Squeezing collective atomic spins with an optical resonator

Abstract

This thesis describes two methods of overcoming the standard quantum limit of signal-to-noise ratio in atomic precision measurements. In both methods, the interaction between an ultracold atomic ensemble and an optical resonator serves to entangle the atoms and deform the uncertainty distribution of the collective hyperfine spin so that it is narrower in some coordinate than would be possible if the atoms were uncorrelated. The first method uses the dispersive shift of the optical resonator's frequency by the atomic index of refraction to perform a quantum non-demolition measurement of the collective spin, projecting it into a squeezed state conditioned on the measurement outcome. The second method exploits the collective coupling of the atoms to the light field in the resonator to generate an effective interaction that entangles the atoms deterministically. Both methods are demonstrated experimentally, achieving metrologically relevant squeezing of 1.5(5) dB and 4.6(6) dB respectively, and simple analytical models, including the effects of scattering into free space, show that much greater squeezing is realistically achievable. To demonstrate the potential usefulness of such squeezing, a proof-of-principle atomic clock whose Allan variance decreases 2.8(3) three times faster than the standard quantum limit is also presented, together with a discussion of the conditions under which squeezing improves its performance.