Correlation measurement of squeezed light

We study the implementation of a correlation measurement technique for the characterization of squeezed light which is nearly free of electronic noise. With two different sources of squeezed light, we show that the sign of the covariance coefficient, revealed from the time-resolved correlation data, is witnessing the presence of squeezing in the system. Furthermore, we estimate the degree of squeezing using the correlation method and compare it to the standard homodyne measurement scheme. We show that the role of electronic detector noise is minimized using the correlation approach as opposed to homodyning where it often becomes a crucial issue.

Figure 1

Schematic of the setup. The beam from the squeezing setup [optical parametric amplifier (OPA) or Kerr-based squeezing setup (see text)] is interfering with the LO on a 50:50 BS, with a relative phase of $\varphi$. D1 and D2 are the analog photodetectors. The photocurrents of the detectors $i_1$ and $i_2$ are analyzed by the acquisition system.

Figure 2

The scheme of the polarization squeezing setup. The beam from the ${\text{Cr}}^{4+}$:yttrium aluminum garnet (YAG) laser is split on the polarization beam splitter (PBS) after polarization rotation, performed by a half-wave plate (HWP). The birefringence compensator is used to provide a temporal overlap between two orthogonally polarized pulses after propagation through a single-mode polarization maintaining fiber. The interference between the pulses is observed by placing a HWP and a PBS in front of two analog photodetectors. The photocurrents of two detectors are further analyzed by the high-speed digitizer.

Figure 3

The scheme of the OPA based setup. A frequency-doubled Nd:YAG laser (fundamental wavelength of 1064 nm) is used to pump the bowlike-shaped OPA with a 10-mm-long periodically poled Potassium Titanium Oxide Phosphate (PPKTP) crystal. The squeezed vacuum field, generated by the OPA, is mixed with the fundamental wave of the pump laser on a 50:50 BS, used as a LO, and further detected by two analog photodetectors (Det 1 and Det 2). The relative phase between the squeezed vacuum field and the LO is controlled by a mirror on a piezostage (not shown). The photocurrents of two detectors are further analyzed by the high-speed digitizer.

Figure 4

The covariance versus the phase of the LO at two different powers of the LO (open and filled circles) for the OPA-based squeezing setup. Positive covariance values correspond to the measurement of the squeezed quadrature, while the negative covariance values correspond to the measurement of the antisqueezed quadrature.

Figure 5

The covariance at the maximally squeezed (open circles) and the maximally antisqueezed quadrature (filled circles) versus the transmittance of the LO $\left(1-\eta \right)$.

Figure 6

(Color online) Effect of the transmittance of the LO $\left(1-\eta \right)$ on the covariance at (a) the maximally squeezed and (b) the maximally antisqueezed quadrature. In both plots we compare the covariance of a squeezed beam (red) to a calibration measurement using a coherent beam (black).

Figure 7

The degree of squeezing (triangles) and antisqueezing (circles) revealed from the correlation analysis versus the transmittance of the LO $\left(1-\eta \right)$ in the OPA-based squeezing setup. The relatively large error bars are mostly due to statistical fluctuations.

Figure 8

Measurement along the squeezed quadrature in the OPA-based squeezing setup using homodyne detection. The plot shows how the degree of squeezing depends on the transmission of the LO $\left(1-\eta \right)$.

Figure 9

Experimental dependence of the amount of squeezing on the transmission $\left(1-\eta \right)$ (a) for homodyne detection and (b) for the covariance method. The solid lines represent the theoretical prediction without accounting for the EN. The horizontal dashed line at zero marks the border between squeezing and classical excess noises.