Schmidt modes in the angular spectrum of bright squeezed vacuum

We investigate both theoretically and experimentally strong correlations in macroscopic (bright) quantum states of light generated via unseeded parametric down-conversion and four-wave mixing. The states generated this way contain only quantum noise, without a classical component, and are referred to as bright squeezed vacuum (BSV). Their important advantage is the multimode structure, which offers a larger capacity for the encoding of quantum information. For the theoretical description of these states and their correlation features we introduce a generalized fully analytical approach, based on the concept of independent collective (Schmidt) modes and valid for the cases of both weak and strong nonlinear interaction. In experiment, we generate states of macroscopic BSV with up to ${10}^{10}$ photons per mode and examine large photon-number spatial correlations that are found to be very well described by our theoretical approach.

Figure 1

The setup used for the study of BSV angular spectra and a typical 2D image on the CCD camera, with the white dashed line showing (a) the direction of the 1D scan, (b) the measured and calculated intensity angular distributions, and the measured and calculated angular distributions of the photon-number difference variance with the angle ${\theta }_0$ fixed at (c) 3 mrad, (d) 4 mrad, and (e) 5 mrad, shown with arrows. Red solid lines: experiment, black dashed lines: theory.

Figure 2

Normalized angular spectra (red solid line) of PDC for two 1 mm crystals separated by 3 mm measured at the pump powers (a) 29 mW and (b) 73 mW. The corresponding theoretical fits (black dashed lines) are calculated for gain values $G=2.1$ and $G=3.3$.

Figure 3

(a) The Schmidt number $K$ and (b) the width of the covariance versus the parametric gain for the same experimental configuration as in Fig. 2.

Figure 4

Angular spectra of PDC from two crystals with (a), (c) the axes parallel and (b), (d) tilted symmetrically with respect to the pump calculated for the gain values (a), (b) ${10}^{-4}$ and (c), (d) 10. On top, the crystals configurations are shown.

Figure 5

The two-crystal scheme and the basic notation. The angular width of radiation from the first crystal amplified in the second crystal, $\Delta \theta$, is determined by the ratio $\sigma /(2L+d)$, where $\sigma$ characterizes the pump width, $L$ is the crystal length and $d$ the distance between the crystals. The transverse components of the wave vectors are denoted by $\mathbf{q}$.