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Low Temperature Physics

Ground state and excitations of a Bose-Einstein condensate of atoms and their diatomic bound states

A. S. Peletminskii, S. V. Peletminskiǐ, Yu. M. Poluéktov

Published Jun 1, 2014• 6 citations
Publisher

Abstract

This is a theoretical study of a many-body system of spin-zero atoms and their diatomic bound states (molecules) which form a single Bose-Einstein condensate at zero temperature. The Gross-Pitaevskii approach is used to analyze the equilibrium states and dynamics of this system. It is shown that, depending on the binding energy of the system, the system can exist in two phases: an atom-molecule condensate and a molecular condensate. The basic thermodynamic characteristics and the criteria for their stability are found. Both phases have two branches of collective excitations, one of which is acoustic, while the other has an activation energy.

DOI
10.1063/1.4883893

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This is a theoretical study of a many-body system of spin-zero atoms and their diatomic bound states (molecules) which form a single Bose-Einstein condensate at zero temperature. The Gross-Pitaevskii approach is used to analyze the equilibrium states and dynamics of this system. It is shown that, depending on the binding energy of the system, the system can exist in two phases: an atom-molecule condensate and a molecular condensate. The basic thermodynamic characteristics and the criteria for their stability are found. Both phases have two branches of collective excitations, one of which is acoustic, while the other has an activation energy.
The occurrence of a molecular Bose-Einstein condensate is studied for an atomic system near a zero energy resonance of the binary scattering process, with a large and positive scattering length. The interaction potential is modeled by a pseudo-potential having one bound state. Using a variational Gaussian ansatz for the NNN-body density operator, we discuss the thermodynamic properties at low temperature and the relative stability of the system towards the formation of an atomic Bose-Einstein condensate. We also derive an approximate Gross-Pitaevskii equation for the molecular condensate leading to the prediction of a Bogoliubov spectrum.
Abstract We study a many-body system of interacting fermionic atoms of two species that are in thermodynamic equilibrium with their condensed heteronuclear bound states (molecules). In order to describe such an equilibrium state, we use a microscopic approach that involves the Bogoliubov model for a weakly interacting Bose gas and approximate formulation of the second quantization method in the presence of bound states of particles elaborated earlier by the authors. This microscopic approach is valid at low temperatures, when the average kinetic energy of all the components in the system is small in comparison with the bound state energy. The coupled equations, which relate the chemical potentials of fermionic components and molecular condensate density, are obtained within the proposed theory. At zero temperature, these equations are analyzed both analytically and numerically, attracting the relevant experimental data. We find the conditions at which a condensate of heteronuclear molecules coexists in equilibrium with degenerate components of a Fermi gas. The ground state energy and single-particle excitation spectrum are found. The boundaries of the applicability of the developed microscopic approach are analyzed.
The dynamics of a two-component dilute Bose-Einstein gas of atoms at zero temperature is described in the mean-field approximation by a two-component Gross-Pitaevskii equation. We solve this equation assuming a Gaussian shape for the wave function, where the free parameters of the trial wave function are determined using a moment method. We derive equilibrium states and the phase diagrams for the stability for positive and negative sss-wave scattering lengths, and obtain the low-energy excitation frequencies corresponding to the collective motion of the two Bose-Einstein condensates.
We model an atom-molecule Bose-Einstein condensate (AMBEC) using simplified set of coupled Gross-Pitaevskii equations (GPE), where we neglect the background (elastic) scattering length of the atoms. We analyze the ground state numerically and analytically, and construct its twin state through transformation δ→−δ,K→−Kδ\rightarrow-δ, K\rightarrow-Kδ→−δ,K→−K. We find that the ground state is a collection of three local eigenstates: all-atom state, mixed (atom-molecule) state, and all-molecule state, while the twin state comprises of mixed state with tunable fraction of atoms including unity but excluding all-molecules. We find the analytic boundaries of the local eigenstates from the stability analysis of the underlying all-molecule and all-atom eigenstate. In the ground state we find either regular oscillations in size and fraction of both condensates, or shrinking of the atomic condensate that resembles the collapse. In the twin state we find rapid irregular disintegration of both condensates. We contrast the properties of the mean-field parametric excitations found in AMBEC with the experimentally observed excitations of the BEC. We discuss some enticing possibilities for creation of atomic BEC of controllable half-width by performing the parameter sweep around the boundary.
This paper investigates the collective excitation and stability of low-dimensional Bose–Einstein condensates with two- and three-body interactions by the variational analysis of the time-dependent Gross–Pitaevskii–Ginzburg equation. The spectrum of the low-energy excitation and the effective potential for the width of the condensate are obtained. The results show that: (i) the repulsive two-body interaction among atoms makes the frequency red-shifted for the internal excitation and the repulsive or attractive three-body interaction always makes it blue-shifted; (ii) the region for the existence of the stable bound states is obtained by identifying the critical value of the two- and three-body interactions.
Bose-Einstein condensation (BEC) of Feshbach molecules in a homogeneous Bose gas is studied at finite temperatures in a single-channel mean-field approach where the Hartree-Fock energy and pairing gap are determined self-consistently. In the molecular-BEC state, the atomic excitation is gapped and the molecular excitation is gapless. The binding energy of Feshbach molecules is shifted from the vacuum value by many-body effects. When the scattering length as{a}_{s}as​ of the atoms is negative, the system is subject to mechanical collapse due to negative compressibility. The system is stable in most regions with positive scattering lengths. However, at low temperatures near the resonance, the molecular-BEC state vanishes, and the coherent mixture of atomic and molecular BEC is subject to mechanical collapse.