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arXiv:1101.0728 · Physical Review Letters

Solitons as the Early Stage of Quasicondensate Formation during Evaporative Cooling

Emilia Witkowska, Piotr Deuar, Mariusz Gajda, Kazimierz Rza̧żewski

Published Mar 30, 2011• 78 citations
arXivHTMLPDF

Abstract

We calculate the evaporative cooling dynamics of trapped one-dimensional Bose-Einstein condensates for parameters leading to a range of condensates and quasicondensates in the final equilibrium state, using the classical fields method. We confirm that solitons are created during the evaporation process by the Kibble-Zurek mechanism, but subsequently dissipate during thermalization. However, their signature remains in the phase coherence length, which is approximately conserved during dissipation in this system.

DOI
10.1103/physrevlett.106.135301

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We calculate the evaporative cooling dynamics of trapped one-dimensional Bose-Einstein condensates for parameters leading to a range of condensates and quasicondensates in the final equilibrium state, using the classical fields method. We confirm that solitons are created during the evaporation process by the Kibble-Zurek mechanism, but subsequently dissipate during thermalization. However, their signature remains in the phase coherence length, which is approximately conserved during dissipation in this system.
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The problem of understanding how a coherent, macroscopic Bose- Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering achievement of BEC in weakly interacting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the BEC number, as well as the development of its coherence. More recently, there has been interest in connecting such experiments to universal aspects of nonequilibrium phase transitions, in terms of both static and dynamical critical exponents. Here, the spontaneous formation of topological structures such as vortices and solitons in quenched cold-atom experiments has enabled the verification of the Kibble-Zurek mechanism predicting the density of topological defects in continuous phase transitions, first proposed in the context of the evolution of the early universe. This chapter reviews progress in the understanding of BEC formation and discusses open questions and future research directions in the dynamics of phase transitions in quantum gases. Introduction The equilibrium phase diagram of the dilute Bose gas exhibits a continuous phase transition between condensed and noncondensed phases. The order parameter characteristic of the condensed phase vanishes above some critical temperature T c and grows continuously with decreasing temperature below this critical point. However, the dynamical process of condensate formation has proved to be a challenging phenomenon to address both theoretically and experimentally. This formation process is a crucial aspect of Bose systems and of direct relevance to all condensates discussed in this book, despite their evident system-specific properties. Important questions leading to intense discussions in the early literature include the time scale for condensate formation and the role of inhomogeneities and finite-size effects in “closed” systems. These issues are related to the concept of spontaneous symmetry breaking, its causes, and implications for physical systems (see, for example, Chapter 5 by Snoke and Daley). In this chapter, we give an overview of the dynamics of condensate formation and describe the present understanding provided by increasingly well-controlled cold-atom experiments and corresponding theoretical advances over the past twenty years. We focus on the growth of BECs in cooled Bose gases, which, from a theoretical standpoint, requires a suitable nonequilibrium formalism.
Summary form only given. We report the first successful use of direct quantum dynamical calculations of the cooling and formation of Bose-Einstein condensates of trapped atoms. The calculations utilize phase-space methods that have already proved successful in laser theory. Some of the computational results are very similar to those already observed experimentally. In particular, we find quantum evaporative cooling, followed by a clear transition to a condensate; this is strongly influenced by non-classical features of the quantum dynamics. The calculations indicate additional structure, which we interpret as spontaneous formation of vortices in small condensates. These originate in the residual orbital angular momentum of the trapped atoms, which was neglected in previous studies - and would provide a significant test of the present theory.
We have simulated the evaporative cooling of a dilute gas of Bose particles including quantum statistics using a Monte Carlo method. This approach can model situations which are far away from quasiequilibrium such as occur during forced evaporative cooling. We have also simulated the dynamical formation of Bose-Einstein condensate for homogeneous and inhomogeneous Bose gases under the random-phase approximation. It was found that the rate of accumulation of Bose particles into low-energy states through collisions is increased by forced evaporation; and a macroscopic population at ground state can be reached at a time scale characterized by classical collision time for an inhomogeneous gas in a harmonic potential. We present the results of simulations for the evaporative cooling and formation of a Bose-Einstein condensate in one-, two-, and three-dimensional position cuts and energy cuts.
Evaporative cooling of trapped atoms is studied based on the quantum kinetic theory. We extend the classical analysis of Luiten et al. [Phys. Rev. A 53, 381 (1996)] to treat Bose statistics of alkali-metal atoms. Dynamics in evaporative cooling process is described by a kinetic equation for the truncated Bose-Einstein distribution function under the assumption that the system is close to the thermal equilibrium. This approach is applicable to the ``slow'' evaporative cooling normally adopted in most experiments for the efficient production of Bose-Einstein condensates. Time-evolution calculations explain the current experiment well with sodium atoms using a slow evaporative cooling and demonstrate a rapid growth of condensate in the cooling process.
Preparation of atomic Bose–Einstein condensate (BEC) with tunable interactions in a quasi-one-dimensional (quasi-1D) optical trap is essential for both the observation of bright matter-wave solitons and the quantum simulation based on the discrete atomic momentum states. However, the quasi-1D BEC has been obtained by a complex process, which includes the creation of a three-dimensional BEC and its adiabatic transform into a quasi-1D trap. Here, we report the direct creation of a quasi-1D BEC of 133Cs atoms by the fast evaporative cooling of ultracold atoms prepared by the degenerated Raman sideband cooling. We produce the pure BEC of up to 5.5×104 atoms in a quasi-1D optical trap with an evaporative time of 6 s. We demonstrate the anisotropic expansion of the atomic cloud after the release from the quasi-1D trap and study the dependence of both the phase space density and the temperature on the number of atoms in the trap during the evaporative cooling. Our study facilitates the promising applications of quasi-1D interacting atomic gases.