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Journal of Modern Optics

Generation of entangled four-photon states by parametric down-conversion

Surya P. Tewari, P. Hariharan

Published Mar 1, 1997• 4 citations
Publisher

Abstract

Pairs of photons are commonly generated in an entangled state by parametric down-conversion of an ultraviolet pump beam in a nonlinear crystal. We show how this process can be extended to generate entangled four-photon states from two pump photons by using two non-collinear pump beams.
DOI
10.1080/09500349708232920

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Summary form only given. We have experimentally demonstrated that the two-photon probability amplitudes of photon pairs generated using spontaneous parametric down conversion from separate nonlinear crystals, under the conditions outlined above, remain independent and cannot be used to engineer more complex quantum states. The spontaneous nature of the down-conversion process prevents pairs of photons generated in unconnected regions of interaction from having a stable phase relationship between components of their probability amplitudes. The experiment has been performed using two BaB/sub 2/O/sub 4/ nonlinear crystals, of lengths 0.5 mm and 1.5 mm respectively. They have been cut to generate phase-matched type-II collinear down conversion.
We study the physics of four-photon states generated in spontaneous parametric down-conversion with a pulsed pump field. In the limit where the coherence time of the photons t ph c is much shorter than the duration of the pump pulse Δt, the four photons can be described as two independent pairs. In the opposite limit, the four photons are in a four-particle entangled state. Any intermediate case can be characterized by a single parameter χ, which is a function of t ph c Δt. We present a direct measurement of χ through a simple experimental set-up. The full theoretical analysis is also provided.
We study the physics of four-photon states generated in spontaneous parametric down-conversion with a pulsed pump field. In the limit where the coherence time of the photons t ph c is much shorter than the duration of the pump pulse Δt, the four photons can be described as two independent pairs. In the opposite limit, the four photons are in a four-particle entangled state. Any intermediate case can be characterized by a single parameter χ, which is a function of t ph c Δt. We present a direct measurement of χ through a simple experimental set-up. The full theoretical analysis is also provided.
The purpose of this project is to set up a system for creating entangled photon pairs for use in various quantum mechanical experiments, including the testing of Bell’s inequalities which demonstrates the fundamentally indeterministic nature of quantum mechanics. The photons are created by pumping a beta barium borate crystal with 405 nm laser light then, due to a process called type 1 spontaneous parametric down conversion, a single pump photon can be converted into two 810 nm photons in an entangled state. In the same lab, a similar set up has already been achieved using a 474 nm pump laser, but by using a shorter wave length, a higher detection rate can be achieved. Two collimators are set up to collect the down converted photons and send them to two photon counting modules. The collimators need to be positioned precisely to detect any down converted photons because they emerge from the crystal in a narrow beam that is at an angle with respect to the pump beam and only a miniscule fraction of pump photons are down converted. The angle at which the down converted photons emerge is a function of how the crystal is prepared and the polarization orientation of the pump beam. It was calculated using a program by National Institute of Standards and Technology.
Entangled photons produced by spontaneous parametric down-conversion have been of paramount importance for our current understanding of quantum mechanics and advances in quantum information. In this process, the quantum correlations of the down-converted photons are governed by the optical properties of the pump beam illuminating the nonlinear crystal. Extensively, the pump beam has been modeled by either coherent beams or by the well-known Gaussian-Schell model, which leads to the natural conclusion that a high degree of optical coherence is required for the generation of highly entangled states. Here, we show that when a novel class of partially coherent Gaussian pump beams is considered, a distinct type of quantum state can be generated for which the amount of entanglement increases inversely with the degree of coherence of the pump beam. This leads to highly incoherent yet highly entangled multiphoton states, which should have interesting consequences for photonic quantum information science.