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Physical Review Letters

Generation and Compression of Chirped Biphotons

Steven Sensarn, G. Y. Yin, Stephen E. Harris

Published Jun 22, 2010• 81 citations
Publisher

Abstract

We describe an experiment demonstrating the radarlike technique of "chirp and compress." Chirped biphotons are generated using a quasi-phase-matched nonlinear crystal where the phase-matched frequency varies linearly with position. Sum frequency generation is used to measure the amplitude of the biphoton wave function. As compared to a nonchirped crystal, compression and an increase in summing efficiency of a factor of 5 is observed.

DOI
10.1103/physrevlett.104.253602

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We describe an experiment demonstrating the radarlike technique of "chirp and compress." Chirped biphotons are generated using a quasi-phase-matched nonlinear crystal where the phase-matched frequency varies linearly with position. Sum frequency generation is used to measure the amplitude of the biphoton wave function. As compared to a nonchirped crystal, compression and an increase in summing efficiency of a factor of 5 is observed.
Chirped biphotons generated via spontaneous parametric down-conversion in chirped quasi-phase-matched nonlinear crystals have ultrabroadband frequency spectra, while their correlation times are not ultranarrow, due to the nonlinear frequency dependence of the phase factor. Based on the idea of Fresnel zone lenses, we propose a Fresnel-inspired binary phase-shaping scheme for tailoring broadband biphoton spectra. By applying binary phase masks to the biphoton spectrum, a Fresnel zone lens was produced in the frequency domain, compressing the broadband temporal wave packets of the chirped biphotons to the Fourier-transform limit due to the effective removal of the quadratic phase. Furthermore, biphoton correlation trains can also be generated by properly shaping the biphoton spectrum with this scheme. This provides a method for biphoton compression and shaping, which avoids the length dependence and the impact of higher-order dispersion in a dispersive medium by using the phase compensation method. Our results could prove useful in quantum metrology, lithography, and coding of entangled photons.
Chirped biphotons generated via spontaneous parametric down-conversion in chirped quasi-phase-matched nonlinear crystals have ultrabroadband frequency spectra. However, the presence of quadratic frequency phase factor restricts their applications in quantum metrology and quantum lithography due to simultaneously lengthening the correlation times of biphotons. The key point to improve the temporal correlation of chirped biphotons is how to compensate for or remove the quadratic frequency phase factor. Phase compensation methods have been demonstrated to solve this problem in earlier reports. But the compressed efficiencies of these methods are strongly dependent on the length of the utilized dispersive medium and decreased by the higher-order dispersion of the dispersive medium. In this paper, based on the phase transform of a lens for a light field in spatial domain, we theoretically propose a method of the equivalent removal of the quadratic phase by realizing a Fresnel-zone lens-like modulation on the biphotons spectrum in frequency domain, thereby compressing the correlation time of chirped biphotons to the Fourier-transform limited width. By analogy to the idea of Fresnel wave zone plate, this lens-like modulation can be realized by dividing the biphoton spectrum into Fresnel frequency zones and applying only binary spectral phase (0, ) sequentially to these zones. The theoretical results show that the correlation time width of chirped biphotons can be reduced, and the correlation signal intensity can be increased compared with the original one, by a factor about 100 and 30, respectively. The physical reason is that these Fresnel frequency zones under binary spectral phase modulation will lead to constructive interference at zero delay and destructive interference elsewhere. This method can significantly enhance biphoton time correlation without biphoton signal loss and avoids the limitations of phase compensation methods. Therefore, we can obtain biphotons with both ultra-broad bandwidth and ultra-short correlation times by using our proposed method. The attainable compression efficiency is constrained by the division resolution of the Fresnel frequency zones and the precision of applied binary phase modulations. It should be noted that a constraint condition about crystal length, chirp parameter and the number of frequency zones is summarized in designing the experimental parameters for the desired compression goal. Since binary spectral phase and 0 are easy to obtain and calibrate in practice, we thus believe that our proposed method is feasible to implement experimentally. Moreover, the proposed method can also be generalized to other fields relating to the quadratic phase factor, such as two-photon absorption, second-harmonic generation and chirped pulse compression.
We study the theory of linearly chirped biphoton wave-packets produced in two basic quasi-phase-matching configurations: chirped photonic-like crystals and aperiodically poled crystals. The novelty is that these structures are considered as definite assembles of nonlinear layers that leads to detailed description of spontaneous parametric down-conversion (SPDC) processes through the discrete Gauss sums. We demonstrate that biphoton spectra for chirped photonic crystals involving a small number of layers consist from definite well-resolved spectral lines. We also discuss the forming of broadband spectra of signal (idler) waves in SPDC for both configurations as number of layers increases as well as in dependence of chirping parameters .
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.
The generation of biphoton wave packets with a broad spectrum owing to quasi-phase-matched spontaneous parametric down-conversion in a crystal with an aperiodic poling has been considered. Biphotons at the exit of such a sample are not Fourier limited; i.e., their correlation time is much larger than the inverse width of the spectrum. It has been shown that if the inverse grating vector varies linearly along the sample length, the generated biphoton wave packets can be compressed in time by transmitting two-photon light through an optical fiber.