Geometric phase for an adiabatically evolving open quantum system

Kamleitner, I.; Cresser, J. D.; Sanders, Barry C.

doi:10.1103/physreva.70.044103

Cited by 29 publications

(28 citation statements)

References 29 publications

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“…Other discussions or experimental demonstrations of geometric phases for mixed states may be found in papers [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Separable states and geometric phases of an interacting two-spin system

Niu

Liu

et al. 2010

Phys. Rev. A

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It is known that an interacting bipartite system evolves as an entangled state in general, even if it is initially in a separable state. Due to the entanglement of the state, the geometric phase of the system is not equal to the sum of the geometric phases of its two subsystems. However, there may exist a set of states in which the nonlocal interaction does not affect the separability of the states, and the geometric phase of the bipartite system is then always equal to the sum of the geometric phases of its subsystems. In this paper, we illustrate this point by investigating a well known physical model. We give a necessary and sufficient condition in which a separable state remains separable so that the geometric phase of the system is always equal to the sum of the geometric phases of its subsystems.

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“…Other discussions or experimental demonstrations of geometric phases for mixed states may be found in papers [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Separable states and geometric phases of an interacting two-spin system

Niu

Liu

et al. 2010

Phys. Rev. A

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“…This is a pure state analysis, so it did not address the problem of geometric phases for mixed states. Toward the geometric phase for mixed states in open systems, the approaches used involve solving the master equation of the system [9,10,11,12,13], employing a quantum trajectory analysis [14,15] or Krauss operators [16], and the perturbative expansions [17,18]. Some interesting results were achieved, briefly summarized as follows: nonhermitian Hamiltonian lead to a modification of Berry's phase [8,17], stochastically evolving magnetic fields produce both energy shift and broadening [18], phenomenological weakly dissipative Liouvillians alter Berry's phase by introducing an imaginary correction [11] or lead to damping and mixing of the density matrix elements [12].…”

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confidence: 99%

Geometric phase in dephasing systems

Wang

2005

Phys. Rev. A

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Beyond the quantum Markov approximation, we calculate the geometric phase of a two-level system driven by a quantized magnetic field subject to phase dephasing. The phase reduces to the standard geometric phase in the weak coupling limit and it involves the phase information of the environment in general. In contrast with the geometric phase in dissipative systems, the geometric phase acquired by the system can be observed on a long time scale. We also show that with the system decohering to its pointer states, the geometric phase factor tends to a sum over the phase factors pertaining to the pointer states.PACS numbers: 03.65. Vf, 03.65.Yz Quantum mechanics tell us that physical states are equivalent up to a global phase, which in general does not contain useful information about the described system and thus can be ignored. This is not the case, however, for a system transported round a circuit by varying the parameters s = (s 1 , s 2 , ...) in its Hamiltonian H( s). As Berry showed [1], the phase can have a component of geometric origin called geometric phase with important observable consequences, such as the Aharonov-Bohm effect [2] and the spin-1 2 particle driven by a rotating magnetic field [1]. The geometric phases that only depend on the path followed by the system during its evolution, have been investigated and tested in a variety of settings and have been generalized in several directions [3]. The geometric phases are attractive both from a theoretical perspective, and from the point of view of possible applications, among which geometric quantum computation [4,5,6,7] is one of the most importance.As realistic systems always interact with their environment, the study on the geometric phase in open systems become interesting. Garrison and Wright [8] were the first to touch on this issue by describing open system evolution in terms of a non-Hermitian Hamiltonian. This is a pure state analysis, so it did not address the problem of geometric phases for mixed states. Toward the geometric phase for mixed states in open systems, the approaches used involve solving the master equation of the system [9,10,11,12,13], employing a quantum trajectory analysis [14,15] or Krauss operators [16], and the perturbative expansions [17,18]. Some interesting results were achieved, briefly summarized as follows: nonhermitian Hamiltonian lead to a modification of Berry's phase [8,17], stochastically evolving magnetic fields produce both energy shift and broadening [18], phenomenological weakly dissipative Liouvillians alter Berry's phase by introducing an imaginary correction [11] or lead to damping and mixing of the density matrix elements [12]. However, almost all these studies are performed for dissipative systems, and thus the representations are applicable for systems whose energy is not conserved. For open systems with conserved energy (dephasing systems), the problem beyond the Markov approximation remains untouched to our best knowledge. Because the systemenvironment interaction H I and the free system Hamilton...

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“…Since the perturbers surrounding the radiating atom do not move along closed paths, the contributions to the Berry phase coming from the time dependence of the perturber coordinates R(t) were assumed to be negligible in these analyses. It was shown, however, by several researches that the geometric phase makes sense also for non-cyclic adiabatic evolution, corresponding to open paths in parameter space [4][5][6][7]. Therefore, in the present work we address ourselves to the following problem:…”

Section: Introductionmentioning

confidence: 99%