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Optics and Spectroscopy

The influence of collective effects on quantum fluctuations of laser radiation

A. A. Kurbatov, Е. А. Титов

Published May 1, 2016• 0 citations
Publisher

Abstract

Quantum fluctuations in a laser with two different relaxation times are considered, i.e., transverse (polarization relaxation) and longitudinal (population relaxation) in the case in which the cavity transmission band half-width is much smaller than the transverse width and much larger than the longitudinal one. The lasing frequency detuning from the transition frequency of a two-level system is assumed to be arbitrary in this case, and it is necessary to take into account the contribution of two-particle correlators into the dispersion and laser linewidth. The results are considered as applied to a semiconductor laser.

DOI
10.1134/s0030400x16050179

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Quantum fluctuations in a laser with two different relaxation times are considered, i.e., transverse (polarization relaxation) and longitudinal (population relaxation) in the case in which the cavity transmission band half-width is much smaller than the transverse width and much larger than the longitudinal one. The lasing frequency detuning from the transition frequency of a two-level system is assumed to be arbitrary in this case, and it is necessary to take into account the contribution of two-particle correlators into the dispersion and laser linewidth. The results are considered as applied to a semiconductor laser.
A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\ensuremath{\alpha}$ above the threshold and for $\ensuremath{\alpha}\ensuremath{\gg}{\ensuremath{\gamma}}_{c}$; however, now the peak heights (widths) are in the ratio 3x3x3x (23x\frac{2}{3x}3x2​), $x=\frac{[{\ensuremath{\gamma}}_{c}+\frac{({T}_{1}^{\ensuremath{-}1}+{T}_{2}^{\ensuremath{-}1})}{3}]}{[2{\ensuremath{\gamma}}_{c}+{T}_{2}^{\ensuremath{-}1}]}$, where ${\ensuremath{\gamma}}_{c}^{\ensuremath{-}1}$ is the correlation time for laser phase fluctuations. For ${\ensuremath{\gamma}}_{c}\ensuremath{\gg}\ensuremath{\alpha}$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.
Although the resonance fluorescence spectrum of coherent light scattering from a two-level atom has been discussed in many papers, the effects of longitudinal, transverse relaxation and optical pumping have not yet been considered simultaneously in the motion equations. By solving the optical Bloch equations including the longitudinal relaxation time T 1 , transverse relaxation time T 2 and optical pumping parameter Δ 0 , in the case T 2 /T 1 <<1, we obtain the spectrum with dip in the central peak besides the familiar spectrum of three peaks. In addition, we find that the parameter Δ 0 and detuning Δω have influence on the symmetry, height and width of the spectrum of the three peaks.
We present a theoretical and experimental investigation of quantum fluctuations in vertical-cavity surface-emitting lasers (VCSELs) having one longitudinal and transverse linearly polarized mode above threshold. We develop the quantum version of the broadly used four-level spin-flip model to take into account the quantum statistics of the pumping process of the active atoms. Our theory allows for arbitrary pumping statistics varying from Poissonian to regular. We compare experimental results obtained with single-mode VCSELs with predictions of our theory and find very good agreement. We demonstrate that the quantum fluctuations of the subthreshold field component polarized orthogonally to the lasing mode have to be taken into account for adequate description of quantum fluctuations in VCSELs. In particular, we show that when the laser light passes through a polarizer, the two orthogonal polarization components of the light wave after passing through the polarizer can be strongly anticorrelated.
Motivated by recent ``circuit QED'' experiments we study the lasing transition and spectral properties of single-qubit lasers. In the strong coupling, low-temperature regime, quantum fluctuations dominate over thermal noise and strongly influence the linewidth of the laser. When the qubit and the resonator are detuned, amplitude and phase fluctuations of the radiation field are coupled and the phase diffusion model, commonly used to describe conventional lasers, fails. We predict pronounced effects near the lasing transition, with an enhanced linewidth and nonexponential decay of the correlation functions. We cover a wide range of parameters by using two complementary approaches, one based on the Liouville equation in a Fock-state basis, covering arbitrarily strong coupling but limited to low photon numbers, the other based on the coherent-state representation, covering large photon numbers but restricted to weak or intermediate coupling.
Abstract A new approach for analytically solving quantum nonlinear Langevin equations is proposed and applied to calculations of spectra of superradiant lasers where collective effects play an important role. We calculate lasing spectra for arbitrary pump rates and recover well-known results such as the pump dependence of the laser linewidth across the threshold region. We predict new sideband peaks in the spectrum of superradiant lasers with large relaxation oscillations as well as new nonlinear structures in the lasing spectra for weak pump rates. Our approach sheds new light on the importance of population fluctuations in the narrowing of the laser linewidth, in the structure of the lasing spectrum, and in the transition to coherent operation.