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Applied Physics Letters

Photon-number squeezing in nano- and microlasers

Mark Anthony Carroll, Giampaolo D’Alessandro, Gian Luca Lippi, Gian‐Luca Oppo, F. Papoff

Published Sep 6, 2021• 16 citations
Publisher

Abstract

Based on theoretical predictions on the appearance of antibunching before the laser threshold at the nano- and microscale, we analyze the amount of photon-number squeezing naturally produced in the laser emission. Up to 3 dB photon number noise reduction is obtained in comparison with the coherent emission, with output power in the range of pW and with negligible effects due to pump fluctuations. The scheme requires a moderately high Q cavity and holds promise for the construction of a simple and effective photon-number squeezed source.

DOI
10.1063/5.0063691

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Based on theoretical predictions on the appearance of antibunching before the laser threshold at the nano- and microscale, we analyze the amount of photon-number squeezing naturally produced in the laser emission. Up to 3 dB photon number noise reduction is obtained in comparison with the coherent emission, with output power in the range of pW and with negligible effects due to pump fluctuations. The scheme requires a moderately high Q cavity and holds promise for the construction of a simple and effective photon-number squeezed source.
We consider the problem of reducing the contributions of pump and spontaneous-emission noise to the output noise of a laser field. We consider two models based on an atomic medium, one analytic, the other involving numerical simulation of a sequence of pump cycles. The predictions of both models are shown to agree. For regular pump excitation the intensity fluctuations of a laser well above threshold may be reduced to zero at the cavity resonance frequency if the ratio of the lifetimes of the upper and lower lasing levels is sufficiently large that spontaneous emission is suppressed. When the atomic lifetimes are comparable, spontaneous emission reduces the amount of noise reduction. For example, for equal atomic lifetimes regular pump excitation will result in a maximum noise reduction in the output field of one-half the shot-noise limit.
The random nature of spontaneous emission leads to unavoidable fluctuations in a laser's output. This is often included through random Langevin forces in laser rate equations, but this approach falls short for nanolasers. In this paper, we show that the laser quantum noise can be quantitatively computed for a very broad class of lasers by starting from simple and intuitive rate equations and merely assuming that the number of photons and excited electrons only takes discrete values. While the approach has seen previous success, we here derive it rigorously from an open quantum system master equation, whereas it was previously introduced only on phenomenological grounds. We further show that in the many-photon limit, the model simplifies to Langevin equations. We perform an extensive comparison of different approaches for computing quantum noise in lasers, identifying the best approach for different system sizes, ranging from nanolasers to macroscopic lasers, and different levels of excitation, i.e., cavity photon number. In particular, we show that below the laser threshold, stochastic fluctuations in the numerical solution to the Langevin equations can drive populations to unphysical negative values, requiring the introduction of population bounds, which in turn skew the noise statistics, leading to inaccuracies. The Laser Markov Chain model, on the other hand, is accurate for all pump values and laser sizes when collective emitter effects are excluded.
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Do Nanolasers Benefit From a High β\betaβ-Factor?
The realization of high-β\betaβ lasers is one of the prime applications of cavity-QED promising ultra-low thresholds, integrability and reduced power consumption in the field of \textit{green photonics}. In such nanolasers spontaneous emission can play a central role even above the threshold. By going beyond rate-equation approaches, we revisit the definition of a laser threshold in terms of the input-output characteristics and the degree of coherence of the emission. We demonstrate that there are new regimes of cavity-QED lasing, realized e.g. in high-QQQ nanolasers with extended gain material, for which the two can differ significantly such that coherence is reached at much higher pump powers than required to observe the thresholdlike intensity jump. Against the common perception, such devices do not benefit from high-β\betaβ factors in terms of power reduction, as a significant amount of stimulated emission is required to quieten the spontaneous emission noise.