Quantum-classical correspondence of a system of interacting bosons in a triple-well potential

E. R. Castro,Lea F. Santos,I. Roditi,Jorge Chávez-Carlos,Jorge G. Hirsch

doi:10.22331/q-2021-10-19-563

Abstract

We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the quantum system and how they could be used for quantum information science. In the integrable limits, our analysis of the stationary points of the semiclassical Hamiltonian reveals critical points associated with second-order quantum phase transitions. In the nonintegrable domain, the system exhibits crossovers. Depending on the parameters and quantities, the quantum-classical correspondence holds for very few bosons. In some parameter regions, the ground state is robust (highly sensitive) to changes in the interaction strength (tilt amplitude), which may be of use for quantum information protocols (quantum sensing).

Highlights

Studies of the quantum-classical correspondence provide insights into the properties of both the quantum system and its classical counterpart
We explore the quantum-classical correspondence for yet another goal, that of locating the quantum phase transition points of a system of interacting bosons in a triple-well potential
With the semiclassical Hamiltonian of our triplewell system, we find the stationary points of the classical dynamics and use them to identify the critical points of quantum phase transitions

Summary

Introduction

Studies of the quantum-classical correspondence provide insights into the properties of both the quantum system and its classical counterpart. The tilt is an additional control parameter that expands the versatility of the model and allows for its possible application as an atomtronic switching device [40] and as a generator of entangled states [41] This is the system that we analyze here, both in its integrable and nonintegrable regimes. We analyze how the quantum-classical correspondence for the lowest energy state depends on the total number of bosons. This point is related with the question of how many particles are needed for a system to reveal many-body features [42, 49], a subject of current experimental interest [50, 51].

Quantum Hamiltonian

Classical Hamiltonian and Stationary Points

Integrable limits

Nonintegrable regime

Discussion

A Equations for the nonintegrable regime