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arXiv:quant-ph/0002007 · Journal of the Optical Society of America B

Coexistence of thermal noise and squeezing in the intensity fluctuations of small laser diodes

Holger Friedrich Hofmann, Ortwin G. Hess

Published Nov 1, 2000• 14 citations
arXivHTMLPDF

Abstract

The intensity fluctuations of laser light are derived from photon number rate equations. In the limit of short times, the photon statistics for small laser devices such as typical semiconductor laser diodes show thermal characteristics, even above threshold. In the limit of long-time averages represented by the low-frequency component of the noise, the same devices exhibit squeezing. It is shown that squeezing and thermal noise can coexist in the multimode output field of laser diodes. This result implies that the squeezed light generated by regularly pumped semiconductor laser diodes is qualitatively different from single-mode squeezed light. In particular, no entanglement between photons can be generated by use of this type of collective multimode squeezing.

DOI
10.1364/josab.17.001926

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The intensity fluctuations of laser light are derived from photon number rate equations. In the limit of short times, the photon statistics for small laser devices such as typical semiconductor laser diodes show thermal characteristics, even above threshold. In the limit of long-time averages represented by the low-frequency component of the noise, the same devices exhibit squeezing. It is shown that squeezing and thermal noise can coexist in the multimode output field of laser diodes. This result implies that the squeezed light generated by regularly pumped semiconductor laser diodes is qualitatively different from single-mode squeezed light. In particular, no entanglement between photons can be generated by use of this type of collective multimode squeezing.
Theoretical and experimental results of investigations into the quantum noise of multimode laser radiation are considered. The feasibility of generating light with a photon-number-squeezed (sub-Poissonian) photon distribution by a multimode laser with a homogeneously broadened line is analyzed. The conditions of noisy and noiseless (regular) pumping are considered. Photon-number fluctuations of the net laser radiation summed over all generated modes are calculated in the approximation of equidistant equal modes, as are photon-number fluctuations in an individual mode inside and outside the resonator. Output-radiation noise spectra and photon-number fluctuations are calculated for solid-state (neodymium glass, Nd:YAG) and semiconductor lasers. Theoretical results are compared with a number of experimental data obtained for semiconductor lasers in recent years.
We report on the experimental observation of a spectrally asymmetric quantum correlation between the intensities of the main mode and a large number of weakly excited side modes in a pump-noise-suppressed laser diode. The total intensity noise of the laser diode results from a generally incomplete cancellation process between these mode intensities, which influences the generation of amplitude squeezed light. Nonlinear gain due to cross mode gain saturation in the semiconductor lasing medium is found to be the origin of the asymmetric intensity noise distribution between short- and long-wavelength side modes. The experimental results are in good agreement with the predictions of a multimode Langevin rate equation model including asymmetric nonlinear gain saturation.
The mechanism for quantum noise suppression in a multimode laser with a homogeneously broadened line is explained. It is shown that the spontaneous emission noise and pump noise contribution to the photon number fluctuations inside the laser cavity may be suppressed infinitely (up to their complete elimination) when the number of modes participating in the generation is increased. Low-frequency spectral squeezing for an individual output field mode in optimal conditions tends to 100% as the total number of modes increases. The low-frequency spectral squeezing for the total output field may reach 50% below the shot noise level under optimal conditions. The noise suppression of the laser light is explained by the saturation effect of an atomic transition and inter-mode correlation. A multimode laser is an accessible source of light with potentially fully suppressed quantum noise.
A new time-domain model using the quantum formalism of the positive-P distribution is used to investigate squeezing in laser diodes, taking into account longitudinal hole burning and distributed noise sources, under steady-state and large-signal modulation. Simulations indicate that the laser structure determines the lowest achievable intensity noise. With losses present or power escaping from the rear facet, this minimum noise may be much higher than expected from the device quantum efficiency. Squeezing appears more difficult in DFB lasers than in Fabry-Perot lasers in our simulations. Mode-partition noise is removed by low-loss passive DBR sections, and such laser diodes are promising sources with low-intensity noise. Intensity noise in the large-signal dynamic regime is also simulated, showing that intensity-squeezed light output is possible.>
Semiconductor lasers are particularly well suited for the implementation of pump-noise suppression, yielding a reduction of the intensity noise in the laser. In this simple picture, the maximal amount of squeezing is equal to the quantum efficiency. However, experimental results on intensity noise reduction by pump-noise suppression are usually above this limit. This discrepancy suggests that additional noise sources must be involved. Here we successfuly interpret the full noise behavior of a single-mode laser diode far above threshold by considering two excess noise sources: the leakage current fluctuations across the laser and the Petermann excess noise. We have estimated the contribution of each noise source using the results of the correlations between the laser output intensity noise and the voltage fluctuations across the laser diode (light-voltage correlations) and obtained good agreement between our theory and experimental results.
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.