Phase effects in coherently stimulated down-conversion with a quantized pump field

Abstract

We investigate the effect of the cumulative phase on the photon statistics of the three-mode state whose evolution is described by the trilinear HamiltonianĤI = i κ âbĉ † −â †b † c , wherein the pump is taken to be quantized (and prepared in a coherent state) and the signal and idler modes are initially seeded with coherent states. We provide a brief review of the two-mode squeezed coherent states generated by non-degenerate coherently-stimulated parametric down-conversion, whereby the nonlinear crystal is driven by a strong classical field. The statistics of the resulting two mode state have been shown to depend greatly on the cumulative phase Φ = θs + θi − 2φ where θ s(i) are the signal(idler) coherent state phases and 2φ is the classical pump phase. Using perturbation theory, we analytically show for short times how the photon statistics and entanglement properties of the resultant state depends strictly on this phase combination. We also present numerical results of the relevant quantities to show the evolution of the three modes and provide a qualitative analysis of the steady state valid for long times.

The parity operator: Applications in quantum metrology

“…On the other hand, the case in which one has parametric down-conversion with coherent states seeding the signal and idler modes, or twomode squeezed coherent states (TMSCS), was considered by Birrittella et al 54 who found a measurement resolution and phase sensitivity dependent on a so-called cumulative phase (the sum of the initial field phases) that yields, for low squeezing, sub-SQL phase sensitivity that does not degrade like the TMSVS does as the phase deviates from zero for the optimal choice of cumulative phase. The cumulative-phasedependent state statistics and entanglement properties of the state resulting from coherently-stimulated down-conversion with a quantized pump field has been studied by Birrittella et al 55 , however the state has not yet been considered in the context of interferometry.…”

Pump Depletion in Parametric Amplification

“…Under typical experimental conditions this is a good approximation as the efficiency of the interaction is very low, however efficiencies are improving all the time and experiments are moving into the regime where depletion effects cannot be neglected [14,15]. Whilst full numerical solutions have been known for many years [16,17] and have been used in theoretical studies [18,20] in conjunction with short time perturbative approaches, these rapidly become intractable when treating realistic systems where the pump power is large.…”