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Harmonic and Subharmonic Association and Dissociation of Universal Dimers in a Thermal Gas

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 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 dissociation in a thermal gas of dimers.