Phase transition kinetics for a Bose Einstein condensate in a periodically driven band system

Abstract

The dynamical transition of an atomic Bose-Einstein condensate from a spatially periodic state to a staggered state with alternating sign in its wavefunction is experimentally studied using a onedimensional phase modulated optical lattice. We observe the crossover from quantum to thermal fluctuations as the triggering mechanism for the nucleation of staggered states. In good quantitative agreement with numerical simulations based on the truncated Wigner method, we experimentally investigate how the nucleation time varies with the renormalized tunneling rate, the atomic density, and the driving frequency. The effective inverted energy band in the driven lattice is identified as the key ingredient which explains the emergence of gap solitons as observed in numerics and the possibility to nucleate staggered states from interband excitations as reported experimentally.

Parametric Instabilities of Interacting Bosons in Periodically Driven 1D Optical Lattices

“…The appearance of instabilities is common in static weakly interacting bosonic lattice systems. For instance, Landau instabilities can occur when the condensate is prepared at a finite quasimomentum, where the effective mass in the band structure is negative; such configurations can also display dynamical instabilities, where Bogoliubov excitations grow exponentially [40][41][42][43][44][45][46]. We emphasize that the origin of such instabilities is different compared to those revealed in this work.…”

“…These instabilities exist even for a condensate initially at rest; in contrast, parametric instabilities originate from the time-dependent nature of the drive. We note that instabilities are not necessarily detrimental but can result in interesting phenomena, such as parametric amplification, four-wave mixing [44][45][46][47], and pattern formation [48][49][50][51].…”

“…Note that α is independent of the modulation frequency ω. The measurements are performed in a strong-driving regime, 1 < α < 2, where the effects of the drive are nonperturbative, while the minimum of the effective dispersion remains at q x ¼ 0 [39,46]. To avoid single-particle interband resonances [61], the modulation frequency is chosen well below the first single-particle band gap of the static lattice, Δ 21 =h ¼ 41.6ð5Þ kHz.…”

Phase transitions in biology: from bird flocks to population dynamics

“…Much of the terminology used in the study of phase transitions was codified by Paul Ehrenfest's work on statistical mechanics in the early twentieth century [1]. The study of phase transitions has been expanded to other physical phenomena ranging from magnetization, which can be described with the well-studied Ising model [1,2], to liquid crystals [3,4], Bose-Einstein condensates [5] and superconductivity [6]. A phase transition, most simply defined, is a shift of a system from one identifiable state of order to another, in response to the alteration of a control parameter such as temperature or the strength of an applied magnetic field [1].…”

Parametric instabilities in resonantly-driven Bose–Einstein condensates

“…Other approaches have been adopted to characterize dynamical instabilities in shaken BECs [41][42][43][44][45], and a recent study even pointed out the possibility of dynamically stabilizing a modulated BEC, inspired by the Kapitza pendulum [46]; the experimental evidence of staggered-states in time-modulated BECs, whose formation also stems from an instability involving the external drive and collective excitations, was recently reported in Ref. [47]; we note that time-modulating the trapping potential can also be exploited to create correlated excitations in BECs [48].…”