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arXiv:1106.0509 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Universal signatures of lasing in the strong coupling regime

Fabrice P. Laussy, Elena del Valle, Jonathan James Finley

Published Feb 3, 2012• 6 citations
arXivHTMLPDF

Abstract

An almost ideal thresholdless laser can be realized in the strong-coupling regime of the light-matter interaction, with Poissonian fluctuations of the field at all pumping powers. Here, we show that this ideal scenario is thwarted by quantum nonlinearities when crossing from the linear to the stimulated emission regime. A universal jump in the normalized intensity correlation function is predicted to occur, the measurement of which could be used to establish a standard fingerprint of the onset of lasing in the strong coupling regime.

DOI
10.1117/12.912732

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An almost ideal thresholdless laser can be realized in the strong-coupling regime of the light-matter interaction, with Poissonian fluctuations of the field at all pumping powers. Here, we show that this ideal scenario is thwarted by quantum nonlinearities when crossing from the linear to the stimulated emission regime. A universal jump in the normalized intensity correlation function is predicted to occur, the measurement of which could be used to establish a standard fingerprint of the onset of lasing in the strong coupling regime.
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The regime of strong light-matter coupling is typically associated with weak excitation. With current realizations of cavity-QED systems, strong coupling may persevere even at elevated excitation levels sufficient to cross the threshold to lasing. In the presence of stimulated emission, the vacuum-Rabi doublet in the emission spectrum is modified and the established criterion for strong coupling no longer applies. We provide a generalized criterion for strong coupling and the corresponding emission spectrum, which includes the influence of higher Jaynes-Cummings states. The applicability is demonstrated in a theory-experiment comparison of a few-emitter quantum-dot--micropillar laser as a particular realization of the driven dissipative Jaynes-Cummings model. Furthermore, we address the question if and for which parameters true single-emitter lasing can be achieved and provide evidence for the coexistence of strong coupling and lasing in our system in the presence of background emitter contributions.
We consider what happens to a laser when all incoherent processes are reduced to the minimum needed to keep emission irreversible. Specifically, we investigate the case where the vacuum Rabi frequency is larger than any decay rate in the laser except for the atomic polarization decay rate. Using a fully quantum description, we show that this laser can be made to go continuously from a regime with a well-defined threshold to the ideal thresholdless regime, where the photon statistics is always Poissonian even for arbitrarily small pump powers. We suggest how a proof-of-principles experiment can be realized in the microwave domain.
Starting from a fully quantized Hamiltonian for an ensemble of identical emitters coupled to the modes of an optical cavity, we determine analytically regimes of thermal, collective anti-bunching and laser emission that depend explicitly on the number of emitters. The lasing regime is reached for a number of emitters above a critical number-which depends on the light-matter coupling, detuning, and the dissipation rates-via a universal transition from thermal emission to collective anti-bunching to lasing as the pump increases. Cases where the second order intensity correlation fails to predict laser action are also presented.
In ultrastrong light-matter coupling regime, it is found theoretically that lasing accompanies odd-order harmonics of radiation field both inside and outside the cavity and even-order harmonics of atomic population. This qualitative difference from the normal laser is generally obtained independent of whether we choose the Coulomb gauge or the electric-dipole one, although quantitative behaviors strongly depend on the gauge choice due to the two-level and single-mode approximations used in our calculation. The lasing also shows a bistability for strong enough light-matter coupling and low enough cavity loss.
It is shown that, introducing quantum-mechanical degrees of freedom for the pump field, one can model optical-pumping processes of a laser with sub-Poissonian statistics. For a class of pump models containing regular pumping at one end of the range and Poissonian pumping at the other, the exact stationary moments for the pump-field-averaged laser field are calculated in the strong-saturation limit of the lasing transition. It is demonstrated that, in a photodetection experiment of the laser output, complete noise suppression in the photocurrent fluctuation spectrum is, at least in principle, achievable. Finally, an approximate Fokker-Planck equation for photon distribution of the laser field with explicit appearance of the pump-light intensity correlation function in the diffusion term is derived and solved in the stationary limit.