Detecting topological exceptional points in a parity-time symmetric system with cold atoms

Xu, Jian; Du, Yan-Xiong; Huang, Wei; Zhang, Dan‐Wei

doi:10.1364/oe.25.015786

Cited by 17 publications

(12 citation statements)

References 45 publications

(48 reference statements)

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“…One such class of open systems can be descried by a non-Hermitian Hamiltonian. This type of system, realizable in various platforms like photonic lattice [34], phononic media [35], LRC circuits [36] and cold atoms [37,38], has attracted great attention in recent years due to their nontrivial dynamical [39][40][41][42][43][44][45][46][47][48], topological [49][50][51][52][53][54][55][56][57][58][59][60][61][62] and transport properties [63][64][65][66][67][68][69][70]. Many of these features can be traced back to non-Hermitian degeneracy (i.e.…”

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confidence: 99%

Dynamical quantum phase transitions in non-Hermitian lattices

et al. 2018

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In closed quantum systems, a dynamical phase transition is identified by nonanalytic behaviors of the return probability as a function of time. In this work, we study the nonunitary dynamics following quenches across exceptional points in a non-Hermitian lattice realized by optical resonators. Dynamical quantum phase transitions with topological signatures are found when an isolated exceptional point is crossed during the quench. A topological winding number defined by a real, noncyclic geometric phase is introduced, whose value features quantized jumps at critical times of these phase transitions and remains constant elsewhere, mimicking the plateau transitions in quantum Hall effects. This work provides a simple framework to study dynamical and topological responses in non-Hermitian systems.Introduction.-Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behavior of physical observables as functions of time [1,2]. These transitions happen in general if the system is ramped through a quantum critical point. As a promising framework to classify quantum dynamics of nonequilibrium many-body systems, DQPTs have been studied intensively in recent years [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The generality and topological feature of DQPTs were demonstrated in both lattice and continuum systems [20], across different spatial dimensions [21][22][23][24][25], and under various dynamical protocols [26][27][28]. The defining features of DQPTs have also been observed in recent experiments [29][30][31].Following the initial proposal, most studies on DQPTs focus on closed quantum systems undergoing unitary time evolution. Efforts have been made to generalize DQPTs to systems prepared in mixed states [32,33]. However, DQPTs in systems with gain and loss, and therefore subject to nonunitary evolution are largely unexplored. One such class of open systems can be descried by a non-Hermitian Hamiltonian. This type of system, realizable in various platforms like photonic lattice [34], phononic media [35], LRC circuits [36] and cold atoms [37,38], has attracted great attention in recent years due to their nontrivial dynamical [39][40][41][42][43][44][45][46][47][48], topological [49][50][51][52][53][54][55][56][57][58][59][60][61][62] and transport properties [63][64][65][66][67][68][69][70]. Many of these features can be traced back to non-Hermitian degeneracy (i.e. exceptional) points mediating gap closing and reopening transitions on the complex plane [71][72][73][74][75][76]. In this work, we explore DQPTs in non-Hermitian systems, with a focus on topological signatures in nonunitary evolution following quenches across exceptional points (EPs).Theory.-We start by summarizing the theoretical framework of DQPTs for systems described by non-Hermitian lattice Hamiltonians. The nonunitary time evolution of the system is governed by a Schrödinger equation i d dt |Ψ(t) = H|Ψ(t) . For concreteness, we present the formalism with a one-dimensional twoband lattice model in mind, while the g...

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Dynamical quantum phase transitions in non-Hermitian lattices

et al. 2018

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“…The exceptional points (EPs) of the non-Hermitian Hamiltonian are the special parameter points where both the eigenvalues and eigenvectors "degenerate" into only one value and vector [32,33]. The EPs exhibit novel properties in both classical and quantum non-Hermitian systems [34][35][36][37][38][39][40][41]. Suppose that λ is the tuning parameter of the non-Hermitian Hamiltonian H(λ).…”

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General properties of fidelity in non-Hermitian quantum systems with PT symmetry

