Measuring Photon Antibunching from Continuous Variable Sideband Squeezing

We present a technique for measuring the second-order coherence function $g^{(2)}(\tau )$ of light using a Hanbury Brown–Twiss intensity interferometer modified for homodyne detection. The experiment was performed entirely in the continuous-variable regime at the sideband frequency of a bright carrier field. We used the setup to characterize $g^{(2)}(\tau )$ for thermal and coherent states and investigated its immunity to optical loss. We measured $g^{(2)}(\tau )$ of a displaced-squeezed state and found a best antibunching statistic of $g^{(2)}(0)=0.11\pm 0.18$.

Figure 1

Schematic of the experimental setup. OPA optical parametric amplifier, $\lambda /2$ half-wave plate, PBS polarizing beam splitter, $x:y$ beam splitter with transmission $x$, $\mathrm{H}1/\mathrm{H}2$ homodyne detectors, AM amplitude modulator, $\omega$ function generator, WNG white-noise generator, $\otimes$ mixer, LP low-pass filter.

Figure 2

The $g^{(2)}(0)$ parameter space for a displaced-squeezed state with squeezing $r$ and displacement $\alpha$. Regions exhibiting photon antibunching are marked progressively darker, with contours giving the precise values.

Figure 3

Experimental measurement of $g^{(2)}(\tau )$ with normalized time delay $\tau$ in units of bandwidth $\pi /\Omega =8.3\mu \mathrm{s}$. (a) displaced-squeezed state, (b) coherent state, (c) biased-thermal state, curves are theoretical predictions.

Figure 4

Experimental measurement of $g^{(2)}(0)$ as a function of displacement ${\alpha }_{\mathrm{in}}$. (a) displaced- squeezed state, (b) weak displaced-squeezed state, (c) coherent state, (d) biased-thermal state, curves are theoretical predictions.