Coherently stimulated parametric down-conversion, phase effects, and quantum-optical interferometry

Abstract

We re-examine the properties of the states produced by nondegenerate coherently stimulated parametric down-conversion wherein the signal and idler modes are seeded with coherent states of light and where the nonlinear crystal is driven by a strong classical field as described by the parametric approximation. The states produced are the two-mode squeezed coherent states defined with a specific ordering of operators, namely, the displacement operators of the two modes acting on the double vacuum state followed by the action of the two-mode squeeze operator representing the down-conversion process. Though mathematically equivalent to the reverse ordering of operators, but with different displacement parameters, the ordering we consider is closely related to what could most easily be implemented in the laboratory. The statistical properties of the state are studied with an emphasis on how they, and its average photon number, are affected by the various controllable phases, namely, those of the classical pump field of the two input coherent states. We then consider the multiphoton interference effects that arise if the two beams are overlapped on a 50:50 beam splitter, investigating the role of the phases in controlling the statistical properties of the output states. Finally, we study the prospects for the application of the states to quantum-optical interferometry to obtain sensitivities in phase-shift measurements beyond the standard quantum limit.

SU(1,1)-type light-atom-correlated interferometer

“…The generated state is similar to the two-mode squeezed vacuum state | = n c n |n ph |n atom , where n is the photon number and the number of atomic collective excitation. If a(0) andb(0) are initially in coherent states, the generated state is similar to a two-mode squeezed coherent state [36]. After RP1, the LCC is not zero, which shows that a strong correlation exists between the number of photon and the number of atomic collective excitation number.…”

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

“…For the method of generation we had in mind, that is, where the two displacement operators act on the double vacuum followed by the action of the two-mode squeezing operation, the average photon number in the quantized output signal and idler beams strongly depends on the arXiv:1910.12124v1 [quant-ph] 26 Oct 2019 combined phase angle Φ. In the reverse ordering of the operators where the two-mode squeezing operator acts on the double vacuum states and where the two displacement operators act on each of the modes of the generated squeezed vacuum states, the phase effects are still there but are somewhat hidden, as pointed out in [6]. Furthermore, the joint photon number distributions for the output signal and idler beams are remarkably altered by changing Φ from 0 to π, with the value of π yielding the greatest average photon number for a given set of parameters.…”

“…In this case a strong classical UV field is used to drive a nonlinear crystal producing pairs of frequency down-converted (infrared) photons in the signal and idler modes, which are initially prepared in vacuum states. Recently, Birrittella et al [6] studied the use of coherently-stimulated parametric down-conversion in the context of quantum optical interferometry, wherein the signal/idler modes are initially seeded with coherent states, and noted the interesting effects of the cumulative phase of the two coherent light fields and the pump field, the latter field assumed to be a classically prescribed field. One can define the cumulative phase from the mixing of the three fields as Φ = θ s + θ i − 2φ, where θ s and θ i are the seeded signal and idler coherent state phases, respectively, and 2φ is the phase of the pump field.…”

“…On the other hands, if the output signal and idler beams are subject to arbitrary unitary transformation, the individual phases may have some affect. As a specific example, it was shown [6] that having the signal and idler modes incident on a 50:50 beam splitter will result in a joint-photon number distribution that depends heavily on the choice of individual phases.…”

“…The work described in [6], as indicated above, is performed within the confines of the parametric approximation in which the pump field is treated as a classical undepleted field. Work has been performed in considering pump depletion with seeded vacuum states [10] with an emphasis on modeling black hole dynamics.…”