Asymmetric steering in coherent transport of atomic population with a three-well Bose-Hubbard model

TL;DR

This paper investigates asymmetric EPR steering in a three-well Bose-Hubbard model during coherent atomic transport, revealing initial state dependence and directional asymmetry in quantum correlations.

Contribution

It demonstrates that EPR steering occurs only with initial Fock states and exhibits time-dependent asymmetry during transport, using phase-space stochastic methods.

Findings

Steering is only observed for initial Fock states.

Steering exhibits directional asymmetry that reverses over time.

Inseparability is confirmed between wells for Fock initial states.

Abstract

We analyse the Einstein-Podolsky-Rosen (EPR) steering properties in a three-well Bose-Hubbard model under the mechanism of coherent transport of atomic population (CTAP). This process, also known as transport without transit (TWT), transfers condensed atoms from one well of a lattice potential to another, non-adjacent well, without macroscopic occupation of the middle well. The dynamics and entanglement properties of this system have previously been analysed and shown to be dependent on the initial quantum state of the atoms in the first well. In this work we utilise the phase-space method of stochastic integration in the positive-P representation. The system demonstrated inseparability between the wells for Fock initial states, and we show that steering is also only found for an initial Fock state. Depending on how we write our steering inequalities, steering is seen at different times, showing a basic asymmetry. This means that for part of the evolution, Alice can steer Bob but not vice versa. After the midpoint of the population transfer, this situation reverses.