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Fermi-type interaction in molecular and atomic Hamiltonians. Application to molecular systems and Bose-Einstein condensates.

Claude Leroy, Artur Mikhailovich Ishkhanyan, Ruzan Sokhoyan, Olga V. Gromova, F. Michelot, Hans Rudolf Jauslin, OLEG N. ULENIKOV, Elena S. Bekhtereva

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

We present a simple prescription to build phenomenological Hamiltonians describing Fermi-type interactions and apply the developed formalism to two distinct physical systems. First, in a very simple way, we derive equations describing time dynamics of two coherently coupled Bose-Einstein condensates. Further, for bent XY2 molecules, we reproduce all the experimental data with an excellent precision.

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arXiv:2106.12274•Jun 23, 2021•0 citations
We present a simple prescription to build phenomenological Hamiltonians describing Fermi-type interactions and apply the developed formalism to two distinct physical systems. First, in a very simple way, we derive equations describing time dynamics of two coherently coupled Bose-Einstein condensates. Further, for bent XY2 molecules, we reproduce all the experimental data with an excellent precision.
The dynamics of coherent Rabi oscillations in coupled atomic and molecular Bose-Einstein condensates is considered taking into account the atom-atom, atom-molecule, and molecule-molecule elastic interactions. The exact solution for the molecule formation probability is derived in terms of the elliptic functions. The two-dimensional space of the involved parameters intensity and detuning is analyzed and divided into two regions where the Rabi oscillations show different characteristics. A resonance curve is found, on which the molecular formation probability monotonically increases as a function of time. The maximum value of the final transition probability on this curve is 1∕21∕21∕2 (i.e., total transition to the molecular state) and it is achieved at high field intensities starting from a minimal threshold defined by the interspecies interaction scattering lights. The explicit form of the resonance curve is determined, and it is shown that the resonance frequency position reveals a nonlinear dependence on the Rabi frequency of the applied field. A singular point is found on the resonance curve, where a power-law time evolution of the system is observed.
Using an exact third-order NL di®erential equation for the molecular state probability, we develop a variational approach which enables us to construct highly accurate analytic approximations describing time dynamics of the coupled atom-molecular system in each of the interaction regimes. We show that the approximation describing time evolution of the molecular state probability both in the weak interaction limit and in the large detuning regime of the strong interaction limit can be written as a sum of two distinct terms; the ¯rst one, being a solution to a limit ¯rst-order NL equation, e®ectively describes the process of the molecule formation while the second one, being a scaled solution to the linear DK problemb (but now with modi¯ed parameters), models the remaining oscillations which come up when the process of molecule formation is over. The graphs of the approximate and numerical solutions are practically indistinguishable for almost all the time range.
Theoretical treatments of nonequilibrium dynamics in strongly interacting Bose-Fermi mixtures are complicated by the inherent non-Gaussian nature of the vacuum two-body physics, invalidating the typical Hartree-Fock-Bogoliubov approximation. Here we apply the cumulant expansion to study nonequilibrium Bose-Fermi mixtures, which allows us to explicitly include the missing non-Gaussian quantum correlations, leading to a consistent dynamical theory of a Bose-Fermi mixture near an interspecies Feshbach resonance. We first apply our theory to a study of atom-pair coherence in the gas, which is significantly enhanced by the competing influences of the Fermi sea and Bose-Einstein condensation, in agreement with analytical calculations. Then we study the depletion of a degenerate Bose-Fermi mixture following a quench to the unitary regime, characterizing the resulting depletion of the Bose-Einstein condensate, the deformation of the Fermi surface, and the production of molecules. We find that at early times, the population dynamics scale quadratically with the hold time, and define an associated characteristic timescale set by the parameters of the mixture and the width of the Feshbach resonance. Published by the American Physical Society 2024
We extend classical-field methods [Blakie et al., Adv. Phys. 57, 363 (2008)] to provide a description of atom-molecule systems. We use a model of Bose-Einstein condensation of atoms close to a Feshbach resonance, in which the tunable scattering length of the atoms is described using a system of coupled atom and molecule fields [Holland et al., Phys. Rev. Lett. 86, 1915 (2001)]. We formulate the basic theoretical methods for a coupled atom-molecule system, including the determination of the phenomenological parameters in our system, the Thomas-Fermi description of Bose-Einstein condensate, the Bogoliubov--de Gennes equations, and the Bogoliubov excitation spectrum for a homogenous condensed system. We apply this formalism to the special case of Bragg scattering from a uniform condensate and find that for moderate and large scattering lengths, there is a dramatic difference in the shift of the peak of the Bragg spectra, compared to that based on a structureless atom model. The result is compatible with the experimental results of Papp et al. [Phys. Rev. Lett 101, 135301 (2008)] for Bragg scattering from a nonuniform condensate.
In the present work we have studied the dynamics of dipolar atom-molecular Bose Einstein Condensates coupled via Feshbach Resonance in a double well potential. We have numerically solved four coupled GP like equations, two for left well and two for right well for this atom molecular coupled system. Our numerical results show that both the long-range dipole-dipole interaction (chosen to be positive) and the coherent coupling interaction (which is positive for bosons) facilitate the transmission of atoms and molecules from left well to the right well when the population in the right well dominates over that in the left well and is trapped for a period of time. Whereas in absence of any one of these interactions probability of transient transmission decreases. However in absence of both the interactions (dipole-dipole and coherent coupling) i.e. when only the repulsive contact interaction is present, it leads to self trapping in the left well for a period of time. It is also shown that the signature of coherent coupling between atoms and molecules on the density distribution of atoms in the double well potential is present both in absence and presence of dipole-dipole interaction.