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Physical Review A

Effect of electrical partition noise on squeezing in semiconductor lasers

Y. Yamamoto, H. A. Haus

Published May 1, 1992• 24 citations
Publisher

Abstract

Amplitude fluctuations in the light from a laser and the partition noise attributable to a beam splitter are analyzed using an equivalent-circuit model that incorporates amplitude squeezing. When the energy is not carried by photons but by electrons and also when electrons can be treated as classical particles, the circuit model need not be changed. One simply applies the general circuit model to low frequencies h\ensuremath{\nu}\ensuremath{\ll}${\mathit{k}}_{\mathit{B}}$T. Conversion of an electric current to photon flux, and vice versa, converts classical sub-shot-noise spectra of electric currents into quantum squeezing of photon fluxes, and vice versa. The sub-shot-noise character of electric currents, unlike that of quantum squeezing, is not necessarily destroyed by current loss.

DOI
10.1103/physreva.45.6596

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Journal of the Optical Society of America B•Feb 1, 1997•8 citations
Amplitude fluctuations in the light from a laser and the partition noise attributable to a beam splitter are analyzed using an equivalent-circuit model that incorporates amplitude squeezing. When the energy is not carried by photons but by electrons and also when electrons can be treated as classical particles, the circuit model need not be changed. One simply applies the general circuit model to low frequencies h\ensuremath{\nu}\ensuremath{\ll}kB{\mathit{k}}_{\mathit{B}}kB​T. Conversion of an electric current to photon flux, and vice versa, converts classical sub-shot-noise spectra of electric currents into quantum squeezing of photon fluxes, and vice versa. The sub-shot-noise character of electric currents, unlike that of quantum squeezing, is not necessarily destroyed by current loss.
The pump amplitude fluctuation of a current-driven semiconductor laser can be suppressed to below the ordinary shot-noise level by ``high-impedance suppression.'' As a result of this pump-fluctuation suppression, the output of a current-driven semiconductor laser exhibits amplitude squeezing in the frequency region below the cavity bandwidth. The noise equivalent circuits and the quantum-mechanical Langevin equations are derived and discussed for clarifying the difference between an ordinary laser oscillator with shot-noise-limited pump fluctuation and a constant-current-driven semiconductor laser.
Low-current, high-impedance microelectronic devices can be affected by electric current shot noise more than they are affected by Nyquist noise, even at room temperature. An approach to implementing a sub-shot noise current source for powering such devices is based on direct conversion of amplitude-squeezed light to photocurrent. The phenomenon of optical squeezing allows for the optical measurements below the fundamental shot noise limit, which would be impossible in the domain of classical optics. This becomes possible by affecting the statistical properties of photons in an optical mode, which can be considered as a case of information encoding. Once encoded, the information describing the photon (or any other elementary excitations) statistics can be also transmitted. In fact, it is such information transduction from optics to an electronics circuit, via photoelectric effect, that has allowed the observation of the optical squeezing. It is very difficult, if not technically impossible, to directly measure the statistical distribution of optical photons except at extremely low light level. The photoelectric current, on the other hand, can be easily analyzed using RF spectrum analyzers. Once it was observed that the photocurrent noise generated by a tested light source in question is below the shot noise limit (e.g. produced by a coherent light beam), it was concluded that the light source in question possess the property of amplitude squeezing. The main novelty of this technology is to turn this well-known information transduction approach around. Instead of studying the statistical property of an optical mode by measuring the photoelectron statistics, an amplitude-squeezed light source and a high-efficiency linear photodiode are used to generate photocurrent with sub-Poissonian electron statistics. By powering microelectronic devices with this current source, their performance can be improved, especially their noise parameters. Therefore, a room-temperature sub-shot noise current source can be built that will be beneficial for a very broad range of low-power, low-noise electronic instruments and applications, both cryogenic and room-temperature. Taking advantage of recent demonstrations of the squeezed light sources based on optical micro-disks, this sub-shot noise current source can be made compatible with the size/power requirements specific of the electronic devices it will support.
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]
Fluctuations of the stored energy and the emitted power of a semiconductor laser are derived by classical corpuscular optical theory. The fundamental noise sources are the shot noise associated with a field’s conversion to emitting or absorbing atoms and the mirror loss noise. The latter is taken into account in the form of partition noise forces linked to laser facet reflection. The theory permits the description of the nonclassical states of light, and its results agree with quantum theory. For quiet pumping conditions and for a high-reflection coated Fabry–Perot laser, 50% of internal photon noise suppression is obtained, whereas nonfluctuating optical output is possible for negligible internal loss. The influence of gain suppression on amplitude squeezing is discussed. The effect of attenuation on the propagation of laser fluctuations is studied by use of the concept of optical partition noise. This leads to the invariance of a suitably defined relative intensity noise, which becomes negative for sub-Poissonian photon statistics. The setup for the intensity noise measurement with the balanced detection technique is analyzed by use of optical partition noise.