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arXiv:0902.2178

Static and Dynamic properties of a Fermi-gas of cooled atoms near a wide Feshbach resonance

Deqiang Sun, Ar. Abanov, V. L. Pokrovsky

Published Feb 12, 2009• 0 citations
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Abstract

We introduce the Global Spin Model to study the static and dynamic properties of the ultracold fermionic gas near the broad Feshbach resonance. We show that the problem of molecular production, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction leads to significant renormalization of the gap between adiabatic levels. In contrast to static problem the close vicinity of exact resonance does not play substantial role. Two main physical results of our theory is the high sensitivity of molecular production to the initial value of magnetic field and generation of a large BCS condensate distributed over a broad range of momenta in a wide range of parameters. We calculate the amplitude of the condensate as function of the initial detuning and the rate of the magnetic field sweep.

DOI
10.48550/arxiv.0902.2178

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We introduce the Global Spin Model to study the static and dynamic properties of the ultracold fermionic gas near the broad Feshbach resonance. We show that the problem of molecular production, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction leads to significant renormalization of the gap between adiabatic levels. In contrast to static problem the close vicinity of exact resonance does not play substantial role. Two main physical results of our theory is the high sensitivity of molecular production to the initial value of magnetic field and generation of a large BCS condensate distributed over a broad range of momenta in a wide range of parameters. We calculate the amplitude of the condensate as function of the initial detuning and the rate of the magnetic field sweep.
\n The problem of molecular production from a degenerate gas of fermions at a broad Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction and induced coherence lead to significant renormalization of the gap between adiabatic levels. The essential region of energies near the resonance contributing to the atom-molecule transformation strongly exceeds the Fermi energy of the weakly interacting gas. The close vicinity of the exact resonance does not play as substantial a role as in the static problem. Our main results are: i) The molecular production is sensitive to the initial magnetic field. ii) In the inverse process of molecule dissociation a large BCS condensate distributed over a broad range of momenta is generated.\n
The problem of molecular production from a degenerate gas of fermions at a broad Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction and induced coherence lead to significant renormalization of the gap between adiabatic levels. The essential region of energies near the resonance contributing to the atom-molecule transformation strongly exceeds the Fermi energy of the weakly interacting gas. The close vicinity of the exact resonance does not play as substantial a role as in the static problem. Our main results are: i) The molecular production is sensitive to the initial magnetic field. ii) In the inverse process of molecule dissociation a large BCS condensate distributed over a broad range of momenta is generated.
We investigate the dynamic response of a highly degenerate ultracold Fermi gas to varying magnetic fields near the Feshbach resonance. Following the experimental practice, we calculate the dynamics of the excitation gap in response to the oscillating and linearly ramped magnetic fields, respectively. For oscillating magnetic fields, depending on the frequencies and the amplitudes of the oscillations, the response of the system shows either linear or rich nonlinear behavior. In addition, both the spectral studies through the linear-response theory and the time-domain simulations suggest the existence of a resonant frequency corresponding to the dissociation threshold of the fermion atom pairs. For linearly ramped magnetic fields, the response of the excitation gap shows damped oscillations, with the final value dependent on the rate of the field sweep. This work may find its applications in exploring the dynamics of the ultracold atom superfluidity near the BCS--Bose-Einstein-condensation crossover region.
This thesis studies the dynamics of Feshbach molecule production from a gas of \nultracold spin polarised Fermi atoms. A magnetic field is used to vary the strength \nof the interaction between the atoms exploring the limits of weakly paired atoms \nand tightly bound diatomic molecules. A mean field approximation is used to \nstudy the thermodynamics and dynamics of the system. \nThe two-body interaction is modelled using a separable potential that reproduces \nthe near threshold behaviour of the system close to a Feshbach resonance. \nFor atoms in the same internal state interactions occur in the p-wave, such that \nthey have one quanta of relative orbital angular momentum (ℓ = 1). The presence \nof a magnetic field fixes a quantisation axis for this angular momentum, leading \nto a splitting of the resonance feature into three components. It is shown that in \ncertain cases these components may be treated separately on both a two-body and \nthermodynamic level. Consequently the many-body dynamics are also treated as \nif these components are distinct. \nIn order to study molecule production the gas is prepared in a state similar to \nthe Bardeen-Cooper-Schrieffer (BCS) state in a superconductor. A linear sweep \nof the magnetic field through a Feshbach resonance is used to convert the weakly \npaired atoms into tightly bound molecules. The variation of the molecule production \nefficiency is studied as the initial temperature, density initial magnetic field \nand final magnetic field are varied. Also studied is the variation of molecule production \nas a function of the rate at which the magnetic field is varied. It is shown \nthat high densities are needed to explore a range of initial magnetic fields and \nsweep rates.
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.