantum Phase Transition2013In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 88, no 1, p. 012310-Article in journal (Refereed)
    Abstract [en]

    Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are respectively the real and imaginary parts of a complex-valued geometric entanglement, which can be investigated in typical quantum interferometry experiments. We argue that the singular behavior of the complex-value geometric entanglement at a quantum critical point is a characteristic of any quantum phase transition, by showing that the underlying mechanism is the occurrence of level crossings associated with the underlying Hamiltonian.

  • 7.
    Azimi Mousolou, Vahid
    et al.
    School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
    Canali, Carlo M.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Theoretical Chemistry. School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Universal Non-adiabatic Holonomic Gates in Quantum Dots and Single-Molecule Magnets2014In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 16, article id 013029Article in journal (Refereed)
    Abstract [en]

    Geometric manipulation of a quantum system offers a method for fast, universal, and robust quantum information processing. Here, we propose a scheme for universal all-geometric quantum computation using non-adiabatic quantum holonomies. We propose three different realizations of the scheme based on an unconventional use of quantum dot and single-molecule magnet devices, which offer promising scalability and robust efficiency. 

  • 8.
    Azimi Mousolou, Vahid
    et al.
    Dept. of Mathematics, Faculty of Science, Univ. of Isfahan, Iran.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory. Uppsala universitet.
    Entangling power of holonomic gates in atom-cavity systems2018In: Article in journal (Other (popular science, discussion, etc.))
    Abstract [en]

    Our goal is to provide a new approach to the construction of geometry-induced entanglement between a pair of Λ type atoms in a system consists of N identical atoms by means of nonadiabatic quantum holonomies. By employing the quantum Zeno effect, we introduce a tripod type interaction Hamiltonian between two selected atoms trapped in an optical cavity, which allows arbitrary geometric entangling power. This would be a substantial step toward resolving the feasibility of realizing universal nonadiabatic holonomic entangling two-qubit gates.

  • 9.
    Azimi Mousolou, Vahid
    et al.
    School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Non-Abelian geometric phases in a system of coupled quantum bits2014In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 89, no 2, p. 022117-Article in journal (Refereed)
    Abstract [en]

    A common strategy to measure the Abelian geometric phase for a qubit is to let it evolve along an `orange slice' shaped path connecting two antipodal points on the Bloch sphere by two different semi-great circles. Since the dynamical phases vanish for such paths, this allows for direct interference measurement of the geometric phase. Here, we generalize the orange slice setting to the non-Abelian case. The proposed method to measure the non-Abelian geometric phase can be implemented in a cyclic chain of four qubits with controllable nearest-neighbor interactions.

  • 10.
    Bengtson, Charlotta
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    The role of quantum coherence in dimer and trimer excitation energy transfer2017In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 19, article id 113015Article in journal (Refereed)
    Abstract [en]

    Recent progress in resource theory of quantum coherence has resulted in measures to quantify coherence in quantum systems. Especially, the l1-norm and relative entropy of coherence have been shown to be proper quantifiers of coherence and have been used to investigate coherence properties in different operational tasks. Since long-lasting quantum coherence has been experimentally confirmed in a number of photosynthetic complexes, it has been debated if and how coherence is connected to the known efficiency of population transfer in such systems. In this study, we investigate quantitatively the relationship between coherence, as quantified by l1 norm and relative entropy of coherence, and efficiency, as quantified by fidelity, for population transfer between end-sites in a network of two-level quantum systems. In particular, we use the coherence averaged over the duration of the population transfer in order to carry out a quantitative comparision between coherence and fidelity. Our results show that although coherence is a necessary requirement for population transfer, there is no unique relation between coherence and the efficiency of the transfer process.

  • 11.
    Bengtson, Charlotta
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Stenrup, Michael
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Quantum nonlocality in the excitation energy transfer in the Fenna-Matthews-Olson complex2016In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 116, p. 1763-1771Article in journal (Refereed)
    Abstract [en]

    The Fenna-Matthews-Olson (FMO) complex - a pigment protein complex involved in photosynthesis in green sulfur bacteria - is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger-than-entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs on the other hand is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems. 

