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Production of bosonic molecules in the nonequilibrium dynamics of a degenerate Fermi gas across a Feshbach resonance

B. Dobrescu

Published Jun 2, 2009• 0 citations
OpenAlex

Abstract

In this thesis I present a nonequilibrium quantum field theory that describes the\nproduction of molecular dimers from a two-component quantum-degenerate atomic\nFermi gas, via a linear downward sweep of a magnetic field across an s-wave Feshbach\nresonance. This problem raises interest because it is presently unclear as to why\ndeviations from the universal Landau-Zener formula for the transition probability at\ntwo-level crossing are observed in the experimentally measured production efficiencies.\nThe approach is based on evaluating real-time Green functions within the Keldysh-\nSchwinger formalism. The effects of quantum statistics associated with Pauli blocking\nfor fermions and induced emission for bosons, characteristic of particle scattering in\na quantum-degenerate many-body medium, are fully accounted for. I show that the\nmolecular conversion efficiency is represented by a power series in terms of a dimensionless\nparameter which, in the zero-temperature limit, depends solely on the initial\ngas density and the Landau-Zener parameter. This result reveals a hindrance of the\ncanonical Landau-Zener transition probability due to many-body effects, and presents\nan explanation for the experimentally observed deviations.\nA second topic treated in this thesis concerns the study of non-adiabatic transitions\nin N-state Landau-Zener systems. In connection to this, I provide a proof of\nthe conjecture put forth by Brundobler and Elser, regarding the survival probability\non the diabatic levels with maximum/minimum slope.

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Adiabatic association of ultracold molecules via magnetic-field tunable interactions

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We consider in detail the situation of applying a time-dependent external magnetic field to a 87 Rb atomic Bose–Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low-energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of Köhler and Burnett (2002 Phys. Rev. A 65 033601) to study the efficiency of the association of molecules in a 87 Rb Bose–Einstein condensate during a linear passage of the magnetic-field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau–Zener, configuration interaction, and two-level mean-field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose–Einstein condensed gas, provided that the magnetic-field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic-field strength, and identify the Landau–Zener coefficient determined by Mies et al (2000 Phys. Rev. A 61 022721) as the main parameter that controls the efficiency.

arXiv:cond-mat/0312178•Journal of Physics B Atomic Molecular and Optical Physics•Aug 24, 2004•102 citations

Many-body effects on nonadiabatic Feshbach conversion in bosonic systems

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We investigate the dynamics of converting cold bosonic atoms to molecules when an external magnetic field is swept across a Feshbach resonance. Our analysis relies on a quantum microscopic model that accounts for many-body effects in the association process. We show that the picture of two-body molecular production depicted by the Landau-Zener model is significantly altered due to many-body effects. In the nonadiabatic regime, we derive an analytic expression for molecular conversion efficiency that explains the discrepancy between the prediction of the Landau-Zener formula and the experimental data [E. Hodby et al., Phys. Rev. Lett. 94, 120402 (2005)]. Our theory is further extended to the formation of heteronuclear diatomic molecules and gives some interesting predictions.

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Dynamics of Feshbach molecule production

Thomas M. Hanna

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.

•Jan 1, 2008•2 citations

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Many-body effects on adiabatic passage through Feshbach resonances

Igor Tikhonenkov, E. Pazy, Y. B. Band +2 more

We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms $\ensuremath{\Gamma}$ on sweep rate $\ensuremath{\alpha}$, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law $\ensuremath{\Gamma}\ensuremath{\propto}\ensuremath{\alpha}$ is obtained when the initial molecular fraction is smaller than the $1∕N$ quantum fluctuations, and a cubic-root power law $\ensuremath{\Gamma}\ensuremath{\propto}{\ensuremath{\alpha}}^{1∕3}$ is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.

