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Physical Review Letters

Cavity Enhanced Spontaneous Parametric Down-Conversion for the Prolongation of Correlation Time between Conjugate Photons

Z. Y. Ou, Y. J. Lu

Published Sep 27, 1999• 264 citations
Publisher

Abstract

By resonating both fields of the spontaneous parametric down-conversion with an optical cavity, the bandwidth of the fields is reduced to a level that can be resolved by photodetectors. This enables us to directly measure the distribution of the time intervals between the two down-converted photons. The correlation time is found inversely proportional to the down-conversion bandwidth. In the meantime, the signal levels of the fields are greatly enhanced by the resonance. Such a two-photon source will find wide application in quantum information processing.

DOI
10.1103/physrevlett.83.2556

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By resonating both fields of the spontaneous parametric down-conversion with an optical cavity, the bandwidth of the fields is reduced to a level that can be resolved by photodetectors. This enables us to directly measure the distribution of the time intervals between the two down-converted photons. The correlation time is found inversely proportional to the down-conversion bandwidth. In the meantime, the signal levels of the fields are greatly enhanced by the resonance. Such a two-photon source will find wide application in quantum information processing.
The theory of the optical parametric oscillator is examined and compared to the experiment in the regime of far below threshold. It is found that the output state has no difference from spontaneous parametric down-conversion except that the bandwidth of down-conversion is reduced to that of the resonator and the conversion rate is enhanced by cavity resonance. The reduction of the bandwidth of the down-converted fields makes it possible for a direct measurement of the time interval distribution between two down-converted photons. The observed distributions are well explained by the theory. Such a narrow-band two-photon source will find wide applications in quantum information processing.
We report the generation of polarization-entangled photons by cavity-enhanced spontaneous parametric down-conversion. The bandwidth of entangled photons is reduced to that of the optical parometric oscillator and the conversion rate is enhanced by cavity. The time interval between the conjugate two photon is prolongated so that it can be directly measured by a common detector. The time correlation function of the entangled-photons pair shows a time-oscillatory characteristic. To demonstrate the entanglement, we experimentally obtain two-photon quantum interference for the polarization variable.
Heralded single-photon sources are the most commonly used sources for optical quantum technology applications. There is strong demand for accurate prediction of their spectral features and temporal correlations with ever-increasing precision. This is particularly important in connection with the intrinsically stochastic photon-pair generation process in heralded sources. Here we present a complete theoretical description of the temporal correlation of a signal-idler, signal-signal, and signal-signal-idler coincidences of photons generated by continuous-wave pumped cavity-enhanced spontaneous parametric down-conversion. The theory excellently predicts the measurements, which has been experimentally confirmed in our setup utilizing single-photon detectors with high temporal resolution. This enables us to resolve and analyze the multiphoton correlation functions in great detail.
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.
A theoretical study is made of the process in which incident pump photons that interact with a nonlinear medium (such as a crystal lacking inversion symmetry) are spontaneously split into lower-frequency signal and idler photons. The down-converted fields are quantized and described by a continuum of modes, a subset of which interacts with each photodetector. It is shown that when two ideal photodetectors are appropriately located so that they receive the conjugate signal and idler photons, then the joint probability of two-photon detection by the two detectors can equal the single-photon detection probability. The time correlation between the two detected photons is shown to be limited either by the resolving time of the detectors, or by the bandwidth of the down-converted light, and to be independent of the coherence time of the pump field or of the length of the nonlinear medium. These conclusions are compared with the results of recent experiments.
Application of quantum sources in communication and information processing are believed to bring a new revolution to the on-going information age. The generation of applicable quantum sources such as single photon state and two-photon state, appears to be one of the most difficult in experimental quantum optics. Spontaneous Parametric Down-Conversion (PDC) is known to generate two-photon state, but bandwidth problem makes it less applicable in quantum information processing. The aim of this work is to generate a narrow band two-photon state and apply it to quantum information processing. We start by developing a cavity enhanced PDC device to narrow the bandwidth of the two-photon state. Direct measurement of the bandwidth of the generated state has been made and the quantum theory of such a device has been investigated. An application of this narrow band two-photon state is to generate anti-bunched photons for quantum cryptography, based on the quantum interference between the two-photon state and a coherent state. The feasibility of this scheme for pulsed pump is also investigated. When applying the concept of mode locking in lasers to a two-photon state, we have mode-locked two-photon state which exhibits a comb-like correlation function and may be used for engineering of quantum states in time domain. Other applications such as demonstration of single photon nonlocality, nonlinear sign gate in quantum computation, and direct measurement of quantum beating, will also be addressed.