  • 12.
    Brown, Harvey R.
    et al.
    Sub-Faculty of Philosophy, Oxford Univ., UK.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Bacciagaluppi, Guido
    Sub-Faculty of Philosophy, Oxford Univ., UK.
    Remarks on identical particles in de Broglie-Bohm theory1999In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 251, no 4, p. 229-235Article in journal (Refereed)
    Abstract [en]

    It is argued that the topological approach to the (anti-) symmetrisation condition for the quantum state of a collection of identical particles, defined in the "reduced" configuration space, is particularly natural from the perspective of de Broglie-Bohm pilot-wave theory.

  • 13.
    Carlsen, Henrik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Goscinski, Osvaldo
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Quantal trajectories for adiabatic and nonadiabatic regimes of vibronic systems1999In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 75, no 4-5, p. 409-416Article in journal (Refereed)
    Abstract [en]

    Exact and averaged nuclear pseudorotational quantal trajectories are compared for Various adiabatic and vibronic states of the Longuet-Higgins E x epsilon Jahn-Teller model. It is argued that the usual averaging over the electronic motion could be understood as being a consequence of ergodicity. The failure of the Born-Oppenheimer factorization to obey the ergodic hypothesis was examined. A quantitative separation of the electronic and nuclear time-scales is, nevertheless, achieved for all regimes. It is shown that the short-time deviations from the global "drift" of the electronic and nuclear motions are perfectly correlated.

  • 14.
    Ericsson, Marie
    et al.
    Centre for Quantum Computation, DAMTP, University of Cambridge, UK.
    Kult, David
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Åberg, Johan
    Centre for Quantum Computation, DAMTP, Cambridge, UK.
    Nodal free geometric phases: concept and application to geometric quantum computation2008In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 372, no 5, p. 596-599Article in journal (Refereed)
    Abstract [en]

    Nodal free geometric phases are the eigenvalues of the final member of a parallel transporting family of unitary operators. These phases are gauge invariant, always well defined, and can be measured interferometrically. Nodal free geometric phases can be used to construct various types of quantum phase gates.

  • 15.
    Ericsson, Marie
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Pati, Arun K.
    Institute of Physics, Bhubaneswar, India.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Brännlund, Johan
    SCFAB, Dept. of Physics, Stockholm Univ., Sweden.
    Oi, Daniel K.L.
    Centre for Quantum Computation, Clarendon Laboratory, University of Oxford, UK.
    Mixed state geometric phases, entangled systems, and local unitary transformations2003In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 91, no 9, p. 090405-Article in journal (Refereed)
    Abstract [en]

    The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution not only depends on the geometry of the path of the system alone but also on a constrained bi-local unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires uni-local transformations and is therefore essentially a property of the system alone.

  • 16.
    Ericsson, Marie
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Comment on `Detecting non-Abelian geometric phases with three-level Λ systems'2013In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 87, no 3, p. 036101-Article in journal (Refereed)
    Abstract [en]

    In their recent paper, Yan-Xiong Du {\it et al.} [Phys. Rev. A {\bf 84}, 034103 (2011)] claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned $\Lambda$ three-level system. They further propose a test to detect the non-commutative feature of this geometric phase. On the contrary, we show that the non-Abelian geometric phase picked up by the energy eigenstates of a $\Lambda$ system is trivial in the adiabatic approximation, while, in the exact treatment of the time evolution, this phase is very small and cannot be separated from the non-Abelian dynamical phase acquired along the path in parameter space.

  • 17.
    Ericsson, Marie
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Dlaczego kot Schrödingera laduje na czterech lapach2001In: Delta, ISSN 0137-3005, no 11, p. 1-Article in journal (Other (popular science, discussion, etc.))
  • 18.
    Ericsson, Marie
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Har vi redan skapat kvantdatorn?2015In: Forskning och Framsteg, no 10, p. 58-63Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    Vissa menar att kvantdatorn redan är verklighet, och syftar på en gåtfull låda som kallas D-wave. Men uppfyller den verkligen kraven? Frågan diskuteras livligt i forskarvärlden. Vad är egentligen en riktig kvantdator? Här hjälper Uppsalaforskarna Marie Ericsson och Erik Sjöqvist till att reda ut begreppen.  

  • 19.
    Ericsson, Marie
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Quantum computation using the Aharonov-Casher set up2002In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 303, no 1, p. 7-10Article in journal (Refereed)
    Abstract [en]

    It is argued that the Aharonov-Casher set up could be used as the basic building block for quantum computation. We demonstrate explicitly in this scenario one- and two-qubit phase shift gates that are fault tolerant to deformations of the path when encircling two sites of the computational system around each other.

