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arXiv:1609.02403 · Physical Review A

Theoretical realization and application of parity-time-symmetric oscillators in a quantum regime

Wenlin Li, Chong Li, He‐Shan Song

Published Feb 14, 2017• 38 citations
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Abstract

In the existing parity-time ($\mathcal{PT}$) symmetry with the balanced gain and loss, the gain is derived from semiclassical but not full quantum theories, which significantly restricts the applications of $\mathcal{PT}$ symmetry in quantum fields. In this work, we propose and analyze a theoretical scheme to realize full quantum oscillator $\mathcal{PT}$ symmetry. The quantum gain is provided by a dissipation optical cavity with a blue-detuned laser field. After adiabatically eliminating the cavity modes, we give an effective master equation, which is a complete quantum description compared with the non-Hermitian Hamiltonian, to reveal the quantum behaviors of such a gain oscillator. This kind of $\mathcal{PT}$ symmetry can eliminate the dissipation effect in the quantum regime. As an example, we apply $\mathcal{PT}$-symmetric oscillators to enhance optomechanically induced transparency.

DOI
10.1103/physreva.95.023827

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In the existing parity-time (PT\mathcal{PT}PT) symmetry with the balanced gain and loss, the gain is derived from semiclassical but not full quantum theories, which significantly restricts the applications of PT\mathcal{PT}PT symmetry in quantum fields. In this work, we propose and analyze a theoretical scheme to realize full quantum oscillator PT\mathcal{PT}PT symmetry. The quantum gain is provided by a dissipation optical cavity with a blue-detuned laser field. After adiabatically eliminating the cavity modes, we give an effective master equation, which is a complete quantum description compared with the non-Hermitian Hamiltonian, to reveal the quantum behaviors of such a gain oscillator. This kind of PT\mathcal{PT}PT symmetry can eliminate the dissipation effect in the quantum regime. As an example, we apply PT\mathcal{PT}PT-symmetric oscillators to enhance optomechanically induced transparency.
We study steady-state continuous-variable entanglement in a three-mode optomechanical system consisting of an active optical cavity (gain) coupled to a passive optical cavity (loss) supporting a mechanical mode. For a driving laser which is blue-detuned, we show that coupling between optical and mechanical modes is enhanced in the unbroken-PT\mathcal{PT}PT-symmetry regime. We analyze the stability and this shows that steady-state solutions are more stable in the gain and loss systems. We use these stable solutions to generate distant entanglement between the mechanical mode and the optical field inside the gain cavity. It results in a giant enhancement of entanglement compared to what is generated in the single lossy cavity. This work offers the prospect of exploring quantum state engineering and quantum information in such systems. Furthermore, such entanglement opens up an interesting possibility to study spatially separated quantum objects.
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PT{\mathscr{PT}}PT -symmetry from Lindblad dynamics in a linearized optomechanical system
Abstract We analyze a lossy linearized optomechanical system in the red-detuned regime under the rotating wave approximation. This so-called optomechanical state transfer protocol provides effective lossy frequency converter (quantum beam-splitter-like) dynamics where the strength of the coupling between the electromagnetic and mechanical modes is controlled by the optical steady-state amplitude. By restricting to a subspace with no losses, we argue that the transition from mode-hybridization in the strong coupling regime to the damped-dynamics in the weak coupling regime, is a signature of the passive parity-time ( PT{\mathscr{PT}}PT PT ) symmetry breaking transition in the underlying non-Hermitian quantum dimer. We compare the dynamics generated by the quantum open system (Langevin or Lindblad) approach to that of the PT{\mathscr{PT}}PT PT -symmetric Hamiltonian, to characterize the cases where the two are identical. Additionally, we numerically explore the evolution of separable and correlated number states at zero temperature as well as thermal initial state evolution at room temperature. Our results provide a pathway for realizing non-Hermitian Hamiltonians in optomechanical systems at a quantum level.
Parity-time (PT\mathcal{PT}PT) symmetric systems, which rely on the balanced gain-loss condition and render the Hamiltonian non-Hermitian, have provided a new platform to engineer effective light-matter interactions in recent years. Here we explore the high-order sideband features of the output fields obtained from a PT\mathcal{PT}PT-symmetric optical system consisting of a passive nonlinear cavity coupled to an active linear cavity. By employing a perturbation technique, we derive analytic formulas used to determine the nonlinear transmission coefficient of optical second-order sideband in this structure. Using experimentally achievable parameters, it is clearly shown that the efficiency of the second-order sideband generation can be greatly enhanced in the PT\mathcal{PT}PT-symmetric dimer, extremely in the vicinity of the transition point from unbroken- to broken-PT\mathcal{PT}PT regimes. Moreover, we further analyzed the influences of the system parameters, including the photon-tunneling rate between two cavities, Kerr nonlinearity strength, and optical detuning, on the second-order sideband generation. Subsequently we investigate the higher-order sideband output spectrum by numerical simulations, where the sideband amplitude also is largely enhanced in the PT\mathcal{PT}PT-symmetric arrangement, compared with the passive-passive double-cavity system. Our obtained results provide a new avenue for acquiring optical high-order sidebands and operating light, which may inspire further applications in chip-scale optical communications and optical frequency combs.
We propose a scheme to realize parity-time (PT) symmetry via electromagnetically induced transparency (EIT). The system we consider is an ensemble of cold four-level atoms with an EIT core. We show that the cross-phase modulation contributed by an assisted field, the optical lattice potential provided by a far-detuned laser field, and the optical gain resulted from an incoherent pumping can be used to construct a PT-symmetric complex optical potential for probe field propagation in a controllable way. Comparing with previous study, the present scheme uses only a single atomic species and hence is easy for the physical realization of PT-symmetric Hamiltonian via atomic coherence.
In standard quantum theory, the Hamiltonian describing a physical system is assumed to be Hermitian in order to guarantee the energy spectrum to be real and the time evolution to be unitary. In recent years, it was recognized that non-Hermitian Hamiltonians with parity-time () symmetry can exhibit entirely real spectra, raising the possibility for extending the quantum theory to complex domain and hence stimulated growing interest in recent years. Many proposals have been presented for realizing -symmetric Hamiltonians in various physical systems. Among them -symmetric coherent atomic gases are special and possess many unique advantages, including the possibility to obtain authentic -symmetric refractive indexes (which have balanced gain and loss in the whole space), the capability to actively control and precisely manipulate system parameters in situ, and the feasibility to acquire large Kerr nonlinearity based on the resonance character between light and atoms. In this article, we review various schemes for the realization of symmetry with coherent atomic gases, elucidate their interesting properties and promising applications. In particular, the non-linear optical effect in the -symmetric atomic gases are described, which may be served as useful building blocks for developing novel photonic devices with active light control at very low power level.