Observation of Feshbach resonances in a Bose–Einstein condensate

Abstract

It has long been predicted that the scattering of ultracold atoms can be altered significantly through a so-called 'Feshbach resonance'. Two such resonances have now been observed in optically trapped Bose-Einstein condensates of sodium atoms by varying an external magnetic field. They gave rise to enhanced inelastic processes and a dispersive variation of the scattering length by a factor of over ten. These resonances open new possibilities for the study and manipulation of Bose-Einstein condensates.Bose-Einstein condensates of atomic gases offer new opportunities for studying quantum-degenerate fluids 1-5 . All the essential properties of Bose condensed systems-the formation and shape of the condensate, the nature of its collective excitations and statistical fluctuations, and the formation and dynamics of solitons and vortices-are determined by the strength of the atomic interactions. In contrast to the situation for superfluid helium, these interactions are weak, allowing the phenomena to be theoretically described from 'first principles'. Furthermore, in atomic gases the interactions can be altered, for instance by employing different species, changing the atomic density, or, as in the present work, merely by varying a magnetic field.At low temperatures, the interaction energy in a cloud of atoms is proportional to the density and a single atomic parameter, the scattering length a which depends on the quantum-mechanical phase shift in an elastic collision. It has been predicted that the scattering length can be modified by applying external magnetic 6-10 , optical 11,12 or radio-frequency 13 (r.f.) fields. Those modifications are only pronounced in a so-called ''Feshbach resonance'' 14 , when a quasibound molecular state has nearly zero energy and couples resonantly to the free state of the colliding atoms. In a timedependent picture, the two atoms are transferred to the quasibound state, 'stick' together and then return to an unbound state. Such a resonance strongly affects the scattering length (elastic channel), but also affects inelastic processes such as dipolar relaxation 6,7 and threebody recombination. Feshbach resonances have so far been studied at much higher energies 15 by varying the collision energy, but here we show that they can be 'tuned' to zero energy to be resonant for ultracold atoms. The different magnetic moments of the free and quasibound states allowed us to tune these resonances with magnetic fields, and as a result, minute changes in the magnetic field strongly affected the properties of a macroscopic system.Above and below a Feshbach resonance, the scattering length a covers the full continuum of positive and negative values. This should allow the realization of condensates over a wide range of interaction strengths. By setting a Ϸ 0, one can create a condensate with essentially non-interacting atoms, and by setting a Ͻ 0 one can make the system unstable and observe its collapse. Rapid tuning of an external magnetic field around a Feshbach resonance will lead to sudden changes of t...

Condensation, excitation, pairing, and superfluid density in high-Tc superconductors: the magnetic resonance mode as a roton analogue and a possible spin-mediated pairing

“…10 (a) and (d)) and the "binding" process ( Fig. 10 (b) and (c)) is reminiscent of the Feshbach resonance [40,84] appearing in the BE-BCS crossover of ultracold atoms. Note that some of these processes in Fig.…”

Stable and mobile two-dimensional dipolar ring-dark-in-bright Bose–Einstein condensate soliton

“…The scattering length can be adjusted to a desired value by the magnetic [33] and optical [34] Feshbach resonance technique. The densities of the different RDB solitons for (a) figure 2.…”

Heteronuclear quantum gas mixtures

“…After the final transfer at these two magnetic field values, the field is ramped to varying values in the immediate vicinity of the resonance either from above or below. The ramp is performed within 50 ms, thereby changing a FB adiabatically with respect to any other time scale in the experiment:ȧ F B /a F B ω i so that the clouds remain in equilibrium within the field ramp [11,106]. We then probe the expansion of the cloud at different values of the heteronuclear scattering length and under different conditions.…”