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arXiv:2304.03471 · Physical Review A

Quantum dynamics of non-Hermitian many-body Landau-Zener systems

Rajesh K. Malla, Julia Cen, Wilton J. M. Kort-Kamp, Avadh Saxena

Published Dec 18, 2023• 6 citations
arXivHTMLPDF

Abstract

We develop a framework to solve a large class of linearly driven non-Hermitian quantum systems. Such a class of models in the Hermitian scenario is commonly known as multistate Landau-Zener models. The non-Hermiticity is due to the anti-Hermitian couplings between the diabatic levels. We find that there exists a conservation law, unique to this class of models, that describes the simultaneous growth of the unnormalized wave functions. These models have practical applications in Bose-Einstein condensates, and they can describe the dynamics of multispecies bosonic systems. The conservation law relates to a pair-production mechanism that explains the dissociation of diatomic molecules into atoms. We provide a general framework for both solvable and semiclassically solvable non-Hermitian Landau-Zener models. Our findings will open alternative avenues for a number of diverse emergent phenomena in explicitly time-dependent non-Hermitian quantum systems.

DOI
10.1103/physreva.108.062217

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We develop a framework to solve a large class of linearly driven non-Hermitian quantum systems. Such a class of models in the Hermitian scenario is commonly known as multistate Landau-Zener models. The non-Hermiticity is due to the anti-Hermitian couplings between the diabatic levels. We find that there exists a conservation law, unique to this class of models, that describes the simultaneous growth of the unnormalized wave functions. These models have practical applications in Bose-Einstein condensates, and they can describe the dynamics of multispecies bosonic systems. The conservation law relates to a pair-production mechanism that explains the dissociation of diatomic molecules into atoms. We provide a general framework for both solvable and semiclassically solvable non-Hermitian Landau-Zener models. Our findings will open alternative avenues for a number of diverse emergent phenomena in explicitly time-dependent non-Hermitian quantum systems.
We propose a simple ansatz that allows us to generate new exactly solvable multistate Landau-Zener models. It is based on a system of two decoupled two-level atoms whose levels vary with time and cross at some moments. Then we consider multiparticle systems with Heisenberg equations for annihilation operators having a similar structure as the Shr\"odinger equation for amplitudes in multistate Landau-Zener models and show that the corresponding Shr\"odinger equation in the multiparticle sector belongs to the multistate Landau-Zener class. This observation allows us to generate new exactly solvable models from already known ones. We discuss possible applications of the new solutions in the problem of the driven charge transport in quantum dots.
Abstract The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians (Sinitsyn et al 2018 Phys. Rev. Lett . 120 190402). Within the multistate Landau–Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models (Sinitsyn and Chernyak 2017 J. Phys. A: Math. Theor . 50 255203). Here we compare both methods by applying them to a new class of exactly solvable MLZ models. This class contains systems with an arbitrary number of interacting states and shows quick growth with N number of exact adiabatic energy crossing points, which appear at different moments of time. At each N , transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with N quickly. We illustrate how common features of solvable MLZ systems appear from quantum integrability and develop an approach to further classification of solvable MLZ problems.
Nanoscale systems have sizes intermediate between atomic and macroscopic ones. Therefore their treatment often requires a combination of methods from atomic and condensed matter physics. The conventional Landau-Zener theory, being a powerful tool in atomic physics, often fails to predict correctly nonadiabatic transition probabilities in various nanostructures because it does not include many-body effects typical for mesoscopics. In this research project the generalizations of the Landau-Zener theory that solve this problem were studied. The multistate, multiparticle and nonunitary extensions of the theory have been proposed and investigated. New classes of exactly solvable models have been derived. I discuss their applications in problems of the molecular condensate dissociation and of the driven charge transport. In application to the physics of nanomagnets new approaches in modeling the influence of the environment on the Landau-Zener evolution are proposed and simple universal formulas are derived for the extensions of the theory that include the coupling to noise and the nuclear spin bath.
Abstract We discuss a class of models that generalize the two-state Landau–Zener Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution can be understood in great detail. Here, we present an approach to classify such solvable models, namely, to identify all their independent families for a given number N of interacting states and prove the absence of such families for some types of interactions. We also discuss how, within a solvable family, one can classify the scattering matrices, i.e., the system’s dynamics. Due to the possibility of such a detailed classification, the multitime Landau–Zener model defines a useful special function of theoretical physics.
We study the dynamics of non-adiabatic transitions in non-Hermitian multi-level parabolic models where the separations of the diabatic energies are quadratic function of time. The model Hamiltonian has been used to describe the non-Hermitian dynamics of two pairs of coupled cavities. In the absence of the coupling between any two pairs of cavities, the wave amplitudes within each subsystem are described by the tri-confluent Heun functions. When all the couplings between the cavities are present, we reduce the dynamics into a set of two coupled tri-confluent Heun equations, from which we derive analytical approximations for the wave amplitudes at different physical limits.
Abstract Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. In addition, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.