Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1210.2317 · Physical Review A

Many-body dynamics of p -wave Feshbach-molecule production: A mean-field approach

L. Austen, L.G. Cook, M. D. Lee, Jordi Mur-Petit

Published Feb 13, 2013• 3 citations
arXivHTMLPDF

Abstract

We study the mean-field dynamics of $p$-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 $p$-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.

DOI
10.1103/physreva.87.023610

Related papers

Production of p-wave Feshbach molecules from an ultra-cold Fermi gas

L. Austen

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.

•Jan 28, 2012•0 citations

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

Adiabatic association of ultracold molecules via magnetic-field tunable interactions

Krzysztof Góral, Thorsten Köhler, S. A. Gardiner +2 more

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

Feshbach-molecule formation in a Bose-Fermi mixture

Tyler D. Cumby, Ruth Shewmon, Ming-Guang Hu +2 more

We investigate magnetoassociation of ultracold fermionic Feshbach molecules in a mixture of ${}^{40}$K and ${}^{87}$Rb atoms, where we can create ${}^{40}$K${}^{87}$Rb molecules with a conversion efficiency as high as 45%. In the limit of fast magnetic sweeps and small molecule fraction, we find that the time scale of molecule production is accurately predicted by a parameter-free model that uses only the atomic densities, masses, and the known Feshbach resonance parameters. We find that molecule production efficiency saturates for slower magnetic sweeps, at which point the maximum number of Feshbach molecules depends primarily on the atoms' phase-space density. At higher temperatures, our measurements agree with a phenomenological model that successfully describes the formation of bosonic molecules from either Bose or Fermi gases. However, for quantum degenerate atom gas mixtures, we measure significantly fewer molecules than this model predicts.

arXiv:1212.0903•Physical Review A•Jan 7, 2013•35 citations

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

Hongwei Xiong, Shujuan Liu, Min Liu +2 more

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.

arXiv:cond-mat/0404565•Apr 23, 2004•0 citations

BCS,BEC states and Feshbach resonance in atomic Fermi gases

呂欣頤

To study the behavior of atomic Fermi gases in the vicinity of Feshbach resonance, M. Holland et al. [12] and S. J. J. M. F. Kokkelmans et al. [22] proposed resonance mean field theory in which the molecules formed by Feshbach resonance are considered in the many-body Hamiltonian. Motivated by microscopic scattering theory and resonance mean field theory, we develop a thermodynamic method to study this system. In this method we treat atomic Fermi gases near resoance as a atom-molecule mixture. We can use BCS Hamiltonian and Bose- Einstein statistics to describe the behavior of atoms and molecules respectively. Chemical equilibrium can be achieved between atoms and molecules due to hypefine interaction. We use this method to study the system behavior under different temperature and detuning energy and find that at low temperature a smooth BCS-BEC crossever can occure with decreasing detuning energy. We further calculate a measurable quantity, molecular condensation fraction, and find its behavior matches qualitatively with the experimental result [16].

臺灣大學物理研究所學位論文•Jan 1, 2004•0 citations
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.
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.
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.
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 magnetoassociation of ultracold fermionic Feshbach molecules in a mixture of 40{}^{40}40K and 87{}^{87}87Rb atoms, where we can create 40{}^{40}40K87{}^{87}87Rb molecules with a conversion efficiency as high as 45%. In the limit of fast magnetic sweeps and small molecule fraction, we find that the time scale of molecule production is accurately predicted by a parameter-free model that uses only the atomic densities, masses, and the known Feshbach resonance parameters. We find that molecule production efficiency saturates for slower magnetic sweeps, at which point the maximum number of Feshbach molecules depends primarily on the atoms' phase-space density. At higher temperatures, our measurements agree with a phenomenological model that successfully describes the formation of bosonic molecules from either Bose or Fermi gases. However, for quantum degenerate atom gas mixtures, we measure significantly fewer molecules than this model predicts.
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.
To study the behavior of atomic Fermi gases in the vicinity of Feshbach resonance, M. Holland et al. [12] and S. J. J. M. F. Kokkelmans et al. [22] proposed resonance mean field theory in which the molecules formed by Feshbach resonance are considered in the many-body Hamiltonian. Motivated by microscopic scattering theory and resonance mean field theory, we develop a thermodynamic method to study this system. In this method we treat atomic Fermi gases near resoance as a atom-molecule mixture. We can use BCS Hamiltonian and Bose- Einstein statistics to describe the behavior of atoms and molecules respectively. Chemical equilibrium can be achieved between atoms and molecules due to hypefine interaction. We use this method to study the system behavior under different temperature and detuning energy and find that at low temperature a smooth BCS-BEC crossever can occure with decreasing detuning energy. We further calculate a measurable quantity, molecular condensation fraction, and find its behavior matches qualitatively with the experimental result [16].