Dynamical quantum phase transitions in non-Hermitian lattices

Abstract

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...

Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory

“…Now, by combining Eqs. (32) and (33), and using the operatorsâ † j , j = 1, 2 instead of the operatorÔ, one obtains the following solution for the TTCF,…”

“…EPs have been discussed in electronics [20], optomechanics [13,21,22], acoustics [23,24], plasmonics [25], and metamaterials [26]. The concept of EPs has been successfully applied in the description of dynamical quantum phase transitions and topological phases of matter in open quantum systems (see, e.g., [27][28][29][30][31][32][33][34][35][36]).…”

Floquet dynamical quantum phase transitions

“…If pre-quench and post-quench systems are in topologically distinct phases, DQPTs may also be characterized by dynamical topological invariants [3][4][5]. As a promising approach to classify quantum states of matter in nonequilibrium situations, DQPTs have been theoretically explored in both closed and open quantum systems at different physical dimensions [2,7,8]. Experimentally, DQPTs have been observed in trapped ions [3,10], cold atoms [11,12], superconducting qubits [13], nanomechanical oscillators [14], and photonic quantum walks [15,16].To date, in most studies of DQPTs, a quantum quench acts as a trigger for initiating nonequilibrium dynamics and then exposing the underlying topological features.…”

Observation of dynamical phase transitions in a topological nanomechanical system

“…Experimentally exploring the bulk-edge relations in quenched dynamics will be an interesting and important problem deserved further study. In addition, our system can be used to study more complicated phenomena including interplay between topology, dissipation and nonequilibrium dynamics 32 .…”