Cavity-enhanced measurement for the generation of spin squeezed states in strontium atom interferometry.

Over the last three decades, atom interferometry has been developed rapidly and has become an important tool in quantum metrology. It has been widely applied both in the test of fundamental physics and in the precise measurement of gravity and gravity gradients. Atom interferometers based on the alkaline-earth (like) atoms such as strontium (Sr) and ytterbium (Yb) have attracted increasing attention due to the existence of narrow intercombination transitions and ultra-narrow clock transitions. The bosonic 88Sr is a good candidate for transportable and space-borne atom interferometers due to the immunity to stray magnetic fields in its electronic ground state, long coherence time and low collision rate. It can therefore be used in space projects for precision measurement of gravity and gravity gradients. However, there is a fundamental limit to the precision in a phase shift measurement with atom interferometers, which is set by the number of atoms involved. This limit is known as the standard quantum limit. It is possible to surpass this limit by introducing correlations in the atomic ensembles thus reducing the phase uncertainty at the expense of an increase in the population uncertainty. In this case the spin-squeezed states are generated and can be used to improve the phase resolution of atom interferometers. In this thesis, a method to generate spin squeezed states in 88Sr momentum states for atom interferometry is considered and the necessary technology that allows its implementation will be presented. Spin squeezing is achieved by resolving the Doppler effect due to momentum state superposition via cavity- enhanced nondestructive measurement. An optical ring cavity is designed and constructed for quantum nondestructive measurements. However, one major obstacle that blocks the way to spin squeezing via cavity-enhanced measurement arises from cavity length fluctuations, which can totally mask the atomic signal if no appropriate scheme is adopted. Therefore, a method to cancel the cavity length fluctuations in measuring the atom-induced phase shift is proposed and close to 30 dB reduction of the cavity noise down to the noise floor has been demonstrated. We further apply the demonstrated noise-reduced measurement scheme in the simulated squeezing experiment, where we mimic the atom-induced cavity phase shift by varying the frequency of one of the two circulating beams. The noise cancellation scheme demonstrates an improvement of a factor of 40 in phase sensitivity with a phase resolution of 0.7 mrad. With this improvement we estimate that the cavity noise will no longer play an important role in a real spin squeezing measurement.