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Physical Review A

Quantum measurement of the photon number via the junction voltage in a semiconductor laser

Wayne H. Richardson, Y. Yamamoto

Published Dec 1, 1991• 14 citations
Publisher

Abstract

The quantum correlation between photon number and junction-voltage fluctuations in a constant-current-driven semiconductor laser is theoretically predicted and experimentally demonstrated. An external electrical circuit has the two functions of pumping to compensate for cavity loss and measuring the photon number. The photon-number noise can be reduced to below the standard quantum limit and even to near that of a number state by referring to the junction-voltage measurements. Phase diffusion incorporates the inherent back action noise of such a measurement process. The number-phase uncertainty principle is conserved between the measurement-induced sub-Poissonian photon-number noise and the Schawlow-Townes phase-diffusion noise.

DOI
10.1103/physreva.44.7702

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Science•Mar 6, 1992•65 citations
The quantum correlation between photon number and junction-voltage fluctuations in a constant-current-driven semiconductor laser is theoretically predicted and experimentally demonstrated. An external electrical circuit has the two functions of pumping to compensate for cavity loss and measuring the photon number. The photon-number noise can be reduced to below the standard quantum limit and even to near that of a number state by referring to the junction-voltage measurements. Phase diffusion incorporates the inherent back action noise of such a measurement process. The number-phase uncertainty principle is conserved between the measurement-induced sub-Poissonian photon-number noise and the Schawlow-Townes phase-diffusion noise.
The photon-number fluctuation of the external field from a semiconductor laser---which was reduced to below the standard quantum limit---is shown to be correlated with the measured junction-voltage noise. The spectral density of the sum of the photon-number fluctuation and junction-voltage fluctuation falls below the squeezed photon-number fluctuation. This confirms the theoretical predictions that this correlation, which originates in the dipole interaction between the internal field and electron-hole pairs, extends into the quantum regime.
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.
The quantum correlation between junction voltage fluctuations1/frequency fluctuations2 and the intensity fluctuations of a semiconductor laser may be used to reduce the intensity noise. Here we address squeezed-state generation discussing both fundamental and practical limitations on noise reduction in conventional semiconductor lasers and microcavity lasers. In conventional semiconductor lasers, starting with intensity noise at the standard quantum limit, ideally a 3-dB amplitude squeezing is possible. This fundamental limit is set by spontaneous emission noise. Another fundamental limit is that noise reduction beyond the level set by optical losses and pump noise is not possible. It is also shown that the number-phase uncertainty in some conditions can reach the ultimate limit set by Heisenberg’s uncertainty principle. These conditions are clarified and a comparison made between junction voltage and frequency noise feedforward. Feedforward schemes realizing intensity noise reduction are discussed.
A new scheme for generating an amplitude-squeezed state is proposed. The photon-flux fluctuation of a semiconductor-laser output wave is measured with a quantum nondemolition (QND) detector, and is negatively fed back to the laser pumping current. The operator Langevin equations are derived by combining the quantum-mechanical analyses on the laser internal-external field fluctuations, the quantum nondemolition detector based on an optical Kerr effect, and a negative-feedback circuit. The output wave features a reduced photon number noise below the standard quantum limit, 〈(\ensuremath{\Delta}n^)2{)}^{2})2〉^〉, and an enhanced phase noise above that, 〈(\ensuremath{\Delta}\ensuremath{\psi}^)2{)}^{2})2〉>(1/4)〈n^${〉}^{\mathrm{\ensuremath{-}}1}$, while the minimum uncertainty product is still preserved. The observed photoelectron statistics in a negative-feedback GaAs laser diode using a conventional p-i-n photodiode (not a QND detector) are shown to exhibit sub-Poissonian statistics with the variance 〈(\ensuremath{\Delta}n^)2{)}^{2})2〉apeq20.26〈n^〉. The measured photocurrent fluctuation spectral density is also indicated to be below the standard quantum limit by a factor of 0.2 (=-7 dB). The experimental results also confirm that such amplitude squeezing is only observed inside the feedback loop and cannot be extracted from the loop unless a quantum nondemolition detector is used.
Both the junction voltage fluctuations and the frequency fluctuations of a semiconductor laser are highly correlated with its intensity noise. We analyze three schemes where the correlation information is used to reduce the intensity noise. In conventional semiconductor lasers, starting with intensity noise at the standard quantum limit, ideally 3-dB amplitude squeezing is possible. The influence of nonideal factors such as parasitics for junction voltage feedforward and the linewidth floor for frequency noise feedforward are discussed. It is shown that under certain conditions the number-phase uncertainty can reach the ultimate limit set by Heisenberg's uncertainty principle. These conditions are clarified, and examples are given for both conventional semiconductor lasers and microcavity lasers.
Electromagnetic fields, with the noise on one quadrature component reduced to below the quantum mechanical zero-point fluctuation level and the noise on the other quadrature component enhanced to above it, are currently of great interest in quantum optics because of their potential applications to various precision measurements. Such squeezed states of light are usually produced by imposing nonlinear unitary evolution on coherent (or vacuum) states. On the other hand, squeezed states with reduced photon number noise and enhanced phase noise are generated directly by a constant current-driven semiconductor laser. This is the simplest scheme for the generation of nonclassical light, and so far it has yielded the largest quantum noise reduction. The mutual coupling between a lasing junction and an external electrical circuit provides opportunities for exploring the macroscopic and microscopic quantum effects in open systems.