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Physical Review A

Two-photon processes in the presence of phase- or frequency-telegraph noise: Experimental study

R. Boscaino, Rosario N. Mantegna

Published Jul 1, 1989• 11 citations
Publisher

Abstract

Stochastic fields with non-Gaussian Markovian phase or frequency jumplike noise are produced at microwave frequency and used to induce two-photon (TP) processes in a S=(1/2 spin system. The influence of the field statistics on the TP-induced second-order response is experimentally investigated in a system with very short relaxation times, in its stationary state and in the weak-field limit. In the case of frequency-telegraph noise the experimental spectra of the nonlinear response are found to reproduce roughly the spectral profiles of the corresponding driving fields but with a larger width. When the telegraph noise modulates the phase of the field, the relationship between input and output spectra depends on the phase-jump amplitude ${\ensuremath{\varphi}}_{0}$. For ${\ensuremath{\varphi}}_{0}$=\ensuremath{\pi}/4 the spectrum of the response is much broader than the input one, whereas it is much narrower for ${\ensuremath{\varphi}}_{0}$=\ensuremath{\pi}/2. The experimental results are interpreted using the calculation of the TP-induced second-order response worked out in the preceding paper [Boscaino and Mantegna, Phys. Rev. A 40, 5 (1989)].

DOI
10.1103/physreva.40.13

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Stochastic fields with non-Gaussian Markovian phase or frequency jumplike noise are produced at microwave frequency and used to induce two-photon (TP) processes in a S=(1/2 spin system. The influence of the field statistics on the TP-induced second-order response is experimentally investigated in a system with very short relaxation times, in its stationary state and in the weak-field limit. In the case of frequency-telegraph noise the experimental spectra of the nonlinear response are found to reproduce roughly the spectral profiles of the corresponding driving fields but with a larger width. When the telegraph noise modulates the phase of the field, the relationship between input and output spectra depends on the phase-jump amplitude \ensuremathφ0{\ensuremath{\varphi}}_{0}\ensuremathφ0​. For \ensuremathφ0{\ensuremath{\varphi}}_{0}\ensuremathφ0​=\ensuremath{\pi}/4 the spectrum of the response is much broader than the input one, whereas it is much narrower for \ensuremathφ0{\ensuremath{\varphi}}_{0}\ensuremathφ0​=\ensuremath{\pi}/2. The experimental results are interpreted using the calculation of the TP-induced second-order response worked out in the preceding paper [Boscaino and Mantegna, Phys. Rev. A 40, 5 (1989)].
Two-photon processes induced by a stochastic field, frequency-modulated by a Gaussian noise, are experimentally investigated in a S=12S=\frac{1}{2}S=21​ spin system at microwave frequency. The shape and the width of the power spectra of the second-order two-photon-induced response of the spin system are measured for wide ranges of the rms amplitude and of the correlation time of the frequency fluctuations of the driving field.
A phase-diffusion stochastic field with frequency fluctuations obeying Gaussian Markovian statistics is produced at microwave frequency and used to drive a two-level spin system. The system is tuned to the two-photon (TP) resonance and its TP-induced second-order response is measured as a function of the characteristic parameters of the frequency noise. It is found that, when the statistics of the driving field are varied from the fast- to the slow-modulation limit, the power spectrum of the nonlinear response of the system varies in a continuous way from a Lorentzian form toward a Gaussian one, and its relative width (normalized to the input spectral width) varies from 4.0\ifmmode\pm\else\textpm\fi{}0.4 to 2.0\ifmmode\pm\else\textpm\fi{}0.2. The experimental results are interpreted on the basis of a semiclassical calculation which takes into account the stochastic nature of the field. The effect of the filter action of the cavity modes is discussed. The relationship with previous experiments and theoretical calculations of TP absorption is also examined.
The nutational regime induced by a stochastic field with phase telegraph noise is experimentally investigated in a two-level system at microwave frequency. Regular oscillations are observed in the average transient response of the system with an effective Rabi frequency whose value depends both on the jump amplitude and on the mean dwell time of the phase noise. Motional-narrowing, weak-damping, and strong-damping regimes are observed on varying the dwell time and the jump amplitude. The experimental results are in fair agreement with theoretical predictions.
We report on an experimental study of strong radiation–matter interactions between a phase-telegraph field and an inhomogeneous S = 1/2 two-level system. The phase-telegraph field is obtained by performing a stochastic phase modulation to control the statistical properties of the radiation field. We detect the average time evolution of the system, and we study the dependence of the effective Rabi frequency on the parameters characterizing the stochastic evolution of the radiation field. Experimental results are in good agreement with a theoretical picture of this process given by Eberly et al. [ Phys. Rev. A30, 2381 ( 1984)].
Measurements of two-photon absorption spectra have been made for the case where the exciting laser has a random-telegraph phase. The resulting spectral shapes are compared to theoretical predictions and to previous data taken with a phase-diffusing laser field [Elliott et al., Phys. Rev. A 32, 887 (1985)]. A striking dependence of the absorption spectrum on the second-order coherence of the field was observed. Using the theory for the propagation of second-order spatial coherence, we draw an analogy between diffraction and two-photon absorption which we use to interpret the two-photon absorption spectra.
Three methods are given for imposing random telegraph phase or frequency noise on a stabilized cw laser thus giving explicit control of the coherence of the laser field. In the case of phase noise, the resulting laser spectrum consists of a carrier part with nearly Lorentzian shaped noise sidebands which have full-width at half maximum up to 14 MHz. Complete suppression of the carrier is possible if the phase is made to jump by π radians. Frequency telegraph noise results in a laser power spectrum that can be single or double peaked, depending on the relative sizes of the average dwell time and the frequency jump. The laser field has been produced for studies of noise in nonlinear spectroscopic interactions. Measurements of the resulting laser spectra are presented. As an example of the application of such a noisy laser, some results from studies of the dependence of two photon absorption on higher-order optical coherences are given.