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arXiv:2109.09275 · Physical Review A

Experimental observation of partial parity-time symmetry and its phase transition with a laser-driven cesium atomic gas

Yongmei Xue, Chao Hang, Yunhui He, Zhengyang Bai, Yuechun Jiao, Guoxiang Huang, Jianming Zhao, Suotang Jia

Published May 17, 2022• 16 citations
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Abstract

Realizing and manipulating parity-time ($\mathcal{PT}$) symmetry in multidimensional systems are highly desirable for the exploration of nontrivial physics and the discovery of exotic phenomena in non-Hermitian systems. Finding non-Hermitian systems that still have all-real spectra even if their Hamiltonians possess only partial $\mathcal{PT}$ symmetry has also attracted tremendous attention in recent years. Here, we report the experimental observation of partial $\mathcal{PT}$ symmetry in a cesium atomic gas coupled with laser fields, where a two-dimensional partially $\mathcal{PT}$-symmetric optical potential for a probe laser beam is created. A transition of the partial $\mathcal{PT}$ symmetry from an unbroken phase to a broken one is observed through changing the beam-waist ratio of the control and probe laser beams, and the domains of unbroken, broken, and nonpartial $\mathcal{PT}$ phases are also discriminated unambiguously. Moreover, we develop a technique to precisely determine the exceptional point location of the partial $\mathcal{PT}$ symmetry breaking by measuring the asymmetry degree of the probe-beam intensity distribution. The findings reported here pave the way for controlling multidimensional laser beams in non-Hermitian systems via laser-induced atomic coherence, and have potential applications for designing light amplifiers and attenuators in different parts of laser beams.

DOI
10.1103/physreva.105.053516

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Realizing and manipulating parity-time (PT\mathcal{PT}PT) symmetry in multidimensional systems are highly desirable for the exploration of nontrivial physics and the discovery of exotic phenomena in non-Hermitian systems. Finding non-Hermitian systems that still have all-real spectra even if their Hamiltonians possess only partial PT\mathcal{PT}PT symmetry has also attracted tremendous attention in recent years. Here, we report the experimental observation of partial PT\mathcal{PT}PT symmetry in a cesium atomic gas coupled with laser fields, where a two-dimensional partially PT\mathcal{PT}PT-symmetric optical potential for a probe laser beam is created. A transition of the partial PT\mathcal{PT}PT symmetry from an unbroken phase to a broken one is observed through changing the beam-waist ratio of the control and probe laser beams, and the domains of unbroken, broken, and nonpartial PT\mathcal{PT}PT phases are also discriminated unambiguously. Moreover, we develop a technique to precisely determine the exceptional point location of the partial PT\mathcal{PT}PT symmetry breaking by measuring the asymmetry degree of the probe-beam intensity distribution. The findings reported here pave the way for controlling multidimensional laser beams in non-Hermitian systems via laser-induced atomic coherence, and have potential applications for designing light amplifiers and attenuators in different parts of laser beams.
Inspired by the discovery of real energy spectra of non-Hermitian Hamiltonians obeying parity-time (PT) symmetry, many proposals and relevant experiments have been suggested and implemented for the realization of PT-symmetric Hamiltonians in various physical systems. Among them PT-symmetric atomic gases are of great interest as they possess many unique advantages, including: (i) the possession of active PT symmetry with balanced optical gain and loss, (ii) the ability to be extended to high-dimensional ones, and (iii) the feasibility to acquire enhanced Kerr nonlinearity based on the resonance character between light and atoms. Here, we review the new progresses made on the study of PT symmetry in coherent atomic gases since our last review paper [Advances in Physics: X, 2, 737–783 (2017)]. Particularly, we focus on the newly emerged research topics in this direction, including nonlocal nonlinear effect, non-Hermitian quantum effect, exceptional point and associated phenomenon, and non-Hermitian skin effect with PT symmetry. Perspectives and potential applications of the subject are also discussed.
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.
Abstract A wide class of non-Hermitian Hamiltonians can possess entirely real eigenvalues when they have parity-time (PT) symmetric potentials. Recently, this family of non-Hermitian systems has attracted considerable attention in diverse areas of physics due to their extraordinary properties, especially in optical systems based on solid-state materials, such as coupled gain–loss waveguides and microcavities. Considering the desired refractive index can be effectively manipulated through atomic coherence, it is important to realize such non-Hermitian optical potentials and further investigate their distinct properties in atomic systems. In this paper, we review the recent theoretical and experimental progress of non-Hermitian optics with coherently prepared multi-level atomic configurations. The realizations of (anti-) PT symmetry with different schemes have extensively demonstrated the special optical properties of non-Hermitian optical systems with atomic coherence.
We present a physical setup for realizing all-real-spectrum optical potentials with arbitrary gain-and-loss distributions in a coherent medium consisting of a cold three-level atomic gas driven by control and probe laser fields. We show that by the interference of Raman resonances and the Stark shift induced by a far-detuned laser field, tunable, non-parity-time (non-PT)\mathcal{PT})PT)-symmetric optical potentials with all-real spectra proposed recently by Nixon and Yang [Phys. Rev. A 93, 031802(R) (2016)] can be actualized physically. We also show that when the real parts of the non-PT\mathcal{PT}PT-symmetric optical potentials are tuned cross certain thresholds, phase transitions---where the eigenspectrum of the system changes from all real to complex---may occur and hence the stability of the probe-field propagation is altered. Our scheme can also be extended to high dimensions and to a nonlinear propagation regime, where stable optical solitons with power of the order of nano-Watts may be generated in the system.
We propose a scheme to realize a parity-time (PT) symmetric nonlinear system in a coherent atomic gas via electromagnetically induced transparency. We show that it is possible to construct an optical potential with PT symmetry due to the interplay among the Kerr nonlinearity stemmed from the atom-photon interaction, the linear potential induced by a far-detuned Stark laser field, and the optical gain originated from an incoherent pumping. Since the real part of the PT-symmetric potential depends only on the intensity of the probe field, the potential is nonlinear and its PT-symmetric properties are determined by the input laser intensity of the probe field. Moreover, we obtain the fundamental soliton solutions of the system and attain their stability region in the system parameter space. The dependence of the exceptional point (EP) location on the soliton maximum amplitude is also illustrated. The research results reported here open a new avenue for understanding the unique properties of PT symmetry of a nonlinear system. They are also promising for designing novel optical devices applicable in optical information processing and transmission.
We propose a scheme to realize parity-time (PT\mathcal{PT}PT) symmetry and nonlocal optical solitons in a cold Rydberg atomic system with electromagnetically induced transparency. We show that a two-dimensional (2D) periodic optical potential with PT\mathcal{PT}PT symmetry can be obtained for the propagation of probe laser field by using an incoherent population pumping between two low-lying levels and spatial modulations of control and assistant laser fields. We also show that, based on the giant nonlocal Kerr nonlinearity originated from the strong, long-range atom-atom interaction, the system supports 2D nonlocal gap solitons with very low light intensity. In particular, we find that the degree of the nonlocality of the Kerr nonlinearity, which can be actively tuned in our system, can be used to manipulate the phase transition of the PT\mathcal{PT}PT symmetry and the behavior of the nonlocal optical solitons. Our study opens a route for developing non-Hermitian nonlinear optics, especially for realizing and controlling high-dimensional weak-light optical solitons through adjustable PT\mathcal{PT}PT symmetry and giant nonlocal optical nonlinearity.