Imaginary phases in two-level model with spontaneous decay

Pinto, A.C. Aguiar; Thomaz, M. T.

doi:10.1088/0305-4470/36/26/316

Cited by 13 publications

(10 citation statements)

References 27 publications

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“…[29,30]. Moreover, two particularly intriguing applications of the theory presented here are to the study of geometric phases in open systems and to quantum adiabatic algorithms, both of which have received considerable recent attention [16,17,38,39,40]. We leave these as open problems for future research.…”

Section: Discussionmentioning

confidence: 99%

Adiabatic approximation in open quantum systems

2005

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We generalize the standard quantum adiabatic approximation to the case of open quantum systems. We define the adiabatic limit of an open quantum system as the regime in which its dynamical superoperator can be decomposed in terms of independently evolving Jordan blocks. We then establish validity and invalidity conditions for this approximation and discuss their applicability to superoperators changing slowly in time. As an example, the adiabatic evolution of a two-level open system is analysed.Comment: v4: 13 pages, 1 figure. Published version. v3: Time condition for adiabaticity improved and references update

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Section: Discussionmentioning

confidence: 99%

Adiabatic approximation in open quantum systems

2005

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“…The topological structure of quantum Hall systems has been conjectured to be a possible resource for fault tolerant quantum computation [29]. These potential applications of geometric phases in quantum information science motivated a number of articles devoted to their implementation in quantum optical systems and their behavior under the influence of different kinds of reservoir [30][31][32][33][34][35][36][37]. Decoherence is recognized as the main difficulty for quantum information protocols in realistic physical systems.…”

Section: Introductionmentioning

confidence: 99%

Topological phase structure of entangled qudits

Khoury¹,

Oxman²

2014

Phys. Rev. A

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We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. 106, 240503 (2011) is detailed and extended to qudits of different dimensions. The topological nature of the phase evolution and its restriction to fractional values are related to both the structure of the projective space of states and entanglement. For maximally entangled states of qudits with the same Hilbert space dimension, the fractional geometric phases are the only ones attainable under local SU(d) operations, an effect that can be experimentally observed through conditional interference.

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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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Imaginary phases in two-level model with spontaneous decay

Cited by 13 publications

References 27 publications

Adiabatic approximation in open quantum systems

Adiabatic approximation in open quantum systems

Topological phase structure of entangled qudits

Geometric phase in dephasing systems

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