Velocimetry, Cooling and Rotation Sensing by Cold-Atom Matterwave Interferometry

Abstract

Interferometric measurement of an atom's velocity allows, by tailoring the impulse imparted by the matterwave-splitting laser pulses, a velocity-dependent force that cools an atomic sample. Differential measurement reveals the sample's acceleration and rotation.OCIS codes: (020.1335) Atom optics; (020.3320) Laser cooling; (120.5790) Sagnac effect; (120.7250) Velocimetry Interferometric velocimetryRaman matterwave interferometry [1] commonly uses pairs of laser beams, similar in frequency but opposite in wavevector, to couple atomic states of similar electronic configuration and energy but different linear momentum. The momentum difference gives the radiative interaction a velocity-dependence, which may be overcome if the interaction is limited to pulses short enough to be broad in bandwidth, but which persists between pulses in the phase drift between the atomic superposition and the laser oscillator. The small frequency difference between the coupled states means that there is negligible spontaneous emission, and that the beam pair can be produced with phase precision by radio-frequency modulation of a single master laser. With these ingredients, atom interferometry has been shown to be a precise means of inertial measurement [2][3][4].The evolution of the wavefunction of an atom, as it moves with respect to, but between the pulses of, an interacting optical field, may be viewed from two perspectives. From that of the optical apparatus, the coupled atomic states differ in kinetic energy, and the phase of their superposition therefore accrues because of the difference in classical action between their trajectories. Viewed from the inertial frame of the atom, the phase of the optical field varies as the apparatus moves and presents different points for the stationary atom to sample. The result is a relative phase φ between the atomic superposition and the optical field which, if the field is resonant for a stationary atom, depends after a time t upon the atom's velocity v:where k eff is the effective wavevector of the Raman field, equal to the wavevector difference between its components, and v R is the recoil velocity ℏk eff /m for atoms of mass m.Whether regarded as interference of the de Broglie matterwave, or of the optical wave transferred via an atomic resonator, the interference fringes of a two-pulse Ramsey interferometer show a sinusoidal dependence of the transferred population upon time, with a periodicity determined by the velocity component along k eff . Single velocity components may be found from the fringes' periodicity, and distributions from their Fourier transform. Interferometric coolingInterferometric measurement of the atomic velocity is accompanied by a radiative impulse, for atoms receive an impulse of ℏk eff when they are transferred between the two interferometer states. By tailoring the interferometer period and introducing an adjustable phase between the two interferometer pulses, it may be arranged that this impulse on average opposes the atom's velocity, and an atomic sampl...