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arXiv:cond-mat/0209634 · Physical Review Letters

Experimental Observation of a Superfluid Gyroscope in a Dilute Bose-Einstein Condensate

E. Hodby, S. A. Hopkins, Gerald Hechenblaikner, N. L. Smith, Christopher J. Foot

Published Aug 27, 2003• 28 citations
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Abstract

We have observed a three-dimensional gyroscopic effect associated with a vortex in a dilute Bose-Einstein condensed gas. A condensate with a vortex possesses a single quantum of circulation, and this causes the plane of oscillation of the scissors mode to precess around the vortex line. We have measured the precession rate of the scissors oscillation. From this we deduced the angular momentum associated with the vortex line and found a value close to Planck's over 2pi per particle, as predicted for a superfluid.

DOI
10.1103/physrevlett.91.090403

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We have observed a three-dimensional gyroscopic effect associated with a vortex in a dilute Bose-Einstein condensed gas. A condensate with a vortex possesses a single quantum of circulation, and this causes the plane of oscillation of the scissors mode to precess around the vortex line. We have measured the precession rate of the scissors oscillation. From this we deduced the angular momentum associated with the vortex line and found a value close to Planck's over 2pi per particle, as predicted for a superfluid.
We investigate the oscillation of a dilute atomic gas generated by a sudden rotation of the confining trap (scissors mode). This oscillation reveals the effects of superfluidity exhibited by a Bose-Einstein condensate. The scissors mode is also investigated in a classical gas above Tc{T}_{c}Tc​ in various collisional regimes. The crucial difference with respect to the superfluid case arises from the occurrence of low frequency components, which are responsible for the rigid value of the moment of inertia. Different experimental procedures to excite the scissors mode are discussed.
The gyroscopic motion of a trapped Bose gas containing a vortex is studied. We model the system as a classical top, as a superposition of coherent hydrodynamic states, by solution of the Bogoliubov equations, and by integration of the time-dependent Gross-Pitaevskii equation. The frequency spectrum of Bogoliubov excitations, including quantum frequency shifts, is calculated and the quantal precession frequency is found to be consistent with experimental results, though a small discrepancy exists. The superfluid precession is found to be well described by the classical and hydrodynamic models. However the frequency shifts and helical oscillations associated with vortex bending and twisting require a quantal treatment. In gyroscopic precession, the vortex excitation modes m = ±1 are the dominant features giving a vortex kink or bend, while the m = +2 is found to be the dominant Kelvin wave associated with vortex twisting. Superfluid atomic gyroscopes 2 1.
The gyroscopic motion of a trapped Bose gas containing a vortex is studied. We model the system as a classical top, as a superposition of coherent hydrodynamic states, by solution of the Bogoliubov equations, and by integration of the time-dependent Gross–Pitaevskii equation. The frequency spectrum of Bogoliubov excitations, including quantum frequency shifts, is calculated and the quantal precession frequency is found to be consistent with experimental results, although a small discrepancy does exist. The superfluid precession is found to be well described by the classical and hydrodynamic models. However, the frequency shifts and helical oscillations associated with vortex bending and twisting require a quantal treatment. In gyroscopic precession, the Kelvin modes m = ±1 are the dominant features giving a vortex kink or bend, while the m = +2 mode is found to be the dominant Kelvin wave associated with vortex twisting.
We study experimentally the line of a single vortex in a rotating prolate Bose-Einstein condensate confined in a harmonic potential. In agreement with predictions, we find that the vortex line is in most cases curved at the ends. We also present measurements of the quadrupole oscillation of the condensate in presence of a single vortex. A theoretical treatment to account for the short time and long time behaviors of these modes is developed. Finally, we use these measurements to infer the angular momentum per particle and relate it to the shape of the vortex line.
By applying a position-dependent detuning to a spin-orbit-coupled Hamiltonian with equal Rashba and Dresselhaus coupling, we exploit the behavior of the angular momentum of a harmonically trapped Bose-Einstein condensed atomic gas and discuss the distinctive role of its canonical and spin components. By developing the formalism of spinor hydrodynamics, we predict the precession of the dipole oscillation caused by the synthetic rotational field, in analogy with the precession of the Foucault pendulum, the excitation of the scissors mode, following the sudden switching off of the detuning, and the occurrence of Hall-like effects. When the detuning exceeds a critical value, we observe a transition from a vortex free, rigidly rotating quantum gas to a gas containing vortices with negative circulation which results in a significant reduction of the total angular momentum.