[Paper Review] Effective Field Theory for Atom-Molecule Systems III: Dynamic Effects of a Feshbach Resonance on Bragg scattering from a Bose-Einstein Condensate

Catarina E. Sahlberg, R. J. Ballagh+1 more|arXiv (Cornell University)|Sep 14, 2011

Cold Atom Physics and Bose-Einstein Condensates5 references3 citations

TL;DR

This paper develops a two-c-field effective field theory incorporating atomic and molecular condensate fields to model Bragg scattering from a 85 Rb Bose-Einstein condensate near a Feshbach resonance. The model captures dynamic molecular bound states and reproduces experimental Bragg spectra quantitatively without fitting parameters, demonstrating that two-field mean-field dynamics are essential for strong interactions beyond standard perturbation theory.

ABSTRACT

We present a theoretical model for Bragg scattering from a Bose-Einstein condensate (BEC) in the vicinity of a magnetic Feshbach resonance, using a two c-field formalism, one c-field for the atom and the other for a molecule formed of two atoms. We use this model to numerically simulate a recent experiment [S. B. Papp et al., Phys. Rev. Lett., 101(13):135301, Sep 2008] investigating the effects of strong interactions on the Bragg spectrum from a 85Rb BEC. Results from these simulations are in very good quantitative agreement with the experimental results, confirming the importance of the resonance bound state in the dynamics of the condensate for fast experiments like Bragg scattering.

Motivation & Objective

• To address the breakdown of standard mean-field and perturbative theories in describing Bragg scattering from a strongly interacting Bose-Einstein condensate near a Feshbach resonance.
• To investigate the role of dynamically generated molecular bound states in modifying the excitation spectrum during fast processes like Bragg scattering.
• To test whether a two-field effective field theory—incorporating both atomic and molecular condensate fields—can quantitatively reproduce experimental Bragg spectra in the strongly interacting regime.
• To provide a non-perturbative theoretical framework that accounts for momentum-dependent scattering and strong correlations in ultracold atomic systems.

Proposed method

• Formulates a two-c-field effective field theory with separate c-fields for atoms and molecules, where molecular formation arises from Feshbach resonance coupling.
• Uses a Hamiltonian formalism that includes interaction terms between atomic and molecular fields, with coupling constants derived from scattering length and binding energy data.
• Applies a stochastic c-field method to simulate the time evolution of the system under Bragg laser pulses, including quantum fluctuations via noise terms.
• Computes the Bragg spectrum by calculating the dynamic structure factor from the time-averaged density-density correlation function.
• Defines the density-weighted density as a key observable to account for inhomogeneities in the harmonic trap, using symmetrized field operator products.
• Validates the initial state by matching the expectation values of atomic and molecular densities and their second moments to the initial coherent and thermal components.

Experimental results

Research questions

• RQ1 How do molecular bound states formed via a Feshbach resonance dynamically influence the Bragg scattering spectrum of a strongly interacting Bose-Einstein condensate?
• RQ2 Can a two-field effective field theory—incorporating both atomic and molecular condensate fields—accurately describe Bragg scattering in the strongly interacting regime where standard mean-field theory fails?
• RQ3 To what extent do momentum-dependent scattering effects and strong correlations modify the excitation spectrum compared to the standard Gross-Pitaevskii prediction?
• RQ4 Why do experimental Bragg spectra near a Feshbach resonance deviate significantly from predictions based on perturbative and simple mean-field theories?
• RQ5 Can a non-perturbative EFT framework reproduce experimental data quantitatively without fitting parameters?

Key findings

• The two-c-field effective field theory reproduces the experimental Bragg spectra from Papp et al. [1] with excellent quantitative agreement, using no fitted parameters.
• The inclusion of molecular field dynamics—specifically the resonance-bound molecular state—is essential to explain the observed spectral shifts and broadening at large scattering lengths.
• The model successfully captures deviations from the standard Bragg formula (ℏω = ℏ²k²/2m + 4πℏ²naₛ/m) when the system enters the non-perturbative regime (naₛ³ ~ 0.125, kξ ~ 2, kaₛ ~ 0.8).
• The density-weighted density, defined as the square of the total density operator averaged over both fields, correctly accounts for inhomogeneities in the harmonic trap and matches the experimental observable.
• The simulation results confirm that the standard mean-field approach fails in the strong interaction regime, but a two-field mean-field description remains valid when molecular degrees of freedom are explicitly included.
• The theory resolves discrepancies with prior theoretical models, including time-dependent Hartree-Fock-Bogoliubov and momentum-independent scattering approximations, which showed only qualitative agreement with experiment.