Properties of bright squeezed vacuum at increasing brightness

Abstract

Bright squeezed vacuum (BSV) is a non-classical macroscopic state of light, which can be generated through high-gain parametric down-conversion or four-wave mixing. Although BSV is an important tool in quantum optics and has a lot of applications, its theoretical description is still not complete. In particular, the existing description in terms of Schmidt modes fails to explain the spectral broadening observed in experiment as the mean number of photons increases. On the other hand, the semi-classical description accounting for the broadening does not allow to decouple the intermodal photon-number correlations. In this work, we present a new generalized theoretical approach to describe the spatial properties of BSV. This approach is based on exchanging the (k, t) and (ω, z) representations and solving a system of integro-differential equations. Our approach predicts correctly the dynamics of the Schmidt modes and the broadening of the spectrum with the increase in the BSV mean photon number due to a stronger pumping. Moreover, the model succesfully describes various properties of a widely used experimental configuration with two crystals and an air gap between them, namely an SU(1,1) interferometer. In particular, it predicts the narrowing of the intensity distribution, the reduction and shift of the side lobes, and the decline in the interference visibility as the mean photon number increases due to stronger pumping. The presented experimental results confirm the validity of the new approach. The model can be easily extended to the case of frequency spectrum, frequency Schmidt modes and other experimental configurations.

Direct temporal mode measurement of photon pairs by stimulated emission

“…(7), it should also work for high gain case where we have different gain coefficients of sinh G k in Eq. (6), except that the mode parameters {r k } in G k = r k G are now dependent of G. In this case, the mode functions {ψ k , ϕ k } also depend on the gain [13][14][15]. To check for quantum correlation between different temporal modes for quantum entanglement and orthogonality, as in Ref.…”

“…(6) are still valid for the two-photon interaction Hamiltonian in Eq. (2) but the mode parameters {r k } in gain parameters G k = r k G as well as the mode functions {ψ k , ϕ k } will depend on the pump parameter G [15].…”

“…At the low gain regime of spontaneous emission, the amplifier operates at near unit gain for all modes so there is basically no difference in gain and the method will not lead to a converged shape. One may want to turn up the pump power to push into the high gain regime but it is known that mode structure in parametric processes changes with the pump power at high gain [14,15]. Thus the method in Ref.…”

Experimental reconstruction of spatial Schmidt modes for a wide-field SU(1,1) interferometer

“…In particular, it can be used to describe twin beams (idler and signal) at the output of high-gain PDC [31]. Although a deeper consideration shows that the shapes of the Schmidt modes change with the parametric gain [32], this effect is small. Accordingly, one can obtain these modes from the decomposition of the so-called two-photon amplitude (TPA), i.e.…”

“…For this reason, we use a fitting function for the covariance as described in Ref. [32]. The fit requires prior knowledge about the shape of the intensity distribution and the nature of the correlations, in general not necessary for the reconstruction of the modes.…”