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Molecular Production in Two Component Atomic Fermi Gases

Jan Chwedeńczuk, Krzysztof Góral, Thorsten Köhler +1 more

We provide a practical approach to the molecular production via linear downward sweeps of Feshbach resonances in degenerate Fermi gases containing incoherent mixtures of two atomic spin states. We show that the efficiency of the association of atoms is determined just by the Landau-Zener parameter in addition to the density of the gas. Our approach of pairwise summation of the microscopic binary transition probabilities leads to an intuitive explanation for the observed saturation of the molecular production and recovers all atomic loss curves of Regal et al. [Nature (London) 427, 47 (2003))]] as well as Strecker et al. [Phys. Rev. Lett. 91, 080406 (2003))]] without adjustable parameters.

arXiv:cond-mat/0409192•Physical Review Letters•Dec 20, 2004•24 citations
In this thesis I present a nonequilibrium quantum field theory that describes the\nproduction of molecular dimers from a two-component quantum-degenerate atomic\nFermi gas, via a linear downward sweep of a magnetic field across an s-wave Feshbach\nresonance. This problem raises interest because it is presently unclear as to why\ndeviations from the universal Landau-Zener formula for the transition probability at\ntwo-level crossing are observed in the experimentally measured production efficiencies.\nThe approach is based on evaluating real-time Green functions within the Keldysh-\nSchwinger formalism. The effects of quantum statistics associated with Pauli blocking\nfor fermions and induced emission for bosons, characteristic of particle scattering in\na quantum-degenerate many-body medium, are fully accounted for. I show that the\nmolecular conversion efficiency is represented by a power series in terms of a dimensionless\nparameter which, in the zero-temperature limit, depends solely on the initial\ngas density and the Landau-Zener parameter. This result reveals a hindrance of the\ncanonical Landau-Zener transition probability due to many-body effects, and presents\nan explanation for the experimentally observed deviations.\nA second topic treated in this thesis concerns the study of non-adiabatic transitions\nin N-state Landau-Zener systems. In connection to this, I provide a proof of\nthe conjecture put forth by Brundobler and Elser, regarding the survival probability\non the diabatic levels with maximum/minimum slope.
We consider in detail the situation of applying a time-dependent external magnetic field to a 87 Rb atomic Bose–Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low-energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of Köhler and Burnett (2002 Phys. Rev. A 65 033601) to study the efficiency of the association of molecules in a 87 Rb Bose–Einstein condensate during a linear passage of the magnetic-field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau–Zener, configuration interaction, and two-level mean-field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose–Einstein condensed gas, provided that the magnetic-field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic-field strength, and identify the Landau–Zener coefficient determined by Mies et al (2000 Phys. Rev. A 61 022721) as the main parameter that controls the efficiency.
We investigate the dynamics of converting cold bosonic atoms to molecules when an external magnetic field is swept across a Feshbach resonance. Our analysis relies on a quantum microscopic model that accounts for many-body effects in the association process. We show that the picture of two-body molecular production depicted by the Landau-Zener model is significantly altered due to many-body effects. In the nonadiabatic regime, we derive an analytic expression for molecular conversion efficiency that explains the discrepancy between the prediction of the Landau-Zener formula and the experimental data [E. Hodby et al., Phys. Rev. Lett. 94, 120402 (2005)]. Our theory is further extended to the formation of heteronuclear diatomic molecules and gives some interesting predictions.
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.
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.
We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms $\ensuremath{\Gamma}$ on sweep rate $\ensuremath{\alpha}$, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law $\ensuremath{\Gamma}\ensuremath{\propto}\ensuremath{\alpha}$ is obtained when the initial molecular fraction is smaller than the 1∕N1∕N1∕N quantum fluctuations, and a cubic-root power law $\ensuremath{\Gamma}\ensuremath{\propto}{\ensuremath{\alpha}}^{1∕3}$ is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.
We provide a practical approach to the molecular production via linear downward sweeps of Feshbach resonances in degenerate Fermi gases containing incoherent mixtures of two atomic spin states. We show that the efficiency of the association of atoms is determined just by the Landau-Zener parameter in addition to the density of the gas. Our approach of pairwise summation of the microscopic binary transition probabilities leads to an intuitive explanation for the observed saturation of the molecular production and recovers all atomic loss curves of Regal et al. [Nature (London) 427, 47 (2003))]] as well as Strecker et al. [Phys. Rev. Lett. 91, 080406 (2003))]] without adjustable parameters.