Cooperative Effects for Measurement - Raman Superradiance Imaging and Quantum States for Heisenberg Limited Interferometry

Abstract

Cooperative effects in many-particle systems can be exploited to achieve measurement outcomes not possible with independent probe particles. We explore two measurement applications based on the cooperative phenomenon of superradiance or on correlated quantum states closely related to superradiance. In the first application we study the off-resonant superradiant Raman scattering of light from an ultracold Bose atomic vapor. We investigate the temperature dependence of superradiance for a trapped vapor and show that in the regime where superradiance occurs on a timescale comparable to a trap frequency, scattering takes place preferentially from atoms in the lowest trap levels due to Doppler dephasing. As a consequence, below the critical temperature for Bose condensation, absorption images of transmitted light serve as a direct probe of the condensed state. Subsequently, we consider a pure condensate and study the time-dependent spatial features of transmitted light, obtaining good qualitative agreement with recent imaging experiments. Inclusion of quantum fluctuations in the initial stages of the superradiant emission accounts well for shot-to-shot fluctuations. Secondly, we have used simulated annealing, a global optimization strategy, to systematically search for correlated quantum interferometer input states that approach the Heisenberg limited uncertainty in estimates of the interferometer phase shift. That limit improves over the standard quantum limit to the phase sensitivity of interferometric measurements by a factor of 1√N, where N is the number of interfering particles. We compare the performance of these states to that of other non-classical states already known to yield Heisenberg limited uncertainty.