Kapitza stabilization of a repulsive Bose-Einstein condensate in an oscillating optical lattice

Abstract

We show that the Kapitza stabilization can occur in the context of nonlinear quantum fields. Through this phenomenon, an amplitude-modulated lattice can stabilize a Bose-Einstein condensate with repulsive interactions and prevent the spreading for long times. We present a classical and quantum analysis in the framework of Gross-Pitaevskii equation, specifying the parameter region where stabilization occurs. Effects of nonlinearity lead to a significant increase of the stability domain compared with the classical case. Our proposal can be experimentally implemented with current cold atom settings. arXiv:1709.07792v3 [cond-mat.quant-gas]

Transverse quasi-modes in periodic potentials

“…It is convenient to recast equation ( 21) as a function of ϕ(x). Temporal integral in equations (10) and ( 11) can now be easily computed [18]…”

“…the problem of a two-state quantum system interacting with a periodic perturbation [1], is used to describe several fundamental processes, such as the spin dynamics in magnetic fields (used for example in the nuclear magnetic resonance) [2,3], electromagnetic interaction with matter [4], stabilization of repulsive Bose-Einstein condensate [5], directional coupler in integrated optics [6], Josephson junction [7], and many others, all of them featuring the Rabi oscillations [8]. In the last years, the problem of waves in periodic potential beyond the perturbative regime is of strong interest, including optical traps for cold atoms [9,10] and higher harmonic generation in nonlinear optics [11]. For example, the possibility to reduce a full 3D nonlinear Schrödinger equation with inhomogeneous coefficients to a simplified 1D version has been demonstrated [12].…”

“…This effect, originally discovered by Kapitza while studying an inverted forced classical pendulum [21,22], originates from the influence of fast varying scales on slow scales [18]. A time-independent potential proportional to the square of the local (in time and space) force arises [20,23,24], providing a way to confine particles (Paul trap [25]) and waves [10], or even realizing scatteringless potential using non-Hermitian potentials [26].…”

Mode selectivity of dynamically induced conformation in many-body chainlike bead-spring models

“…The existence of two timescales, the slow pendulum and the fast pivot, is the key mechanism of this stabilization. Owing to the importance of the mechanism, this highly nonintuitive stabilization is applied in a wide variety of fields: many-body coupled pendulums [5], microscopic objects with a surrounding medium [6], particles on a toroidal helix [7], liquid [8,9], control [10,11], localized wave packets in a repulsive Bose-Einstein condensate [12], optical molasses [13], quantum versions [14][15][16][17], and complex potential versions [18].…”

Parametric instabilities in resonantly-driven Bose–Einstein condensates

“…On the one hand, at very short times, time-modulated BECs are believed to be mostly affected by strong parametric instabilities, which are characterized by an exponential growth of collective (Bogoliubov) excitations and are accompanied with a fast decay of the BEC; such processes were thoroughly characterized in our previous work [40], where instability rates, stability diagrams and robust physical signatures of such processes were obtained for simple non-resonant shaken systems. 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].…”