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:1504.06573 · Physical Review A

Harmonic and subharmonic association of universal dimers in a thermal gas

Abhishek Mohapatra, Eric Braaten

Published Jul 28, 2015• 8 citations
arXivHTMLPDF

Abstract

In a gas of ultracold atoms whose scattering length is controlled by a magnetic Feshbach resonance, atoms can be associated into universal dimers by an oscillating longitudinal magnetic field. In addition to the harmonic resonance with frequency near that determined by the dimer binding energy, there is a subharmonic resonance with half that frequency. If the thermal gas contains dimers, they can be dissociated into unbound atoms by the oscillating magnetic field. We show that the transition rates for association and dissociation can be calculated by treating the oscillating magnetic field as a sinusoidal time-dependent perturbation proportional to the contact operator. Many-body effects are taken into account through transition matrix elements of the contact operator. We calculate both the harmonic and subharmonic transition rates analytically for association in a thermal gas of atoms and for dissociation in a thermal gas of dimers.

DOI
10.1103/physreva.92.013425

Related papers

Association and Dissociation of Ultracold Fermions Using an Oscillating Magnetic Field

Abhishek Mohapatra

The pairwise interactions of ultracold atoms can be resonantly enhanced by tuning the scattering length to infinity using a Feshbach resonance.In a gas of ultracold atoms whose scattering length is controlled by a magnetic Feshbach resonance, the atoms can be associated into universal dimers and the dimers can be dissociated into unbound atoms by using an oscillating longitudinal magnetic field with frequency near the binding energy of a dimer.If the gas of ultracold atoms are fermions, the oscillating magnetic field with frequency near the pairing gap can dissociate Cooper pairs into pairs of unbound atoms.In this thesis, we show that the transition rates for association and dissociation can be calculated by treating the oscillating magnetic field as a sinusoidal time-dependent perturbation proportional to the contact operator.We calculate both the harmonic and subharmonic transition rates analytically for association in a thermal gas of atoms and for dissociation in a thermal gas of dimers.We also calculate the harmonic transition rate analytically for the dissociation of Cooper pairs into pairs of unbound atoms in the BCS limit.Our results for the dissociation rate of Cooper pairs can be used to make a direct measurement of the pairing gap for fermionic atoms.

•Jan 1, 2018•0 citations

Association of Atoms into Universal Dimers Using an Oscillating Magnetic Field

Christian B. Langmack, Dane Hudson Smith, Eric Braaten

In a system of ultracold atoms near a Feshbach resonance, pairs of atoms can be associated into universal dimers by an oscillating magnetic field with a frequency near that determined by the dimer binding energy. We present a simple expression for the transition rate that takes into account many-body effects through a transition matrix element of the contact. In a thermal gas, the width of the peak in the transition rate as a function of the frequency is determined by the temperature. In a dilute Bose-Einstein condensate of atoms, the width is determined by the inelastic scattering rates of a dimer with zero-energy atoms. Near an atom-dimer resonance, there is a dramatic increase in the width from inelastic atom-dimer scattering and from atom-atom-dimer recombination. The recombination contribution provides a signature for universal tetramers that are Efimov states consisting of two atoms and a dimer.

arXiv:1406.7313•Physical Review Letters•Mar 11, 2015•16 citations

Feshbach molecule formation through an oscillating magnetic field: subharmonic resonances

S. Brouard, Jesús Plata

Abstract The conversion of ultracold atoms to molecules via a magnetic Feshbach resonance with a sinusoidal modulation of the field is studied. Different practical realizations of this method in Bose atomic gases are analyzed. Our model incorporates many-body effects through an effective reduction of the complete microscopic dynamics. Moreover, we simulate the experimental conditions corresponding to the preparation of the system as a thermal gas and as a condensate. Some of the experimental findings are clarified. The origin of the observed dependence of the production efficiency on the frequency, amplitude, and application time of the magnetic modulation is elucidated. Our results uncover also the role of the atomic density in the dynamics, specifically, in the observed saturation of the atom–molecule conversion process.

arXiv:1503.01700•Journal of Physics B Atomic Molecular and Optical Physics•Mar 4, 2015•5 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

Resonant Floquet Scattering of Ultracold Atoms

Dane Hudson Smith

In systems of ultracold atoms, pairwise interactions are resonantly enhanced by the application of an oscillating magnetic field that is parallel to the spin-quantization axis of the atoms. The resonance occurs when the frequency of the applied field is precisely tuned near the transition frequency between the scattering atoms and a diatomic molecule. The resulting cross section can be made more than two orders of magnitude larger than the cross section in the absence of the oscillating field. The low momentum resonance properties have a universal description that is independent of the atomic species. To arrive at these conclusions, we first develop a formal extension of Floquet theory to describe scattering of atoms with time-periodic, short-range interaction potentials. We then calculate the atomic scattering properties by modeling the atomic interactions with a square well potential with oscillating depth and then explicitly solving the time-dependent Schrodinger equation. We then apply the Floquet formalism to the case of atoms scattering with a contact interaction described by a time-periodic scattering length, obtaining analytic results that agree with those obtained by solving the time-dependent Schrodinger equation.