  • 20.
    Ericsson, Marie
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Towards a quantum Hall effect for atoms using electric fields2002In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 65, no 1, p. 013607-Article in journal (Refereed)
    Abstract [en]

    An atomic analogue of Landau quantization based on the Aharonov-Casher (AC) interaction is developed. The effect provides a first step towards an atomic quantum Hall system using electric fields, which may be realized in a Bose-Einstein condensate.

  • 21.
    Ericsson, Marie
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Brännlund, Johan
    Stockholm University, SCFAB, Fysikum, Sweden .
    Oi, Daniel K.L.
    Centre for Quantum Computation, Clarendon Laboratory, University of Oxford, UK.
    Pati, Arun K.
    Institute of Physics, Bhubaneswar, India .
    Generalization of the geometric phase to completely positive maps2003In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 67, no 2, p. 020101(R)-Article in journal (Refereed)
    Abstract [en]

    We generalize the notion of relative phase to completely positive maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference effect is embodied in a set of interference patterns defined by flipping the environment state in one of the two paths. We show for the qubit that this structure gives rise to interesting additional information about the geometry of the evolution defined by the CP map.

  • 22.
    Ericsson, Marie
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Goscinski, Osvaldo
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Degree of electron-nuclear entanglement in the E x e Jahn-Teller system1999In: Proceedings of the XIV International Symposium on Electron-Phonon Dynamics and Jahn-Teller Effect: Erice, Italy, 7-13 July 1998 / [ed] G. Bevilacqua, L. Martinelli, N. Terzi, Singapore: World Scientific Publishing , 1999, p. 20-Conference paper (Other academic)
    Abstract [en]

    Jahn-Teller systems exhibit strong coupling between the electronic and nuclear degrees of freedom. We analyse how linear and quadratic coupling affect the electron-nuclear entanglement in the $E\otimes \epsilon$ system. A measure of quantum entanglement, recently developed by Shimony [Ann. New York Acad. Sci. 755, 675 (1995)], is used. States in the adiabatic regime with quadratic coupling are analysed. The electron-nuclear entanglement in vibronic states of the linear Exe model is calculated numerically. The physical significance of electron-nuclear entanglement is discussed in terms of reduction factors and magnetic vibrational circular dichroism.

  • 23.
    Eriksson, Karl-Erik
    et al.
    Division of Physical Resource Theory, Department of Space, Earth and Environment, Chalmers University of Technology, Göteborg, Sweden.
    Cederwall, Martin
    Division of Theoretical Physics, Department of Physics, Chalmers University of Technology, Göteborg, Sweden.
    Lindgren, Kristian
    Division of Physical Resource Theory, Department of Space, Earth and Environment, Chalmers University of Technology, Göteborg, Sweden .
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory. Uppsala universitet.
    Bifurcation in Quantum Measurement2017In: Article in journal (Other academic)
    Abstract [en]

    We present a generic model of (non-destructive) quantum measurement. It consists of two-level system μ interacting with a larger system A, in such a way that if μ is initially in one of the chosen basis states, it does not change but makes A change into a corresponding state (entanglement). The μA-interaction is described as a scattering process. Internal (unknown) variables of A may influence the transition amplitudes. It is assumed that the statistics of these variables is such that, in the mean, the μA-interaction is neutral with respect to the chosen basis states. It is then shown that, for a given initial state of μ, in the limit of a large system A, the statistics of the ensemble of available initial states leads to a bifurcation: those initial states of A that are efficient in leading to a final state, are divided into two separated subsets. For each of these subsets, μ ends up in one of the basis states. The probabilities in this branching confirm the Born rule.

  • 24.
    Filipp, Stefan
    et al.
    Atominstitut, Vienna, Austria.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Off-diagonal generalization of the mixed-state geometric phase2003In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 68, no 4, p. 042112-Article in journal (Refereed)
    Abstract [en]

    The concept of off-diagonal geometric phases for mixed quantal states in unitary evolution is developed. We show that these phases arise from three basic ideas: (1) fulfillment of quantum parallel transport of a complete basis, (2) a concept of mixed state orthogonality adapted to unitary evolution, and (3) a normalization condition. We provide a method for computing the off-diagonal mixed state phases to any order for unitarities that divide the parallel transported basis of Hilbert space into two parts: one part where each basis vector undergoes cyclic evolution and one part where all basis vectors are permuted among each other. We also demonstrate a purification based experimental procedure for the two lowest order mixed state phases and consider a physical scenario for a full characterization of the qubit mixed state geometric phases in terms of polarization-entangled photon pairs. An alternative second order off-diagonal mixed state geometric phase, which can be tested in single-particle experiments, is proposed.

