Multiphoton Effects Enhanced due to Ultrafast Photon-Number Fluctuations

The rate of an $n$-photon effect generally scales as the $n$th order autocorrelation function of the incident light, which is high for light with strong photon-number fluctuations. Therefore, “noisy” light sources are much more efficient for multiphoton effects than coherent sources with the same mean power, pulse duration, and repetition rate. Here we generate optical harmonics of the order of 2–4 from a bright squeezed vacuum, a state of light consisting of only quantum noise with no coherent component. We observe up to 2 orders of magnitude enhancement in the generation of optical harmonics due to ultrafast photon-number fluctuations. This feature is especially important for the nonlinear optics of fragile structures, where the use of a noisy pump can considerably increase the effect without overcoming the damage threshold.

Figure 1

(a) The normalized correlation function determining the enhancement of an $n$-photon effect as a function of $n$ in the case of coherent (black), thermal (red), and BSV (blue) light used as a pump. (b) The experimental setup. The BSV is obtained via high-gain PDC in a BBO crystal and filtered spatially with a slit and spectrally with a $4f$ system containing two diffraction gratings (DG), two lenses, and a slit. After the filtering, a small part of the BSV is tapped off by a beam sampler (BS) for monitoring the mean photon number per pulse and the statistics, and the rest is tightly focused on the surface of a lithium niobate crystal (${\mathrm{LiNbO}}_3$). All optical harmonics are generated without phase matching, filtered from the BSV radiation with short-pass (SP) and bandpass filters and registered by a detector. (c) Measured dependence of the SHG (red), THG (green), and FHG (blue) photon flux on the pump flux with the pump being the BSV (solid squares) and pseudocoherent light (empty circles). The detection and transmission losses are taken into account [30]. Theoretical fits with the quadratic, cubic, and quartic functions (lines) show the correct power dependence for each harmonic.

Figure 2

SHG (a), THG (b), and FHG (c) statistical efficiencies ${\xi }^{(n)}$ (points) as well as the corresponding correlation functions (solid lines) measured versus the BSV wavelength. For comparison, the expected efficiencies for coherent light are shown by dashed lines.

Figure 3

Statistical efficiencies ${\xi }^{(n)}$ of SHG (left), THG (middle), and FHG (right) from a broadband BSV show linear dependences on the corresponding correlation functions, measured with narrow-band filtering. The correlation functions are varied by changing the orientation of the BBO crystal and hence the efficiency of BSV generation in the same crystal. Low values of the correlation functions are obtained with the BSV generated efficiently, so that the second-harmonic generation in BBO reduces the photon-number fluctuations. In the opposite case, with inefficient BSV generation, its superbunched statistics is almost perfectly preserved, and the correlation functions are high.

Figure 4

Measured second-order autocorrelation functions $g_{n\omega }^{(2)}$ for the harmonics generated from a superbunched (solid circles) and a thermal (empty circles) BSV show extremely high fluctuations of the harmonic radiation, which increase with the number of the harmonic. The theoretical values are shown by solid and shaded color bars, respectively.