Nonlinear Schrödinger-Liouville Equation with Antihermitian Terms

Mizrahi, S. S.; Dodonov, V. V.; Otero, D.

doi:10.1088/0031-8949/57/1/003

Cited by 9 publications

(8 citation statements)

References 41 publications

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“…[21][22][23] for pure states. Note that the covariance-type structure in (1) has also appeared in the contexts of approach to thermal equilibrium [24], dissipative motion [25,26], and constrained quantum dynamics [27]. Key properties of the evolution equation ( 1) can be summarised as follows: (i) It preserves the overall probability so that tr(ρ t ) = 1 for all t ≥ 0.…”

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confidence: 99%

Mixed-State Evolution in the Presence of Gain and Loss

2012

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A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the space of density matrices corresponding to the fixed points of the dynamics are identified, and the existence of a transition between the phase in which gain and loss are balanced and the phase in which this balance is lost is illustrated in terms of the time average of observables. The model is extended to include a noise term that results from a uniform random perturbation generated by white noise. Numerical studies of example systems show the emergence of equilibrium states that suppress the phase transition.PACS numbers: 03.65. Ca, 05.30.Rt, 03.65.Yz Over the past decade there have been considerable research interests, both theoretical and experimental, into the static and dynamic properties of classical and quantum systems for which gain and loss are present [1,2]. This is in part motivated by the realisation that when a system is placed in a configuration in which its energy or amplitude is transferred into its environment through one channel, but at the same time is amplified by the same amount through another channel, the resulting dynamics can exhibit features that are similar to those seen in Hamiltonian dynamical systems. The time evolution of such a system can be described by a Hamiltonian that is symmetric under a space-time reflection, that is, invariant under the parity-time (PT) reversal.Interest in the theoretical study of PT symmetry was triggered by the discovery that complex PT-symmetric quantum Hamiltonians can possess entirely real eigenvalues [3]. One distinguishing feature of PT-symmetric quantum systems is the existence of phase transitions associated with the breakdown of the symmetry. That is, depending on the values of the matrix elements of the Hamiltonian, its eigenstates may or may not be symmetric under the parity-time reversal. In the 'unbroken phase' where the eigenstates respect PT symmetry, the eigenvalues are real and there exists a similarity transformation that maps a local PT-symmetric Hamiltonian into a typically nonlocal Hermitian Hamiltonian [4,5]; whereas in the 'broken phase' the eigenvalues constitute complex conjugate pairs. The transition between these phases is similar to second-order phase transitions in statistical mechanics, accompanied by singularities in the covariance matrix of the estimators for the parameters in the Hamiltonian (this can be seen by using methods of information geometry [6]).Experimental realisations of these phenomena are motivated in part by the observation that the presence of a loss, which traditionally has been viewed as an undesirable feature, can positively be manipulated so as to generate unexpected interesting effects (cf. [7]). In particular, PT phase transitions have been predicted or observed in laboratory experiments for a range of systems; most notably in optical waveguides [8][9][10], but ...

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confidence: 99%

Mixed-State Evolution in the Presence of Gain and Loss

2012

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“…Here the Hermitian part and anti-Hermitian part characterize the unitary evolution, and gain/loss of the system, respectively. The master equation governing the evolution of the joint density matrix of the system ( ρ) may be written as [343][344][345]…”

Section: Magnon-photon Entanglementmentioning

confidence: 99%

Quantum magnonics: when magnon spintronics meets quantum information science

Yuan

2022

Preprint

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Spintronics and quantum information science are two promising candidates for innovating information processing technologies. The combination of these two fields enables us to build solid-state platforms for studying quantum phenomena and for realizing multi-functional quantum tasks. For a long time, however, the intersection of these two fields was limited due to the distinct properties of the classical magnetization, that is manipulated in spintronics, and quantum bits, that are utilized in quantum information science. This situation has changed significantly over the last few years because of the remarkable progress in coding and processing information using magnons. On the other hand, significant advances in understanding the entanglement of quasi-particles and in designing high-quality qubits and photonic cavities for quantum information processing provide physical platforms to integrate magnons with quantum systems. From these endeavours, the highly interdisciplinary field of quantum magnonics emerges, which combines spintronics, quantum optics and quantum information science. Here, we give an overview of the recent developments concerning the quantum states of magnons and their hybridization with mature quantum platforms. First, we review the basic concepts of magnons and quantum entanglement and discuss the generation and manipulation of quantum states of magnons, such as single-magnon states, squeezed states and quantum many-body states including Bose-Einstein condensation and the resulting spin superfluidity. We discuss how magnonic systems can be integrated and entangled with quantum platforms including cavity photons, superconducting qubits, nitrogen-vacancy centers, and phonons for coherent information transfer and collaborative information processing. The implications of these hybrid quantum systems for non-Hermitian physics and parity-time symmetry are highlighted, together with applications in quantum memories and high-precision measurements. Finally, we present an outlook on some of the challenges and opportunities in quantum magnonics.

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“…The last term in equation ( 1): 2 tr(ρ t B • σ)ρ t which is non-linear in ρ t is a direct consequence of the norm preservation constraint. Extensive exploration of this type of equation have been done in many contexts like dissipative quantum evolution [60], constrained quantum motion [61], approach to thermal equilibrium [62], non-Hermitian quantum motion and dissipation [63,64], and also has been realized experimentally [53,55,65]. The formal solution of the equation ( 1) is given by:…”

Section: Non-hermitian Bloch Equationmentioning

confidence: 99%

Temporal correlation beyond quantum bounds in non-Hermitian PT- symmetric dynamics of a two level system

Mohanty

Das

2021

J. Phys. A: Math. Theor.

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We study the dynamics of a non-Hermitian PT- symmetric Hamiltonian of a two level system (TLS) which has real eigenvalues. Within the framework of Hermitian quantum mechanics, it is known that maximal violation of Leggett–Garg inequality (LGI) is bounded by K 3 = 3/2 (Luder’s bound). We show that this absolute bound can be evaded when dynamics is governed by non-Hermitian PT- symmetric Hamiltonians with real eigenvalues. Moreover, the extent of violation can be optimized to asymptotically approach the algebraic maximum of K 3 max = 3 , which is otherwise observed for Hermitian Hamiltonian with infinite dimensional Hilbert space. The extreme violation of LGI is shown to be directly related to the two basic ingredients: (i) the Bloch equation for the TLS having a non-linear terms which allow for accelerated dynamics of states on the Bloch sphere exceeding all known quantum speed limits of state evolution; and (ii) quantum trajectory of states lie on a great circle (geodesic path) on the Bloch sphere at all times. We demonstrate that such extreme temporal correlation of TLS can be simulated in realistic system by embedding the TLS into a higher dimensional Hilbert space such that the composite system obeys unitary dynamics. Specifically we show that a four dimensional embedding of non-Hermitian PT- symmetric TLS is enough to host K 3 → 3 limit. We also discuss the effect of random noise on our results. Finally we conclude with a comparative study of our results with existing experimental realization of embedding.

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Nonlinear Schrödinger-Liouville Equation with Antihermitian Terms

Cited by 9 publications

References 41 publications

Mixed-State Evolution in the Presence of Gain and Loss

Mixed-State Evolution in the Presence of Gain and Loss

Quantum magnonics: when magnon spintronics meets quantum information science

Temporal correlation beyond quantum bounds in non-Hermitian PT- symmetric dynamics of a two level system

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