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arXiv:1412.0182 · Physical Review Letters

Classical-to-Quantum Transition with Broadband Four-Wave Mixing

Rafi Z. Vered, Yaakov Shaked, Yelena Ben-Or, M. Rosenbluh, Avi Pe’er

Published Feb 10, 2015• 42 citations
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Abstract

A key question of quantum optics is how nonclassical biphoton correlations at low power evolve into classical coherence at high power. Direct observation of the crossover from quantum to classical behavior is desirable, but difficult due to the lack of adequate experimental techniques that cover the ultrawide dynamic range in photon flux from the single photon regime to the classical level. We investigate biphoton correlations within the spectrum of light generated by broadband four-wave mixing over a large dynamic range of ∼80 dB in photon flux across the classical-to-quantum transition using a two-photon interference effect that distinguishes between classical and quantum behavior. We explore the quantum-classical nature of the light by observing the interference contrast dependence on internal loss and demonstrate quantum collapse and revival of the interference when the four-wave mixing gain in the fiber becomes imaginary.

DOI
10.1103/physrevlett.114.063902

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A key question of quantum optics is how nonclassical biphoton correlations at low power evolve into classical coherence at high power. Direct observation of the crossover from quantum to classical behavior is desirable, but difficult due to the lack of adequate experimental techniques that cover the ultrawide dynamic range in photon flux from the single photon regime to the classical level. We investigate biphoton correlations within the spectrum of light generated by broadband four-wave mixing over a large dynamic range of ∼80 dB in photon flux across the classical-to-quantum transition using a two-photon interference effect that distinguishes between classical and quantum behavior. We explore the quantum-classical nature of the light by observing the interference contrast dependence on internal loss and demonstrate quantum collapse and revival of the interference when the four-wave mixing gain in the fiber becomes imaginary.
We observe at record-high speed the nonclassical nature of ultra-broadband bi-photons, reducing the measurement time by four orders of magnitude compared to standard techniques of Hong–Ou–Mandel interference or sum-frequency generation. We measure the quantum wave-function of the broadband bi-photons, amplitude and phase, with a pairwise 'Mach–Zehnder' quantum interferometer, where bi-photons that are generated in one nonlinear crystal are enhanced (constructive interference) or diminished (destructive interference) in another crystal, depending on the bi-photon phase. We verify the quantum nature of the interference by observing the dependence of the fringe visibility on internal loss. Since destructive interference is equivalent to an attempt to annihilate in the second crystal (by up-conversion) the bi-photons that were created in the first crystal (by down-conversion), the fringe visibility is a measure of the quantum bi-photon purity of the broadband light. The measurement speed-up is due to the large homodyne-like gain from the strong pump (∼10 7–9 ) in the up-conversion efficiency of single bi-photons, which enables the use of simple photo-detection of the full, ultra-high photon flux instead of single-photon/coincidence counting.
Quantum correlations in four-wave-mixing from ensembles of cold two-level atoms may prevail without filtering over background light with well-known classical interpretations, such as Rayleigh scattering, as recently experimentally demonstrated in Phys. Rev. Lett. 128, 083601 (2022). Here we provide an extended investigation of this effect, in which we detail the experimental procedure and the variation of the quantum correlation with various parameters of the system. Particularly, we show that the decay rate of the quantum correlations changes with the number of atoms in the sample, providing another indication of its superradiance-like nature. The nonclassical aspects of the signal occur for short timescales, but the long timescales carry as well a lot of information on the classical correlations of the system. This slow classical regime presents also two clearly distinct timescales, which we explain by two different pathways for the creation of biphotons. From the global analysis of the data in all its timescales, we are able to derive an empirical expression to fit the data, resulting in information on, among other parameters, the sample's temperature and superradiant-like acceleration. In general, the reported quantum correlations present a dependence on critical parameters of the system, such as optical depth and excitation power, that is quite different from other systems used for biphoton generation, and are more robust to changes in these parameters. This opens the possibility of exploring this process for efficient generation of narrow-band biphotons or of other quantum-correlated photonic states of higher order.
We observe at record-high speed the nonclassical nature of ultra-broadband bi-photons, reducing the measurement time by four orders of magnitude compared to standard techniques of Hong-Ou-Mandel interference or sum-frequency generation. We measure the quantum state of the broadband bi-photons, amplitude and phase, with a pairwise Mach-Zehnder quantum interferometer, where bi-photons that are generated in one nonlinear crystal are enhanced (constructive interference) or diminished (destructive interference) in another crystal, depending on the bi-photon phase. We verify the quantum nature of the interference by observing the dependence of the fringe visibility on internal loss. Since destructive interference is equivalent to an attempt to annihilate in the second crystal (by up-conversion) the bi-photons that were created in the first crystal (by down-conversion), the fringe visibility is a measure for the quantum bi-photon purity of the broadband light. The measurement speed-up is due to the large homodyne-like gain from the strong pump ( ⁣∼ ⁣107−9\!\sim\!10^{7-9}∼107−9) in the up-conversion efficiency of single bi-photons, which enables the use of simple photo-detection of the full, ultra-high photon flux instead of single-photon / coincidence counting.