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arXiv:cond-mat/0408254 · Physical Review A

Radio-frequency transitions on weakly bound ultracold molecules

Cheng Chin, Paul S. Julienne

Published Jan 27, 2005• 96 citations
arXivHTMLPDF

Abstract

We show that radio-frequency spectroscopy on weakly bound molecules is a powerful and sensitive tool to probe molecular energy structure as well as atomic scattering properties. An analytic expression of the excitation line shape is derived, which in general contains a bound-free component and a bound-bound component. In particular, we show that the bound-free process strongly depends on the sign of the scattering length in the outgoing channel and acquires a Fano-type profile near a Feshbach resonance. The derived line shapes provide an excellent fit to both numerical calculations and recent experimental measurements based on $^{6}\mathrm{Li}_{2}$.

DOI
10.1103/physreva.71.012713

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We show that radio-frequency spectroscopy on weakly bound molecules is a powerful and sensitive tool to probe molecular energy structure as well as atomic scattering properties. An analytic expression of the excitation line shape is derived, which in general contains a bound-free component and a bound-bound component. In particular, we show that the bound-free process strongly depends on the sign of the scattering length in the outgoing channel and acquires a Fano-type profile near a Feshbach resonance. The derived line shapes provide an excellent fit to both numerical calculations and recent experimental measurements based on 6Li2^{6}\mathrm{Li}_{2}6Li2​.
We employ radio-frequency spectroscopy on weakly bound (6)Li(2) molecules to precisely determine the molecular binding energies and the energy splittings between molecular states for different magnetic fields. These measurements allow us to extract the interaction parameters of ultracold (6)Li atoms based on a multichannel quantum scattering model. We determine the singlet and triplet scattering lengths to be a(s) = 45.167(8)a(0) and a(t) = -2140(18)a(0) (1a(0) = 0.052 917 7 nm), and the positions of the broad Feshbach resonances in the energetically lowest three s-wave scattering channels to be 83.41(15), 69.04(5), and 81.12(10) mT.
We create weakly bound Feshbach molecules in ultracold Fermi gas 4~K by sweeping a magnetic field across a broad Feshbach resonance point 202.2 G with a rate of 20 ms/G and perform the dissociation process using radio-frequency （RF） technology. From RF spectroscopy, we obtain the binding energy of the weakly bound molecules in the vicinity of Feshbach resonance. Our measurement also shows that the number of atoms generated from the dissociation process is different at various magnetic fields with the same RF amplitude, which gives us a deeper understanding of weakly bound Feshbach molecules.
We create weakly bound Feshbach molecules in ultracold Fermi gas 40 K by sweeping a magnetic field across a broad Feshbach resonance point 202.2 G with a rate of 20 ms/G and perform the dissociation process using radio-frequency (RF) technology. From RF spectroscopy, we obtain the binding energy of the weakly bound molecules in the vicinity of Feshbach resonance. Our measurement also shows that the number of atoms generated from the dissociation process is different at various magnetic fields with the same RF amplitude, which gives us a deeper understanding of weakly bound Feshbach molecules.
We perform radio-frequency dissociation spectroscopy of weakly bound 6Li2 Feshbach molecules using low-density samples of about 30 molecules in an optical dipole trap. Combined with a high magnetic field stability, this allows us to resolve the discrete trap levels in the radio-frequency dissociation spectra. This novel technique allows the binding energy of Feshbach molecules to be determined with unprecedented precision. We use these measurements as an input for a fit to the 6Li scattering potential using coupled-channel calculations. From this new potential, we determine the pole positions of the broad 6Li Feshbach resonances with an accuracy better than 7×10(-4) of the resonance widths. This eliminates the dominant uncertainty for current precision measurements of the equation of state of strongly interacting Fermi gases. As an important consequence, our results imply a corrected value for the Bertsch parameter ξ measured by Ku et al. [Science 335, 563 (2012)], which is ξ=0.370(5)(8).
Spectroscopic measurements are made and obtained for three molecular levels within 50 MHz of the atomic continuum, along with their variation of magnetic field in ultracold 40 K Fermi gases. We use spectroscopic measurements to modify the scattering properties near magnetic Fano–Feshbach resonances with a radio-frequency (RF) field by measuring the loss profile versus magnetic field. This work provides the high accuracy locations of ground molecular states near the s-wave Fano–Feshbach resonance, which can be used to study the crossover regime from a Bose–Einstein condensate to a Bardeen–Cooper–Schrieffer superfluid in the presence of an RF field.
Optical Feshbach resonances allow one to control cold atomic scattering, produce ultracold molecules, and study atomic interactions via photoassociation spectroscopy. In the limit of ultracold sss-wave collisions, the strength of an optical Feshbach resonance can be expressed via an energy-independent parameter called the optical length. Here we give fully analytic approximate expressions for its magnitude applicable to near-threshold bound states of an excited molecular state dominated by a single resonant-dipole or van der Waals interaction. We express these magnitudes in terms of intuitive quantities, such as the laser intensity, the excited-state binding energy, the sss-wave scattering length, and the Condon point. Additionally, we extend the utility of the optical length to associative stimulated Raman adiabatic passage in three-dimensional optical lattices by showing that the free-bound Rabi frequency induced by a laser coupling a pair of atoms in an optical lattice site can be approximately related to the trap frequency and the optical length.