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# Onset of non-Gaussian quantum physics in pulsed squeezing with mesoscopic fields

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## Abstract

We study the emergence of non-Gaussian quantum features in pulsed squeezed light generation with a mesoscopic number (i.e., dozens to hundreds) of pump photons. Due to the strong optical nonlinearities necessarily involved in this regime, squeezing occurs alongside significant pump depletion, compromising the predictions made by conventional semiclassical models for squeezing. Furthermore, nonlinear interactions among multiple frequency modes render the system dynamics exponentially intractable in na\"ive quantum models, requiring a more sophisticated modeling framework. To this end, we construct a nonlinear Gaussian approximation to the squeezing dynamics, defining a "Gaussian interaction frame" (GIF) in which non-Gaussian quantum dynamics can be isolated and concisely described using a few dominant (i.e., principal) supermodes. Numerical simulations of our model reveal non-Gaussian distortions of squeezing in the mesoscopic regime, largely associated with signal-pump entanglement. We argue that the state of the art in nonlinear nanophotonics is quickly approaching this regime, providing an all-optical platform for experimental studies of the semiclassical-to-quantum transition in a rich paradigm of coherent, multimode nonlinear dynamics. Mesoscopic pulsed squeezing thus provides an intriguing case study of the rapid rise in dynamic complexity associated with semiclassical-to-quantum crossover, which we view as a correlate of the emergence of new information-processing capacities in the quantum regime.

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We generate pulsed, two-mode squeezed states in a single spatiotemporal mode with mean photon numbers up to 20. We directly measure photon-number correlations between the two modes with transition edge sensors up to 80 photons per mode. This corresponds roughly to a state dimensionality of 6400. We achieve detection efficiencies of 64% in the technologically crucial telecom regime and demonstrate the high quality of our measurements by heralded nonclassical distributions up to 50 photons per pulse and calculated correlation functions up to 40th order.
Article
We study time ordering corrections to the description of spontaneous parametric down-conversion (SPDC), four wave mixing (SFWM) and frequency conversion (FC) using the Magnus expansion. Analytic approximations to the evolution operator that are unitary are obtained. They are Gaussian preserving, and allow us to understand order-by-order the effects of time ordering. We show that the corrections due to time ordering vanish exactly if the phase matching function is sufficiently broad. The calculation of the effects of time ordering on the joint spectral amplitude of the photons generated in spontaneous SPDC and SFWM are reduced to quadrature.
Article
A model is presented to describe spontaneous type-II parametric down-conversion pumped by a broadband source. This process differs from the familiar cw-pumped down-conversion in that a broader range of pump energies is available for down-conversion. The properties of the nonlinear crystal determine how these energies are distributed into the down-converted photons. Because the two photons are polarized along different crystal axes, they have different spectral characteristics and are no longer exactly anticorrelated. As the pump bandwidth is increased, this effect becomes more pronounced. A fourth-order interference experiment is proposed, illustrating some of the features of broadband pumped down-conversion.
Article
By embedding an atom capable of electromagnetically induced transparency inside an appropriate photonic-crystal microcavity it may become possible to realize an optical nonlinearity that can impart a π-rad-peak phase shift in response to a single-photon excitation. Such a device, if it operated at high fidelity, would then complete a universal gate set for all-optical quantum computation. It is shown here that the causal, noninstantaneous behavior of any χ(3) nonlinearity is enough to preclude such a high-fidelity operation. In particular, when a single-photon-sensitive χ(3) nonlinearity has a response time that is much shorter than the duration of the quantum computer’s single-photon pulses, essentially no overall phase shift is imparted to these pulses by cross-phase modulation. Conversely, when this nonlinearity has a response time that is much longer than this pulse duration a single-photon pulse can induce a π-rad overall phase shift through cross-phase modulation, but the phase noise injected by the causal, noninstantaneous response function precludes this from being a high-fidelity operation.
Article
The properties of a unique set of quantum states of the electromagnetic field are reviewed. These 'squeezed states' have less uncertainty in one quadrature than a coherent state. Proposed schemes for the generation and detection of squeezed states as well as potential applications are discussed.
Article
The Einstein-Podolsky-Rosen paradox is demonstrated experimentally for dynamical variables having a continuous spectrum. As opposed to previous work with discrete spin or polarization variables, the continuous optical amplitudes of a signal beam are inferred in turn from those of a spatially separated but strongly correlated idler beam generated by nondegenerate parametric amplification. The uncertainty product for the variances of these inferences is observed to be 0.70±0.01, which is below the limit of unity required for the demonstration of the paradox.