  • 25.
    Filipp, Stefan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Off-diagonal geometric phases for mixed states2003In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 90, no 5, p. 050403-Article in journal (Refereed)
    Abstract [en]

    We extend the off-diagonal geometric phase [Phys. Rev. Lett. 85, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase [Phys. Rev. Lett. 85, 2845 (2000)]. Extension to higher dimensional Hilbert spaces is delineated. A physical scenario for the off-diagonal mixed state geometric phase in polarization-entangled two-photon interferometry is proposed.

  • 26.
    Filipp, Stefan
    et al.
    Atominstitut, Vienna, Austria .
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Off-diagonal quantum holonomy along density operators2005In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 342, no 3, p. 205-212Article in journal (Refereed)
    Abstract [en]

    Uhlmann's concept of quantum holonomy for paths of density operators is generalised to the off-diagonal case providing insight into the geometry of state space when the Uhlmann holonomy is undefined. Comparison with previous off-diagonal geometric phase definitions is carried out and an example comprising the transport of a Bell-state mixture is given.

  • 27.
    Friedenauer, Axel
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Noncyclic geometric quantum computation2003In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 67, no 2, p. 024303-Article in journal (Refereed)
    Abstract [en]

    Geometric quantum computation is extended to the noncyclic case. Adiabatic NMR implementations of geometric phase shift gates at any precession angle and their concomitant fault tolerance with respect to the amplitude of the oscillating field are analysed. Nonadiabatic one-qubit geometric quantum computation is considered from the noncyclic perspective, with particular emphasis on errors in precession angles.

  • 28.
    Garcia de Polavieja, Gonzalo
    et al.
    Physical and Theoretical Chemistry Laboratory, Oxford, UK.
    Sjöqvist, Erik
    Sub-Faculty of Philosophy, Oxford University, UK.
    Extending the quantal adiabatic theorem: Geometry of noncyclic motion1998In: American Journal of Physics, ISSN 0002-9505, E-ISSN 1943-2909, Vol. 66, no 5, p. 431-438Article in journal (Refereed)
    Abstract [en]

    We show that a noncyclic phase of geometric origin has to be included in the approximate adiabatic wave function. The adiabatic noncyclic geometric phase for systems exhibiting a conical intersection as well as for an Aharonov–Bohm situation is worked out in detail. A spin-1/2 experiment to measure the adiabatic noncyclic geometric phase is discussed. We also analyze some misconceptions in the literature and textbooks concerning noncyclic geometric phases.

  • 29.
    Gürkan, Nilhan
    et al.
    Department of Industrial Engineering, Gediz University, Menemen-Izmir, Turkey.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Realization of a holonomic quantum computer in a chain of three-level systems2015In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 379, no 47-48, p. 3050-3053Article in journal (Refereed)
    Abstract [en]

    Holonomic quantum computation is the idea to use non-Abelian geometric phases to implement universal quantum gates that are robust to fluctuations in control parameters. Here, we propose a compact design for a holonomic quantum computer based on coupled three-level systems. The scheme does not require adiabatic evolution and can be implemented in arrays of atoms or ions trapped in tailored standing wave potentials. 

  • 30.
    Gürkan, Nilhan
    et al.
    Department of Industrial Engineering, Gediz University, Menemen-Izmir, Turkey.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy. Uppsala universitet.
    Hessmo, Björn
    Centre for Quantum Technologies, NUS, Singapore.
    Grémaud, Benoit
    Centre for Quantum Technologies, NUS, Singapore.
    Towards a measurement of the effective gauge field and the Born-Huang potential with atoms in chip traps2016Article in journal (Other academic)
    Abstract [en]

    We study magnetic traps with very high trap frequencies where the spin is coupled to the motion of the atom. This allows us to investigate how the Born-Oppenheimer approximation fails and how effective magnetic and electric fields appear as the consequence of the non-adiabatic dynamics. The results are based on exact numerical diagonalization of the full Hamiltonian describing the coupling between the internal and external degrees of freedom. The position in energy and the decay rate of the trapping states correspond to the imaginary part of the resonances of this Hamiltonian and are computed using the complex rotation method. 

