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arXiv:cond-mat/0403652

Dimers of ultracold two-component Fermi gases on magnetic-field Feshbach resonance

Hongwei Xiong, Shujuan Liu, Mingsheng Zhan

Published Mar 26, 2004• 0 citations
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Abstract

At the location of a magnetic-field Feshbach resonance, a mixture gas of fermionic atoms and dimers of fermionic atom pairs is investigated in the unitarity limit where the absolute value of the scattering length is much larger than the mean distance between atoms. The dynamic equilibrium of the mixture gases is characterized by the minimum of the Gibbs free energy. For the fermionic atoms and dimers with divergent scattering length, it is found that the fraction of the dimers based on a very simple theory agrees with the high fraction of zero-momentum molecules observed in a recent experiment (M. W. Zwierlein et al, Phys. Rev. Lett. 92, 120403 (2004)). The dimeric gas can be also used to interpret the frequency of the radial breathing mode observed in the experiment by J. Kinast et al (Phys. Rev. Lett. 92, 150402 (2004)).

DOI
10.48550/arxiv.cond-mat/0403652

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•Jun 5, 2014•0 citations
At the location of a magnetic-field Feshbach resonance, a mixture gas of fermionic atoms and dimers of fermionic atom pairs is investigated in the unitarity limit where the absolute value of the scattering length is much larger than the mean distance between atoms. The dynamic equilibrium of the mixture gases is characterized by the minimum of the Gibbs free energy. For the fermionic atoms and dimers with divergent scattering length, it is found that the fraction of the dimers based on a very simple theory agrees with the high fraction of zero-momentum molecules observed in a recent experiment (M. W. Zwierlein et al, Phys. Rev. Lett. 92, 120403 (2004)). The dimeric gas can be also used to interpret the frequency of the radial breathing mode observed in the experiment by J. Kinast et al (Phys. Rev. Lett. 92, 150402 (2004)).
The condensate fraction of molecules for ultracold Fermi gases is investigated for the magnetic field below the Feshbach resonant magnetic field. Assuming that there is no loss of particles and energy during the adiabatic magnetic-field sweep, a simple theory is used to interpret the measured condensate fraction in the experiments by JILA group (Phys. Rev. Lett. 92, 040403 (2004)) and MIT group (Phys. Rev. Lett. 92, 120403 (2004)). Our theory shows that the condensate fraction of molecules is dependent on the initial condition of the system and especially on the process of the magnetic-field sweep.
The thermodynamic properties of two-component Fermi gases with divergent scattering length is investigated and the transition temperature for the emergence of a stable dimeric gas is obtained by a simple theoretical model where the unique property of the dimers (i.e. fermionic atom pairs) with divergent scattering length is considered. Below the transition temperature, through the investigation of the overall entropy for the mixture gas of fermionic atoms and dimers, we calculate the relation between the energy and temperature of the system. In the limit of zero temperature, based on the chemical equilibrium condition, the fraction of the dimers is investigated and the role of the dimers in the collective excitations of the system is also discussed. It is found that our theoretical results agree with the condensate fraction, collective excitations, transition temperature and heat capacity investigated by the recent experiments about the strongly interacting two-component Fermi gases.
Magnetically tunable Feshbach resonances are an indispensable tool for experiments with atomic quantum gases. We report on 37 thus far unpublished Feshbach resonances and four further probable Feshbach resonances in spin mixtures of ultracold fermionic 40K^{40}\mathrm{K}40K with temperatures well below 100 nK. In particular, we locate a broad resonance at B=389.7GB=389.7\phantom{\rule{0.16em}{0ex}}\text{G}B=389.7G with a magnetic width of 26.7G26.7\phantom{\rule{0.28em}{0ex}}\text{G}26.7G. Here $1\phantom{\rule{0.28em}{0ex}}\text{G}={10}^{\ensuremath{-}4}\phantom{\rule{0.16em}{0ex}}\text{T}$. Furthermore, by exciting low-energy spin waves, we demonstrate a means to precisely determine the zero crossing of the scattering length for this broad Feshbach resonance. Our findings allow for further tunability in experiments with ultracold 40K^{40}\mathrm{K}40K quantum gases.
Abstract In a previous paper [Phys. Rev. A 95, 060 701(R) (2017)], we demonstrated that a new type of two-body interaction, which depends on the center of mass (CoM) momentum, can be realized for ultracold atoms via laser-modulated magnetic Feshbach resonance (MFR). Further studies (e.g. L He et al, Phys. Rev. Lett. 120, 045 302 (2018)) show that various interesting phenomena, such as Fulde–Ferrell superfluids, can be induced by scattering between ultracold atoms with this interaction. In this work we investigate the shallow bound states of two ultracold atoms with this type of interaction. We show that when the magnetic field B is below the MFR point B 0, two shallow bound states can appear in this system. Namely, a ‘two-component dimer’ or a dimer with pseudo-spin 1/2 can be formed by two atoms. Furthermore, the dispersion curve of the dimer may have either single or double minimums in the CoM momentum space. The latter case can be explained as a result from significant pseudo-spin-orbital coupling (SOC) effects. Our results show that the ultracold gases with CoM momentum dependent interaction may be a candidate for quantum simulations with ultracold two-component molecules, especially the molecule gases with SOC.
Motivated by a recent experiment by ENS group on the mixture of Bose and Fermi superfluids (arxiv:1404.2548), we investigate the effective scattering between a bosonic atom and a molecule(dimer) of fermion atoms. It is found that the mean-field prediction of the atom-dimer scattering length (aada_{ad}aad​), as simply given by the boson-fermion scattering length (abfa_{bf}abf​), generically fails. Instead, aada_{ad}aad​ crucially depends on the ratio between abfa_{bf}abf​ and affa_{ff}aff​ (the fermion-fermion scattering length), and in addition log-periodically depends on the three-body parameter. We identify the universal parameters in characterizing aada_{ad}aad​ for a wide range of affa_{ff}aff​ in the molecular side of the fermion-fermion Feshbach resonance, and further demonstrate that the atom-dimer many-body system can become unstable against either phase separation or collapse as tuning affa_{ff}aff​. Our results have practical implications to the atom loss and collective mode measurement in ENS experiment.