Tilted optical lattices with defects as realizations of PT symmetry in Bose-Einstein condensates

TL;DR

This paper proposes an experimental setup using a tilted optical lattice with defects to realize PT symmetry in Bose-Einstein condensates, providing a practical approach to emulate complex quantum systems.

Contribution

It introduces a method to implement PT symmetry in BECs via a tilting optical lattice with defects, bridging theoretical models and experimental realization.

Findings

Mapping of the system to a matrix model enables analysis of PT symmetry conditions.

Conditions for two wells to emulate PT-symmetric behavior are derived.

Stepwise increase of system size demonstrates scalability of the approach.

Abstract

A PT-symmetric Bose-Einstein condensate can theoretically be described using a complex optical potential, however, the experimental realization of such an optical potential describing the coherent in- and outcoupling of particles is a nontrivial task. We propose an experiment for a quantum mechanical realization of a PT-symmetric system, where the PT-symmetric currents are implemented by an accelerating Bose-Einstein condensate in a titled optical lattice. A defect consisting of two wells at the same energy level then acts as a PT-symmetric double-well if the tilt in the energy offsets of all further wells in the lattice is varied in time. We map the time-dependence of the amplitudes of a frozen Gaussian variational ansatz to a matrix model and increase the system size step by step starting with a six-well setup. In terms of this simple matrix model we derive conditions under which two wells of the Hermitian multi-well system behave exactly as the two wells of the PT-symmetric system.