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arXiv:0707.3630 · Europhysics Letters (EPL)

Molecular production at a broad Feshbach resonance in a Fermi gas of cooled atoms

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

Published Jun 12, 2008• 18 citations
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Abstract

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.

DOI
10.1209/0295-5075/83/16003

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Molecular production at a broad Feshbach resonance in Fermi-gas of cooled atoms

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

\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

Bulletin of the American Physical Society•Mar 13, 2008•0 citations

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

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

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.

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Dynamics of Feshbach molecule production

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The variation of a magnetic field in the vicinity of a zero-energy resonance allows highly vibrationally excited molecules (‘Feshbach molecules’) to be produced from an ultracold atomic gas. In this thesis, we study the dynamics of this process. We begin by studying the dissociation of Feshbach molecules, showing that in the limit of a sudden jump the shape of the spectrum of dissociated atoms can act as a probe of the zero-energy resonance. For some resonances, such jumps are within reach of current experiments. We also study the intermediate region between sudden jumps and asymptotically wide, linear ramps. It is shown from a precise derivation how the latter limit leads to a universal spectrum with a shape independent of the implementation of the two-body physics, provided that the near-resonant scattering properties are correctly modelled. We then turn to the dynamics of Feshbach molecule production from thermal and condensed gases. Our microscopic quantum dynamics approach includes the exact twobody evolution as an input to the many-body calculations. We show that in the long-time limit, and the Markov limit for the interactions, the non-Markovian Boltzmann equation (NMBE) we derive for the one-body density matrix reduces to the normal Boltzmann equation. In the limit of short times and small depletion of the atomic gas, the molecule production efficiency can be calculated by thermally averaging the two-body transition probability density. This thermal averaging technique is applied to studies of the formation of Feshbach molecules using a magnetic field modulation that is near-resonant with the molecular bound state energy. The continuum is shown to have a significant effect on both the dynamics and efficiency of this process. We examine the dependence of the molecule production efficiency on the duration, amplitude and frequency of the modulation, as well as the temperature and density of the gas. This method of producing molecules is effective for a wide range of bound state energies, but requires sufficient variation of the two-body energy levels with magnetic field. Lastly, we implement the NMBE for the case of a fast linear ramp across a Feshbach resonance. The solution of this equation is made feasible by including a large part of the required computation in the kernel, which is calculated in advance. The NMBE allows predictions of the molecule production efficiency which go beyond the thermal averaging technique by accounting for the depletion and rethermalisation of the continuum. In the limit of small depletions, the two approaches give the same results. As the depletion increases, the two approaches differ due to many-body effects limiting the maximum possible molecule production efficiency. We have observed this in our simulations by considering higher-density gases. We have therefore shown the suitability and practicability of this beyond mean-field approach for application to further problems in the production of Feshbach molecules from ultracold gases.

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Enhanced magnetoassociation of $^6$Li in the quantum degenerate regime

Vineetha Naniyil, Yijia Zhou, Guy Simmonds +3 more

We study magnetic Feshbach resonance of ultracold $^6$Li atoms in a dipole trap close to quantum degeneracy. The experiment is carried out by linearly ramping down the magnetic field from the BCS to the BEC side around the broad resonance at $B_r=834.1$G. The Feshbach molecule formation efficiency depends strongly on the temperature of the atomic gas and the rate at which the magnetic field is ramped across the Feshbach resonance. The molecular association process is well described by the Landau-Zener transition while above the Fermi temperature, such that two-body physics dominates the dynamics. However, we observe an enhancement of the atom-molecule coupling as the Fermionic atoms reach degeneracy, demonstrating the importance of many-body coherence not captured by the conventional Landau-Zener model. We develop a theoretical model that explains the temperature dependence of the atom-molecule coupling. Furthermore, we characterize this dependence experimentally and extract the atom-molecule coupling coefficient as a function of temperature, finding qualitative agreement between our model and experimental results. Accurate measurement of this coupling coefficient is important for both theoretical and experimental studies of atom-molecule association dynamics.

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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.