  • 31.
    Herterich, Emmi
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Single-loop multiple-pulse nonadiabatic holonomic quantum gates2016In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 94, no 5, article id 052310Article in journal (Refereed)
    Abstract [en]

    Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [New J. Phys. 14, 103035 (2012)] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our one-qubit gate is realized by dividing the loop into path segments, each of which is generated by a Λ-type Hamiltonian. We demonstrate that two path segments are sufficient to realize arbitrary single-loop holonomic one-qubit gates. We describe how our scheme can be implemented experimentally in a generic atomic system exhibiting a three-level Λ-coupling structure, by utilizing carefully chosen laser pulses. 

  • 32.
    Hessmo, Björn
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Quantal phase for nonmaximally entangled photons2000In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 62, no 6, p. 062301-Article in journal (Refereed)
    Abstract [en]

    We calculate the Pancharatnam phase difference obtained when entangled two-photon states interfere. This phase depends nontrivially on the degree of entanglement between the photons forming the two-photon state. We outline an experiment where the entanglement dependence of the two-photon phase may be studied interferometrically. Also we propose how a cyclic version of this phase may be useful for implementing an efficient quantum gate.

  • 33.
    Hyllus, Philipp
    et al.
    Institut für Theoretische Physik, Universität Hannover, Germany.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Comment on `Complementarity between Local and Nonlocal Topological Effects'2002In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 89, no 19, p. 198901-Article in journal (Other academic)
  • 34.
    Hyllus, Philipp
    et al.
    Institut für Theoretische Fysik, Universität Hannover, Germany.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Precession and interference in the Aharonov-Casher and scalar Aharonov-Bohm effect2003In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 33, no 7, p. 1085-1105Article in journal (Refereed)
    Abstract [en]

    The ideal scalar Aharonov-Bohm (SAB) and Aharonov-Casher (AC) effect involve a magnetic dipole pointing in a certain fixed direction: along a purely time dependent magnetic field in the SAB case and perpendicular to a planar static electric field in the AC case. We extend these effects to arbitrary direction of the magnetic dipole. The precise conditions for having nondispersive precession and interference effects in these generalized set ups are delineated both classically and quantally. Under these conditions the dipole is affected by a nonvanishing torque that causes pure precession around the directions defined by the ideal set ups. It is shown that the precession angles are in the quantal case linearly related to the ideal phase differences, and that the nonideal phase differences are nonlinearly related to the ideal phase differences. It is argued that the latter nonlinearity is due the appearance of a geometric phase associated with the nontrivial spin path. It is further demonstrated that the spatial force vanishes in all cases except in the classical treatment of the nonideal AC set up, where the occurring force has to be compensated by the experimental arrangement. Finally, for a closed space-time loop the local precession effects can be inferred from the interference pattern characterized by the nonideal phase differences and the visibilities. It is argued that this makes it natural to regard SAB and AC as essentially local and nontopological effects.

  • 35.
    Johansson, Markus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    Ericsson, Marie
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    Singh, Kuldip
    Centre for Quantum Technologies, NUS, Singapore.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    Williamson, Mark S.
    Centre for Quantum Technologies, NUS, Singapore.
    Correlation-induced non-Abelian quantum holonomies2011In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 44, no 14, p. 145301-Article in journal (Refereed)
    Abstract [en]

    In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the Lévay geometric phase (2004 J. Phys. A: Math. Gen. 37 1821) in the case of two-qubit systems undergoing local SU(2) evolutions.

