Creation and Characterization of Matter-Wave Breathers.

We report the creation of quasi-1D excited matter-wave solitons, "breathers," by quenching the strength of the interactions in a Bose-Einstein condensate with attractive interactions. We characterize the resulting breathing dynamics and quantify the effects of the aspect ratio of the confining potential, the strength of the quench, and the proximity of the 1D-3D crossover for the two-soliton breather. Furthermore, we demonstrate the complex dynamics of a three-soliton breather created by a stronger interaction quench. Our experimental results, which compare well with numerical simulations, provide a pathway for utilizing matter-wave breathers to explore quantum effects in large many-body systems.

Monopole excitations of a harmonically trapped one-dimensional Bose gas from the ideal gas to the Tonks-Girardeau regime.

Using a time-dependent modified nonlinear Schrödinger equation (MNLSE)-where the conventional chemical potential proportional to the density is replaced by the one inferred from Lieb-Liniger's exact solution-we study frequencies of the collective monopole excitations of a one-dimensional Bose gas. We find that our method accurately reproduces the results of a recent experimental study [E. Haller et al., Science 325, 1224 (2009)] in the full spectrum of interaction regimes from the ideal gas, through the mean-field regime, through the mean-field Thomas-Fermi regime, all the way to the Tonks-Giradeau gas. While the former two are accessible by the standard time-dependent NLSE and inaccessible by the time-dependent local density approximation, the situation reverses in the latter case. However, the MNLSE is shown to treat all these regimes within a single numerical method.

Memory of the initial conditions in an incompletely chaotic quantum system: universal predictions with application to cold atoms.

Two zero-range-interacting atoms in a circular, transversely harmonic waveguide are used as a test bench for a quantitative description of the crossover between integrability and chaos in a quantum system with no selection rules. For such systems we show that the expectation value after relaxation of a generic observable is given by a linear interpolation between its initial and thermal expectation values. The variable of this interpolation is universal; it governs this simple law to cover the whole spectrum of the chaotic behavior from integrable regime through the well-developed quantum chaos. The predictions are confirmed for the waveguide system, where the mode occupations and the trapping energy were used as the observables of interest; a variety of the initial states and a full range of the interaction strengths have been tested.

One-dimensional Bose chemistry: effects of nonintegrability.

Three-body collisions of ultracold identical Bose atoms under tight cylindrical confinement are analyzed. A Feshbach resonance in two-body collisions is described by a two-channel zero-range interaction. Elimination of the closed channel in the three-body problem reduces the interaction to a one-channel zero-range one with an energy-dependent strength. The related integrable Lieb-Liniger-McGuire (LLMG) model, with an energy-independent strength, forbids all chemical processes, such as three-atom association and diatom dissociation, as well as reflection in atom-diatom collisions. The resonant case is analyzed by a numerical solution of the Faddeev equations. The results demonstrate that as the internal symmetry of the LLMG model is lifted, reflection and chemical reactions become allowed and may be observed in experiments.

Atom-Atom Scattering under Cylindrical Harmonic Confinement: Numerical and Analytic Studies of the Confinement Induced Resonance.

It was recently predicted [Phys. Rev. Lett. 81, 938 (1998)]] that atom-atom scattering under transverse harmonic confinement is subject to a "confinement-induced resonance" where the effective one-dimensional coupling strength diverges at a particular ratio of the confinement and scattering lengths. As the initial prediction made use of the zero-range pseudopotential approximation, we now report numerical results for finite-range interaction potentials that corroborate this resonance. In addition, we now present a physical interpretation of this effect as a novel type of Feshbach resonance in which the transverse modes of the confining potential assume the roles of "open" and "closed" scattering channels.

Field-induced magnetic order in quantum spin liquids.

We study magnetic-field-induced three-dimensional ordering transitions in low-dimensional quantum spin liquids, such as weakly coupled, antiferromagnetic spin- 1/2 Heisenberg dimers and ladders. Using stochastic series expansion quantum Monte Carlo simulations, we obtain the critical scaling exponents which dictate the power-law dependence of the transition temperature on the magnetic field. These are compared with recent experiments on candidate materials and with predictions for the Bose-Einstein condensation of magnons. The critical exponents deviate from isotropic mean-field theory and exhibit different scaling behavior at the lower and upper critical magnetic fields.

Bosons in cigar-shaped traps: Thomas-Fermi regime, Tonks-Girardeau regime, and in between.

We present a quantitative analysis of the experimental accessibility of the Tonks-Girardeau gas in present-day experiments with cigar-trapped alkalis. For this purpose we derive, using a Bethe ansatz generated local equation of state, a set of hydrostatic equations describing one-dimensional, delta-interacting Bose gases trapped in a harmonic potential. The resulting solutions cover the entire range of atomic densities.