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arXiv:2506.20835 · Physical Review A

Nonequilibrium quench dynamics of Bose-Einstein condensates of microwave-shielded polar molecules

Abdelâali Boudjemâa

Published Jun 11, 2025• 5 citations
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Abstract

We theoretically investigate the nonequilibrium dynamics of homogeneous ultracold Bose gases of microwave-shielded polar molecules following a sudden quench of the scattering length at zero temperature. We calculate in particular the quantum depletion, the anomalous density, the condensate fluctuations, and the pair-correlation function using both the time-dependent Bogoliubov approach and the self-consistent time-dependent Hartree-Fock-Bogoliubov approximation. During their time evolution, these quantities exhibit slow or fast oscillations depending on the strength of the shielding interactions. We find that at long timescales the molecular condensate is characterized by nonequilibrium steady-state momentum distribution functions, with depletion, anomalous density, and correlations that deviate from their corresponding equilibrium values. We demonstrate that the pair correlations expand diffusively at short times while they spread ballistically at long times.

DOI
10.1103/6b82-sb2j

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We theoretically investigate the nonequilibrium dynamics of homogeneous ultracold Bose gases of microwave-shielded polar molecules following a sudden quench of the scattering length at zero temperature. We calculate in particular the quantum depletion, the anomalous density, the condensate fluctuations, and the pair-correlation function using both the time-dependent Bogoliubov approach and the self-consistent time-dependent Hartree-Fock-Bogoliubov approximation. During their time evolution, these quantities exhibit slow or fast oscillations depending on the strength of the shielding interactions. We find that at long timescales the molecular condensate is characterized by nonequilibrium steady-state momentum distribution functions, with depletion, anomalous density, and correlations that deviate from their corresponding equilibrium values. We demonstrate that the pair correlations expand diffusively at short times while they spread ballistically at long times.
Recent advances in the tunability of ultracold atomic gases have created opportunities for studying interesting quantum many-body systems. Fano-Feshbach resonances, in particular, allow experimenters to freely adjust the scattering of atoms by controlling an external magnetic field. By rapidly changing this field near a resonance, it is possible to drive systems out of equilibrium towards novel quantum states where correlations between atoms change dynamically. In this thesis, we take a wave-function-based approach to theoretically examine the response of several interesting systems to suddenly-switched, or "quenched", interactions.\nWe first calculate the time evolution of a Bose-Einstein condensate that is quenched to the unitarity regime, where the scattering length 'a' diverges. Working within the time-dependent variational formalism, we find that the condensate does not deplete as quickly as the usual Bogoliubov theory would suggest. We also make a quantitative prediction for the dynamics of short-range pair correlations, encoded in Tan's contact. We then consider the dynamics of these correlations for quenches to small 'a', and we find that bound states can cause high-contrast oscillations of the contact. These dynamics can be modelled quantitatively at short times by using a properly-chosen two-body model. Finally, we characterize the nonlocal correlation waves that are generated by an interaction quench in arbitrary dimensionality. Our analysis demonstrates that the large-momentum limit of the post-quench momentum distribution can sometimes include contributions from both the short range and the long range, depending on the quench protocol.
Bose-Einstein condensation of dipolar molecules can be achieved by shielding loss channels with microwave fields. The microwave coupling can be approximated by effective dipole-dipole interactions with a short-range repulsion. We study properties and stability of these molecular Bose gases with a many-body variational method, the hypernetted-chain Euler-Lagrange method for a wide range of densities and repulsion strengths of the microwave shield. We find a homogeneous gas-like phase which, however, is unstable at low density against density waves: at a critical density, which depends on the repulsion strength, the dipolar fluid undergoes a phase transition to a layer phase. Thus, if the molecular condensate is expanded adiabatically by decreasing the confinement strength, it will spontaneously form layers at the critical density. These quasi-two-dimensional layers can be self-bound, hence form two-dimensional liquids. By varying the microwave shield, the predicted equilibrium densities span more than an order of magnitude.
We explore the dynamics of a Bose gas following its quench to a strongly interacting regime near a Feshbach resonance. Within a self-consistent Bogoliubov analysis we find that after the initial condensate-quasiparticle Rabi oscillations, at long time scales the gas is characterized by a nonequilibrium steady-state momentum distribution function, with depletion, condensate density, and contact that deviate strongly from their corresponding equilibrium values. These are in a qualitative agreement with recent experiments on 85{}^{85}85Rb by Makotyn et al. Our analysis also suggests that for sufficiently deep quenches close to the resonance the nonequilibrium state undergoes a phase transition to a fully depleted state, characterized by a vanishing condensate density.
We investigate the ground-state phases of ultracold gases composed of bosonic microwave-shielded polar molecules (MSPMs). Using a translational symmetry-breaking variational ansatz with Jastrow correlations, we characterize the many-body correlations arising from the large shielding core of the two-body potential in a dense gas. We show that the molecular gases are always stabilized by the shielding potential and support a self-bound gas phase and an expanding gas phase. Furthermore, we find that, analogous to liquid ^{4}He, the condensate fraction is significantly reduced when the size of the shielding core of the two-body potential becomes comparable to the intermolecular distance. For experimental detection, we also identify a bimodal feature in the momentum distribution. Our work invalidates the application of the Gross-Pitaevskii equation to molecular gases and establishes a universal framework to reveal the many-body correlations in dense molecular gases.
We calculate the dynamics of one- and two-body correlation functions in a homogeneous Bose gas at zero temperature following a sudden change in the interaction strength, in the continuum and in a lattice. By choosing suitable examples, we highlight features in the correlation functions that emerge due to the interactions and the band structure. We find that interactions dramatically change the way correlations build up and subsequently decay following a quench. For example, the Bogoliubov dispersion induces a crossover from diffusive spreading of short-range correlations to ballistic spreading of longer-range correlations. In the lattice, the correlation functions develop additional features absent in the continuum. Most strikingly, the lattice induces an additional velocity scale and some features propagate with that velocity. Finally, we discuss the ultra-short-range properties of the density-density correlation function following a quench, and the implications for experiments using this quantity to probe the ``contact.'' Our calculations, which can be readily tested in current experiments, suggest that the dynamics of correlations may be a useful tool for extracting many-body parameters.
We investigate the finite-temperature phase diagram of polar molecules shielded by dual microwave fields using the path integral Monte Carlo method combined with the worm algorithm. We determine the critical temperature T c for Bose-Einstein condensations (BECs) and identify two distinct phases below T c : the expanding gas (EG) phase and the self-bound gas (SBG) phase. We further analyze the temperature and interaction-strength dependence of the condensate and superfluid fractions. Notably, in contrast to dilute atomic BECs, the SBG phase displays a low condensate fraction and a high superfluid fraction, resembling the behavior of strongly correlated 4 He superfluids. These significant many-body correlations arise from the interplay between long-range dipole-dipole interactions and the short-range shielding potential. Furthermore, we demonstrate that the aspect ratio of the gas provides a characteristic geometric signature to accurately determine the EG-to-SBG transition, robust against external trapping potentials. Our findings provide unbiased and numerically exact results to guide upcoming experiments with polar molecules.