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Physical Review A

Amplitude squeezing in a semiconductor laser using quantum nondemolition measurement and negative feedback

Y. Yamamoto, N. Imoto, S. Machida

Published May 1, 1986• 205 citations
Publisher

Abstract

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^${)}^{2}$〉^〉, and an enhanced phase noise above that, 〈(\ensuremath{\Delta}\ensuremath{\psi}^${)}^{2}$〉>(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^${)}^{2}$〉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.

DOI
10.1103/physreva.33.3243

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•May 21, 1990•0 citations
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^〉\ensuremath−1{〉}^{\mathrm{\ensuremath{-}}1}〉\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.
Quantum statistical properties of laser light have been extensively studied for the last thirty years by using an operator Langevin equation, a density operator master equation, and a quantum mechanical Fokker-Planck equation. It has been generally accepted among physicists and quantum electronics engineers that an ideal laser operating at far above the threshold generates a coherent state of light. Various experimental facts such as the Poissonian photoelectron statistics, the shot noise limited photocurrent fluctuations, and the Gaussian distributions of optical homodyne detector output seem to support this. However, recent careful studies on a semiconductor laser have revealed that a semiconductor laser does not necessarily produce a coherent state of light, but generates a number-phase squeezed state, in which the photon-number noise is smaller than the standard quantum limit (shot noise limit or Poisson limit). This paper reviews the theoretical and experimental aspects of number-phase squeezed state generation by a semiconductor laser.
If the idler photon flux is continuously measured in a photon-counting detector and the photocurrent fluctuations are fed back to control the pump intensity, the output signal state will be an amplitude-squeezed state (near-number state) at low frequencies and high feedback loop gain. Electromagnetic field in number-phase minimum-uncertainty states (amplitude- squeezed states), and its limit (photon-number states) have potential applications in optical communication, precision measurement, and atomic spectroscopy, and gravitational wave detection. These states have been the focus of considerable attention.
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.
This thesis describes the phase and amplitude noise properties of semiconductor lasers subjected to weak, dispersive optical feedback. In the first half, experiments demonstrating reductions in the laser frequency noise power spectrum and spectral linewidth by several orders of magnitude are presented. Weak optical feedback is applied to the laser by an external cavity containing an atomic vapor. The presence of the vapor adds to the dispersion of the cavity and simultaneously locks the laser to a fixed frequency reference. The role of 1/f frequency noise in limiting the effectiveness of this linewidth reduction technique is investigated and 1/f noise is found to be the dominant contribution to the linewidth under strong optical feedback conditions. An electronic feedback scheme utilizing FM sideband locking is then implemented alongside the optical feedback, and an additional reduction in the low frequency 1/f frequency noise power spectrum by over two orders of magnitude is obtained. With both systems operating simultaneously, the spectral linewidth is narrowed from its free-running value of about 20 MHz to 1.4 kHz. Excellent absolute frequency stability is also achieved. In the second half, the effects of optical feedback on the quantum mechanical amplitude noise properties of the laser are examined. A fully quantum mechanical theory of amplitude and phase noise for a semiconductor laser with weak optical feedback is developed, and the nature and limits of the noise reduction using this technique are established. Particular attention is given to the feedback-induced enhancement of the amplitude squeezing which can be obtained in a pump-suppressed semiconductor laser: an improvement in the squeezing by 3 dB is predicted under moderate pumping. Somewhat larger noise reductions are expected when the laser is operating closer to threshold. Measurements performed on a laser biased close to threshold are then described and a reduction in the low frequency amplitude noise power spectrum by 7 dB is obtained. An experimental investigation of the effects of optical feedback on the amplitude squeezing in a semiconductor laser is then discussed. The low frequency squeezing in a room temperature device is increased from 3% below the standard quantum limit (SQL) under free-running conditions to 19% below the SQL with optimal feedback. The experimental results are found to agree poorly with the single-mode model and a multi-mode model including the effects of asymmetrical cross-mode non-linear gain is developed to explain the discrepancy. Finally, further experimental investigation into the generation of amplitude squeezed light is presented using a commercial laser with no intentional external modifications. Squeezing as large as 29% below the SQL is measured using a balanced homodyne detector with the laser operating near room temperature, corresponding to 41% below the SQL at the output facet of the laser.
Number states of the electromagnetic field are ideal for optical communication and for a variety of high precision measurements. It has been shown theoretically that the light from a semiconductor laser can opproach a number state1. In previous experiments2,3 the observed amplitude noise reduction, below the standard quantum limit, was at most 1.5 db. In this experiment we have been able to reduce the effects of optical feedback, increase the collection efficiency and consequently further elucidate the basic device physics necessary for improvement in the noise reduction. We have observed that the measured squeezing is not limited by the laser overall quantum efficiency but only by the optical output coupling efficiency. An explanation is advanced based on the premise that current division does not introduce Poissonian noise but thermal noise.