We present numerical results from solving the time-dependent nonlinear Schrödinger equation (NLSE) that describes an inhomogeneous, weakly interacting Bose-Einstein condensate in a small harmonic trap potential at zero temperature. With this method we are able to find solutions for the NLSE for ground state condensate wave functions in one dimension or in three dimensions with spherical symmetry. These solutions corroborate previous ground state results obtained from the solution of the time-independent NLSE. Furthrmore, we can examine the time evolution of the macroscopic wave function even when the trap potential is changed on a time scale comparable to that of the condensate dynamics, a situation that can be easily achieved in magneto-optical traps. We show that there are stable solutions for atomic species with both positive and negative s-wave scattering lengths in one-dimensional (1D) and 3D systems for a fixed number of atoms. In both the 1D and 3D cases, these negative scattering length solutions have solitonlike properties. In 3D, however, these solutions are only stable for a modest range of nonlinearities. We analyze the prospects for diagnosing Bose-Einstein condensation in a trap using several experiments that exploit the time-dependent behavior of the condensate.

Atomtronics deals with matter-wave circuits of ultracold atoms manipulated through magnetic or laser-generated guides with different shapes and intensities. In this way, new types of quantum networks can be constructed in which coherent fluids are controlled with the know-how developed in the atomic and molecular physics community. In particular, quantum devices with enhanced precision, control, and flexibility of their operating conditions can be accessed. Concomitantly, new quantum simulators and emulators harnessing on the coherent current flows can also be developed. Here, the authors survey the landscape of atomtronics-enabled quantum technology and draw a roadmap for the field in the near future. The authors review some of the latest progress achieved in matter-wave circuits' design and atom-chips. Atomtronic networks are deployed as promising platforms for probing many-body physics with a new angle and a new twist. The latter can be done at the level of both equilibrium and nonequilibrium situations. Numerous relevant problems in mesoscopic physics, such as persistent currents and quantum transport in circuits of fermionic or bosonic atoms, are studied through a new lens. The authors summarize some of the atomtronics quantum devices and sensors. Finally, the authors discuss alkali-earth and Rydberg atoms as potential platforms for the realization of atomtronic circuits with special features.

We apply linear-response analysis of the Gross-Pitaevskii equation to obtain the excitation frequencies of a Bose-Einstein condensate confined in a time-averaged orbiting potential trap. Our calculated values are in excellent agreement with those observed in a recent experiment.

We present a numerical technique to solve the time-independent nonlinear Schrödinger equation with an external potential. We apply it to the case of a dilute Bose-condensed assembly of trapped neutral atoms where the potential varies on the same scale as the condensate. This situation should soon be accessible to experimental observation.

We analyze and experimentally demonstrate a new (temporal) Talbot effect, where a pulsed phase grating is applied to a cloud of cold atoms (Bose-Einstein condensate). In contrast to the usual (spatial) Talbot effect, our atoms gain kinetic energy when diffracted by the pulsed grating. The energy gain and the matter-wave-dispersion relation result in an exact (no paraxial approximation) Talbot effect where the initial wave front is reconstructed at multiples of a “Talbot time” $T_{\mathrm{T}}$. We demonstrate the Talbot effect by applying a second pulsed phase grating after a variable delay. When this second grating is applied at even (odd) multiples of $T_{\mathrm{T}}/2\mathrm{}$, it doubles (cancels) the effect of the first pulsed grating.

We present experimental and theoretical studies of the coherence properties of a Bose-Einstein condensate (BEC) using an interference technique. Two optical standing wave pulses of duration 100 ns and separation $\Delta t$ are applied to a condensate. Each standing wave phase grating makes small copies of the condensate displaced in momentum space. The quantum mechanical amplitudes of each copy interfere, depending on $\Delta t$ and on spatial phase variations across the condensate. We find that the behavior of a trapped BEC is consistent with a uniform spatial phase. A released BEC, however, exhibits large phase variation across the condensate.