Perpetual emulation threshold of PT-symmetric Hamiltonians

TL;DR

This paper presents a method to emulate PT-symmetric Hamiltonians with gain and loss using unitary dynamics of a larger quantum system, enabling indefinite emulation time through amplitude recycling.

Contribution

It introduces an amplitude recycling scheme that allows indefinite emulation of PT-symmetric Hamiltonians within a larger quantum system, overcoming non-unitary limitations.

Findings

Successfully emulates PT-symmetric dynamics with indefinite duration.

Proposes a realistic implementation with ultracold atoms.

Extends the emulation time despite non-unitary nature.

Abstract

We describe a technique to emulate a two-level \PT-symmetric spin Hamiltonian, replete with gain and loss, using only the unitary dynamics of a larger quantum system. This we achieve by embedding the two-level system in question in a subspace of a four-level Hamiltonian. Using an \textit{amplitude recycling} scheme that couples the levels exterior to the \PT-symmetric subspace, we show that it is possible to emulate the desired behaviour of the \PT-symmetric Hamiltonian without depleting the exterior, reservoir levels. We are thus able to extend the emulation time indefinitely, despite the non-unitary \PT dynamics. We propose a realistic experimental implementation using dynamically decoupled magnetic sublevels of ultracold atoms.