Statistical Floquet prethermalization of the Bose-Hubbard model

Abstract

The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, such exponential suppression of heating has been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.

Floquet States in Open Quantum Systems

“…The Floquet prethermalization has also been shown to occur in classical systems (74)(75)(76) and boson systems (77,78), which are not covered by rigorous results. Floquet prethermalization has also been observed in recent experiments (79,80).…”

Floquet States in Open Quantum Systems

“…The Floquet prethermalization has also been shown to occur in classical systems [68][69][70] and boson systems [71,72], which are not covered by rigorous results. Floquet prethermalization has also been observed in recent experiments [73,74].…”

Stable Many-Body Resonances in Open Quantum Systems

“…This regime allows us to describe the particle/excitation hopping processes within the semi-classical picture as discussed in Refs. [29,38].…”

“…Nonequilibrium quantum phases without static analogs have become an active area of research because programmable quantum simulators [1] such as cold atoms [2][3][4][5] and superconducting circuits [6][7][8][9][10][11] allow the preparation of exotic states of matter into a states out of equilibrium. Paradigmatic examples of nonequilibrium states are discrete time crystals [12][13][14][15][16][17][18][19][20][21] and Floquet prethermalization [22][23][24][25][26][27][28][29]. The search for nonequilibrium states of matter is challenging because one needs to move beyond standard quantum statistical mechanics [30][31][32][33][34], and simulations of quantum many-body systems in classical computers [35][36][37].…”

“…Furthermore, renowned quantum machine learning algorithms center around the Harrow-Hassidim-Lloyd (HHL) algorithm [66] and quantum principal component analysis [67], which require the physical realization of quantum random access memory [68,69]. Here, we recognize a substantial overlap with localized nonequilibrium states of matter, such as prethermal states [22][23][24][25][26][27][28][29] and many-body localization [70][71][72]. Moreover, because localized nonequilibrium states of matter retain information about their initial state, they may be used as quantum memories [73].…”