Generating Mesoscopic Bell States via Collisions of Distinguishable Quantum Bright Solitons

Abstract

We investigate numerically the collisions of two distinguishable quantum matter-wave bright solitons in a one-dimensional harmonic trap. We show that such collisions can be used to generate mesoscopic Bell states which can reliably be distinguished from statistical mixtures. Calculation of the relevant s-wave scattering lengths predicts that such states could potentially be realized in quantum-degenerate mixtures of 85 Rb and 133 Cs. In addition to fully quantum simulations for two distinguishable two-particle solitons, we use a mean-field description supplemented by a stochastic treatment of quantum fluctuations in the soliton's center of mass: We demonstrate the validity of this approach by comparison to a mathematically rigorous effective potential treatment of the quantum many-particle problem. Generating quantum entanglement between mesoscopic objects over mesoscopic distances allows exploration of a fascinating "middle-ground" between quantum and classical physics [1,2], and promises significant advances in quantum-enhanced interferometry [3]. The high degree of experimental control offered by quantum-degenerate gases makes them an ideal platform with which to explore such multi-particle entanglement [4,5]. From a fundamental perspective, the creation of maximally-entangled many-particle Bell states in quantum-degenerate gases presents an intriguing proposition. The generation of similar macroscopic Bell states of many photons is an area of current theoretical and experimental research [6,7]. In addition to their inherent fundamental interest, such states are of potential application as a resource in quantum information [7].Previously, the scattering of quantum bright matterwave solitons [8][9][10][11][12][13][14][15][16][17] in quasi-one-dimensional (1D) trapping geometries has been suggested as a way to create mesoscopic entangled states in single-species BoseEinstein condensates (BECs) [13,18,19]. In this Letter we consider a dual-species BEC [20,21] where |A, B (|B, A ) signifies that the BEC A is on the left (right) and the BEC B is on the right (left). In particular, we show that a favorable combination of interand intra-species s-wave scattering lengths means that such states may be realized using 85 Rb and 133 Cs mixtures. We also show that the interference properties of these bright-soliton Bell states distinguish them from statistical mixtures. In contrast to the Bell ground states associated with double-well potentials, our collisionallygenerated Bell states are robust to the presence of asymmetries. While distinguishable solitons are essential to produce Bell states, entanglement generation for solitons of the same species was investigated in [13].For our quasi-1D system, we consider an experimentally motivated harmonic confinement ω = 2πf . Mixtures of ultracold gases can be confined in a common optical trap with the same trap frequencies [24], yieldingwhere m A (m B ) is the atomic mass of species A (B); the interactions g = hf ⊥ a are set by the scattering lengths a and the perpendicular tra...

Beyond-mean-field behavior of large Bose-Einstein condensates in double-well potentials

“…As the ACSs are not orthogonal the associated N -particle state (7) has a certain extension in phase space that gets smaller with increasing particle number N and eventually vanishes in the mean field (2). To account for these quantum mechanical uncertainties often semiclassical methods, where a phase-space distribution is propagated, are used [24][25][26][27][28][29][30][31][32]. On the N -particle level it was demonstrated in [22] that a hyperbolic fixed point acts as a generator of mesoscopic entanglement.…”

“…One approach to explain parts of the behavior of quantum systems is to average over mean-field solutions, so-called truncated Wigner methods [25,[28][29][30][31][32]. For a BEC in a double well, the Husimi distribution (10) can be used to average over mean-field solutions (Refs.…”

“…In general, situations with important quantum correlations, where a mean-field approach is no longer adequate, are in the focus of current research, e.g., many-particle entanglement [15], the experimental realization * b.gertjerenken@uni-oldenburg.de of entangled squeezed states [16], mesoscopic quantum superpositions [17][18][19][20][21], and mean-field chaos [22,23]. In order to estimate time scales on which the mean-field dynamics still agrees with N -particle quantum dynamics, classical-field methods can be used to approximate the quantum dynamics by averaging over mean-field solutions [24][25][26][27][28][29][30][31][32], thus mimicking quantum uncertainties that disappear in the mean-field limit (2) but will always be present for finite particle numbers.…”

Bright-soliton quantum superpositions: Signatures of high- and low-fidelity states

“…tinguishable solitons [13], and collision dynamics and entanglement generation of two initially independent and indistinguishable boson pairs [28]. While a mean-field description has been found to successfully describe many aspects in the scattering dynamics of bright solitons for high kinetic energies [15,20,29] considerably deviating behavior has been predicted for lower kinetic energies.…”

“…Recent suggestions for realizations of nonlocal mesoscopic superpositions include Bose-Einstein condensates (BECs) [3], cavity quantum optomechanical systems [4] and topological defects [5]. Bright solitons 1 , self-bound matter-waves generated from Bose-Einstein condensates [6,7] are, in their quantum version [8][9][10], a particularly promising system to generate quantum superpositions [11][12][13].…”