Survival, decay, and topological protection in non-Hermitian quantum transport

Rudner, Mark S.; Levin, Michael; Levitov, Leonid S.

doi:10.48550/arxiv.1605.07652

Cited by 22 publications

(50 citation statements)

References 22 publications

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“…As the nonlinear coefficient increases from zero, the mean displacement deviates from the quantized behavior gradually. In particular, the original "topological trivial" region (where ∆m = 0 in the linear case [1,3]) almost disappears upon increasing U , with the values of ∆m approaching unity over the whole parametric range. In other words, the particle always hops to the right unit cell for large enough U , regardless of the relative values of µ and ν.…”

Section: Nonlinearity Induced Trivial-nontrivial Transitionmentioning

confidence: 99%

“…We start by briefly reviewing the original RL model [1,3,4], where each unit cell of the one-dimensional dimerized lattice contains a lossy site A and a neutral site B, as shown in Fig. 1.…”

Section: The Rudner-levitov Modelmentioning

confidence: 99%

“…This is equivalent to the winding number of the relative phase between components of the Bloch wave function [i.e., the eigenstate of the Fourier transformation of H(m)] and is thus topologically protected [1,3,28,29]. Specifically, if one initializes a single particle at a neutral site, the mean displacement ∆m takes the value of 0 for ν < µ and takes the value of 1 for ν > µ, which precisely predicts the topological phase transition of this model.…”

Section: The Rudner-levitov Modelmentioning

confidence: 99%

“…Specifically, if one initializes a single particle at a neutral site, the mean displacement ∆m takes the value of 0 for ν < µ and takes the value of 1 for ν > µ, which precisely predicts the topological phase transition of this model. Such an archetype model has been well investigated both theoretically [1,3] and experimentally [4], and has also been extended in many directions [23,24,[30][31][32][33][34][35][36][37][38]. In the following, we generalize the RL model to a few instances with nonlinear hopping terms and study the quantum transport therein.…”

Section: The Rudner-levitov Modelmentioning

confidence: 99%

“…The Rudner-Levitov (RL) model [1], which can be viewed as a simple non-Hermitian extension of the Su-Schrieffer-Heeger (SSH) model [2], has been predicted to support quantized quantum transport with topological protection [1,3] has been verified experimentally in a lattice of optical waveguides [4]. This important feature not only shows the possibility of accessing nontrivial topological phases in physical systems where dissipations are intrinsic and unavoidable, but also provides a direct way to detect the topology of such systems by monitoring their bulk properties.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Quantum transport in nonlinear Rudner-Levitov models

Du,

Wu,

Artoni

et al. 2021

Preprint

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Quantum transport in a class of nonlinear extensions of the Rudner-Levitov model is numerically studied in this paper. We show that the quantization of the mean displacement, which embodies the quantum coherence and the topological characteristics of the model, is markedly modified by nonlinearities. Peculiar effects such as a "trivial-nontrivial" transition and unidirectional longrange quantum transport are observed. These phenomena can be understood on the basis of the dynamic behavior of the effective hopping terms, which are time and position dependent, containing contributions of both the linear and nonlinear couplings.d nonlinear couplings.

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Section: Nonlinearity Induced Trivial-nontrivial Transitionmentioning

confidence: 99%

Section: The Rudner-levitov Modelmentioning

confidence: 99%

Section: The Rudner-levitov Modelmentioning

confidence: 99%

Section: The Rudner-levitov Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantum transport in nonlinear Rudner-Levitov models

Du,

Wu,

Artoni

et al. 2021

Preprint

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Tuning of topological interface modes in an elastic beam array system with inerters

Cajić

Christensen

Adhikari

2021

International Journal of Mechanical Sciences

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Fixed Points and Dynamic Topological Phenomena in a Parity-Time-Symmetric Quantum Quench

Qiu

Deng

et al. 2019

iScience

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We identify emergent topological phenomena such as dynamic Chern numbers and dynamic quantum phase transitions in quantum quenches of the non-Hermitian Su-Schrieffer-Heeger Hamiltonian with parity-time (PT ) symmetry. Their occurrence in the non-unitary dynamics are intimately connected with fixed points in the Brillouin zone, where the states do not evolve in time. We construct a theoretical formalism for characterizing topological properties in non-unitary dynamics within the framework of biorthogonal quantum mechanics, and prove the existence of fixed points for quenches between distinct static topological phases in the PT -symmetry-preserving regime. We then reveal the interesting relation between different dynamic topological phenomena through the momentumtime spin texture characterizing the dynamic process. For quenches involving Hamiltonians in the PT -symmetry-broken regime, these topological phenomena are not ensured.The exploration of topological matter constitutes a major theme in modern physics [1,2]. With rapid progress in the discovery and understanding of topological phases in solid-state materials, a challenging quest lies in extending the study of conventional topological matter to novel regimes. Prominent examples include the investigation of emergent topological properties in out-of-equilibrium dynamics [3-28] and the characterization of topological phases in non-Hermitian systems [29? -40]. With the flexible controls afforded by synthetic systems such as ultracold atoms and engineered photonic configurations, the experimental implementation of these interesting scenarios is already within reach [41][42][43][44][45][46][47][48][49][50].An exemplary situation for the study of topological properties in out-of-equilibrium dynamics is the quantum quench of a topological system, where the ground state of the initial Hamiltonian H i is subject to a unitary time evolution governed by the final Hamiltonian H f . Whereas the topological invariant characterizing the instantaneous state is unchanged during the unitary dynamics [8,9], previous studies have revealed the emergence of intriguing phenomena such as dynamic quantum phase transitions (DQPTs) [13-18, 45, 51] and quantized non-equilibrium Hall responses in quench processes [19][20][21]. Further, in a series of recent theoretical and experimental studies, it has been established that dynamic topological invariants can be defined in unitary quantum quenches, which are related to the topology of initial and final Hamiltonians in equilibrium [23][24][25]44].Here arises an interesting question: what if the quench dynamics is non-unitary and governed by non-Hermitian Hamiltonians? The question is particularly relevant in light of recent studies on topological phenomena in parity-time(PT )-symmetric non-Hermitian systems [32][33][34][46][47][48]. Under PT symmetry, eigenenergies of a non-Hermitan Hamiltonian are entirely real in the PTsymmetry-preserving regime, in contrast to regimes with spontaneously broken PT symmetry [52][53][54]. Whereas it has be...

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Survival, decay, and topological protection in non-Hermitian quantum transport

Cited by 22 publications

References 22 publications

Quantum transport in nonlinear Rudner-Levitov models

Quantum transport in nonlinear Rudner-Levitov models

Tuning of topological interface modes in an elastic beam array system with inerters

Fixed Points and Dynamic Topological Phenomena in a Parity-Time-Symmetric Quantum Quench

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