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arXiv:1211.4556 · Physical Review A

Optical control of the scattering length and effective range for magnetically tunable Feshbach resonances in ultracold gases

Haibin Wu, John E. Thomas

Published Dec 20, 2012• 32 citations
arXivHTMLPDF

Abstract

We describe two-field optical techniques to control interactions in Feshbach resonances for two-body scattering in ultracold gases. These techniques create a molecular dark state in the closed channel of a magnetically tunable Feshbach resonance, greatly suppressing optical scattering compared to single optical field methods. The dark-state method enables control of the effective range, by creating narrow features that modify the energy dependence of the scattering phase shift, as well as control of the elastic and inelastic parts of the zero-energy $s$-wave scattering amplitude. We determine the scattering length and the effective range from an effective range expansion, by calculating the momentum-dependent scattering phase shift from the two-body scattering state.

DOI
10.1103/physreva.86.063625

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•Feb 2, 2016•0 citations
We describe two-field optical techniques to control interactions in Feshbach resonances for two-body scattering in ultracold gases. These techniques create a molecular dark state in the closed channel of a magnetically tunable Feshbach resonance, greatly suppressing optical scattering compared to single optical field methods. The dark-state method enables control of the effective range, by creating narrow features that modify the energy dependence of the scattering phase shift, as well as control of the elastic and inelastic parts of the zero-energy sss-wave scattering amplitude. We determine the scattering length and the effective range from an effective range expansion, by calculating the momentum-dependent scattering phase shift from the two-body scattering state.
We propose a general method for optical control of magnetic Feshbach resonances in ultracold atomic gases with more than one molecular state in an energetically closed channel. Using two optical frequencies to couple two states in the closed channel, inelastic loss arising from spontaneous emission is greatly suppressed by destructive quantum interference at the two-photon resonance, i.e., dark-state formation, while the scattering length is widely tunable by varying the frequencies and/or intensities of the optical fields. This technique is of particular interest for a two-component atomic Fermi gas, which is stable near a Feshbach resonance.
The scattering length is commonly used to characterize the strength of ultracold atomic interactions, since it is the leading parameter in the low-energy expansion of the scattering phase shift. Its value can be modified via a magnetic field, by using a Feshbach resonance. However, the effective range term, which is the second parameter in the phase shift expansion, determines the width of the resonance and gives rise to important properties of ultracold gases. Independent control over this parameter is not possible by using a magnetic field only. We demonstrate that a combination of magnetic and electric fields can be used to get independent control over both parameters, which leads to full control over elastic ultracold interactions.
We control magnetic Feshbach resonances in an optically trapped mixture of the two lowest hyperfine states of a ^{6}Li Fermi gas, using two optical fields to create a dark state in the closed molecular channel. In the experiments, the narrow Feshbach resonance is tuned by up to 3 G. For the broad resonance, the spontaneous lifetime is increased to 0.4 s at the dark-state resonance, compared to 0.5 ms for single-field tuning. We present a new model of light-induced loss spectra, employing continuum-dressed basis states, which agrees in shape and magnitude with loss measurements for both broad and narrow resonances. Using this model, we predict the trade-off between tunability and loss for the broad resonance in ^{6}Li, showing that our two-field method substantially reduces the two-body loss rate compared to single-field methods for the same tuning range.
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 propose that the long-sought Fulde-Ferrell superfluidity with nonzero momentum pairing can be realized in ultracold two-component Fermi gases of ^{40}K or ^{6}Li atoms by optically tuning their magnetic Feshbach resonances via the creation of a closed-channel dark state with a Doppler-shifted Stark effect. In this scheme, two counterpropagating optical fields are applied to couple two molecular states in the closed channel to an excited molecular state, leading to a significant violation of Galilean invariance in the dark-state regime and hence to the possibility of Fulde-Ferrell superfluidity. We develop a field theoretical formulation for both two-body and many-body problems and predict that the Fulde-Ferrell state has remarkable properties, such as anisotropic single-particle dispersion relation, suppressed superfluid density at zero temperature, anisotropic sound velocity, and rotonic collective mode. The latter two features can be experimentally probed using Bragg spectroscopy, providing a smoking-gun proof of Fulde-Ferrell superfluidity.
Abstract : During this period, we made important breakthroughs in the optical control of two-body interactions in ultra-cold gases. We have studied magnetic Feshbach resonances in an optically-trapped mixture of the two lowest hyperfine states of a 6Li Fermi gas, using two optical fields to create a darkstate in the closed molecular channel. In the experiments, the narrow Feshbach resonance is tuned by up to 3 G. For the broad resonance, thespontaneous lifetime is increased from 0.5 ms for single field tuning to 0.4 s at the dark state resonance, despite the large background scatteringlength.A major breakthrough in our understanding is the experimental verification of a new model of light-induced loss spectra, employing continuum-dressed basis states, which agrees in shape and magnitude with all of our loss measurements for both broad and narrow resonances.Using this model, we show that our method substantially reduces the two-body loss rate compared to single field methods for same tuning range.