Tu¹,

Jang²,

Chang³

et al. 2022

Preprint

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The fidelity susceptibility is a tool for studying quantum phase transitions in the Hermitian condensed matter systems. Recently, it has been generalized with the biorthogonal basis for the non-Hermitian quantum systems. From the general perturbation description with the constrain of parity-time (PT) symmetry, we show that the fidelity F is always real for the PT-symmetric states. For the PT-broken states, the real part of the fidelity susceptibility equals to one half of the sum of the fidelity susceptibility of the PT-broken and the PT-partner states, Re[XF ] = 1 2 (XF + XF ). The negative infinity of the fidelity susceptibility is explored by the perturbation theory when the parameter approaches the exceptional point (EP). Moreover, at the second-order EP where two eigenstates and eigenenergies coalesce, we prove that the real part of the fidelity between PTsymmetric and PT-broken states is ReF = 1 2 . We demonstrate these general properties for noninteracting and interacting systems by two examples: the two-legged non-Hermitian Su-Schrieffer-Heeger (SSH) model and the non-Hermitian XXZ spin chain.

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“…While the energy eigenvalues for non-Hermitian Hamiltonians are complex in general, the PT -symmetry of a Hamiltonian ensures either all real (PT -symmetric) or complex conjugate pairs (PT -broken) of complex eigenvalues, with two regions separated by an exceptional point [35,36]. In ultracold atomic gases, the physical realization [40][41][42][43] as well as associated single particle physics [44][45][46][47][48][49][50] of PTsymmetry have been investigated in both theory and experiment. Recently non-Hermitian fermionic superfluidity at zero temperature with complex-valued interactions or PT -symmetric pairing states have been studied in theory [51][52][53][54].…”

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$\mathcal{PT}$-Symmetry Enhanced Berezinskii-Kosterlitz-Thouless Superfluidity

Li,

Luo,

Zhang

2021

Preprint

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Berezinskii-Kosterlitz-Thouless (BKT) transition, the topological phase transition to a quasilong range order in a two-dimensional (2D) system, is a hallmark of low-dimensional topological physics. The recent emergence of non-Hermitian physics, particularly parity-time (PT ) symmetry, raises a natural question about the fate of low-dimensional orders (e.g., BKT transition) in the presence of complex energy spectrum. Here we investigate the BKT phase transition in a 2D degenerate Fermi gas with an imaginary Zeeman field obeying PT -symmetry. Despite complex energy spectrum, PT -symmetry guarantees that the superfluid density and many other quantities are real. Surprisingly, the imaginary Zeeman field enhances the superfluid density, yielding higher BKT transition temperature than that in Hermitian systems. In the weak interaction region, the transition temperature can be much larger than that in the strong interaction limit. Our work showcases a surprising interplay between low-dimensional topological defects and non-Hermitian effects, paving the way for studying non-Hermitian low-dimensional phase transitions.Berezinskii-Kosterlitz-Thouless (BKT) transition, first discovered in the two-dimensional (2D) XY spin model [1-4], is a cornerstone for studying lowdimensional condensed matter physics [5]. In 2D systems, while Mermin-Wagner theorem forbids the emergence of a true long range order due to thermal fluctuations, BKT physics permits a topological phase transition to a quasi-long range order of topological defects (i.e., vortices) at very low temperature. Specifically, across a critical temperature T BKT , free vortices bind together spontaneously and form bound vortex-antivortex (V-AV) pairs, giving rising to a quasi-long range order. BKT transitions have been experimentally studied in a wide range of systems, including liquid helium films [6], 2D magnets [7-10], superconducting thin films [11][12][13][14], and 2D atomic hydrogen [15], where only macroscopic properties of the systems can be measured. In recent years, ultracold atomic superfluids have emerged as a versatile playground for the studies of BKT physics [16][17][18][19][20][21][22][23][24][25][26][27][28][29] with access to the underlying microscopic phenomena such as the visualization of the proliferation of free vortices. Experimental signatures of BKT physics have been observed in harmonically trapped , and the recent realization of ultracold superfluids in box potentials [30][31][32][33][34] offers a uniform platform for exploring BKT transitions.

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Detecting topological exceptional points in a parity-time symmetric system with cold atoms

Cited by 17 publications

References 45 publications

Dynamical quantum phase transitions in non-Hermitian lattices

Dynamical quantum phase transitions in non-Hermitian lattices

General properties of fidelity in non-Hermitian quantum systems with PT symmetry

$\mathcal{PT}$-Symmetry Enhanced Berezinskii-Kosterlitz-Thouless Superfluidity

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