Parametric instabilities in resonantly-driven Bose–Einstein condensates

Abstract

Shaking optical lattices in a resonant manner offers an efficient and versatile method to devise artificial gauge fields and topological band structures for ultracold atomic gases. This was recently demonstrated through the experimental realization of the Harper-Hofstadter model, which combined optical superlattices and resonant time-modulations. Adding inter-particle interactions to these engineered band systems is expected to lead to strongly-correlated states with topological features, such as fractional Chern insulators. However, the interplay between interactions and external timeperiodic drives typically triggers violent instabilities and uncontrollable heating, hence potentially ruling out the possibility of accessing such intriguing states of matter in experiments. In this work, we study the early-stage parametric instabilities that occur in systems of resonantly-driven Bose-Einstein condensates in optical lattices. We apply and extend an approach based on Bogoliubov theory [PRX 7, 021015 (2017)] to a variety of resonantly-driven band models, from a simple shaken Wannier-Stark ladder to the more intriguing driven-induced Harper-Hofstadter model. In particular, we provide ab initio numerical and analytical predictions for the stability properties of these topical models. This work sheds light on general features that could guide current experiments to stable regimes of operation. * samuel.lellouch@univ-lille1.fr † ngoldman@ulb.ac.be arXiv:1711.08832v1 [cond-mat.quant-gas]

Asymptotic Prethermalization in Periodically Driven Classical Spin Chains

“…Presenting a major bottleneck at the forefront of present-date experimental research, heating processes play an important role in many-body Floquet systems, and understanding the underlying physics is expected to offer significant advances in the field. Unlike single-particle quantum systems, such as the kicked rotor [42] and weakly-interacting bosonic models [43,44], it is believed that generic isolated clean periodically-driven quantum many-body systems heat up to an infinite-temperature state [45][46][47][48][49][50], although the debate is not fully settled [51][52][53][54][55][56]. Heating rates have been shown to be at least exponentially suppressed in the drive frequency [57,58].…”

Dynamics and density correlations in matter-wave jet emission of a driven condensate

“…We now show that the exponential growth can be attributed to a certain dynamical instability associated with the interaction modulation. We note that analogous instabilities exhibit in BECs for which other parts of the Hamiltonian are modulated periodically [26][27][28][29][30][31][32]. Letting u k (t) = u k e −iΩt/2 and v k (t) = v k e iΩt/2 , and adopting the rotating wave approximation (i.e., terms oscillating at multiples of Ω are neglected in the equations for u k and v k ), Eqs.…”

Parametric Heating in a 2D Periodically Driven Bosonic System: Beyond the Weakly Interacting Regime

“…In this appendix, we briefly revisit the derivation for the most unstable mode within FBdG theory [26], and extend the results to diagonal and circular drives. The takehome message is that the critical saturation frequency ω c , which defines the position of hte cusp in the instability rate curves, coincides for the linear and circular drives; for the diagonal drive the value is twice as large on the square lattice.…”

“…Additionally, interaction-mediated heating is itself an interesting nontrivial quantum manybody process. Energy absorption and entanglement production in periodically driven systems have recently been the focus of theoretical studies [16,[22][23][24][25][26][27][28][29] and experimental investigations [5,9,20,21]. It was predicted that, whenever the drive frequency is larger than all singleparticle energy scales of the problem, heating succumbs to a stable long-lived prethermal steady state, before it can occur at exponentially-long times [25,[30][31][32][33][34][35].…”