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arXiv:2503.18465 · Physical Review Research

Degree of simplicity of Floquet states of a periodically driven Bose-Hubbard dimer

Steffen Seligmann, Hamed Koochaki Kelardeh, Martin Holthaus

Published Jul 18, 2025• 1 citation
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Abstract

We demonstrate longtime coherent subharmonic motion of a many-boson system subjected to an external time-periodic driving force. The underlying mechanism is exemplified numerically through analysis of a periodically driven Bose-Hubbard dimer, and clarified conceptually by semiclassical requantization of invariant tubes pertaining to the system’s mean-field description. In this way, one arrives at pre-Floquet states that relate to the actual many-body Floquet states in a manner similar to the relation of site-localized Wannier states to lattice-extended Bloch states in solid-state physics. It is argued that even high-order subharmonic response can be systematically engineered, and be observed experimentally, with weakly interacting Floquet condensates comprising a sufficiently large number of particles.

DOI
10.1103/nqg9-788r

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We demonstrate longtime coherent subharmonic motion of a many-boson system subjected to an external time-periodic driving force. The underlying mechanism is exemplified numerically through analysis of a periodically driven Bose-Hubbard dimer, and clarified conceptually by semiclassical requantization of invariant tubes pertaining to the system’s mean-field description. In this way, one arrives at pre-Floquet states that relate to the actual many-body Floquet states in a manner similar to the relation of site-localized Wannier states to lattice-extended Bloch states in solid-state physics. It is argued that even high-order subharmonic response can be systematically engineered, and be observed experimentally, with weakly interacting Floquet condensates comprising a sufficiently large number of particles.
We explore prethermal Floquet steady states and instabilities of the weakly interacting two-dimensional Bose-Hubbard model subject to periodic driving. We develop a description of the nonequilibrium dynamics, at arbitrary drive strength and frequency, using a weak-coupling conserving approximation. We establish the regimes in which conventional (zero-momentum) and unconventional [(π,π)-momentum] condensates are stable on intermediate time scales. We find that condensate stability is enhanced by increasing the drive strength, because this decreases the bandwidth of quasiparticle excitations and thus impedes resonant absorption and heating. Our results are directly relevant to a number of current experiments with ultracold bosons.
Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases.While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinitetemperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system-leading to long-lived "prethermal" regimes.In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model.By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude.The tunability of the lattice potentials allows us to explore one-and twodimensional systems in a range of different interacting regimes.Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension.Our results show experimental evidence of the phenomenon of Floquet prethermalization and provide insight into the characterization of heating for driven bosonic systems.
We suggest that nonequilibrium Bose-Einstein condensates may occur in time-periodically driven interacting Bose gases. Employing the model of a periodically forced bosonic Josephson junction, we demonstrate that resonance-induced ground-state-like many-particle Floquet states possess an almost perfect degree of coherence, as corresponding to a mesoscopically occupied, explicitly time-dependent single-particle orbital. In marked contrast to the customary time-independent Bose-Einstein condensates, the order parameter of such systems is destroyed by violent fluctuations when the particle number becomes too large, signaling the nonexistence of a proper mean-field limit.
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.
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, the exponential suppression of heating has also 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.
Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system -- leading to long-lived 'prethermal' regimes. In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model. By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude. The tunability of the lattice potentials allows us to explore one- and two-dimensional systems in a range of different interacting regimes. Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension. Our results show experimental evidence of the phenomenon of Floquet prethermalization, and provide insight into the characterization of heating for driven bosonic systems.