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Physical Review A

Phase-noise influence on coherent transients and hole burning

R. N. Shakhmuratov, Alex Szabo

Published Oct 1, 1998• 7 citations
Publisher

Abstract

Resonant excitation of an inhomogeneously broadened ensemble of two-level atoms (TLA) by a stochastic field with phase noise is theoretically investigated. Free-induction decay (FID), hole burning (HB), and transient nutation (TN) are studied. We consider two kinds of driving fields, one with a free walking phase and another with the phase locked in a limited domain. It is shown that the resonant excitation behavior depends strongly on the noise property. Noise induced by a walking phase gives a simple contribution to the dephasing time, ${T}_{2},$ of two-level atoms whereas phase locking qualitatively changes the laser-atom interaction. In the latter case, it is shown that even when the central part of the driving field spectrum is narrower than homogeneous absorption line of the TLA, the wide, low intensity wings of the spectrum (sidebands produced by the locked phase noise), have a strong effect on the FID, TN, and HB induced by the central, narrow part of the spectrum. The influence of sidebands on photon echoes is also discussed.

DOI
10.1103/physreva.58.3099

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Physical Review A•Oct 1, 1990•16 citations
Resonant excitation of an inhomogeneously broadened ensemble of two-level atoms (TLA) by a stochastic field with phase noise is theoretically investigated. Free-induction decay (FID), hole burning (HB), and transient nutation (TN) are studied. We consider two kinds of driving fields, one with a free walking phase and another with the phase locked in a limited domain. It is shown that the resonant excitation behavior depends strongly on the noise property. Noise induced by a walking phase gives a simple contribution to the dephasing time, T2,{T}_{2},T2​, of two-level atoms whereas phase locking qualitatively changes the laser-atom interaction. In the latter case, it is shown that even when the central part of the driving field spectrum is narrower than homogeneous absorption line of the TLA, the wide, low intensity wings of the spectrum (sidebands produced by the locked phase noise), have a strong effect on the FID, TN, and HB induced by the central, narrow part of the spectrum. The influence of sidebands on photon echoes is also discussed.
Steady-state free induction decay (FID), hole burning (HB) and transient nutations (TN) decay are investigated in ensemble of two-level particles with inhomogeneously broadened spectrum. The influence of x- and y-noise components induced by the coherent field exciting the resonant transition is considered. It is shown that 'longitudinal' (x) and 'transverse' (y) noises give the contribution to both T1 and T2 relaxation processes. This effect accelerates TN decay and changes the saturation broadening seen in HB and FID. It is found that when field-noise contributions to 1/T2 and 1/T1 relaxation rates are dominant and equal to each other, the Bloch's saturation is changed to Redfield's saturation. Comparison with experimentally observed FID and TN in nearly ideal spin system (color centers in quartz and silica) is discussed.
Free induction decay and transient nutations are investigated in a system of two-level particles with an inhomogeneously broadened spectrum. The influence of the x (real) and y (imaginary) parts of the complex amplitude of the noise, induced by the driving field in the sample, is considered. It is shown that both noises affect T1{T}_{1}T1​ and T2{T}_{2}T2​ relaxation processes. When field-noise contributions to 1/T2{1/T}_{2}1/T2​ and 1/T1{1/T}_{1}1/T1​ relaxation rates are dominant and equal to each other, Bloch's saturation is changed to Redfield's saturation. This effect also accelerates transient nutation decay. Comparison with experimentally observed free induction decay and transient nutation in color centers in quartz is discussed.
We demonstrate the possibility of quenching the effects of noisy lasers by intense coherent fields. For this purpose, we study the spectrum of resonance fluorescence from two-level atoms irradiated by bichromatic fields, where one field is coherent and the other stochastic. The spectrum is seen to be very sensitive to the frequencies of the two fields. In particular, we find a dramatic narrowing of the Rabi sidebands in the spectrum when the fluctuating field is tuned to the frequency of the Rabi sideband in the spectrum. We interpret the results in a dressed-state representation, revealing that the atom is sensitive to the fluctuating field, only when that field can induce resonant transitions between the dressed levels. Our calculation of the decay rates of the dressed levels predicts a narrowing of the sidebands by a factor of 4, when the driving field is broadband, while at the same time the central peak in the spectrum is broadened. Surprisingly, we find that there is the possibility of observing very narrow resonances even when noisy lasers interact with the atom.
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.
We have measured the variance in fluorescence intensity and the spectrum of those fluctuations for two-level atoms in a phase-diffusing laser field. We compare our results with recent theoretical predictions that have been extended to include the effects of Doppler broadening and spatial variation of the laser intensity. Our study includes the effects of laser power, bandwidth, and shape (Lorentzian and non-Lorentzian) of the laser spectrum. At lower laser intensities, our measured variances versus detuning are in quantitative agreement with the theoretical predictions. At intensities above saturation, the variance is sensitive to inhomogeneities in the distribution of laser intensity in the interaction region, and only qualitative agreement is achieved. Asymmetries in the variance versus detuning resulting from correlated amplitude and phase noise have been observed. Spectra of the phase-noise-induced fluorescence-intensity fluctuations are shown to contain contributions from transients excited by the phase noise and are more sensitive to artifacts in the noise modulation process than the intensity spectrum of the laser field itself.
A consistent explanation of recent studies by Szabo and Muramoto [Phys. Rev. A 39, 3992 (1989); 38, 5928 (1988)] on the experimental test of modified optical Bloch equations is presented. It is shown that the observed peculiarities of optical transients in solids are connected with the mechanism of relaxation in systems with slow stochastic modulation. A theory of laser-modified relaxation and analysis of free induction decay (FID), hole burning, and rotary echo (RE) in such systems are presented. The universal character of the FID time dependence and field-independent RE decay is predicted.