  • 36.
    Johansson, Markus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    Ericsson, Marie
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    Singh, Kuldip
    Centre for Quantum Technologies, NUS, Singapore.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    Williamson, Mark S.
    Centre for Quantum Technologies, NUS, Singapore.
    Topological phases and multiqubit entanglement2012In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 85, no 3, p. 032112-1-032112-11Article in journal (Refereed)
    Abstract [en]

    Global phase factors of topological origin, resulting from cyclic local $\rm{SU}$ evolution, called topological phases, were first described in [Phys. Rev. Lett. {\bf 90}, 230403 (2003)], in the case of entangled qubit pairs. In this paper we investigate topological phases in multi-qubit systems as the result of cyclic local $\rm{SU(2)}$ evolution. These phases originate from the topological structure of the local $\rm{SU(2)}$-orbits and are an attribute of most entangled multi-qubit systems. We discuss the relation between topological phases and SLOCC-invariant polynomials and give examples where topological phases appear. A general method to find the values of the topological phases in an $n$-qubit system is described and a complete list of these phases for up to seven qubits is given.

  • 37.
    Johansson, Markus
    et al.
    Centre for Quantum Technologies, NUS, Singapore.
    Ericsson, Marie
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Osterloh, Andreas
    Fakultät für Physik, Universität Duisburg-Essen, Germany.
    Classification scheme of pure multipartite states based on topological phases2014In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 89, no 1, p. 012320-Article in journal (Refereed)
    Abstract [en]

    We investigate the connection between the concept of a-balancedness introduced in [Phys. Rev A. 85, 032112 (2012)] and polynomial local SU invariants and the appearance of topological phases respectively. It is found that different types of a-balancedness correspond to different types of local SU invariants analogously to how different types of balancedness as defined in [New J. Phys. 12, 075025 (2010)] correspond to different types of local SL invariants. These different types of SU invariants distinguish between states exhibiting different topological phases. In the case of three qubits the different kinds of topological phases are fully distinguished by the three-tangle together with one more invariant. Using this we present a qualitative classification scheme based on balancedness of a state. While balancedness and local SL invariants of bidegree $(2n,0)$ classify the SL-semistable states [New J. Phys. 12, 075025 (2010), Phys. Rev. A 83, 052330 (2011)], a-balancedness and local SU invariants of bidegree (2n-m,m) gives a more fine grained classification. In this scheme the a-balanced states form a bridge from the genuine entanglement of balanced states, invariant under the SL-group, towards the entanglement of unbalanced states characterized by U invariants of bidegree (n,n). As a by-product we obtain generalizations to the W-state, states that are entangled, but contain only globally distributed entanglement of parts of the system.

  • 38.
    Johansson, Markus
    et al.
    Centre for Quantum Technologies, NUS, Singapore.
    Khoury, Antonio
    Instituto de Fisica, Universidade Federal Fluminense, Rio de Janeiro, Brazil.
    Singh, Kuldip
    Centre for Quantum Technologies, NUS, Singapore.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.
    Three-qubit topological phase on entangled photon pairs2013In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 87, no 4, p. 042112-Article in journal (Refereed)
    Abstract [en]

    We propose an experiment to observe the topological phases associated with cyclic evolutions, generated by local SU(2) operations, on three-qubit entangled states prepared on different degrees of freedom of entangled photon pairs. The topological phases reveal the nontrivial topological structure of the local SU(2) orbits. We describe how to prepare states showing different topological phases, and discuss their relation to entanglement. In particular, the presence of a π/2 phase shift is a signature of genuine tripartite entanglement in the sense that it does not exist for two-qubit systems. 

  • 39.
    Johansson, Markus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    Andersson, Mauritz
    Dept. of Applied Physics, KTH, Sweden.
    Ericsson, Marie
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    Hessmo, Björn
    Centre for Quantum Technologies, NUS, Singapore.
    Singh, Kuldip
    Centre for Quantum Technologies, NUS, Singapore.
    Tong, Dianmin
    Physics Dept., Shandong University, China.
    Robustness of nonadiabatic holonomic gates2012In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 86, no 6, p. 062322-Article in journal (Refereed)
    Abstract [en]

    The robustness to different sources of error of the scheme for non-adiabatic holonomic gates proposed in [arXiv:1107.5127v2] is investigated. Open system effects as well as errors in the driving fields are considered. It is found that the gates can be made more error resilient by using sufficiently short pulses. The principal limit of how short the pulses can be made is given by the breakdown of the quasi-monochromatic approximation. A comparison with the resilience of adiabatic gates is carried out.

  • 40.
    Johansson, Niklas
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Optimal topological test for degeneracies of real Hamiltonians2004In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 92, no 6, p. 060406-Article in journal (Refereed)
    Abstract [en]

    We consider adiabatic transport of eigenstates of real Hamiltonians around loops in parameter space. It is demonstrated that loops that map to nontrivial loops in the space of eigenbases must encircle degeneracies. Examples from Jahn-Teller theory are presented to illustrate the test. We show furthermore that the proposed test is optimal.

