Effects of Interactions on the Generalized Hong–Ou–Mandel Effect

We numerically investigate the influence of interactions on the generalized Hong–Ou–Mandel (HOM) effect for bosonic particles in a (quasi-)one-dimensional set-up with weak harmonic confinement and show results for the cases of N = 2, N = 3 and N = 4 bosons interacting with a beam splitter, whose role is played by a δ-barrier. In particular, we focus on the effect of attractive interactions and compare the results with the repulsive case, as well as with the analytically available results for the non-interacting case (that we use as a benchmark). We observe a fermionization effect both for growing repulsive and attractive interactions, i.e., the dip in the HOM coincidence count is progressively smeared out, for increasing interaction strengths. The role of input asymmetries is also explored

Progress towards quantum-enhanced interferometry with harmonically trapped quantum matter-wave bright solitons

We model the dynamics of attractively interacting ultracold bosonic atoms in a quasi-one-dimensional wave guide with additional harmonic trapping. Initially, we prepare the system in its ground state and then shift the zero of the harmonic trap and switch on an additional narrow scattering potential near the center of the trap. After colliding with the barrier twice, we propose to measure the number of atoms opposite the initial condition. Quantum-enhanced interferometry with quantum bright solitons allows us to predict detection of an offset of the scattering potential with considerably increased precision as compared to single-particle experiments. In a future experimental realization this might lead to measurement of weak forces caused, for example, by small horizontal gradients in the gravitational potential—with a resolution of several micrometers given essentially by the size of the solitons. Our numerical simulations are based on the rigorously proved effective potential approach developed in previous papers [Phys. Rev. Lett. 102, 010403 (2009) and Phys. Rev. Lett. 103, 210402 (2009)]. We choose our parameters such that the prerequisite of the proof (that the solitons cannot break apart, for energetic reasons) is always fulfilled, thus exploring a parameter regime inaccessible to the mean-field description via the Gross-Pitaevskii equation due to Schrödinger-cat states occurring in the many-particle quantum dynamics

Generating and Manipulating Quantized Vortices On-Demand in a Bose-Einstein Condensate: a Numerical Study

We numerically investigate an experimentally viable method, that we will refer to as the “chopsticks method”, for generating and manipulating on-demand several vortices in a highly oblate atomic Bose-Einstein condensate (BEC) in order to initialize complex vortex distributions for studies of vortex dynamics. The method utilizes moving laser beams (the “chopsticks”) to generate, capture and transport vortices inside and outside the BEC. We examine in detail this methodology and show a wide parameter range of applicability for the prototypical two-vortex case, and show case examples of producing and manipulating several vortices for which there is no net circulation, equal numbers of positive and negative circulation vortices, and for which there is one net quantum of circulation. We find that the presence of dissipation can help stabilize the pinning of the vortices on their respective laser beam pinning sites. Finally, we illustrate how to utilize laser beams as repositories that hold large numbers of vortices and how to deposit individual vortices in a sequential fashion in the repositories in order to construct superfluid flows about the repository beams with several quanta of circulation

Generating Mesoscopic Bell States via Collisions of Distinguishable Quantum Bright Solitons

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 that 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 Rb85 and Cs133. 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

Interactions of solitons with a Gaussian barrier: splitting and recombination in quasi-one-dimensional and three-dimensional settings

The interaction of matter–wave solitons with a potential barrier is a fundamentally important problem, and the splitting and subsequent recombination of the soliton by the barrier is the essence of soliton matter–wave interferometry. We demonstrate the three-dimensional (3D) character of the interactions in the case relevant to ongoing experiments, where the number of atoms in the soliton is relatively close to the collapse threshold. We examine the soliton dynamics in the framework of the effectively one-dimensional (1D) nonpolynomial Schr¨odinger equation (NPSE), which admits the collapse in a modified form, and in parallel we use the full 3D Gross–Pitaevskii equation (GPE). Both approaches produce similar results, which are, however, quite different from those produced in recent work that used the 1D cubic GPE. Basic features, produced by the NPSE and the 3D GPE alike, include (a) an increase in the first reflection coefficient for increasing barrier height and decreasing atom number; (b) large variation of the secondary reflection/recombination probability versus barrier height; (c) pronounced asymmetry in the oscillation amplitudes of the transmitted and reflected fragments; and (d) enhancement of the transverse excitations as the number of atoms is increased. We also explore effects produced by variations of the barrier width and outcomes of the secondary collision upon phase imprinting on the fragment in one arm of the interferometer

Reproducible mesoscopic superpositions of Bose-Einstein condensates and mean-field chaos

In a parameter regime for which the mean-field (Gross-Pitaevskii) dynamics becomes chaotic, mesoscopic quantum superpositions in phase space can occur in a double-well potential, which is shaken periodically. For experimentally realistic initial states, such as the ground state of some 100 atoms, the emergence of mesoscopic quantum superpositions in phase space is investigated numerically. It is shown to be reproducible, even if the initial conditions change slightly. Although the final state is not a perfect superposition of two distinct phase states, the superposition is reached an order of magnitude faster than in the case of the collapse-and-revival phenomenon. Furthermore, a generator of entanglement is identified