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Frontiers of Physics

Many-body effects on atom−molecule conversion in a Floquet spin-boson model

Yan Qin, Rong Chang, Sheng-Chang Li

Published Jan 1, 2025• 1 citation
Publisher

Abstract

We investigate the quantum many-body dynamics of ultracold atom−molecule conversion using a Floquet spin-boson model, where the periodic energy detuning between molecules and atomic pairs is utilized to explore various dynamical regimes. We find that the upper bound of the adiabatic driving frequency increases continuously with the strength of molecule−molecule interactions, indicating that many-body interactions are beneficial in meeting the requirement of the adiabatic condition, thereby facilitating the realization of adiabatic atom−molecule conversion. This enhancement of the fulfillment of the adiabatic condition is further evidenced by the stabilization of periodic oscillations in the mean molecule number over time, protected by these interactions, even when the frequency lies within the localized regime. Interestingly, in the diffusive regime, while the many-body interaction has little effect on the dynamical equilibrium of atom−molecule conversion, it significantly expands the diffusive regime. In the high-frequency limit, many-body interactions are found to completely suppress atom−molecule conversion. Our results shed light on how molecule−molecule interactions influence the boundaries between different dynamical regimes.

DOI
10.15302/frontphys.2025.052202

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We investigate the quantum many-body dynamics of ultracold atom−molecule conversion using a Floquet spin-boson model, where the periodic energy detuning between molecules and atomic pairs is utilized to explore various dynamical regimes. We find that the upper bound of the adiabatic driving frequency increases continuously with the strength of molecule−molecule interactions, indicating that many-body interactions are beneficial in meeting the requirement of the adiabatic condition, thereby facilitating the realization of adiabatic atom−molecule conversion. This enhancement of the fulfillment of the adiabatic condition is further evidenced by the stabilization of periodic oscillations in the mean molecule number over time, protected by these interactions, even when the frequency lies within the localized regime. Interestingly, in the diffusive regime, while the many-body interaction has little effect on the dynamical equilibrium of atom−molecule conversion, it significantly expands the diffusive regime. In the high-frequency limit, many-body interactions are found to completely suppress atom−molecule conversion. Our results shed light on how molecule−molecule interactions influence the boundaries between different dynamical regimes.
We have investigated the dynamics of atom-molecule conversion using a periodically driven spin-boson model both quantum mechanically and semiclassically. The semiclassical dynamics is fully chaotic for small driving frequencies, so that the regular atom-molecule conversion gradually vanishes. In quantum mechanics, however, the periodic conversion takes place at small frequencies since the quantum adiabatic condition is fulfilled. Moreover, it survives for rather larger frequencies that breaks the adiabatic condition, which is understood by considering the so-called dynamical localization. It implies that the periodic atom-molecule conversion is more robust than we expect from the semiclassical approximation. We also show that for much larger frequencies delocalization takes place so that the dynamics becomes diffusive.
Abstract We adopt a modified spin-boson model to investigate the quantum phase transition in an ultracold atom-molecule conversion system involving molecule–molecule interaction. We explore the properties of ground state, entanglement entropy, and many-body dynamics, which confirm that the system exhibits a second-order phase transition from a pure atom phase to a mixed atom-molecule phase when the energy detuning is below a critical value. We obtain three scaling laws and the corresponding two critical exponents to characterize the phase transition. In particular, we discuss the effects of both the speed of ground-state dynamical evolution and the strength of molecular interaction on the phase transition. The adiabatic evolution condition is obtained as well. Our results show that the molecular interaction can greatly reduce the upper bound of the adiabatic condition, which provides a theoretical basis for easier observation of the phase transition in experiments.
