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Journal of Modern Optics

Quantum-correlation metrology with biphotons: where is the limit?

Dmitry Strekalov, Andrey B. Matsko, Anatoliy A. Savchenkov, Lute Maleki

Published Nov 10, 2005• 15 citations
Publisher

Abstract

Theoretical analysis shows that the correlation time of a photon pair is closely related to the spectrum of two-photon light. This entails limitations on the shortest achievable two-photon correlation time. These limitations are important for quantum optical metrology and information processing applications, especially those involving quasi-monochromatic light. In this paper we present a more rigorous proof of the fact that the shortest possible two-photon correlation time is limited by approximately the inverse width of the optical spectrum. We further show that this limit can be closely approached with Type-I spontaneous parametric down-conversion at a specific pump wavelength. This study also results in the prediction of very unusual parametric down-conversion spectra, suggesting a method for engineering of frequency-entangled two-photon states.

DOI
10.1080/09500340500275827

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Theoretical analysis shows that the correlation time of a photon pair is closely related to the spectrum of two-photon light. This entails limitations on the shortest achievable two-photon correlation time. These limitations are important for quantum optical metrology and information processing applications, especially those involving quasi-monochromatic light. In this paper we present a more rigorous proof of the fact that the shortest possible two-photon correlation time is limited by approximately the inverse width of the optical spectrum. We further show that this limit can be closely approached with Type-I spontaneous parametric down-conversion at a specific pump wavelength. This study also results in the prediction of very unusual parametric down-conversion spectra, suggesting a method for engineering of frequency-entangled two-photon states.
We show theoretically that two-photon correlation time for a biphoton, a pair of entangled photons generated in the process of parametric down conversion, is limited by the inverse frequency width of the single-photon spectrum, which is limited by the dispersion of the nonlinear material used for the pair generation. The dispersion is determined by the transparency window of the material, which provides the ultimate limitation for the two-photon correlation time. We discuss several experimental approaches enabling realization of such a limiting case.
A concept for an ultra-broad-band optical parametric amplifier or oscillator has emerged as a by-product of a theoretical study in fundamental quantum optics. The study was originally intended to address the question of whether the two-photon temporal correlation function of light [in particular, light produced by spontaneous parametric down conversion (SPDC)] can be considerably narrower than the inverse of the spectral width (bandwidth) of the light. The answer to the question was found to be negative. More specifically, on the basis of the universal integral relations between the quantum two-photon temporal correlation and the classical spectrum of light, it was found that the lower limit of two-photon correlation time is set approximately by the inverse of the bandwidth. The mathematical solution for the minimum two-photon correlation time also provides the minimum relative frequency dispersion of the down-converted light components; in turn, the minimum relative frequency dispersion translates to the maximum bandwidth, which is important for the design of an ultra-broad-band optical parametric oscillator or amplifier. In the study, results of an analysis of the general integral relations were applied in the case of an optically nonlinear, frequency-dispersive crystal in which SPDC produces collinear photons. Equations were found for the crystal orientation and pump wavelength, specific for each parametric-down-converting crystal, that eliminate the relative frequency dispersion of collinear degenerate (equal-frequency) signal and idler components up to the fourth order in the frequency-detuning parameter
Generation of two-photon light with given spectral and temporal properties is of great interest for quantum communication and quantum metrology applications. In particular, preparation of biphotons with ultra-narrow correlation time is a very important task. In a recent series of papers, our group analyzed the generation of twophoton wavepackets, produced by Spontaneous Parametric Down Conversion, in crystals with linearly chirped quasi-phase matching grating. Wavepackets present very broad spectra but a broad spectrum does not necessarily imply small correlation times, although the inverse is true. Indeed, the spectrum broadening induced by the grating is inhomogeneous; for this reason, the two-photon spectral amplitude present a phase (a frequency chirp) that depend nonlinearly on the frequency. Hence, the two-photon wavepackets are not Fourier transform-limited. As suggested in, the ideal way to make the wavepacket perfectly transform limited is to insert in the path of the biphotons a proper optical medium that compensates the non-linear part of the phase factor present in the spectral amplitude. In our work, we investigate the non-local temporal compression of the photons induced by the insertion of a standard optical fibre in the path of one of the two photons. We present and discuss a systematic study of this phenomenon and some optimal situation where the full numerical calculation shows an effect that can be clearly observed with a realistic set-up. The study has open the way to the practical realization of this idea.
Quantum light is a key resource for promoting quantum technology. One such class of technology aims to improve the precision of optical measurements using engineered quantum states of light. In this study, we investigate transmission measurement of frequency-entangled broadband photon pairs generated via parametric down-conversion with a monochromatic laser. It is observed that state-to-state dynamics in the system under study are temporally resolved by adjusting the path difference between the entangled twin beams when the entanglement time is sufficiently short. The non-classical photon correlation enables time-resolved spectroscopy with monochromatic pumping. It is further demonstrated that the signal corresponds to the spectral information along anti-diagonal lines of, for example, two-dimensional Fourier-transformed photon-echo spectra. This correspondence inspires us to anticipate that more elaborately engineered photon states would broaden the availability of quantum light spectroscopy.
This work is focused on the engineering and characterization of the frequency-time properties of photon pairs generated with a semiconductor source. This device emits photons propagating in opposite directions at telecom wavelengths using spontaneous parametric down-conversion at room temperature. A microcavity integrated in the source allows the resonance of the transverse pump beam, enhancing the efficiency of the nonlinear interaction. We give a theoretical description of the down-conversion process in the source and we show how the spatial and spectral properties of the pump beam impact the properties of the photons, in particular their degree of entanglement in frequency allowing a versatile engineering. The variety of states that can be produced is illustrated using the Joint Spectral Amplitude. Two techniques allowing the characterization of the Joint Spectral Intensity have been implemented. The first one is a single photon spectrograph. The second one, based on the stimulation of the down-conversion process showed a dramatic improvement in terms of resolution and integration time. Both techniques allowed the demonstration of the frequency correlation engineering by varying the waist and curvature radius of the pump beam. Examples of more exotic states and a technique to characterize their chronocyclic Wigner function are theoretically investigated. The relationship between time-frequency properties and degree of entanglement in polarization of the biphoton is also explored.
We report the generation and characterization of a frequency anti-correlated entangled biphoton source at the wavelength of 1560nm via a continuous-wave laser pumped spontaneous parametric down-conversion process. The spectra of the signal and idler photons are measured to have their center wavelength being 1559.7nm and 1559.8nm while their 3-dB bandwidths being 3.2nm and 3.15nm respectively. The joint spectrum of the photon pair is observed to be frequency anti-correlated and have a spectral bandwidth of 0.5nm. According to the ratio of the single-photon spectral bandwidth to the joint spectral bandwidth of the photon pairs, the degree of frequency entanglement is quantified to be 6.4. By investigating the relative overlap between the achieved two-photon spectral intensity function and its transpose, the spectral indisinguishablity of the photon pairs is expected to be 90%. Based on a HOM interferometric coincidence measurement setup, a visibility of 89.8% is demonstrated, which shows a good agreement with the expectation.