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arXiv:cond-mat/0404565

Condensate fraction of molecules for a spin mixture of ultracold fermionic atoms

Hongwei Xiong, Shujuan Liu, Min Liu, Kelin Gao, Mingsheng Zhan

Published Apr 23, 2004• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/0404565

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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.
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)).
We determine the adiabatic phase diagram of a resonantly-coupled system of Fermi atoms and Bose molecules confined in the harmonic trap by using the local density approximation. The adiabatic phase diagram shows the fermionic condensate fraction composed of condensed molecules and Cooper pair atoms. The key idea of our work is conservation of entropy through the adiabatic process, extending the study of Williams et al. [Williams et al., New J. Phys. 6, 123 (2004)] for an ideal gas mixture to include the resonant interaction in a mean-field theory. We also calculate the molecular conversion efficiency as a function of initial temperature. Our work helps to understand recent experiments on the BCS-BEC crossover, in terms of the initial temperature measured before a sweep of the magnetic field.
Fast sweep projection onto Feshbach molecules has been widely used as a probe to explore the properties of fermionic condensates, in particular the condensate fraction. By determining the exact dynamics of a pair of atoms in time varying magnetic fields across a Feshbach resonance, we calculate the number of condensed and noncondensed molecules created after fast magnetic field sweeps from the BCS to the BEC side of the resonance. We analyse the dependence of the molecular conversion efficiency for condensed and noncondensed molecules on the sweep rate, and on the initial and final magnetic fields, for 40^{40}40K and 6^{6}6Li resonances; and discuss the relation between the initial fermionic condensate fraction and the molecular condensate fraction measured after the sweep.
Fast-sweep projection onto Feshbach molecules has been widely used as a probe of fermionic condensates. By determining the exact dynamics of a pair of atoms in time-varying magnetic fields, we calculate the number of condensed and noncondensed molecules created after fast magnetic field sweeps from the BCS to the Bose-Einstein condensate side of the resonances in 40K and 6Li, for different sweep rates and a range of initial and final fields. We discuss the relation between the initial fermionic condensate fraction and the molecular condensate fraction measured after the sweep.
We have observed Bose-Einstein condensation of pairs of fermionic atoms in an ultracold 6Li gas at magnetic fields above a Feshbach resonance, where no stable 6Li2 molecules would exist in vacuum. We accurately determined the position of the resonance to be 822+/-3 G. Molecular Bose-Einstein condensates were detected after a fast magnetic field ramp, which transferred pairs of atoms at close distances into bound molecules. Condensate fractions as high as 80% were obtained. The large condensate fractions are interpreted in terms of preexisting molecules which are quasistable even above the two-body Feshbach resonance due to the presence of the degenerate Fermi gas.
We study the mean-field dynamics of ppp-wave Feshbach-molecule production in an ultracold gas of Fermi atoms in the same internal state. We derive a separable potential to describe the low-energy scattering properties of such atoms, and use this potential to solve the mean-field dynamics during a magnetic-field sweep. Initially, on the negative scattering length side of a Feshbach resonance the gas is described by the BCS theory. We adapt the method by Szyma\ifmmode \acute{n}\else \'{n}\fi{}ska et al. [Phys. Rev. Lett. 94, 170402 (2005)] to ppp-wave interacting Fermi gases and model the conversion dynamics of the gas into a Bose-Einstein condensate of molecules on the other side of the resonance under the influence of a linearly varying magnetic field. We have analyzed the dependence of the molecule production efficiency on the density of the gas, temperature, initial value of the magnetic field, and magnetic-field ramp speed. Our results show that in this approximation molecule production by a linear magnetic-field sweep is highly dependent on the initial state.