  • 41.
    Johansson, Niklas
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Searching for degeneracies of real Hamiltonians using homotopy classification of loops in SO(n)2005In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 71, no 1, p. 012106-Article in journal (Refereed)
    Abstract [en]

    Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. 92, 060406 (2004)] for degeneracies of real Hamiltonian matrices. This test relies on the existence of nontrivial loops in the space of eigenbases SO$(n)$. We develop necessary means to determine the homotopy class of a given loop in this space. Furthermore, in cases where the dimension of the relevant Hilbert space is large the application of the original test may not be immediate. To remedy this deficiency, we put forward a condition for when the test is applicable to a subspace of Hilbert space. Finally, we demonstrate that applying the methodology of [Phys. Rev. Lett. 92, 060406 (2004)] to the complex Hamiltonian case does not provide any new information.

  • 42.
    Kult, David
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Geometry of decomposition dependent evolutions of mixed states2004In: International Journal of Quantum Information, ISSN 0219-7499, Vol. 2, no 2, p. 247-256Article in journal (Refereed)
    Abstract [en]

    We examine evolutions where each component of a given decomposition of a mixed quantal state evolves independently in a unitary fashion. The geometric phase and parallel transport conditions for this type of decomposition dependent evolution are delineated. We compare this geometric phase with those previously defined for unitarily evolving mixed states, and mixed state evolutions governed by completely positive maps.

  • 43.
    Kult, David
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Åberg, Johan
    Centre for Quantum Computation, DAMTP, Cambridge, UK.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Holonomy for quantum channels2008In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 77, no 1, p. 012114-Article in journal (Refereed)
    Abstract [en]

    A quantum holonomy reflects the curvature of some underlying structure of quantum-mechanical systems, such as that associated with quantum states. Here, we extend the notion of holonomy to families of quantum channels, i.e., trace-preserving completely positive maps. By the use of the Jamiolkowski isomorphism, we show that the proposed channel holonomy is related to the Uhlmann holonomy. The general theory is illustrated for specific examples. We put forward a physical realization of the channel holonomy in terms of interferometry. This enables us to identify a gauge-invariant physical object that directly relates to the channel holonomy. Parallel transport condition and concomitant gauge structure are delineated in the case of smoothly parametrized families of channels. Finally, we point out that interferometer tests that have been carried out in the past to confirm the 4 pi rotation symmetry of the neutron spin can be viewed as early experimental realizations of the channel holonomy.

  • 44.
    Kult, David
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Åberg, Johan
    Centre for Quantum Computation, DAMTP, Univ. of Cambridge, UK.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Non-Abelian generalization of off-diagonal geometric phases2007In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 78, no 6, p. 60004-Article in journal (Refereed)
    Abstract [en]

    If a quantum system evolves in a noncyclic fashion the corresponding geometric phase or holonomy may not be fully defined. Off-diagonal geometric phases have been developed to deal with such cases. Here, we generalize these phases to the non-Abelian case, by introducing off-diagonal holonomies that involve evolution of more than one subspace of the underlying Hilbert space. Physical realizations of the off-diagonal holonomies in adiabatic evolution and interferometry are put forward.

  • 45.
    Kult, David
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Åberg, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Noncyclic geometric changes of quantum states2006In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 74, no 2, p. 022106-Article in journal (Refereed)
    Abstract [en]

    Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the Abelian Berry phase. Apart from being a general phenomenon displayed in various subfields of quantum physics, the use of holonomies has lately been suggested as a robust technique to obtain quantum gates; the building blocks of quantum computers. Non-Abelian holonomies are usually associated with cyclic changes of quantum systems, but here we consider a generalization to noncyclic evolutions. We argue that this open-path holonomy can be used to construct quantum gates. We also show that a structure of partially defined holonomies emerges from the open-path holonomy. This structure has no counterpart in the Abelian setting. We illustrate the general ideas using an example that may be accessible to tests in various physical systems.

