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arXiv:1604.04025 · Physical Review Letters

Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices

Zhaoyang Zhang, Yiqi Zhang, Jiteng Sheng, Liu Shuan Yang, Mohammad‐Ali Miri, Demetrios N. Christodoulides, Bing He, Yanpeng Zhang, Min Xiao

Published Sep 13, 2016• 340 citations
arXivHTMLPDF

Abstract

We experimentally demonstrate PT-symmetric optical lattices with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system. By appropriately tuning the pertinent atomic parameters, the onset of PT-symmetry breaking is observed through measuring an abrupt phase-shift jump between adjacent gain and loss waveguides. The experimental realization of such a readily reconfigurable and effectively controllable PT-symmetric waveguide array structure sets a new stage for further exploiting and better understanding the peculiar physical properties of these non-Hermitian systems in atomic settings.

DOI
10.1103/physrevlett.117.123601

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Journal of Optics•Feb 1, 2021•4 citations
We experimentally demonstrate PT-symmetric optical lattices with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system. By appropriately tuning the pertinent atomic parameters, the onset of PT-symmetry breaking is observed through measuring an abrupt phase-shift jump between adjacent gain and loss waveguides. The experimental realization of such a readily reconfigurable and effectively controllable PT-symmetric waveguide array structure sets a new stage for further exploiting and better understanding the peculiar physical properties of these non-Hermitian systems in atomic settings.
Abstract Since the periodic parity‐time (PT)‐symmetric potential can possess unique properties compared to a single PT cell (with only two coupled components), various schemes have been proposed to realize PT symmetry in optical lattices. Here, a PT‐symmetric optical lattice is experimentally constructed with simultaneous gain and loss in an atomic medium. The gain and loss arrays are created in the four‐level N‐type configurations excited by spatially alternating strong and weak pump fields, respectively, which do not require discrete diffractions and can be realized more easily with more relaxed operating conditions. Also, the gain and loss coefficients can be modified independently. The dynamical behaviors of the system are investigated by measuring the phase difference between two adjacent gain and loss channels. The demonstrated PT‐symmetric lattice with easy accessibility and better tunability shows obvious advantages in exploiting more peculiar properties and great improvements in practical applications of periodic PT‐symmetric potentials.
We propose that a coherently prepared four-level atomic medium can provide a versatile platform for realizing parity-time (PT\mathcal{PT}PT) symmetric optical potentials. Different types of PT\mathcal{PT}PT-symmetric potentials are proposed by appropriately tuning the exciting optical fields and the pertinent atomic parameters. Such reconfigurable and controllable systems may open up new avenues in observing PT\mathcal{PT}PT-related phenomena with appreciable gain-loss contrast in coherent atomic media.
Analysis of fundamentally open systems which exhibit both spatial reflection (parity) and time-reversal symmetry, called PT-symmetric [1] systems, has played an important role in understanding the dynamics of a broad class of non-Hermitian systems. Such systems support distinct regimes of stability and instability respectively, and the transition between these plays an important role in the system dynamics. We investigate a variety of non-Hermitian systems which exhibit a PT-symmetry breaking transition in both classical and quantum contexts using an array of theoretical and numerical approaches which are directly amenable to physical experiments. Organizationally, we divide these studies into those done on classical and quantum systems. Specifically for classical systems we analyze several interesting phenomena in the context of optical waveguide arrays. These provide an important testing ground for much of the discrete, PT-symmetric theory. In our case, we analyze PT-symmetric extensions of several interesting lattice models. Firstly, we explore single gain/loss pair, PT-symmetric extensions of the Su-Schreiffer-Heeger (SSH) model [2] and the Aubry-Andre-Harper (AAH) model [3,4]. In both cases, we find a veiled symmetry which is responsible for the PT-symmetry. Secondly we expand upon the Rudner-Levitov (RL) model [5,6], a non-Hermitian extension of the SSH model with multiple gain/loss pairs, and we explore the dependence of topological phenomena on changes in the initial state as well as their robustness in the presence of gain-induced nonlinearity. For quantum systems, we explore the rich PT-symmetric phase diagram resulting from time-periodic, Floquet PT-symmetry [7,8]. This is experimentally implementable in ultracold atomic systems [9], and features a reentrant PT-symmetric phase. Secondly, we examine quantum multi-photon statistics for a simple non-Hermitian model which is transformed and mapped to a system with unitary evolution via a unitary dilation, and is fully realizable on a small-scale quantum simulator [10].
Rb atomic system both experimentally and theoretically. Such an instantaneously reconfigurable anti-PT-symmetric photonic lattice is "written" by two one-dimensional coupling fields, which are arranged alternately along the x direction and can modulate the refractive index of the atomic vapor in a spatially periodical manner via controllable atomic coherence. By properly adjusting the relevant atomic parameters, the phase shift between two adjacent lattice channels occurs in the constructed non-Hermitian photonic system. Such a readily reconfigurable anti-PT-symmetric photonic lattice may open the door for demonstrating the discrete characteristics of the optical waves in periodic anti-PT-symmetric photonic systems.
Abstract We propose a physical scheme to realize optical lattices that are symmetric under a combination of parity and time ( ) reversal. The -symmetric structures can be constructed with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system under the effects of cross-Kerr nonlinearity and Doppler broadening. The atoms are considered in the Gaussian density distribution loaded into the dipole traps of one- and two-dimensional optical lattices. The spatial modulation of the probe field susceptibility is achieved by a proper combination of standing wave strong control fields. With proper detunings and coupling field Rabi frequencies, we find the conditions of achieving -symmetry in optical lattices of nonlinear atoms. We show that the -symmetry can be realized when the cross-Kerr nonlinearity is significantly enhanced, and further demonstrate that it survives the Doppler broadening. Our model is based on experimentally observable and effectively controllable scheme which may find potential applications in optical information processing.