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Photonics and Micro- and Nano-structured Materials

Three-photon entanglement in structured χ(2) media

T. V. Gevorgyan, Gagik Yu. Kryuchkyan

Published Jan 20, 2012• 0 citations
Publisher

Abstract

We investigate production of three-photon states in cascaded parametric down-conversion (PDC). The analysis includes preparation of Greenberger-Horne-Zeilinger polarization-entangled states in cascaded type-II and type-I PDC in the framework of considering the dual-grid structure that involves two periodically poled crystals. Considering cascaded optical parametric oscillator (OPO) driven by a sequence of laser pulses with Gaussian time-dependent envelopes, we investigate quantum statistical properties of high intensity mode generated in intracavity three-photon splitting. Calculating the normalized third-order correlation function below-and at the generation threshold, we demonstrate that in the pulsed regime, depending on the duration of pulses and the time-interval separations between them, the degree of three-photon-number correlation essentially exceed the analogous one for the case of continuous pumping.

DOI
10.1117/12.923124

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We investigate production of three-photon states in cascaded parametric down-conversion (PDC). The analysis includes preparation of Greenberger-Horne-Zeilinger polarization-entangled states in cascaded type-II and type-I PDC in the framework of considering the dual-grid structure that involves two periodically poled crystals. Considering cascaded optical parametric oscillator (OPO) driven by a sequence of laser pulses with Gaussian time-dependent envelopes, we investigate quantum statistical properties of high intensity mode generated in intracavity three-photon splitting. Calculating the normalized third-order correlation function below-and at the generation threshold, we demonstrate that in the pulsed regime, depending on the duration of pulses and the time-interval separations between them, the degree of three-photon-number correlation essentially exceed the analogous one for the case of continuous pumping.
Generating multi-photon entangled states is a primary task for applications of quantum information processing. We investigate production of photon-triplet in a regime of light amplification in second-order nonlinear media under action of a pulsed laser beam. For this goal the process of cascaded three-photon splitting in an optical cavity driven by a sequence of laser pulses with Gaussian time-dependent envelopes is investigated. Considering production of photon-triplet for short-time regime and in the cascaded three-wave collinear configuration Generating multi-photon entangled states is a primary task for applications of quantum information processing. We investigate production of photon-triplet in a regime of light amplification in second-order nonlinear media under action of a pulsed laser beam. For this goal the process of cascaded three-photon splitting in an optical cavity driven by a sequence of laser pulses with Gaussian time-dependent envelopes is investigated. Considering production of photon-triplet for short-time regime and in the cascaded three-wave collinear configuration we shortly analyze preparation of polarization-non-product states looking further applications of these results in the cascaded optical parametric oscillator. It is also demonststed the nonclassical characteritics of the photon-triplet in phase-space on the base of the Wigner function. Calculating the normalized third-order correlation functions below-and at the generation threshold of cascaded optical parametric oscillator, we demonstrate that in the pulsed regime, depending on the duration of pulses and the time-interval separations between them, the degree of three-photon-number correlation essentially exceed the analogous one for the case of continuous pumping.
It has been a longstanding goal in quantum optics to realize controllable sources generating joint multiphoton states, particularly photon triplet with arbitrary spectral characteristics. We demonstrate that such sources can be realized via cascaded parametric down-conversion (PDC) in superlattice structures of nonlinear and linear segments. We consider a scheme that involves two parametric processes---${\ensuremath{\omega}}_{0}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$, ${\ensuremath{\omega}}_{2}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{1}$ under pulsed pump---and investigate the spontaneous creation of a photon triplet as well as the generation of high-intensity mode in intracavity three-photon splitting. We show the preparation of Greenberger-Horne-Zeilinger polarization-entangled states in cascaded type-II and type-I PDC in the framework of considering the dual-grid structure that involves two periodically poled crystals. We demonstrate the method of compensation of the dispersive effects in nonlinear segments by appropriately chosen linear dispersive segments of superlattice for preparation of the heralded joint states of two polarized photons. In the case of intracavity three-photon splitting, we concentrate on the investigation of photon-number distributions, third-order photon-number correlation function, as well as the Wigner functions. These quantities are observed both for short interaction time intervals and the over-transient regime, when dissipative effects are essential.
We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO present two χ^2 level oscillation thresholds that are therefore remarkably lower than for a χ^3 OPO. This is promising for reaching the regime of an effective third-order nonlinearity well above both thresholds. Such a χ^2 cascaded device also has potential applications in frequency conversion to far infra-red regimes. But, most importantly, it can generate novel multi-partite quantum correlations in the output radiation, which represent a step beyond squeezed or entangled light. The output can be highly non-Gaussian, and therefore not describable by any semi-classical model.
We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO presents two ${\ensuremath{\chi}}^{(2)}$-level oscillation thresholds that are therefore much lower than for a ${\ensuremath{\chi}}^{(3)}$ OPO. This is promising for reaching the regime of an effective third-order nonlinearity well above both thresholds. Such a ${\ensuremath{\chi}}^{(2)}$ cascaded device also has potential applications in frequency conversion to far-infrared regimes. But, most importantly, it can generate novel multipartite quantum correlations in the output radiation, which represent a step beyond squeezed or entangled light. The output can be highly non-Gaussian and therefore not describable by any semiclassical model. In this paper, we derive quantum stochastic equations in the positive-PPP representation and undertake an analysis of steady-state and dynamical properties of this system.
We investigate production of three-photon and four-photon states in cascaded parametric processes of photon splitting and summing in χ (2)nonlinear media, under action of pump field. Generation of photon triplets using simultaneously phase matched three-photon processes: ω0↔ω1+ω2 , ω2↔ω1+ω1 , is considered in dual-grating layered structure that involves nonlinear and linear segments. The production of heralded two-photon entangled states from three-photon states is analyzed for this configuration by using the method of conditional detection of auxiliary photons. Cascaded four-photon downconversion based on simultaneously phase matched three-photon processes: ω0↔ω2 +ω2 , ω2↔ω1+ω1 is arranged for phase-reversed configuration. The effects of correlation between photons in both three-photon and four-photon states is analyzed in the regimes of amplification of corresponding modes at the frequency of three-photon downconversion ω1 = ω0/3 and the frequency of four-photon down-conversion ω1 = ω0/4respectively for both cascaded systems.
We consider the quantum state of light produced via direct parametric decay of pump photons into photon triples in a medium with cubic nonlinearity. For this state generated in the near-collinear frequency-degenerate regime, the third- and second-order Glauber's correlation functions are calculated and the intensity distribution over frequency and wave vector is found. It is shown that the number of photons generated into a single mode via the three-photon down-conversion is proportional to the width of the frequency-angular intensity distribution for the corresponding two-photon phase matching (spontaneous parametric down-conversion). The intensity of three-photon parametric down-conversion is shown to have an extremely broad frequency spectrum, even for a fixed angle of scattering.