  • 46.
    Larson, Jonas
    et al.
    NORDITA, Stockholm, Sweden.
    Martikainen, Jani-Petri
    NORDITA Stockholm, Sweden.
    Collin, Anssi
    NORDITA Stockholm, Sweden.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    Spin-orbit-coupled Bose-Einstein condensate in a tilted optical lattice2010In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 82, no 4, p. 043620-Article in journal (Refereed)
    Abstract [en]

    Bloch oscillations appear for a particle in a weakly tilted periodic potential. The intrinsic spin Hall effect is an outcome of a spin-orbit coupling. We demonstrate that both of these phenomena can be realized simultaneously in a gas of weakly interacting ultracold atoms exposed to a tilted optical lattice and to a set of spatially dependent light fields inducing an effective spin-orbit coupling. It is found that both the spin Hall and the Bloch oscillation effects may coexist, showing, however, a strong correlation between the two. These correlations are manifested as a transverse spin current oscillating in-phase with the Bloch oscillations. On top of the oscillations originating from the periodicity of the model, a trembling motion is found which is believed to be atomic Zitterbewegung. It is argued that the damping of these Zitterbewegung oscillations may to a large extent be prevented in the present setup considering a periodic optical lattice potential.

     

     

  • 47.
    Larson, Jonas
    et al.
    NORDITA, Stockholm, Sweden.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical Chemistry, Quantum Chemistry.
    Jahn-Teller-induced Berry phase in spin-orbit-coupled Bose-Einstein condensates2009In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 79, p. 043627-Article in journal (Refereed)
    Abstract [en]

    We demonstrate that Berry phases may greatly affect the dynamics of spin-orbit coupled Bose-Einstein condensates. The effective model Hamiltonian under consideration is shown to be equivalent to the Exe Jahn-Teller model first introduced in molecular physics. The corresponding conical intersection is identified and the Berry phase acquired for a wave packet encircling the intersection is studied. It is found that this phase manifests itself in the density profile of the condensate, making it a directly measurable quantity via time-of-flight detection. Moreover, the non-Abelian gauge structure of the system is addressed and we verify how it affects the dynamics.

  • 48.
    Larsson, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Measuring Pancharatnam's relative phase for SO(3) evolutions using spin polarimetry2003In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 68, no 4, p. 042109-Article in journal (Refereed)
    Abstract [en]

    In polarimetry, a superposition of internal quantal states is exposed to a single Hamiltonian and information about the evolution of the quantal states is inferred from projection measurements on the final superposition. In this framework, we here extend the polarimetric test of Pancharatnam's relative phase for spin-1/2 proposed by Wagh and Rakhecha [Phys. Lett. A 197, 112 (1995)] to spin j>1/2 undergoing noncyclic SO(3) evolution. We demonstrate that the output intensity for higher spin values is a polynomial function of the corresponding spin-1/2 intensity. We further propose a general method to extract the noncyclic SO(3) phase and visibility by rigid translation of two \pi/2 spin flippers. Polarimetry on higher spin states may in practice be done with spin polarized atomic beams.

  • 49.
    Larsson, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Sjöqvist, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
    Noncyclic mixed state phase in SU(2) polarimetry2003In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 315, no 1-2, p. 12-15Article in journal (Refereed)
    Abstract [en]

    We demonstrate that Pancharatnam's relative phase for mixed spin-1/2 states in noncyclic SU(2) evolution can be measured polarimetrically.

  • 50.
    Lundberg, Tomas
    et al.
    Dept. of Physics and Measurement Technology, Linköping Univ., Sweden.
    Sjöqvist, Erik
    Sub-Faculty of Philosophy, Oxford University, UK .
    Berggren, Karl-Fredrik
    Dept. of Physics and Measurement Technology, Linköping Univ., Sweden.
    Analysis of electron transport in a two-dimensional structure using quantal trajectories1998In: Journal of Physics: Condensed Matter, ISSN 0953-8984, E-ISSN 1361-648X, Vol. 10, no 25, p. 5583-5594Article in journal (Refereed)
    Abstract [en]

    Ballistic and dissipative electron transport through a two-dimensional geometry is studied in the de Broglie-Bohm quantal trajectory model. The dissipative effect, incorporated to simulate inelastic scattering, is introduced via an imaginary potential term in the Hamiltonian. The relation between the conductance and the local behaviour of the quantal trajectories is discussed. The vortex-like structure of the de Broglie-Bohm trajectories in the vicinity of wavefunction nodes is studied.

123 1 - 50 of 113
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