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arXiv:2112.12302 · Physical Review Letters

Coherent Reaction between Molecular and Atomic Bose-Einstein Condensates: Integrable Model

Rajesh K. Malla, Vladimir Chernyak, Chen Sun, Nikolai A. Sinitsyn

Published Jul 11, 2022• 14 citations
arXivHTMLPDF

Abstract

We solve a model that describes a stimulated conversion between ultracold bosonic atoms and molecules. The reaction is triggered by a linearly time-dependent transition throughout the Feshbach resonance. Our solution predicts a dependence, with a dynamic phase transition, of the reaction efficiency on the transition rate for both atoms-to-molecule pairing and molecular dissociation processes. We find that for the latter process with a linear energy dispersion of atomic modes, the emerging phase can have a thermalized energy distribution of noninteracting bosons with the temperature defined by the rate of the transition. This provides a simple interpretation of the phase transition in terms of the creation of equilibrium Bose-Einstein condensate.

DOI
10.1103/physrevlett.129.033201

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We solve a model that describes a stimulated conversion between ultracold bosonic atoms and molecules. The reaction is triggered by a linearly time-dependent transition throughout the Feshbach resonance. Our solution predicts a dependence, with a dynamic phase transition, of the reaction efficiency on the transition rate for both atoms-to-molecule pairing and molecular dissociation processes. We find that for the latter process with a linear energy dispersion of atomic modes, the emerging phase can have a thermalized energy distribution of noninteracting bosons with the temperature defined by the rate of the transition. This provides a simple interpretation of the phase transition in terms of the creation of equilibrium Bose-Einstein condensate.
We map the phase diagram of a two-mode atom-molecule Bose-Einstein condensate with Fano-Feshbach and coherent three-body recombination (cTBR) terms. The standard second order phase transition observed as the molecular energy is tuned through the Feshbach resonance, is replaced by a first order transition when cTBR becomes prominent, due to a double-well structure in the free energy landscape. This transition is associated with atom-molecule entanglement, bistability, and molecular metastability. Our results establish cTBR as a powerful knob for quantum state engineering and control of reaction dynamics in ultracold chemistry.
A set of nonlinear evolution equations describing the dynamics of atoms, molecules, and photons in the course of stimulated atomic-molecular conversion in a Bose-Einstein condensate is derived and studied in the mean-field approximation. It is shown that conversion can be periodic or aperiodic in time, the rate of the process being determined to a considerable extent by the initial density of particles and by the initial phase difference. Depending on the initial conditions, various conversion modes can be realized. The possibility of stabilization of a special state (of rest) of the system for nonzero initial number densities of particles is predicted. It is pointed out that coherence of a Bose condensate of atoms, molecules, and photons predetermines the possibility of phase control of the conversion process.
Preparation of molecular quantum gas promises novel applications including quantum control of chemical reactions, precision measurements, quantum simulation and quantum information processing. Experimental preparation of colder and denser molecular samples, however, is frequently hindered by fast inelastic collisions that heat and deplete the population. Here we report the formation of two-dimensional Bose-Einstein condensates (BECs) of spinning g−g-g−wave molecules by inducing pairing interactions in an atomic condensate. The trap geometry and the low temperature of the molecules help reducing inelastic loss to ensure thermal equilibrium. We determine the molecular scattering length to be +220(30)+220(30)+220(30)~Bohr and investigate the unpairing dynamics in the strong coupling regime. Our work confirms the long-sought transition between atomic and molecular condensates, the bosonic analog of the BEC-BCS (Bardeen-Cooper-Schieffer superfluid) crossover in a Fermi gas.
The ultracold molecular conversion rate occurring in an adiabatic ramp through a Fano-Feshbach resonance is studied and compared in two statistical models. One model, the so-called stochastic phase-space sampling (SPSS) [Hodby et al., Phys. Rev. Lett. 94, 120402 (2005)] evaluates the overlap of two atomic distributions in phase space by sampling atomic pairs according to a phase-space criterion. The other model, the chemical equilibrium theory (ChET) [Watabe and Nikuni, Phys. Rev. A 77, 013616 (2008)] considers atomic and molecular distributions in the limit of the chemical and thermal equilibrium. The present study applies SPSS and ChET to a prototypical system of K+K$\ensuremath{\rightarrow}$ K2{}_{2}2​ in all the symmetry combinations, namely Fermi-Fermi, Bose-Bose, and Bose-Fermi cases. To examine implications of the phase-space criterion for SPSS, the behavior of molecular conversion is analyzed using four distinct geometrical constraints. Our comparison of the results of SPSS with those of ChET shows that while they appear similar in most situations, the two models give rise to rather dissimilar behaviors when the presence of a Bose-Einstein condensate strongly affects the molecule formation.
Advances in atomic physics have led to the possibility of a coherent transformation between ultracold atoms and molecules including between completely bosonic condensates. Such transformations are enabled by the magneto-association of atoms at a Feshbach resonance which results in a passage through a quantum critical point. In this study, we show that the presence of generic interaction between the constituent atoms and molecules can fundamentally alter the nature of the critical point, change the yield of the reaction and the order of the consequent phase transition. We find that the correlations introduced by this interaction induce nontrivial many-body physics such as coherent oscillations between atoms and molecules, and a selective formation of squeezed molecular quantum states and quantum cat states. We provide analytical and numerical descriptions of these effects, along with scaling laws for the reaction yield in non-adiabatic regimes.