Chirped Biphotons and their Compression in Optical Fibers

Abstract

We show that broadband biphoton wavepackets produced via Spontaneous Parametric DownConversion (SPDC) in crystals with linearly aperiodic poling can be easily compressed in time using the effect of group-velocity dispersion in optical fibres. This result could foster important developments in quantum metrology and lithography.PACS numbers: 42.50. Dv, 03.67.Hk, 42.62.Eh One of the central problems in quantum optics is generation of nonclassical light with given spectral and spatiotemporal properties. In particular, for the needs of quantum metrology and quantum lithography it is important to obtain two-photon wavepackets with small correlation times. Such wavepackets should naturally manifest a broad frequency spectrum. Several ideas have been put forward in this direction, all based on two-photon states produced via Spontaneous Parametric Down-Conversion (SPDC). Among them, one can mention prisms or diffraction gratings introducing a frequency chirp [1], SPDC in aperiodically poled crystals [2,3,4], and SPDC in crystals with temperature gradients [5]. However, a broad spectrum of two-photon light does not necessarily imply small correlation times, although the inverse is true [6,7,8]. This is similar to the fact that a broadband pulse does not have to be short in time, although the spectrum of a short pulse is always broad. The spectrum broadening introduced in Refs [1, 4, 5] is in fact inhomogeneous; as a result, the two-photon spectral amplitude in all these cases has a phase depending nonlinearly on the frequency. This phase (a frequency chirp [9]) makes two-photon wavepackets not Fourier transformlimited. Therefore, they are not short in time despite their broad frequency spectrum. As it was mentioned in Ref. [3], time compression of such two-photon wavepackets requires compensation for their frequency chirp. At the same time, the way to eliminate the chirp was not specified.In this paper we show that, under certain conditions, biphoton wavepackets can be made nearly Fourier transform-limited and hence compressed by injecting one of the photons of a pair in a standard optical fibre and exploiting the effect of group-velocity dispersion (GVD). No specially engineered fibres (for instance, with negative GVD) are necessary. This suggests an easy way of achieving extremely short correlation times for twophoton light.Consider generation of two-photon light via spontaneous parametric down-conversion (SPDC) from a cw pump in an aperiodically poled crystal. From the viewpoint of applications and for simplifying the calculation, it is convenient to assume that signal and idler photons are distinguishable, due to either frequency nondegenerate or type-II phase matching. Below, we consider phase matching to be type-II, collinear, and frequency degenerate, with idler (extraordinary) and signal (ordinary) radiations centered at frequency ω 0 . The two-photon state can be written aswhere |ω i(s) denotes the idler (signal) photon state with frequency ω. The two-photon spectral amplitude (TPSA) F (Ω) determines all spect...

Biphoton compression in a standard optical fiber: Exact numerical calculation

“…No frequency expansion of the wavevector is involved, in contrast to Ref. [15] where the analysis was performed analytically and only up to second-order terms in frequency. Fig.…”

“…[15] it was shown that, in some specific cases, this can be achieved by passing one of the two photon through a normal-dispersion medium, for example a standard optical fiber. This result opens a perspective of a real implementation of the method suggested in Ref.…”

“…In [15] it was shown that within the second-order frequency series expansion of φ(ω s , ω p − ω s ), perfect temporal compression of G (2) meas (τ ) can be achieved with normal dispersive media. Let us now discuss the effect of higher-order terms in the expansion on the width of the compressed G meas (τ ) at the output of the crystal, with no dispersive medium inserted, while the right-hand part illustrates the effect of a 1.06 m long fiber inserted into the SPDC signal channel.…”

“…[9] it was mentioned that time compression of such two-photon wavepackets requires compensation for their frequency chirp, although the way to eliminate the chirp was not specified. Recently we have demonstrated [15] that broadband biphoton wave packets produced via SPDC in APPC can be compressed in time by using group-velocity dispersion (GVD) in standard optical fiber. A Fourier limited compression was obtained in [15] via an analytical calculation within the approximation of large difference in the group velocities of the two SPDC photons and neglecting third-order GVD of the fiber.…”

“…Recently we have demonstrated [15] that broadband biphoton wave packets produced via SPDC in APPC can be compressed in time by using group-velocity dispersion (GVD) in standard optical fiber. A Fourier limited compression was obtained in [15] via an analytical calculation within the approximation of large difference in the group velocities of the two SPDC photons and neglecting third-order GVD of the fiber. Furthermore, we have given an example of a complete numerical calculation demonstrating that higher orders do not change this result.…”