Dynamical quantum phase transition of a two-component Bose-Einstein condensate in an optical lattice

📝 Abstract

We study dynamics of a two-component Bose-Einstein condensate where the two components are coupled via an optical lattice. In particular, we focus on the dynamics as one drives the system through a critical point of a first order phase transition characterized by a jump in the internal populations. Solving the time-dependent Gross-Pitaevskii equation, we analyze; breakdown of adiabaticity, impact of non-linear atom-atom scattering, and the role of a harmonic trapping potential. Our findings demonstrate that the phase transition is resilient to both contact interaction between atoms and external trapping confinement.

💡 Analysis

We study dynamics of a two-component Bose-Einstein condensate where the two components are coupled via an optical lattice. In particular, we focus on the dynamics as one drives the system through a critical point of a first order phase transition characterized by a jump in the internal populations. Solving the time-dependent Gross-Pitaevskii equation, we analyze; breakdown of adiabaticity, impact of non-linear atom-atom scattering, and the role of a harmonic trapping potential. Our findings demonstrate that the phase transition is resilient to both contact interaction between atoms and external trapping confinement.

📄 Content

arXiv:0908.2792v1 [cond-mat.quant-gas] 19 Aug 2009 Dynamical quantum phase transition of a two-component Bose-Einstein condensate in an optical lattice Anssi Collin, Jani-Petri Martikainen, and Jonas Larson∗ NORDITA, 106 91 Stockholm, Sweden (Dated: November 19, 2018) We study dynamics of a two-component Bose-Einstein condensate where the two components are coupled via an optical lattice. In particular, we focus on the dynamics as one drives the system through a critical point of a first order phase transition characterized by a jump in the internal populations. Solving the time-dependent Gross-Pitaevskii equation, we analyze; breakdown of adi- abaticity, impact of non-linear atom-atom scattering, and the role of a harmonic trapping potential. Our findings demonstrate that the phase transition is resilient to both contact interaction between atoms and external trapping confinement. PACS numbers: 03.75.Mn,64.60.Ht,64.70.Tg,67.85.Hj I. INTRODUCTION Since the pioneering experiments on Bose-Einsten con- densates (BEC) [1], the field of ultracold atomic gases has seen a tremendous development [2]. Nowadays, prepa- ration and manipulation of BECs is a standard proce- dure providing a versatile testbed for the study of var- ious quantum effects. Spinor condensates, where inter- nal atomic Zeeman levels play an important role for the dynamics, have been experimentally studied by numer- ous groups [3]. More recent experiments on spinor con- densates include; coherent transport [4], spin-mixing [5], inherent spin tunneling [6], and symmetry breaking [7]. Placing the condensate in an optical lattice formed by counter propagating laser beams greatly affects its char- acteristics and exciting phenomena, e.g. Bloch oscilla- tions [8], gap and colliding solitons [9, 10], self-trapping [11], superfluid instability [12], vortices [13], Anderson lo- calization [14], and for more strongly correlated systems the superfluid-Mott insulator phase transition (PT) [15], arise. Most theoretical works studying PTs consider systems at strict thermal equilibrium. However, a more appropri- ate picture capturing the underlying physics of real ex- periments is often encountered by a dynamical approach. Indeed, the great experimental progress seen in the recent past on correlated ultracold atomic systems [16], calls for a deeper theoretical understanding of non-equilibrium PTs. Much of the theoretical works are devoted to dy- namics across a critical point in various spin models [17, 18, 19, 20, 21]. Also the dynamics of phase tran- sitions in lattice many-body systems such as the Bose- Hubbard model have been considered [22, 23]. To de- rive an estimate of the adiabatic breakdown, the Landau- Zener formula, giving a measure of transition probabili- ties across an avoided level crossing [24], has been utilized in most of the above works [17, 18, 19, 20, 22]. Moreover, ∗Electronic address: jolarson@kth.se in Refs. [17, 18, 19, 22, 23] the Kibble-Zurek mechanism of quench induced transitions was employed. In this paper we consider a spinor condensate in an optical lattice. Apart from providing an effective peri- odic potential, in this model the lattice also induces a coupling between the internal atomic states. The cor- responding many-body model, without atom-atom inter- actions, was first introduced in Ref. [25], and the occur- rence of a first order PT between different internal states was demonstrated. The system was further investigated in [26] by taking interaction between the atoms into ac- count. Both of these works consider thermodynamical equilibrium. Since the single particle ground state of the present model is not gapped, even small time-dependent perturbations of the Hamiltonian might well cause non- adiabatic excitations. Driven through the critical point, such excitations might wash out the signatures of the PT. One goal of the present paper is to study the im- portance of these non-adiabatic contributions. Moreover, the model automatically takes into account the effects de- riving from atom-atom interactions, and the state chang- ing collisions they bring about. This aspect was left as an open question in [25]. In addition, the sensitivity to external harmonic trapping is also considered. The outline of the paper is as follows. In the next section, we present the one dimensional single particle Hamiltonian. After first discussing some general prop- erties in Subsec. II A, we numerically diagonalize the Hamiltonian and give the spectrum in Subsec. II B. Us- ing the spectrum, we demonstrate the equilibrium PT in Subsec. II C. The following Sec. III is devoted to our main results; the dynamics when the system is driven through the critical point. The numerical method for solving the Gross-Pitaevskii equations is outlined, and first the thermal equilibrium PT is studied by means of the partial-state fidelity susceptibility. In Subsec. III A we calculate the order parameter for different dimensions, whereby the following Subsection considers t

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