Quantum Correlation Between the Junction Voltage Fluctuation and the Photon Number Fluctuation in a Semiconductor Laser

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 v ^ n and the external field amplitude fluctuation Δ 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 C v r = 〈 ( v ^ n Δ r ^ † ) s y m 〉 / ( 〈 v ^ n 2 〉 〈 Δ r ^ 2 〉 ) 1 / 2 . At the pump rate required to produce a beam at the standard quantum limit (SQL), C vr is − 1 / 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 ± g r Δ r = ( 〈 v ^ n ± g r Δ r ^ 〉 2 ) 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 Δ r was less than ( 〈 v ^ n 2 〉 + g r 2 〈 Δ r ^ 2 〉 ) . This is indicative of a quantum correlation, since the laser amplitude noise was already below the SQL. Furthermore S v n + g r Δ r was less than g r 2 S Δ 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.