Ring-shaped spectra of parametric downconversion and entangled photons that never meet

Abstract

We report on the observation of an unusual type of parametric down-conversion. In the regime where collinear degenerate emission is in the anomalous range of group-velocity dispersion, its spectrum is restricted in both angle and wavelength. Detuning from exact collinear-degenerate phasematching leads to a ring shape of the wavelength-angular spectrum, suggesting a new type of spatiotemporal coherence and entanglement of photon pairs. By imposing a phase varying in a specific way in both angle and wavelength, one can obtain an interesting state of an entangled photon pair, with the two photons being never at the same point at the same time.Parametric down-conversion (PDC) is the main source of entangled photon pairs and twin beams. It is also used in optical parametric oscillators as a source of tunable radiation. Its importance for quantum and nonlinear optics can hardly be over-estimated.PDC has a very specific shape of the wavelengthangular spectra. So far, two types of such spectra have been observed. One, corresponding to type-I PDC, has a typical shape of a 'cross' around the degenerate collinear point and becomes similar to two hyperbolas as the crystal orientation changes (Fig. 1). This 'X-shape' of the spectrum is known since the 1970-s and has been many times described in the literature since then [1][2][3]. Importantly, the spectrum is practically unbounded, both in the wavelength and in the angle. In the other wellknown case, the one of type-II PDC [4], the spectra are also almost unbounded but do not have the typical 'X' shape.It has been shown theoretically [5,6] that another type of wavelength-angular spectra exists for type-I PDC. Namely, if the degenerate wavelength coincides with the zero dispersion wavelength (ZDW), the frequency spectrum of collinear type-I PDC is extremely broadband, due to the phase mismatch depending only on higher powers of the frequency mismatch. This fact is used in works on parametric generation and amplification [7][8][9]. Even more interesting is the fact that, for PDC both at ZDW and beyond it (in the anomalous group-velocity dispersion (GVD) range), the wavelength-angular spectrum is bounded. This happens because in the anomalous GVD range, frequency detuning from the degenerate collinear PDC cannot be compensated by the noncollinear emission, as in the normal GVD range. As a result, collinear frequency-degenerate type-I PDC has a 'spot-like' wavelength-angular spectrum [10] and the nondegenerate/noncollinear phasematching leads to a ringshaped spectrum [5,6].Below, we demonstrate the first experimental observation of the ring-type of wavelength-angular spectrum, discuss its most interesting features and suggest some important applications.As a pump, we use the radiation of an amplified Tisapphire laser with the central wavelength 800 nm, pulse duration 1.2 ps, and repetition rate 5 kHz. For the simplicity of detection, we work in the high-gain regime of PDC achieved by using a mean power of 1.1 W. PDC is generated in a 10-mm BBO crystal cut at 19.9• to the optic a...

Multiphoton Effects Enhanced due to Ultrafast Photon-Number Fluctuations

“…The pump is focused into the crystal by a cylindrical lens with a focal length of 700 mm, so that the beam remains unfocused in the plane of the optic axis and the pump walkoff [19] is not pronounced. The crystal is cut at 19.9 • degrees to the optic axis, which provides type-I collinear phase-matching around the degenerate wavelength 1600 nm [20]. After the crystal we cut off the pump by dichroic mirrors and two FEL1200 long-pass filters.…”

“…The spectral filtering is made by a 4f-monochromator, which allows the wavelength to be scanned from 1550 nm to 1650 nm and the bandwidth around the degenerate wavelength 1600 nm to be changed. Although the bandwidth of unfiltered BSV is 400 nm [20], the largest bandwidth allowed by filtering is 75 nm.…”

“…Exceptionally interesting in this connection is bright squeezed vacuum (BSV) produced via high-gain parametric down-conversion (PDC). It can be extremely bright -up to hundreds of mW mean power [19,20] -and has highly fluctuating photon number. In fact, this state has no coherent component and only consists of quantum noise.…”

Broadband pseudothermal states with tunable spectral coherence generated via nonlinear optics

“…High-gain SPDC can be extremely bright for a parametric process-up to hundreds of mW mean power [28,55,56]. This is close to the ∼1 W achievable via non-parametric processes [18], and is bright enough to study interesting non-classical phenomena such as the interplay between spectral and photonnumber coherence.…”

Study of broadband multimode light via non-phase-matched sum frequency generation

“…Our experimental setup is shown in figure 2(top). PDC is produced in a 10 mm BBO crystal with type-I collinear and frequency degenerate phase matching [25]. The pump, propagating at ∼19.9°w.r.t.…”