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arXiv:1503.02688 · Physical Review Letters

Inducing Resonant Interactions in Ultracold Atoms with a Modulated Magnetic Field

Dane Hudson Smith

Published Nov 3, 2015• 23 citations
arXivHTMLPDF

Abstract

In systems of ultracold atoms, pairwise interactions can be resonantly enhanced by a new mechanism that does not rely upon a magnetic Feshbach resonance. In this mechanism, interactions are controlled by tuning the frequency of an oscillating parallel component of the magnetic field close to the transition frequency between the scattering atoms and a two-atom bound state. The real part of the resulting s-wave scattering length a is resonantly enhanced when the oscillation frequency is close to the transition frequency. The resonance parameters can be controlled by varying the amplitude of the oscillating field. The amplitude also controls the imaginary part of a, which arises because the oscillating field converts atom pairs into molecules. The real part of a can be made much larger than the background scattering length without introducing catastrophic atom losses from the imaginary part. For the case of a shallow bound state in the scattering channel, the dimensionless resonance parameters are universal functions of the dimensionless oscillation amplitude.

DOI
10.1103/physrevlett.115.193002

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In systems of ultracold atoms, pairwise interactions can be resonantly enhanced by a new mechanism that does not rely upon a magnetic Feshbach resonance. In this mechanism, interactions are controlled by tuning the frequency of an oscillating parallel component of the magnetic field close to the transition frequency between the scattering atoms and a two-atom bound state. The real part of the resulting s-wave scattering length a is resonantly enhanced when the oscillation frequency is close to the transition frequency. The resonance parameters can be controlled by varying the amplitude of the oscillating field. The amplitude also controls the imaginary part of a, which arises because the oscillating field converts atom pairs into molecules. The real part of a can be made much larger than the background scattering length without introducing catastrophic atom losses from the imaginary part. For the case of a shallow bound state in the scattering channel, the dimensionless resonance parameters are universal functions of the dimensionless oscillation amplitude.
In systems of ultracold atoms, pairwise interactions can be resonantly enhanced by a new mechanism which does not rely upon a magnetic Feshbach resonance. In this mechanism, interactions are controlled by tuning the frequency of an oscillating parallel component of the magnetic field close to the Bohr frequency for the transition to a two-atom bound state. The real part of the s-wave scattering length a has a resonance as a function of the oscillation frequency near the Bohr frequency. The resonance parameters can be controlled by varying the amplitude of the oscillating field. The amplitude also controls the imaginary part of a which arises predominantly because the oscillating field converts atom pairs into molecules. For the case of a shallow bound state in the scattering channel, the dimensionless resonance parameters are universal functions of the dimensionless oscillation amplitude.
In systems of ultracold atoms, pairwise interactions can be resonantly enhanced by a new mechanism which does not rely upon a magnetic Feshbach resonance. In this mechanism, interactions are controlled by tuning the frequency of an oscillating parallel component of the magnetic field close to the Bohr frequency for the transition to a two-atom bound state. The real part of the s-wave scattering length aaa has a resonance as a function of the oscillation frequency near the Bohr frequency. The resonance parameters can be controlled by varying the amplitude of the oscillating field. The amplitude also controls the imaginary part of aaa which arises predominantly because the oscillating field converts atom pairs into molecules. For the case of a shallow bound state in the scattering channel, the dimensionless resonance parameters are universal functions of the dimensionless oscillation amplitude.
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.
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.
It is crucial to control the collision between ultracold atoms by applying external fields. We developed a theoretical model for investigating the s-wave scattering of ultracold atoms controlled by the magnetic field and laser field. The calculation is performed by using the close-coupling method and mapped Fourier grid method. Due to the interference between the photoassociation and bound-to-bound transitions, the bound state in the continuum, which is a resonance with a vanishing width, occurs at the magnetic field position near the magnetic Feshbach resonance. The widths of resonances in the neighborhood of the bound state in the continuum are narrow. Changing the laser intensity can shift the magnetic field position where the bound state in the continuum occurs through modifying the ground molecular state to induce wide resonances at desired magnetic field positions. By increasing the resonance width, the tunability of the real part of the scattering length at resonances can be significantly improved. Changing the laser intensity can also adjust the coupling between the ground and excited molecular states. When the coupling between the ground and excited molecular states approaches zero, a resonance is induced, and the photoassociation and bound-to-bound transitions are both significantly suppressed at this resonance. Therefore, the atomic loss peak due to spontaneous emission does not appear at this resonance. The magnetic field position of this resonance is stable against the change in laser frequency.
We present a simple technique for studying the collisions of ultracold atoms in the presence of a magnetic field and radiofrequency (rf) radiation. Resonant control of scattering properties can be achieved by using rf to couple a colliding pair of atoms to a bound state. We show, using the example of 6 Li, that in some ranges of rf frequency and magnetic field this can be done without giving rise to losses. We also show that halo molecules of large spatial extent allow resonant control with much less rf power than deeply bound states. Another way to exert resonant control is with a set of rf-coupled bound states, linked to the colliding pair through the molecular interactions that give rise to magnetically tunable Feshbach resonances. This was recently demonstrated for 87 Rb (Kaufman et al 2009 Phys. Rev. A 80 050701) [1]. We examine the underlying atomic and molecular physics that made this possible. Lastly, we consider the control that may be exerted over atomic collisions by placing atoms in superpositions of Zeeman states, and suggest that it could be useful where small changes in scattering length are required. We suggest other species for which rf and magnetic field control could together provide a useful tuning mechanism.