Generating persistent-current superpositions in Bose-Einstein condensates using dynamic optical potentials

TL;DR

The paper addresses how to generate persistent-current superpositions in Bose-Einstein condensates using dynamic optical potentials. It introduces a wave function engineering approach that independently controls amplitude and phase through time-dependent trapping and phase imprinting, and demonstrates, via 2D Gross-Pitaevskii simulations, high-fidelity engineering of ring-state superpositions approximating cosine-azimuthal profiles. The work shows that the ENG state can closely match the target OAM state with robustness to weak self-interactions, and it develops a simple two-state model to explain stability and mode coupling, confirming practical feasibility with existing light-sculpting techniques. These results have implications for compact, portable atom interferometers and rotation sensing, and open avenues for engineering arbitrary motional states in quantum information tasks.

Abstract

Precise and flexible manipulation of the motional state of ultracold atoms is a fundamental enabling technology for diverse applications such as quantum sensing and quantum computation. In this paper we propose a general, simple and highly efficient method to engineer the motional state of a Bose-Einstein condensate with time-dependent optical fields, which can be realized experimentally with existing light sculpting techniques. We demonstrate numerically how to engineer superpositions of persistent currents in a toroidal trap, achieving very high fidelity. We also study in detail the stability of the state over time, and we present an analytical two-state model that approximates well the evolution of the state in presence of self-interactions.

Figures (9)

• Figure 1: Wave function engineering in a linear trap $V_\text{box}(x)$. (a) The initial state is the ground state of potential $V_\text{box,b}(x)$. (b) We suddenly remove the barriers and, at the same time, apply a $\pi$-phase imprint to the $2^\text{nd}$ and $4^\text{th}$ lobes of the wave function. (c) Final state: the phase imprint flips the corresponding parts of the wave function, so that the resulting state closely approximates the $3^\text{rd}$ excited state of $V_\text{box}(x)$.
• Figure 2: Wave function engineering in a ring trap. The red circle indicates the ring radius. The barriers are created with linear repulsive potentials. In this case, we populate an $|\textrm{OAM} \rangle$ state with $m=3$.
• Figure 3: Fidelity $F = |\langle \textrm{OAM}| \textrm{ENG} \rangle|^2$ as a function of barrier height for a non-interacting condensate, and for interacting condensates with $N=10^3,10^4$. The two cases $m=3$ and $m=9$ are shown.
• Figure 4: Square modulus of the autocorrelation function for the $|\textrm{OAM} \rangle$ and $|\textrm{ENG} \rangle$ states with no self-interactions. The two cases $m=3$ and $m=9$ are shown. The insets represent the atomic density for the $| \textrm{ENG} \rangle$ states with $m=3,9$ at $t=2$ s.
• Figure 5: Square modulus of the autocorrelation function for the $|\textrm{ENG} \rangle$ state in presence of self-interactions, for $m = 3,9$ and $N = 10^3, 10^4$. The insets represent the atomic density at chosen times for $N=10^4$.