We show that solitons occur generically in the thermal equilibrium state of a weakly-interacting elongated Bose gas, without the need for external forcing or perturbations. This reveals a major new quality to the experimentally widespread quasicondensate state, usually thought of as primarily phase-fluctuating. Thermal solitons are seen in uniform 1D, trapped 1D, and elongated 3D gases, appearing as shallow solitons at low quasicondensate temperatures, becoming widespread and deep as temperature rises. This behaviour can be understood via thermal occupation of the Type II excitations in the Lieb-Liniger model of a uniform 1D gas. Furthermore, we find that the quasicondensate phase includes very appreciable density fluctuations, while leaving phase fluctuations largely unaltered from the standard picture derived from a density-fluctuation-free treatment.Solitons, or non-destructible local disturbances, are important features of many one-dimensional (1D) nonlinear wave phenomena. In ultra-cold gases, they have long been sought, and were first observed to be generated by phaseimprinting [1, 2]. More recently, their spontaneous formation in 1D gases was predicted as a result of the Kibble-Zurek mechanism [3, 4], rapid evaporative cooling [5], and dynamical processes after a quantum quench [6]. Here we show that they actually occur generically in the thermal equilibrium state of a weakly-interacting elongated Bose gas, without the need for external forcing or perturbations. This reveals a major new quality to the experimentally widespread quasicondensate state. It can be understood via thermal occupation of the famous and somewhat elusive Type II excitations in the Lieb-Liniger model of a uniform 1D gas [7].A mathematically distinct class of soliton equations are the completely integrable systems. Among them, the GrossPitaevskii[8, 9] equation describes weakly interacting bosons in a 1D geometry in the mean field approximation. The corresponding multi-atom Lieb-Liniger model of N bosons on the circumference of a circle interacting by contact forces [10] has elementary excitations of two kinds: those of a Bogoliubov type and an additional "Type II" branch [7]. These additional excitations have been associated with solitons of the mean field [11][12][13][14]. Although the trapping potential removes integrability, from the early days experimenters have searched for gray solitons. See [15] for a review.Typically, by irradiating one part of the condensate, one engineers a phase difference with the remainder, and a dark soliton forms at the interface between the phase domains[1, 2]. Other proposed schemes involve taking the system away from equilibrium [3][4][5][6]. Our results show that solitons are in fact present spontaneously even in equilibrium. However, engineered solitons have been easier to identify with the standard destructive imaging measurements because their position does not vary from shot to shot.Here we generate a classical field ensemble that describes the weakly interacting Bose gas at thermal equilibri...
We investigate the ground state properties of a polarized dipolar Bose-Einstein condensate trapped in a triple-well potential. By solving the dipolar Gross-Pitaevskii equation numerically for different geometries we identify states which reveal the non-local character of the interaction. Depending on the strength of the contact and dipolar interaction we depict the stable and unstable regions in parameter space.
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