Abstract

Quantum correlation between two observables are of fundamental importance in the measurement of quantum mechanical systems. We introduce here a new type of quantum correlation, that between the junction voltage fluctuation ${\widehat{v}}_n$ and the external field amplitude fluctuation $\Delta \widehat{r}$, in a semiconductor laser. A measure of the correlation, which originates in the dipole interaction between the internal field and the electron-hole system, is given by ${\text{C}}_{vr}=〈\left({\widehat{v}}_n\Delta {\widehat{r}}^{†}\right)sym〉/{\left(〈{\widehat{v}}_n{}^{\text{2}}〉〈\Delta {\widehat{r}}^2〉\right)}^{1/2}$. At the pump rate required to produce a beam at the standard quantum limit (SQL), C_vr is $-1/\sqrt{2}$, while classically the correlation is abscent. In the experiment, the amplified a.c junction voltage was combined with the voltage associated with the photocurrent, due to the output field, at a wideband 180° hybrid. Seperate measurement of the spectral densities of the sum and difference of the amplitude $S{v}_n\pm g_r\Delta r=\left({〈{\widehat{v}}_n\pm g_r\Delta \widehat{r}〉}^2\right)$ taken from the respective ports of the hybrid TEE confirm, for the first time, that the correlation is negative. The relative electrical gain is denoted by g_r. Additionally $S{v}_n+g_r\Delta r$ was less than $\left(〈{\widehat{v}}_n{}^2〉+g_r^2〈\Delta {\widehat{r}}^2〉\right)$. This is indicative of a quantum correlation, since the laser amplitude noise was already below the SQL. Furthermore $S{v}_n+g_r\Delta r$ was less than $g_r{}^2{S}_{\Delta r}$, indicating that the correlation already in the quantum regime has crossed the so called second threshold. The optimum measured C_vr was −0.40 ±.02.

© 1990 Optical Society of America