We numerically demonstrate the dynamic stabilization of a strongly interacting many-body bosonic system which can be realized by coupled ultracold atom-molecule gases. The system is initialized to an unstable equilibrium state corresponding to a saddle point in the classical phase space, where subsequent free evolution gives rise to atom-molecule conversion. To control and stabilize the system, periodic modulation is applied that suddenly shifts the relative phase between the atomic and the molecular modes and limits their further interconversion. The stability diagram for the range of modulation amplitudes and periods that stabilize the dynamics is given. The validity of the phase diagram obtained from the time-average calculation is discussed by using the orbit tracking method, and the difference in contrast with the maximum absolute deviation analysis is shown as well. A brief quantum analysis shows that quantum fluctuations can put serious limitations on the applicability of the mean-field results.
We investigate the conversion dynamics of ultracold bosonic atoms to molecules in an external field with a Gaussian temporal shape and a linear frequency sweep. Under the mean-field theory, we study the atom–molecule conversion efficiency and the dynamics in the conversion process. By using the Fock-state basis, we further research the quantum many-body dynamics, wherein the many-body effect on the conversion is discussed. We find that the atom–molecule conversion dynamics depend on the particle interaction, peak coupled strength, sweep rate, and total particle number. Notably, some analytical results are derived in the regime without particle interactions and in the sudden limit, respectively. Our theory indicates that the ultracold atom–molecule conversion can be achieved stably and efficiently in the Gaussian external field model.
Controlling and manipulating complex many-body quantum systems will be a key ingredient \nfor the development of next-generation technologies. While the realisation of a \nuniversal quantum machine is still out of reach, in recent years experimental systems of \nultracold atoms have already evolved into a vivid field of research for quantum simulation. \nCrucially, such systems even allow for the successful quantum engineering of targeted \nmany-body systems by means of coherent periodic driving. The essential properties of \nthese Floquet systems encompass two main aspects: fast driving facilitates the simulation \nof effective static systems, and interactions lead to unique heating effects as energy is only \nconserved modulo the driving frequency. Within this thesis we theoretically study both \nof these aspects in respective model systems. \nIn part I of this thesis, we investigate the dynamics of excitations of a bosonic Mott \ninsulator in a designed one-dimensional Floquet system. Here, periodic driving in combination \nwith breaking all mirror symmetries of the system can induce directed motion of \nparticles. In the limit of small excitation densities, the effectively non-interacting quantum \nratchet determines the motion of holes and doublons in the Mott insulator and can in fact \nbe used to manipulate the dynamics of such. This little quantum machine can also be \nused to drive particles against an external force, where transport is possible but requires \nthe fulfilment of a commensurability condition for long times. \nIn part II, we discuss the role of interactions for periodically driven systems by means \nof a Floquet version of the Boltzmann equation. Starting from the Keldysh approach, \nwe develop this semiclassical formalism based on a clear separation of time scales. The \nresult is a description of the dynamics and the scattering of Floquet quasiparticles in \nsuch systems. Here, the property of discrete energy violation is naturally encoded in our \nformalism predicting the heating of interacting Floquet systems to infinite temperatures in \nthe long-time limit. As a first application of this approach, we investigate a cold atom setup \nrealising the Haldane model by means of periodic shaking. While homogeneous systems \nheat up globally, a confining potential evokes thermoelectric transport effects resulting \nfrom spatially dependent heating characteristics. Moreover, we show that the interplay \nof intrinsic heating, macroscopic diffusion and non-trivial topological properties of the \nHaldane model lead to an anomalous Floquet-Nernst effect, which describes anomalous \nparticle transport as the result of developing temperature gradients. \nIn part III, we elaborate on the quantum simulator aspect of ultracold atoms by providing \na theoretical framework for a possible simulation of a topological edge state in a \none-dimensional optical lattice. In this case, the one-dimensional Dirac equation with \nspatially varying mass is important, which captures the topological properties of a corresponding \nsystem of the BDI symmetry class. We analytically discuss such system and \ninvestigate the role of mean-field interaction effects. We also identify the emergence of \ndynamical instabilities in a realisation with bosonic atoms.
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.