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Conference on Lasers and Electro-Optics

Three-photon parametric oscillator: semiclassical and quantum signatures

Gagik Yu. Kryuchkyan, L. A. Manukyan, Naira T. Muradyan

Published Aug 29, 2005• 0 citations
Publisher

Abstract

Summary form only given. Parametric down-conversion is the most standard source of pairs of polarization-entangled photons, which is relevant to many problems of quantum information. However, the realization of the entanglement between three or more photons is considered so far as a difficult problem. In this report we present a novel scheme for producing three-photon entangled states. The scheme involves cascaded second-order /spl chi//sup (2)/-nonlinearities inside the same twice resonant cavity pumped by a frequency /spl omega/.

DOI
10.1109/iqec.2000.908063

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The search for new methods to produce entangled photons is a subject of great interest in quantum optics. We show theoretically that two_photon entangled states may be generated through a cascaded nonlinear optical process in a quasiperiodic optical superlattice. When an idler photon ωi produced from spontaneous parametric down conversion (ωp=ωs+ωi) combines with a pum p photon to produce a sum frequency photon ωb(ωb=ωi+ω p), the latter is entangled with the remaining signal photon ωi. Both a pulsed and a cw 532nm laser have been used to pump a quasi_phase matched LiTaO 3 crystal to generate simultaneously 630nm signal photons through parametric d own conversion and 460nm sum frequency photons. The advantage of this method is that entangled photons of short wavelength may be produced.

Acta Physica Sinica•Jan 1, 2005•1 citation
Summary form only given. Parametric down-conversion is the most standard source of pairs of polarization-entangled photons, which is relevant to many problems of quantum information. However, the realization of the entanglement between three or more photons is considered so far as a difficult problem. In this report we present a novel scheme for producing three-photon entangled states. The scheme involves cascaded second-order /spl chi//sup (2)/-nonlinearities inside the same twice resonant cavity pumped by a frequency /spl omega/.
Summary form only given. The use of parametric down-conversion as a convenient source of correlated photon pairs dates back to the early 1970's but it Was not until the late 1980's and early 1990's that these Sources were shown to be useful for fundamental studies of the phenomenon of two particle entanglement. In recent experiments three photon interference effects have been studied by entangling initially separate photons which has led on to demonstration of quantum teleportation and three photon entangle via GHz states. Due to the necessity for overlapping weak beams of randomly timed photon pairs the triple coincidence rates in these experiments is low. Furthermore the three-photon interference effects are post-selected from a product state of two-photon entanglements which opens the experiments to criticism from a local realistic viewpoint. An improved source would create entangled states of three photons directly in a way analogous to two-photon downconversion. This work extends the quantum theory of spontaneous two-photon downconversion in the presence of a /spl chi//sup (2)/ non-linearity to the three photon case based on the nonlinear susceptibility /spl chi//sup (3)/. The resulting gain is much lower and the efficiency for the three-photon creation process is small. However we show by simple arguments that the number of modes scale quadratically with bandwidth. This leaves us with the hope of detecting of order one three photon per second when phase matching.
Non-classical states of light are of fundamental importance for emerging quantum technologies. All optics experiments producing multi-qubit entangled states have until now relied on outcome post-selection, a procedure where only the measurement results corresponding to the desired state are considered. This method severely limits the usefulness of the resulting entangled states. fiere, we show the direct production of polarization- entangled photon triplets by cascading two entangled down-conversion processes[1]. First, a Sagnac source [2] produces non-degenerate entangled photon pairs at 776 nm and 842 nm in a Bell state. The 776 nm photon is sent through a polarizing Mach-Zehnder interferometer with a down-conversion crystal in each arm. If it is down-converted, a photon pair is created in modes 2 and 3 with a polarization state depending on the pump photon. The quantum stete describing the photon triplets is:
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.
This thesis deals with the production of entangled photons using spontaneous parametric down-conversion (SPDC). We start with a short overview of some important theoretical concepts. First we provide a brief reminder of the theory of entanglement. We then discuss how the state of quantum systems can be determined using quantum state tomography. We also explain SPDC, the physical process which we use to produce entangled photons. Finally, we give an overview of the methods which have been used to produce entangled photons in the past, both for two- and three-photon entanglement. \n \nThe first experiment is the design of an efficient source of entangled photon pairs based on a polarizing Sagnac interferometer configuration. With this configuration, we can use quasi-phasematched materials which allow for higher efficiencies than standard bulk nonlinear materials. The source is pumped by a low-power continuous-wave laser diode, and produces degenerate photon pairs at 809nm. It has a spectral brightness of 87,500 pairs/(s mW nm), and the fidelity of the produced quantum states with a Bell state is 98.9%. The source is used for experiments in quantum key distribution, cluster state quantum computing, remote state preparation, state discrimination, and entanglement-enhanced classical communication. \n \nThe second experiment discussed in this thesis is the generation of photon triplets using cascaded SPDC. In this experiment, a primary SPDC source is pumped with a low-power, continuous-wave laser diode, producing photon pairs. Single photons from these pairs serve as the pump for a second down-conversion, resulting in photon triplets. This is the first demonstration of the direct production of photon triplets, and the first observation of SPDC at the single photon level. This method could potentially be used to produce entangled photon triplets without post-selection, and as a source of triggered Bell pairs.
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.
The search for new methods to produce entangled photons is a subject of great interest in quantum optics. We show theoretically that two_photon entangled states may be generated through a cascaded nonlinear optical process in a quasiperiodic optical superlattice. When an idler photon ωi produced from spontaneous parametric down conversion (ωp=ωs+ωi) combines with a pum p photon to produce a sum frequency photon ωb(ωb=ωi+ω p), the latter is entangled with the remaining signal photon ωi. Both a pulsed and a cw 532nm laser have been used to pump a quasi_phase matched LiTaO 3 crystal to generate simultaneously 630nm signal photons through parametric d own conversion and 460nm sum frequency photons. The advantage of this method is that entangled photons of short wavelength may be produced.