arXiv:1611.05412•Nov 16, 2016•0 citations

Dimers of ultracold two-component Fermi gases on magnetic-field Feshbach resonance

Hongwei Xiong, Shujuan Liu, Mingsheng Zhan

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)).

arXiv:cond-mat/0403652•Mar 26, 2004•0 citations
In a gas of ultracold atoms whose scattering length is controlled by a magnetic Feshbach resonance, atoms can be associated into universal dimers by an oscillating longitudinal magnetic field. In addition to the harmonic resonance with frequency near that determined by the dimer binding energy, there is a subharmonic resonance with half that frequency. If the thermal gas contains dimers, they can be dissociated into unbound atoms by the oscillating magnetic field. We show that the transition rates for association and dissociation can be calculated by treating the oscillating magnetic field as a sinusoidal time-dependent perturbation proportional to the contact operator. Many-body effects are taken into account through transition matrix elements of the contact operator. We calculate both the harmonic and subharmonic transition rates analytically for association in a thermal gas of atoms and for dissociation in a thermal gas of dimers.
The pairwise interactions of ultracold atoms can be resonantly enhanced by tuning the scattering length to infinity using a Feshbach resonance.In a gas of ultracold atoms whose scattering length is controlled by a magnetic Feshbach resonance, the atoms can be associated into universal dimers and the dimers can be dissociated into unbound atoms by using an oscillating longitudinal magnetic field with frequency near the binding energy of a dimer.If the gas of ultracold atoms are fermions, the oscillating magnetic field with frequency near the pairing gap can dissociate Cooper pairs into pairs of unbound atoms.In this thesis, we show that the transition rates for association and dissociation can be calculated by treating the oscillating magnetic field as a sinusoidal time-dependent perturbation proportional to the contact operator.We calculate both the harmonic and subharmonic transition rates analytically for association in a thermal gas of atoms and for dissociation in a thermal gas of dimers.We also calculate the harmonic transition rate analytically for the dissociation of Cooper pairs into pairs of unbound atoms in the BCS limit.Our results for the dissociation rate of Cooper pairs can be used to make a direct measurement of the pairing gap for fermionic atoms.
In a system of ultracold atoms near a Feshbach resonance, pairs of atoms can be associated into universal dimers by an oscillating magnetic field with a frequency near that determined by the dimer binding energy. We present a simple expression for the transition rate that takes into account many-body effects through a transition matrix element of the contact. In a thermal gas, the width of the peak in the transition rate as a function of the frequency is determined by the temperature. In a dilute Bose-Einstein condensate of atoms, the width is determined by the inelastic scattering rates of a dimer with zero-energy atoms. Near an atom-dimer resonance, there is a dramatic increase in the width from inelastic atom-dimer scattering and from atom-atom-dimer recombination. The recombination contribution provides a signature for universal tetramers that are Efimov states consisting of two atoms and a dimer.
Abstract The conversion of ultracold atoms to molecules via a magnetic Feshbach resonance with a sinusoidal modulation of the field is studied. Different practical realizations of this method in Bose atomic gases are analyzed. Our model incorporates many-body effects through an effective reduction of the complete microscopic dynamics. Moreover, we simulate the experimental conditions corresponding to the preparation of the system as a thermal gas and as a condensate. Some of the experimental findings are clarified. The origin of the observed dependence of the production efficiency on the frequency, amplitude, and application time of the magnetic modulation is elucidated. Our results uncover also the role of the atomic density in the dynamics, specifically, in the observed saturation of the atom–molecule conversion process.
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.
In systems of ultracold atoms, pairwise interactions are resonantly enhanced by the application of an oscillating magnetic field that is parallel to the spin-quantization axis of the atoms. The resonance occurs when the frequency of the applied field is precisely tuned near the transition frequency between the scattering atoms and a diatomic molecule. The resulting cross section can be made more than two orders of magnitude larger than the cross section in the absence of the oscillating field. The low momentum resonance properties have a universal description that is independent of the atomic species. To arrive at these conclusions, we first develop a formal extension of Floquet theory to describe scattering of atoms with time-periodic, short-range interaction potentials. We then calculate the atomic scattering properties by modeling the atomic interactions with a square well potential with oscillating depth and then explicitly solving the time-dependent Schrodinger equation. We then apply the Floquet formalism to the case of atoms scattering with a contact interaction described by a time-periodic scattering length, obtaining analytic results that agree with those obtained by solving the time-dependent Schrodinger equation.
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)).