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Feshbach molecule production in fermionic atomic gases

Victor Gurarie

This paper examines the problem of molecule production in an atomic fermionic gas close to an $s$-wave Feshbach resonance by means of a magnetic field sweep through the resonance. In the solvable case of a narrow resonance, the density of molecules at the end of the process is derived for a slow sweep. It is shown that the density of the produced molecules is lower than what an application of a naive Landau-Zener formula for level crossing would imply. However, in the limit of a very slow sweep it is still possible to achieve full conversion of fermions into the molecules. It appears that the origin of the failure of the Landau-Zener picture of the molecule production is due to the fact that the sweep goes through a quantum phase transition in the limit of an infinitely narrow resonance, in agreement with general results recently discussed in the literature. However, the precise connection of this problem to other problems with this feature is not established.

arXiv:0812.4474•Physical Review A•Aug 31, 2009•14 citations
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.\n
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.
The variation of a magnetic field in the vicinity of a zero-energy resonance allows highly vibrationally excited molecules (‘Feshbach molecules’) to be produced from an ultracold atomic gas. In this thesis, we study the dynamics of this process. We begin by studying the dissociation of Feshbach molecules, showing that in the limit of a sudden jump the shape of the spectrum of dissociated atoms can act as a probe of the zero-energy resonance. For some resonances, such jumps are within reach of current experiments. We also study the intermediate region between sudden jumps and asymptotically wide, linear ramps. It is shown from a precise derivation how the latter limit leads to a universal spectrum with a shape independent of the implementation of the two-body physics, provided that the near-resonant scattering properties are correctly modelled. We then turn to the dynamics of Feshbach molecule production from thermal and condensed gases. Our microscopic quantum dynamics approach includes the exact twobody evolution as an input to the many-body calculations. We show that in the long-time limit, and the Markov limit for the interactions, the non-Markovian Boltzmann equation (NMBE) we derive for the one-body density matrix reduces to the normal Boltzmann equation. In the limit of short times and small depletion of the atomic gas, the molecule production efficiency can be calculated by thermally averaging the two-body transition probability density. This thermal averaging technique is applied to studies of the formation of Feshbach molecules using a magnetic field modulation that is near-resonant with the molecular bound state energy. The continuum is shown to have a significant effect on both the dynamics and efficiency of this process. We examine the dependence of the molecule production efficiency on the duration, amplitude and frequency of the modulation, as well as the temperature and density of the gas. This method of producing molecules is effective for a wide range of bound state energies, but requires sufficient variation of the two-body energy levels with magnetic field. Lastly, we implement the NMBE for the case of a fast linear ramp across a Feshbach resonance. The solution of this equation is made feasible by including a large part of the required computation in the kernel, which is calculated in advance. The NMBE allows predictions of the molecule production efficiency which go beyond the thermal averaging technique by accounting for the depletion and rethermalisation of the continuum. In the limit of small depletions, the two approaches give the same results. As the depletion increases, the two approaches differ due to many-body effects limiting the maximum possible molecule production efficiency. We have observed this in our simulations by considering higher-density gases. We have therefore shown the suitability and practicability of this beyond mean-field approach for application to further problems in the production of Feshbach molecules from ultracold gases.
Enhanced magnetoassociation of 6^66Li in the quantum degenerate regime
We study magnetic Feshbach resonance of ultracold 6^66Li atoms in a dipole trap close to quantum degeneracy. The experiment is carried out by linearly ramping down the magnetic field from the BCS to the BEC side around the broad resonance at Br=834.1B_r=834.1Br​=834.1G. The Feshbach molecule formation efficiency depends strongly on the temperature of the atomic gas and the rate at which the magnetic field is ramped across the Feshbach resonance. The molecular association process is well described by the Landau-Zener transition while above the Fermi temperature, such that two-body physics dominates the dynamics. However, we observe an enhancement of the atom-molecule coupling as the Fermionic atoms reach degeneracy, demonstrating the importance of many-body coherence not captured by the conventional Landau-Zener model. We develop a theoretical model that explains the temperature dependence of the atom-molecule coupling. Furthermore, we characterize this dependence experimentally and extract the atom-molecule coupling coefficient as a function of temperature, finding qualitative agreement between our model and experimental results. Accurate measurement of this coupling coefficient is important for both theoretical and experimental studies of atom-molecule association dynamics.
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.
This paper examines the problem of molecule production in an atomic fermionic gas close to an sss-wave Feshbach resonance by means of a magnetic field sweep through the resonance. In the solvable case of a narrow resonance, the density of molecules at the end of the process is derived for a slow sweep. It is shown that the density of the produced molecules is lower than what an application of a naive Landau-Zener formula for level crossing would imply. However, in the limit of a very slow sweep it is still possible to achieve full conversion of fermions into the molecules. It appears that the origin of the failure of the Landau-Zener picture of the molecule production is due to the fact that the sweep goes through a quantum phase transition in the limit of an infinitely narrow resonance, in agreement with general results recently discussed in the literature. However, the precise connection of this problem to other problems with this feature is not established.