Non-Hermitian Quantum Dynamics of a Two-Level System and Models of Dissipative Environments

Sergi, Alessandro; Zloshchastiev, Konstantin G.

doi:10.1142/s0217979213501634

Cited by 104 publications

(176 citation statements)

References 60 publications

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“…because the observers live in the conventional quantum world [15,29,30]. The quantum average of an observable A can then be calculated as…”

Section: Fig 1: (Color Online)mentioning

confidence: 99%

Increase of entanglement by localPT-symmetric operations

Chen

2014

Phys. Rev. A

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Entanglement plays a central role in the field of quantum information science. It is well known that the degree of entanglement cannot be increased under local operations. Here, we show that the concurrence of a bipartite entangled state can be increased under the local PT -symmetric operation. This violates the property of entanglement monotonicity. We also use the Bell-CHSH and steering inequalities to explore this phenomenon.

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“…because the observers live in the conventional quantum world [15,29,30]. The quantum average of an observable A can then be calculated as…”

Section: Fig 1: (Color Online)mentioning

confidence: 99%

Increase of entanglement by localPT-symmetric operations

Chen

2014

Phys. Rev. A

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“…The theoretical investigations are also undergoing rapid developments: non-Hermitian quantum mechanics has been investigated within a relativistic framework [31] and it has been adopted by various researchers as a means to describe open quantum systems [32][33][34][35][36][37][38][39][40][41][42]. Moreover, it seems that a few theoretical studies have been dedicated to the statistical mechanics and dynamics of systems with non-Hermitian Hamiltonians [43][44][45][46][47][48][49][50][51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

Embedding quantum systems with a non-conserved probability in classical environments

Sergi

2015

Theor Chem Acc

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Quantum systems with a non-conserved probability can be described by means of non-HermitianHamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and heavy masses is treated. A classical limit over the heavy coordinates is taken in order to embed the non-unitary dynamics of the subsystem in a classical environment. Such a classical environment, in turn, acts as an additional source of dissipation (or noise), beyond that represented by the non-unitary evolution. The non-Hermitian dynamics of a Heisenberg two-spin chain, with the spins independently coupled to harmonic oscillators, is considered in order to illustrate the formalism.

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“…In the present letter, we use a more general von Neumann approach [18][19][20][21] which allows for violation of number conservation due to the non-Hermitian nature of the system. These two approaches are not equivalent to each other and von Neumann approach is proper treatp-1 ment of non-conservative systems with the non-Hermitian models.…”

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confidence: 99%

“…The general formulation for the time evolution of quantum systems under non-Hermitian Hamiltonians can be found in [18][19][20][21]. A non-Hermitian Hamiltonian operator can be partitioned into Hermitian and anti-Hermitian parts:…”

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confidence: 99%

Non-Hermitian quantum dynamics and entanglement of coupled nonlinear resonators

Karakaya¹,

Altintas²,

Güven³

et al. 2014

EPL

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-We consider a generalization of recently proposed non-Hermitian model for resonant cavities coupled by a chiral mirror by taking into account number non-conservation and nonlinear interactions. We analyze non-Hermitian quantum dynamics of populations and entanglement of the cavity modes. We find that an interplay of initial coherence and non-Hermitian coupling leads to a counterintuitive population transfer. While an initially coherent cavity mode is depleted, the other empty cavity can be populated more or less than the initially filled one. Moreover, presence of nonlinearity yields population collapse and revival as well as bipartite entanglement of the cavity modes. In addition to coupled cavities, we point out that similar models can be found in PT symmetric Bose-Hubbard dimers of Bose-Einstein condensates or in coupled soliton-plasmon waveguides. We specifically illustrate quantum dynamics of populations and entanglement in a heuristic model that we propose for a soliton-plasmon system with soliton amplitude dependent asymmetric interaction. Degree of asymmetry, nonlinearity and coherence are examined to control plasmon excitations and soliton-plasmon entanglement. Relations to PT symmetric lasers and Jahn-Teller systems are pointed out.Introduction. -Recently, an intriguing quantum optical model for resonant cavities coupled by a chiral mirror has been proposed [1]. The chiral mirror is a planar metamaterial array of asymmetric split rings, through which transmission of circularly polarized electromagnetic waves becomes different in the opposite direction without violating Lorentz reciprocity principle [2]. The transmission matrix of such a mirror is a two dimensional non-Hermitian matrix. The proposed quantum optical system is then described by a non-Hermitian Hamiltonian. As a special class of non-Hermitian systems, parity-time (PT ) symmetric systems have been attracted much attention [3][4][5]. More recently, it is shown that hybridized metamaterials can simulate effectively spontaneous symmetry breaking in PT -symmetric non-Hermitian quantum systems [6]. Nonreciprocal light transmission in PT -symmetry broken phase using whispering-gallery microcavities has been observed very recently [7].

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Non-Hermitian Quantum Dynamics of a Two-Level System and Models of Dissipative Environments

Cited by 104 publications

References 60 publications

Increase of entanglement by localPT-symmetric operations

Increase of entanglement by localPT-symmetric operations

Embedding quantum systems with a non-conserved probability in classical environments

Non-Hermitian quantum dynamics and entanglement of coupled nonlinear resonators

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