Quantum Behavior of a 
          
            
              PT
            
          
        -Symmetric Two-Mode System with Cross-Kerr Nonlinearity

Peřina, Jan; Lukš, A.

doi:10.3390/sym11081020

Cited by 10 publications

(8 citation statements)

References 50 publications

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“…These exotic phenomena have been observed in different experimental platforms, based on electronics [34], optomechanics [29,35,36], acoustics [37,38], plasmonics [39], and metamaterials [40]. Moreover, the concept of EPs has been successfully exploited in describing dynamical quantum phase transitions and topological phases of condensed matter in open quantum systems [41][42][43][44][45][46][47][48][49], and its relation to nonclassicality in photonic systems [50,51].…”

Section: Exceptional Pointsmentioning

confidence: 99%

Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between PT and anti- PT symmetries

et al. 2020

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Usually, when investigating exceptional points (EPs) of an open Markovian bosonic system, one deals with spectral degeneracies of a non-Hermitian Hamiltonian (NHH), which can correctly describe the system dynamics only in the semiclassical regime. A recently proposed quantum Liouvillian framework enables to completely determine the dynamical properties of such systems and their EPs (referred to as Liouvillian EPs, or LEPs) in the quantum regime by taking into account the effects of quantum jumps, which are ignored in the NHH formalism. Moreover, the symmetry and eigenfrequency spectrum of the NHH become a part of much larger Liouvillian eigenspace. As such, the EPs of an NHH form a subspace of the LEPs. Here we show that once an NHH of a dissipative linear bosonic system exhibits an EP of a certain finite order n, it immediately implies that the corresponding LEP can become of any higher order m ≥ n, defined in the infinite Hilbert space. Most importantly, these higher-order LEPs can be identified by the coherence and spectral functions at the steady state. The coherence functions can offer a convenient tool to probe extreme system sensitivity to external perturbations in the vicinity of higher-order LEPs. As an example, we study a linear bosonic system of a bimodal cavity with incoherent mode coupling to reveal its higher-order LEPs; particularly, of second and third order via first-and second-order coherence functions, respectively. Accordingly, these LEPs can be additionally revealed by squared and cubic Lorentzian spectral lineshapes in the power and intensity-fluctuation spectra. Moreover, we demonstrate that these EPs can also be associated with spontaneous parity-time (PT ) and anti-PT -symmetry breaking in the system studied. These symmetries can be switched in the output fields (the so-called supermodes) of an additional linear coupler with a properly chosen coupling strength. Thus, we show that the initial loss-loss dynamics for the supermodes can be equivalent to the balanced gain-loss evolution.

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Section: Exceptional Pointsmentioning

confidence: 99%

Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between PT and anti- PT symmetries

et al. 2020

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“…Our idea here (see Fig. 1) is to avoid measurements and feedforward by resorting to nonlinear intermode coupling [42][43][44]. This conceptually novel HM mechanism can autonomously concentrate the heat energy of thermal-input modes preferentially in a desired output mode and suppress the energy in other output modes.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear interferometry enables coherent heat machine operation

Opatrný¹,

Bräuer²,

Kofman³

et al. 2021

Preprint

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We propose a novel principle of operating heat machines in a fully unitary (coherent) fashion by mixing few hot and cold thermal field modes in nonlinear interferometers. Such devices, specifically, interferometers containing Kerr-nonlinear intermode cross-couplers, are shown to enable autonomous concentration of the energy predominantly in a desired output mode, at the expense of the other modes. Their phase-coherent operation is reversible and it is approximately reversible even if intermode entanglement is neglected. Such few-mode coherent heat machines radically depart from the existing thermodynamic paradigm which treats heat machines as open systems dissipated by heat baths.

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“…Nevertheless, it may be successfully applied also in investigations of quantum systems described by the nonlinear Heisenberg-Langevin equations provided that a suitable operator linearization of the nonlinear operator equations is applied, e.g. around a stationary state or a classical time-dependent solution [46,51,52,53].…”

Section: Spectra Of Eigenfrequencies For a Doubly Degenerated Qep -Qhpmentioning

confidence: 99%

Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach

Peřina¹,

Miranowicz²,

Chimczak³

et al. 2022

Quantum

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Equivalent approaches to determine eigenfrequencies of the Liouvillians of open quantum systems are discussed using the solution of the Heisenberg-Langevin equations and the corresponding equations for operator moments. A simple damped two-level atom is analyzed to demonstrate the equivalence of both approaches. The suggested method is used to reveal the structure as well as eigenfrequencies of the dynamics matrices of the corresponding equations of motion and their degeneracies for interacting bosonic modes described by general quadratic Hamiltonians. Quantum Liouvillian exceptional and diabolical points and their degeneracies are explicitly discussed for the case of two modes. Quantum hybrid diabolical exceptional points (inherited, genuine, and induced) and hidden exceptional points, which are not recognized directly in amplitude spectra, are observed. The presented approach via the Heisenberg-Langevin equations paves the general way to a detailed analysis of quantum exceptional and diabolical points in infinitely dimensional open quantum systems.

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Quantum Behavior of a PT -Symmetric Two-Mode System with Cross-Kerr Nonlinearity

Cited by 10 publications

References 50 publications

Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between PT and anti- PT symmetries

Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between PT and anti- PT symmetries

Nonlinear interferometry enables coherent heat machine operation

Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach

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