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Giant Coherence Revivals in a Driven Bose--Einstein Condensate on a Non-Orientable

Cinque McFarlane - Blake

Published Nov 27, 2025• 0 citations
Publisher

Abstract

We report numerical evidence that a clean, periodically driven Bose--Einstein condensate (BEC) on a non-orientable (M"obius-like) lattice exhibits sustained breathing dynamics with giant global phase-coherence revivals at thousands of Floquet cycles. Using an RK4 integration of a driven Gross--Pitaevskii-type model on a $30\times30$ lattice with Möbius boundary flips and a slow spiral rotating potential, we observe an initial decay into a breathing regime followed by a pronounced revival reaching $\sim$64% global phase coherence near period $\sim4896$, and retained coherence $\sim29%$ at 5000 cycles. We analyze winding-number observables and demonstrate that the revivals are topologically driven by the interplay of non-orientability and spiral drive rather than disorder, prethermalization, or measurement feedback. The phenomenon suggests a new class of geometry-protected Floquet coherence with potential experimental realizations in neutral-atom platforms.

DOI
10.5281/zenodo.17741986

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We report numerical evidence that a clean, periodically driven Bose--Einstein condensate (BEC) on a non-orientable (M"obius-like) lattice exhibits sustained breathing dynamics with giant global phase-coherence revivals at thousands of Floquet cycles. Using an RK4 integration of a driven Gross--Pitaevskii-type model on a 30×3030\times3030×30 lattice with Möbius boundary flips and a slow spiral rotating potential, we observe an initial decay into a breathing regime followed by a pronounced revival reaching ∼\sim∼64% global phase coherence near period ∼4896\sim4896∼4896, and retained coherence ∼29\sim29%∼29 at 5000 cycles. We analyze winding-number observables and demonstrate that the revivals are topologically driven by the interplay of non-orientability and spiral drive rather than disorder, prethermalization, or measurement feedback. The phenomenon suggests a new class of geometry-protected Floquet coherence with potential experimental realizations in neutral-atom platforms.
We investigate the dynamics of Bose-Einstein condensates in a tilted one-dimensional periodic lattice within the mean-field (Gross-Pitaevskii) description. Unlike in the linear case the Bloch oscillations decay because of nonlinear dephasing. Pronounced revival phenomena are observed. These are analyzed in detail in terms of a simple integrable model constructed by an expansion in Wannier-Stark resonance states. We also briefly discuss the pulsed output of such systems for stronger static fields.
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.
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.
We investigate the Gross–Pitaevskii equation which describes an atomic Bose–Einstein condensate confined in an optical lattice and driven by a spatiotemporal periodic laser field. It is demonstrated that the exact Floquet states appear when the external time-dependent potential is balanced by the nonlinear mean-field interaction. The balance region of parameters is divided into a phase-continuing region and a phase-jumping one. In the latter region, the Floquet states are spatiotemporal vortices of nontrivial phase structures and zero-density cores. Due to the velocity singularities of vortex cores and the blowing-up of perturbed solutions, the spatiotemporal vortices are unstable periodic states embedded into chaos. The stability and instability of these Floquet states are numerically explored by the time evolution of fidelity between the exact and numerical solutions. It is numerically illustrated that the stable Floquet states in the phase-continuing region could be prepared from the uniformly initial states by slow growth of the external potential. 1.
We investigate the Gross-Pitaevskii equation for a classically chaotic system, which describes an atomic Bose-Einstein condensate confined in an optical lattice and driven by a spatiotemporal periodic laser field. It is demonstrated that the exact Floquet states appear when the external time-dependent potential is balanced by the nonlinear mean-field interaction. The balance region of parameters is divided into a phase-continuing region and a phase-jumping one. In the latter region, the Floquet states are spatiotemporal vortices of nontrivial phase structures and zero-density cores. Due to the velocity singularities of vortex cores and the blowing-up of perturbed solutions, the spatiotemporal vortices are unstable periodic states embedded in chaos. The stability and instability of these Floquet states are numerically explored by the time evolution of fidelity between the exact and numerical solutions. It is numerically illustrated that the stable Floquet states could be prepared from the uniformly initial states by slow growth of the external potential.
I present a disorder-free, two-dimensional Floquet stabilization mechanism that maintains a clean periodic orbit for more than5000\mathbf{5 0 0 0}5000cycles on a30×3030 \times 3030×30square lattice. The drive consists of a global transverse field and a purely imaginary nearest-neighbor interaction with a slow spiral phase profile of maximum amplitudeπ/512\pi / 512π/512. Mean-field product-state simulations (size 1800, fourth-order Runge-Kutta, 200 steps per period) show that this imaginary phase twist passively suppresses Floquet heating for thousands of periods without disorder, feedback, or long-range couplings. A hardware test on a3×33 \times 33×3patch of an IBM superconducting device (50\mathbf{5 0}50periods, approximately 106physical gates) produced no detectable subharmonic response, consistent with the expected sensitivity of the mechanism to global coherence and the destructive effect of individual addressing. To verify that the stabilized orbit encodes an effective logical manifold, I applied a global logical-XXXoperation across three qualitatively distinct initial states (polarized, Néel, and random). In all cases the sign of the logical magnetizationZLZ_{L}ZL​inverts while the magnitude remains small (∼10−3\sim 10^{-3}∼10−3), indicating that the operation acts as a symmetry of the Floquet orbit rather than a state-preparation artifact. The resulting drive maps directly to a single global radio-frequency field plus a static magneticfield gradient on current two-dimensional trapped-ion platforms, suggesting a route toward robust low-frequency logical qubits and potential applications in isotope- or chirality-selective sensing.