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arXiv:quant-ph/0505102 · Physical Review A

Scattering-length determination from trapped pairs of atoms

Sanjiv Shresta, Eite Tiesinga, Carl J. Williams

Published Aug 2, 2005• 2 citations
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Abstract

A method is described for estimating effective scattering lengths via spectroscopy on a trapped pair of atoms. The method relies on the phenomena that the energy levels of two atoms in a harmonic trap are shifted by their collisional interaction. The amount of shift depends on the strength of the interaction (i.e., scattering length). By combining the spectra of the trap state energy levels and a suitable model for the effective scattering length, an estimate for the latter may be inferred. Two practical methods for measuring the trap spectra are proposed and illustrated in examples. The accuracy of the scheme is analyzed and requirements on measurement precision are given.

DOI
10.1103/physreva.72.022701

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A method is described for estimating effective scattering lengths via spectroscopy on a trapped pair of atoms. The method relies on the phenomena that the energy levels of two atoms in a harmonic trap are shifted by their collisional interaction. The amount of shift depends on the strength of the interaction (i.e., scattering length). By combining the spectra of the trap state energy levels and a suitable model for the effective scattering length, an estimate for the latter may be inferred. Two practical methods for measuring the trap spectra are proposed and illustrated in examples. The accuracy of the scheme is analyzed and requirements on measurement precision are given.
We propose a scheme for the measurement of the sss-wave scattering length aaa of an atom or molecule with significant dipole-dipole interaction with an accuracy at the percent level. The frequencies of the collective oscillations of a Bose-Einstein condensate are shifted by the magnetic dipole interaction. The shift is polarization dependent and proportional to the ratio ${\ensuremath{\epsilon}}_{\mathrm{dd}}$ of dipolar and sss-wave coupling constants. Measuring the differences in the frequencies for different polarization we can extract the value of ${\ensuremath{\epsilon}}_{\mathrm{dd}}$ and thus measure aaa. We calculate the frequency shifts for a large variety of nonaxisymmetric harmonic traps in the Thomas-Fermi limit and find optimal trapping geometries to maximize the shifts.
We consider the problem of cold atomic collisions in tight traps, where the absolute scattering length may be larger than the trap size. As long as the size of the trap ground state is larger than a characteristic length of the van der Waals potential, the energy eigenvalues can be computed self-consistently from the scattering phase shift for untrapped atoms. By comparing with the exact numerical eigenvalues of the trapping plus interatomic potentials, we verify that our model gives accurate eigenvalues up to milliKelvin energies for single-channel s-wave scattering of 23Na{}^{23}\mathrm{Na}23Na atoms in an isotropic harmonic trap, even when outside the Wigner threshold regime. Our model works also for multichannel scattering, where the scattering length can be made large due to a magnetically tunable Feshbach resonance.
The energy level spectrum of a many-body system containing two shared, collective Rydberg excitations is measured using cold atoms in an optical dipole trap. Two pairs of independently tunable laser pulses are employed to spectroscopically probe the spectrum in a double-resonance excitation scheme. Depending on the magnitude of an applied electric field, the Rydberg-atom interactions can vary from resonant dipole-dipole to attractive or repulsive van der Waals, leading to characteristic signatures in the measured spectra. Our results agree with theoretical estimates of the magnitude and sign of the interactions.
Employing a short-range two-channel description, we derive an analytic model of atoms in isotropic and anisotropic harmonic traps at a Feshbach resonance. On this basis we obtain a parametrization of the energy-dependent scattering length that differs from the one previously employed. We validate the model by comparison to full numerical calculations for 6Li^{6}\mathrm{Li}6Li-87Rb^{87}\mathrm{Rb}87Rb and explain quantitatively the experimental observation of a resonance shift and trap-induced molecules in exited bands. Finally, we analyze the bound state admixture and Landau-Zener transition probabilities.
We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length aosc{a}_{\mathrm{o}\mathrm{s}\mathrm{c}}aosc​. The atoms are assumed to interact through a short-range potential with a scattering length aaa, and the short-distance behavior of the three-body wave function is characterized by a parameter $\ensuremath{\theta}$. For large positive a/aosca/{a}_{\mathrm{o}\mathrm{s}\mathrm{c}}a/aosc​, the energies of states that, in the absence of the trap, correspond to three free atoms approach values independent of aaa and $\ensuremath{\theta}$. For other states, the $\ensuremath{\theta}$ dependence of the energy is strong, but the energy is independent of aaa for $|a/{a}_{\mathrm{o}\mathrm{s}\mathrm{c}}|\ensuremath{\gg}1$.