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International Journal of Modern Physics B

QUANTUM STATE CONTROL IN SEMICONDUCTOR p-n JUNCTIONS (I) — SQUEEZED STATE GENERATION IN SEMICONDUCTOR LASERS

Y. Yamamoto, Shuichiro Inoue, Wayne H. Richardson, S. MACHIDA

Published Apr 1, 1993• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s021797929300250x

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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.
The signal to noise ratio of optical systems is ultimately limited by the shot noise due to the Poissonian statistics of the light field. In recent years there has been a considerable effort to find ways to overcome this limitation by generating non-classical light with sub-shot noise statistics. Several groups have demonstrated non-classical light generation in diode lasers or light emitting diodes, and the amplitude fluctuations have been reduced substantially below the shot noise level [1,2]. However, for phase-sensitive measurements it is necessary to generate the more general quadrature squeezed states. Such quadrature squeezed light can be generated either by second-order or third-order nonlinear processes provided the nonlinear material has very low losses at the optical wavelength. To date, the successful generation schemes for quadrature squeezed light have been restricted to atomic vapours, optical fibres, or second-order nonlinear crystals [3]. The possibility of using the large χ(3) nonlinearities of semiconductors at frequencies below the band gap where the optical absorption is small has been discussed in the literature, but so far there have been no successful experiments [4-6]. In this paper we report measurements on GaAs/Al0.3Ga0.7As multiple quantum well waveguides and bulk ZnS in the wavelength range 750 - 890nm. Although we measure much larger nonlinearities in the quantum wells, the strong two-photon absorption is detrimental for squeezed light generation. However, in the ZnS where the laser frequency is below the two- photon absorption edge, we have succeeded in generating quadrature squeezed light in a semiconductor for the first time. On the basis of our results, we would expect that squeezed light could be generated in many other semiconductor systems provided the photon energy is less than half the band-gap energy.
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.
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.
In this dissertation measurements are presented that extend our understanding of the important noise processes involved in the semiconductor laser generation of photon-number squeezed light. Strong sub-shot noise correlations between photon-number fluctuations on orthogonal polarization axes are observed in the output of a low temperature injection-locked quantum-well laser. Such polarization dependent effects are accounted for by intrinsic correlations generated in the laser gain medium and polarization mixing due to birefringence. Using polarization preserving balanced homodyne detection, up to 4.5 dB of photon-number squeezing is reported, which is within 95% of the expected maximum squeezing based on the device quantum efficiency. The work in this dissertation demonstrates the application of such nonclassical fields to practical measurements that achieve sub-shot noise sensitivity. Coherent nonlinear optical spectroscopy with a photon-number squeezed probe field is used to measure the Urbach tail and exciton resonances in a GaAs/AlGaAs multiple quantum well with sensitivity below the semiclassical shot-noise limit. Direct drive current modulation of an injection-locked room temperature laser results in a nonclassical amplitude modulated field with a signal to noise ratio that exceeds the maximum ratio permitted for a classical source under equivalent modulation conditions.
Summary form only given. Optical phase is conjugate to the photon-number in quantum optics and therefore is important for nonclassical states in which the photon-number operator is reduced below the semiclassical shot noise limit, i.e., for photon-number squeezed states. Nonclassical emission from semiconductor lasers has the added facet that excess phase fluctuations are correlated with fluctuations in the photon-number through the nonlinear gain, and this correlation extends below shot noise. In this experiment, quantum-limited number-phase correlations are examined using an external-cavity semiconductor laser with heavily suppressed (>40 dB) side modes and near ideal single-mode laser characteristics. A feedforward gain matching condition is found to limit the observation of a strong nonclassical effect.