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Journal of Modern Optics

Cavity-enhanced parametric down-conversion as a source of correlated photons

P. Hariharan, Barry C. Sanders

Published Aug 1, 2000• 6 citations
Publisher

Abstract

The most common way of generating correlated photons is by parametric down-conversion in a nonlinear crystal in free space. However, a drawback of this technique is the extremely low photon flux available. We present a simple analysis which shows that cavity-enhanced parametric downconversion, using an arrangement similar to an optical parametric oscillator and operated well below threshold, can yield a substantially higher photon flux without significantly degrading the correlation between photons.

DOI
10.1080/09500340008231422

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The most common way of generating correlated photons is by parametric down-conversion in a nonlinear crystal in free space. However, a drawback of this technique is the extremely low photon flux available. We present a simple analysis which shows that cavity-enhanced parametric downconversion, using an arrangement similar to an optical parametric oscillator and operated well below threshold, can yield a substantially higher photon flux without significantly degrading the correlation between photons.
There has been increasing interest in the generation of such photon pairs using a spontaneous parametric down-conversion (SPDC) source inside an optical cavity to enhance the down-conversion into modes resonant to the cavity, each of the modes having a MHz spectrum. These optical parametric oscillators (OPO) operated far below threshold also provide a well defined spatial mode. Our setup consists of a bow-tie cavity with a periodically poled KTP crystal as nonlinear medium, phase-matched for parametric down-conversion. This photon-pair source is designed to provide photons suitable for interaction with atoms. These photons could be directly used in applications towards a quantum memory of light, like in experiments on slow light or the storage of single photons in EIT media. In this way an optical polarization rotation in an atomic sample could be measured achieving super-resolution.
In this paper we study photon pairs generated in a nonlinear cavity composed of a nonlinear crystal surrounded by mirrors, by the process of spotaneous parametric downconversion. We analyze two different regimes: singly-resonant cavities where the signal and idler modes are resonant and doubly-resonant cavities where the pump mode is also resonant. We present analytic expressions for the joint spectral amplitude in these two cases and study the reduction in emission bandwidth as the cavity coefficient finesse is increased. We also study the enhancement of the source brightness from the presence of the cavity.
This paper presents an experiment on single-photon spectrum generation using an optical parametric oscillator device with cavity-enhanced parametric down-conversion. A PPKTP crystal inside a cavity far below threshold is pumped in order to create signal-idler photon pairs. Triple-resonance of pump, signal, and idler fields are achieved using a compensating KTP crystal. Long-term stability, ultra-high brightness (14000 biphotons/s per mW), and MHz signal bandwidth behind a single-mode fiber on the cesium D1 line (894.3 nm) are attained by locking the cavity length of the pump via the Hansch-Couillaud method. The spectral width of the parametric fluorescence is also derived using the signal-to-idler cross-correlation measurements, and has been found to be < 3 MHz.
Photons as flying qubits are ideal carriers of quantum information. However, efficient quantum interfaces which transfer flying into stationary qubits and vice versa are needed to realize complex quantum networks. Stationary qubit systems (atoms, ions, or solid state implementations) couple to photons via characteristic optical transitions. In order to establish key quantum operations, such as coherent photon storage, entanglement swapping, etc., high-quality photons with a tailored spectral, spatial, and temporal mode are needed. One way to generate these photons is to use the stationary qubit systems themselves. Another approach which does not impose limitations in terms of the photon’s wavelength or bandwidth relies on all-optical single photon sources. An example is spontaneous parametric down conversion (SPDC) inside an optical cavity with well-defined linewidth. In SPDC, a pump photon incident on a nonlinear medium is split into two photons of lower energy that are often referred to as signal and idler. Resonating the fluorescent fields, the setup becomes an optical parametric oscillator (OPO) far below the threshold. The usually THz broad emission spectrum of SPDC then follows the Airy function of the resonator. The spectral bandwidth of the generated photons can easily reach values of several MHz, which is comparable to atom resonance linewidths. By introducing additional losses or simply changing the cavity mirror reflectivities the bandwidth is tunable up to several 100 MHz. This is comparable to the bandwidth of single photons generated by e.g. quantum dots.
We present a single-resonant optical parametric oscillator pumped far below threshold as a source for narrow-band single photons. Spontaneous generation of single photons via parametric downconversion is modified and follows the cavity transfer function. Cross-correlation measurements between signal and idler beams show a cavity bandwidth of 62MHz. As the main improvement to prior realizations, our cavity is locked to the pump beam via the Hänsch-Couillaud method and therefore allows the continuous generation of heralded single photons with long-term stability.
A theory of spontaneous parametric downconversion in a nonlinear crystal that is placed inside a microcavity in the degenerate, collinear, type I arrangement is given. Both atom and field variables are fully quantized. The photon-correlation function for the entangled photon pairs produced has a much longer correlation time (~0.4 ns) than that without the cavity (of the order of subpicoseconds) and can be measured directly with fast photodetectors. We also calculate the resonant suppression and enhancement in the photon-pair count rate as a function of cavity length. The results are in qualitative agreement with recent downconversion experiments [Phys. Rev. Lett. 85, 2556 (1999)] in a 4.5-mm cavity.