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arXiv:1103.1183 · Physical Review A

Sensitivity of ultracold-atom scattering experiments to variation of the fine-structure constant

Anastasia Borschevsky, K. Beloy, V. V. Flambaum, Peter Schwerdtfeger

Published May 19, 2011• 14 citations
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Abstract

We present numerical calculations for cesium and mercury to estimate the sensitivity of the scattering length to the variation of the fine-structure constant $\ensuremath{\alpha}$. The method used follows the ideas of Chin and Flambaum [Phys. Rev. Lett. 96, 230801 (2006)], where the sensitivity to the variation of the electron-to-proton mass ratio $\ensuremath{\beta}$ was considered. We demonstrate that for heavy systems, the sensitivity to the variation of $\ensuremath{\alpha}$ is of the same order of magnitude as to the variation of $\ensuremath{\beta}$. Near narrow Feshbach resonances, the enhancement of the sensitivity may exceed nine orders of magnitude.

DOI
10.1103/physreva.83.052706

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We present numerical calculations for cesium and mercury to estimate the sensitivity of the scattering length to the variation of the fine-structure constant \ensuremathα\ensuremath{\alpha}\ensuremathα. The method used follows the ideas of Chin and Flambaum [Phys. Rev. Lett. 96, 230801 (2006)], where the sensitivity to the variation of the electron-to-proton mass ratio \ensuremathβ\ensuremath{\beta}\ensuremathβ was considered. We demonstrate that for heavy systems, the sensitivity to the variation of \ensuremathα\ensuremath{\alpha}\ensuremathα is of the same order of magnitude as to the variation of \ensuremathβ\ensuremath{\beta}\ensuremathβ. Near narrow Feshbach resonances, the enhancement of the sensitivity may exceed nine orders of magnitude.
Scattering length, which can be measured in Bose-Einstein condensate and Feshbach molecule experiments, is extremely sensitive to the variation of fundamental constants, in particular, the electron-to-proton mass ratio (m(e)/m(p) or m(e)/Lambda(QCD), where Lambda(QCD), is the QCD scale). Based on single- and two-channel scattering models, we show how the variation of the mass ratio propagates to the scattering length. Our results suggest that variation of m(e)/m(p) on the level of 10(-11) - 10(-14) on the level of can be detected near a narrow magnetic or an optical Feshbach resonance by monitoring the scattering length on the 1% level. Derived formulas may also be used to estimate the isotopic shift of the scattering length.
Ultracold molecules offer brand new opportunities to probe the variation of fundamental constants with unprecedented sensitivity. This paper summarizes theoretical background and current constraints on the variation of the fine structure constant and electron-to-proton mass ratio, as well as proposals and experimental efforts to measure the variations based on ultracold molecules. In particular, we describe two novel spectroscopic schemes on ultracold molecules that have greatly enhanced sensitivity to fundamental constants: resonant scattering near Feshbach resonances and spectroscopy on close-lying energy levels of ultracold molecules.
We present a theoretical analysis of numerous magnetically tunable Feshbach resonances measured by Chin et al. [preceding Letter, Phys. Rev. Lett. 85, 2717 (2000)] at fields of up to 25mT25\mathrm{mT}25mT. This analysis provides the most accurate characterization of the collisional properties of ground state Cs atoms currently available and clearly shows, in contrast to previous work, that Bose-Einstein condensation of 133Cs{}^{133}\mathrm{Cs}133Cs cannot be ruled out. The ${X}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and ${a}^{3}{\ensuremath{\Sigma}}_{u}$ scattering lengths are constrained to $(280\ifmmode\pm\else\textpm\fi{}10){a}_{0}$ and $(2400\ifmmode\pm\else\textpm\fi{}100){a}_{0}$, respectively ( 1a0=0.0529177nm{1a}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.0529177\mathrm{nm}1a0​=0.0529177nm), and the van der Waals C6{C}_{6}C6​ coefficient to $6890\ifmmode\pm\else\textpm\fi{}35\mathrm{a}.\mathrm{u}.(1\mathrm{a}.\mathrm{u}.\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.0957345\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\mathrm{J}\ifmmode \dot{}\else \.{}\fi{}{\mathrm{nm}}^{6})$.
In this Letter, we study bosonic atoms at large scattering lengths using a variational method where the condensate amplitude is a variational parameter. We further examine momentum distribution functions, chemical potentials, the speed of sound, and spatial density profiles of cold bosonic atoms in a trap in this limit. The latter two properties turn out to bear similarities to those of Fermi gases. The estimates obtained here are applicable near Feshbach resonances, particularly when the fraction of atoms forming three-body structures is small and can be tested in future cold atom experiments.
We study ultracold three-body collisions of bosons and fermions when the interatomic interaction is tuned near a narrow Feshbach resonance. We show that the width of the resonance has a substantial impact on the collisional properties of ultracold gases in the strongly interacting regime. From our numerical and analytical analyses, we identify universal features dependent on the resonance width. Remarkably, we find that all inelastic processes near narrow resonances leading to deeply bound states in bosonic systems are suppressed, while those for fermionic systems are enhanced. As a result, narrow resonances present a scenario that is the reverse of that found for broad resonances, opening up the possibility of creating stable samples of ultracold bosonic gases with large scattering lengths.
Precision measurements with ultracold molecules require development of robust and sensitive techniques to produce and interrogate the molecules. With this goal, we theoretically analyze factors that affect frequency measurements between rovibrational levels of the Sr2{\mathrm{Sr}}_{2}Sr2​ molecule in the electronic ground state. This measurement can be used to constrain the possible time variation of the proton-electron mass ratio. Sr2{\mathrm{Sr}}_{2}Sr2​ is expected to be a strong candidate for achieving high precision due to the spinless nature and ease of cooling and perturbation-free trapping of Sr [T. Zelevinsky et al., Phys. Rev. Lett. 100, 043201 (2008)]. The analysis includes calculations of two-photon transition dipole moments between deeply and weakly bound vibrational levels, lifetimes of intermediate excited states, and Stark shifts of the vibrational levels by the optical lattice field, including possibilities of Stark-cancellation trapping.