When a system crosses a second-order phase transition on a finite timescale, spontaneous symmetry breaking can cause the development of domains with independent order parameters, which then grow and approach each other creating boundary defects. This is known as Kibble-Zurek mechanism. Originally introduced in cosmology, it applies both to classical and quantum phase transitions, in a wide variety of physical systems. Here we report on the spontaneous creation of solitons in Bose-Einstein condensates via the Kibble-Zurek mechanism. We measure the power-law dependence of defects number with the quench time, and provide a check of the Kibble-Zurek scaling with the sonic horizon. These results provide a promising test bed for the determination of critical exponents in Bose-Einstein condensates.The Kibble-Zurek mechanism (KZM) describes the spontaneous formation of defects in systems that cross a second-order phase transition at finite rate [1][2][3][4]. The mechanism was first proposed in the context of cosmology to explain how during the expansion of the early Universe the rapid cooling below a critical temperature induced a cosmological phase transition resulting in the formation domain structures. In fact, the KZM is ubiquitous in nature and regards both classical and quantum phase transitions [5,6]. Experimental evidences have been observed in superfluid 4 He [7,8] and 3 He [9,10], in superconducting films [11] and rings [12][13][14][15][16] and in ion chains [17,18]. Bose-Einstein condensation in trapped cold gases has been considered as an ideal platform for the KZM [19][20][21][22][23]; the system is extremely clean and controllable and particularly suitable for the investigation of interesting effects arising from the spatial inhomogeneities induced by the confinement. Quantized vortices produced in a pancake-shaped condensate by a fast quench across the transition temperature have been already observed [24], but their limited statistics prevented the test of the KZM scaling. The KZM has been studied across the quantum superfluid to Mott insulator transition with atomic gases trapped in optical lattices [25]. Here we report on the observation of solitons resulting from phase defects of the order parameter, spontaneously created in an elongated Bose-Einstein condensate (BEC) of sodium atoms. We show that the number of solitons in the final condensate grows according to a power-law as a function of the rate at which the BEC transition is crossed, consistent with the expectations of the KZM, and provide the first check of the KZM scaling with the sonic horizon. We support our observations by comparing the estimated speed of the transition front in the gas to the speed of the sonic causal horizon, showing that solitons are produced in a regime of inhomogeneous Kibble-Zurek mechanism (IKZM) [21]. Our measurements can open the way to the determination of the critical exponents of the BEC transition in trapped gases, for which so far little information is available [26].The KZM predicts the formation of independen...

We observe solitonic vortices in an atomic Bose-Einstein condensate (BEC) after free expansion. Clear signatures of the nature of such defects are the twisted planar density depletion around the vortex line, observed in absorption images, and the double dislocation in the interference pattern obtained through homodyne techniques. Both methods allow us to determine the sign of the quantized circulation. Experimental observations agree with numerical simulations. These solitonic vortices are the decay product of phase defects of the BEC order parameter spontaneously created after a rapid quench across the BEC transition in a cigar-shaped harmonic trap and are shown to have a very long lifetime.

We study the real-time dynamics of vortices in a large elongated Bose-Einstein condensate (BEC) of sodium atoms using a stroboscopic technique. Vortices are produced via the Kibble-Zurek mechanism in a quench across the BEC transition and they slowly precess keeping their orientation perpendicular to the long axis of the trap as expected for solitonic vortices in a highly anisotropic condensate. Good agreement with theoretical predictions is found for the precession period as a function of the orbit amplitude and the number of condensed atoms. In configurations with two or more vortices, we see signatures of vortex-vortex interaction in the shape and visibility of the orbits. In addition, when more than two vortices are present, their decay is faster than the thermal decay observed for one or two vortices. The possible role of vortex reconnection processes is discussed.

Reconnections and interactions of filamentary coherent structures play a fundamental role in the dynamics of fluids, redistributing energy and helicity among the length scales and inducing fine-scale turbulent mixing. Unlike ordinary fluids, where vorticity is a continuous field, in quantum fluids vorticity is concentrated into discrete (quantized) vortex lines turning vortex reconnections into isolated events, making it conceptually easier to study. Here we report experimental and numerical observations of three-dimensional quantum vortex interactions in a cigar-shaped atomic Bose-Einstein Condensate. In addition to standard reconnections, already numerically and experimentally observed in homogeneous systems away from boundaries, we show that double reconnections, rebounds and ejections can also occur as a consequence of the non-homogeneous, confined nature of the system.

We present a compact source of cold sodium atoms suitable for the production of quantum degenerate gases and versatile for a multi-species experiment. The magnetic field produced by permanent magnets allows to simultaneously realize a Zeeman slower and a two-dimensional magneto-optical trap (MOT) within an order of magnitude smaller length than standard sodium sources. We achieve an atomic flux exceeding 4 × 10(9) atoms/s loaded in a MOT, with a most probable longitudinal velocity of 20 m/s, and a brightness larger than 2.5 × 10(12) atoms/s/sr. This atomic source allows us to produce pure Bose-Einstein condensates with more than 10(7) atoms and a background pressure limited lifetime of 5 min.