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:1503.01700 · Journal of Physics B Atomic Molecular and Optical Physics

Feshbach molecule formation through an oscillating magnetic field: subharmonic resonances

S. Brouard, Jesús Plata

Published Mar 4, 2015• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0953-4075/48/6/065002

Related papers

Ultracold Molecule Production via a Resonant Oscillating Magnetic Field

S. T. Thompson, E. Hodby, Carl Wieman

A novel atom-molecule conversion technique has been investigated. Ultracold 85Rb atoms sitting in a dc magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field. There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy. We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the phase space density of the sample. This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements. Efficiencies of 55% have been observed for pure Bose-Einstein condensates.

arXiv:cond-mat/0505567•Physical Review Letters•Nov 2, 2005•135 citations

Ultracold Molecule Production via a Resonant Oscillating Magnetic Field

Sarah T. Thompson, E. Hodby, Carl Wieman

A novel atom-molecule conversion technique has been investigated.Ultracold 85 Rb atoms sitting in a DC magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field.There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy.We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the initial phase space density of the sample.This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements.

WORLD SCIENTIFIC eBooks•Jan 1, 2008•1 citation

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

Shapiro-like resonance in ultracold molecule production via an oscillating magnetic field

Bin Liu, Libin Fu, Jie Liu

We study the process of the production of ultracold molecules from ultracold atoms using a sinusoidally oscillating magnetic-field modulation. Our study is based on a two-mode mean-field treatment of the problem. When the magnetic field is resonant roughly with the molecular binding energy, Shapiro-like resonances are observed. Their resonance profiles are well fitted by the Lorentzian functions. The linewidths depend on both the amplitude and the duration of the applied modulations and are found to be dramatically broadened by the thermal dephasing effect. The resonance centers shift due to both the many-body effect and the finite temperature effect. Our theory is consistent with a recent experiment [S. T. Thompson, E. Hodby, and C. E. Wieman, Phys. Rev. Lett. 95, 190404 (2005)]. Our model predicts a $1/3$ ceiling for the molecular production yield in uncondensed ultracold atomic clouds for a long coupling time, while for condensed atoms the optimal conversion yield could be beyond the limit.

arXiv:0905.2890•Physical Review A•Jan 4, 2010•12 citations

Controlled interference of association paths in the conversion of ultracold atoms into molecules

Jesús Plata

Abstract We present a proposal for controlling the conversion of ultracold atoms into molecules by fixing the phase difference between two oscillating magnetic fields. The scheme is based on the use of a magnetic Feshbach resonance with a field modulation that incorporates terms oscillating with frequencies corresponding to the main resonance and one of the subharmonics. The interference between the two association processes activated by the oscillating terms is controlled via the phase difference. As a result, significant increase or decrease of the effective interaction strength can be achieved. The realization of the proposal is feasible under standard technical conditions. In particular, the method is found to be robust against the effect of the sources of decoherence present in the practical setup. The applicability of the approach to deal with quadratic terms in the field modulation is discussed.

arXiv:1511.01401•Journal of Physics B Atomic Molecular and Optical Physics•Nov 3, 2015•0 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
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.
A novel atom-molecule conversion technique has been investigated. Ultracold 85Rb atoms sitting in a dc magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field. There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy. We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the phase space density of the sample. This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements. Efficiencies of 55% have been observed for pure Bose-Einstein condensates.
A novel atom-molecule conversion technique has been investigated.Ultracold 85 Rb atoms sitting in a DC magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field.There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy.We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the initial phase space density of the sample.This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements.
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 study the process of the production of ultracold molecules from ultracold atoms using a sinusoidally oscillating magnetic-field modulation. Our study is based on a two-mode mean-field treatment of the problem. When the magnetic field is resonant roughly with the molecular binding energy, Shapiro-like resonances are observed. Their resonance profiles are well fitted by the Lorentzian functions. The linewidths depend on both the amplitude and the duration of the applied modulations and are found to be dramatically broadened by the thermal dephasing effect. The resonance centers shift due to both the many-body effect and the finite temperature effect. Our theory is consistent with a recent experiment [S. T. Thompson, E. Hodby, and C. E. Wieman, Phys. Rev. Lett. 95, 190404 (2005)]. Our model predicts a 1/31/31/3 ceiling for the molecular production yield in uncondensed ultracold atomic clouds for a long coupling time, while for condensed atoms the optimal conversion yield could be beyond the limit.
Abstract We present a proposal for controlling the conversion of ultracold atoms into molecules by fixing the phase difference between two oscillating magnetic fields. The scheme is based on the use of a magnetic Feshbach resonance with a field modulation that incorporates terms oscillating with frequencies corresponding to the main resonance and one of the subharmonics. The interference between the two association processes activated by the oscillating terms is controlled via the phase difference. As a result, significant increase or decrease of the effective interaction strength can be achieved. The realization of the proposal is feasible under standard technical conditions. In particular, the method is found to be robust against the effect of the sources of decoherence present in the practical setup. The applicability of the approach to deal with quadratic terms in the field modulation is discussed.
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.