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arXiv:1011.1577 · Physical Review A

Three-photon states in nonlinear crystal superlattices

Diana A. Antonosyan, T. V. Gevorgyan, Gagik Yu. Kryuchkyan

Published Apr 8, 2011• 29 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.83.043807

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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---\ensuremathω0\ensuremath→\ensuremathω1+\ensuremathω2{\ensuremath{\omega}}_{0}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}\ensuremathω0​\ensuremath→\ensuremathω1​+\ensuremathω2​, \ensuremathω2\ensuremath→\ensuremathω1+\ensuremathω1{\ensuremath{\omega}}_{2}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{1}\ensuremathω2​\ensuremath→\ensuremathω1​+\ensuremathω1​ 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 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.
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.
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.
We demonstrate a general method of engineering the joint quantum state of photon pairs produced in spontaneous parametric down-conversion. The method makes use of a superlattice structure of nonlinear and linear materials, in conjunction with a broadband pump, to manipulate the group delays of the signal and idler photons relative to the pump pulse, and realizes photon pairs described by a joint spectral amplitude with arbitrary degree of entanglement. This method of group-delay engineering has the potential of synthesizing a broad range of states including factorizable states crucial for quantum networking and states optimized for Hong-Ou-Mandel interferometry. Experimental results for the latter case are presented, illustrating the principles of this approach.
Two spatially separated type-I nonlinear crystals are pumped by femtosecond laser pulses to create entangled photon pairs in the process of spontaneous parametric down-conversion. The two-photon entangled state exhibits high-visibility quantum interference for both polarization and space-time variables without the need of stringent spectral postselection by using narrow-band filters. The visibility is insensitive to the thickness of the crystals, unlike in the case of pulse pumped type-II parametric down-conversion; therefore the intensity can be easily increased by using thick nonlinear crystals. This method will be indispensable in experiments that require a pulsed source of entangled photon pairs, such as generation of multiphoton entangled states, quantum teleportation, and quantum communications.
Summary form only given. Parametric downconversion (PDC) allows the generation of highly coherent, spectrally pure single photons for quantum photonics. In a typical heralded PDC source, the signal photon emerges in a spectrally mixed state due to strong (anti)correlation in the joint spectrum of PDC photon pairs.One method for reducing spectral correlations is spectral filtering, but this compromises the heralding efficiency and the brightness of the source. A more sophisticated method for increasing the heralded photon purity is group-velocity matching, which works by erasing part of the timing information between the pump and PDC photons. What group-velocity matching cannot address, however, are the remaining correlations in the joint spectrum that come from the sinc-shaped phase-matching function (PMF) typical to standard PDC crystals. Further source engineering is therefore required to remove these correlations. Several studies have introduced domain-engineering techniques for shaping the phase matching function (PMF) in periodically poled crystals to improve single photon purities [1-4]. We present a new technique for tailoring crystal nonlinearities which combines the advantages of a deterministic method for domain engineering [4] and an annealing method developed for classical applications in higher-harmonic generation [5]. In our method, we first choose each domain orientation such that the generated field amplitude along the crystal matches the target field amplitude obtained by integrating the desired nonlinearity profile. Using a one-block structure instead of a two-blocks structure (as in [4]) results in a higher flexibility of the algorithm in tracking the target function and yields to more accurate results. We then use an annealing algorithm to slightly vary the width of each domain, further improving the effective PMF. Our technique outperforms its predecessors, particularly for short crystals, leading to high single photon purities, as shown in Fig.1. We experimentally characterise our method through a high-precision measurement of multiphoton interference between two heralded photons generated by two independent sources.We also notice that by considering a complex target field amplitude function it is possible to generalise the algorithm in [5] to any constant domain width (not necessarily equal to the coherence length), leading to a better approximation of the desired phase matching function, especially in the very short crystal regime. Moreover, tracking both the real and imaginary components of the target function allows us to approximate more exotic cases such as chirped nonlinearity profiles. Since scalable quantum photonics will require integrated architectures in which nonlinear processes are typically employed for single-photon generation, it will be interesting to explore new techniques similar to in-fibre Bragg grating structures which might yield quasi-periodic four-wave mixing and apply our algorithm to these new platforms.