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arXiv:1301.4234 · Physical Review A

Controlling the group velocity of colliding atomic Bose-Einstein condensates with Feshbach resonances

Ranchu Mathew, Eite Tiesinga

Published May 10, 2013• 6 citations
arXivHTMLPDF

Abstract

We report on a proposal to reduce the group velocity of a small ``laser'' Bose-Einstein condensate upon passing through a larger ``medium'' condensate of the same isotopic species in analogy to slowing of light passing through dispersive media. We make use of ultracold collisions near a magnetic Feshbach resonance, which gives rise to a sharp variation in scattering length with collision energy and thereby changes the group velocity. A generalized Gross-Pitaevskii equation is used to derive an expression for the group velocity in a homogeneous medium as well as for the spatial delay $\ensuremath{\delta}$, through a finite-sized medium BEC with a Thomas-Fermi density distribution. We predict a maximum reduction of the group velocity by a half, which physically corresponds to freely propagating Feshbach molecules. For typical narrow Feshbach resonances and a medium with number density ${10}^{15}$ cm${}^{\ensuremath{-}3}$, up to $85%$ of the lower bound can be achieved, making the effect experimentally observable. We also derive constraints on the experimental realization of our proposal.

DOI
10.1103/physreva.87.053608

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We report on a proposal to reduce the group velocity of a small laser'' Bose-Einstein condensate upon passing through a larger medium'' condensate of the same isotopic species in analogy to slowing of light passing through dispersive media. We make use of ultracold collisions near a magnetic Feshbach resonance, which gives rise to a sharp variation in scattering length with collision energy and thereby changes the group velocity. A generalized Gross-Pitaevskii equation is used to derive an expression for the group velocity in a homogeneous medium as well as for the spatial delay \ensuremathδ\ensuremath{\delta}\ensuremathδ, through a finite-sized medium BEC with a Thomas-Fermi density distribution. We predict a maximum reduction of the group velocity by a half, which physically corresponds to freely propagating Feshbach molecules. For typical narrow Feshbach resonances and a medium with number density 1015{10}^{15}1015 cm\ensuremath−3{}^{\ensuremath{-}3}\ensuremath−3, up to 8585%85 of the lower bound can be achieved, making the effect experimentally observable. We also derive constraints on the experimental realization of our proposal.
Abstract We theoretically investigate light propagation through a Feshbach-resonant atom–molecule coupled system. We show that when a diatomic molecular state in an electronically ground-state potential is coupled to the continuum of Feshbach-resonant atom–atom scattering states via an excited molecular state with a control (strong) and a probe (weak) laser field, the dispersive behaviour of the medium is significantly influenced by the Feshbach resonance. In particular, a Feshbach resonance helps to make the dispersion characteristics quite sharp, leading to the subluminal propagation of the probe. Our model calculations with realistic parameters show that it is possible to reduce the group velocity to 50 m s −1 with nearly 80% transmission. Furthermore, we demonstrate that it is possible to achieve significant enhancement of the delay-bandwidth product (DBP) of the probe by narrowing the width of the resonance, opening up new prospects for using a resonant atom–molecule coupled medium for efficient slow-light production and applications.
Due to atomic interactions, a dilute gas Bose-Einstein condensate acquires a self- energy proportional to the two-body scattering length a. This self-energy strongly influences the stability, formation rate, size and shape, collective excitations, and other properties of a condensate. For a given atomic species at zero magnetic field, the scattering length is fixed, and this had led to a rather limited range of interaction strengths in experiments. However, it has been predicted that a magnetically tunable Feshbach resonance could be used to strongly modify scattering lengths [1]. We have observed such a Feshbach resonance in collisions of ultracold 85Rb(f =2, mf=−2) atoms in a magnetic field B. From our measured resonance position and width, we infer that the scattering length a2,−2 for collisions of these atoms has the dispersive resonance form.
This thesis reports on the first observation of optical tuning of interactions in an ultracold atomic gas. To control the elastic interactions, we use optically induced scattering resonances. They are realized by coupling pairs of atoms to a bound molecular state with the help of laser light. In comparison to the well-known magnetic Feshbach resonances, these optical Feshbach resonances allow a very fast switching of interactions in a spatially resolved way. This is because laser light can be switched on and off much faster than magnetic fields and because the light intensity can be spatially structured. Our experiments are performed with a Bose-Einstein condensate (BEC) of Rb atoms, which we produce in our new BEC setup. This apparatus has been constructed in the framework of this thesis and offers excellent optical access to the ultracold atom cloud. To investigate the tunability of atomic interactions with single-frequency laser light, we optically couple pairs of free atoms to an electronically excited molecular state. The coupling is achieved with a laser that is tuned close to the respective free-bound photoassociation transition. By changing the laser detuning we are able to adjust the atomic scattering length to any value between 10 a0 and 190 a0, where a0 denotes the Bohr radius. The atomic scattering length is a single quantity that fully describes ultracold elastic interactions. Since laser induced atom losses restrict the duration of our experiments, Bragg spectroscopy is employed as a fast method to measure the scattering length. We also demonstrate that optical Feshbach resonances can be realized with a two-color Raman coupling scheme. To implement this scheme, a second laser is added that couples the excited molecular state to a weakly bound molecular level in a ground state potential. Tuning the second laser results in a modification of the atomic scattering length similar to the one observed with a single laser. In addition, this scheme allows to control the width of the resonance via the detuning of the first laser. For the one-color and two-color coupling schemes, we investigate how the elastic scattering properties depend on the different available parameters, i.e. the laser detunings and intensities. Our experimental findings can successfully be described with an available theoretical model, which treats ultracold collisions in the presence of laser light. Optical Feshbach resonances have the possibility of becoming a valuable tool for fast switching of interactions. This is of special interest in quantum computation schemes with neutral atoms, where interactions between different atomic qubits need to be controlled.
We rapidly change the scattering length as{a}_{s}as​ of a 87{}^{87}87Rb Bose-Einstein condensate by means of a Feshbach resonance, simultaneously releasing the condensate from its harmonic trapping potential. When as{a}_{s}as​ is changed from positive to negative, the subsequent collapse of the condensate is stabilized by the kinetic energy imparted during the release, resulting in a deceleration of the loss rate near the resonance. We also observe an increase in the Thomas-Fermi radius, near the resonance, that cannot be understood in terms of a simple scaling model. Instead, we describe this behavior using the Gross-Pitaevskii equation, including three-body recombination, and hypothesize that the increase in cloud radius is due to self-interference of the condensate resulting in the formation of concentric shells.
We present a theoretical analysis of the optical tuning of the scattering length in a Bose-Einstein condensate in which ultracold atoms in the ground state are exposed to laser light which is off-resonant with the transition frequency to an open-channel excited state. The scattering length can be altered by changing the intensity and frequency of the laser. Experimentally relevant systems are studied in detail, with particular reference to the possibility of Feshbach molecule creation in these systems.
We consider the stability of an ultracold trapped Bose-Einstein condensate near a Feshbach resonance. Using a modified Gross-Pitaevskii equation that includes higher-order terms and a multichannel model of Feshbach resonances, we find regions where stability can be enhanced or suppressed around experimentally measured resonances. We suggest a number of ways to probe the stability diagram. Using scattering length zero crossings huge deviations are found for the critical particle number. Effects are enhanced for narrow resonances or tighter traps. Macroscopic tunneling of the condensate is another possible probe for higher-order interactions; however, to see this requires very narrow resonances or very small particle numbers.