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Laser Physics

Dynamic spectral filter

Anatoly Viktorovich Masalov

Published Aug 1, 2009• 0 citations
Publisher

Abstract

Results of the discussions with N.B. Delone on the perturbation of the atomic transition by a strong nonresonant noise field of electromagnetic radiation are presented. Four examples that are conceptually and mathematically close to each other are considered: spectrum of radiation with the diffusion of phase, spectrum of radiation with the sine phase modulation, atomic absorption lineshape in the presence of a strong nonresonant noise field, and the spectral filter whose maximum-transmission frequency is varied with time (dynamic spectral filter). For all of the examples, the counterintuitive scenario of the formation of the resulting spectrum is demonstrated: the instantaneous radiation frequencies (or the instantaneous positions of the perturbed level) are not summarized in the output spectrum. The analysis is based on the limitation that is typical of the Fourier transform and lies in the fact that significant time is needed for the observation of small frequency shifts.

DOI
10.1134/s1054660x0916004x

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Results of the discussions with N.B. Delone on the perturbation of the atomic transition by a strong nonresonant noise field of electromagnetic radiation are presented. Four examples that are conceptually and mathematically close to each other are considered: spectrum of radiation with the diffusion of phase, spectrum of radiation with the sine phase modulation, atomic absorption lineshape in the presence of a strong nonresonant noise field, and the spectral filter whose maximum-transmission frequency is varied with time (dynamic spectral filter). For all of the examples, the counterintuitive scenario of the formation of the resulting spectrum is demonstrated: the instantaneous radiation frequencies (or the instantaneous positions of the perturbed level) are not summarized in the output spectrum. The analysis is based on the limitation that is typical of the Fourier transform and lies in the fact that significant time is needed for the observation of small frequency shifts.
We have seen in Section 1.2 that a transition between two discrete levels | i 〉 and | k 〉 is possible when the system is submitted to a perturbation which has a non-zero Fourier component close to the Bohr frequency ω 0 = ( E k − E i )/ħ of the transition. This is the case when the perturbation Ĥ 1 ( t ) is sinusoidal, of the form Ĥ 1 ( t ) = Ŵ cos(ω t + φ), and oscillates at a frequency ω close to ω 0 . But in many real physical situations, the perturbation is not perfectly mastered: it is a pure sine function only for times shorter than a limit, called the coherence time . At longer times, the oscillating perturbation has a phase and an amplitude that vary randomly. This is, for example, the case when the perturbation is due to an incident electromagnetic wave produced by a thermal lamp, in which the thermal fluctuations induce random variations of the amplitude and phase of the wave. As the perturbation is no longer a pure sinusoidal wave, its Fourier spectrum is no longer a Dirac delta function. It has some finite width around a mean frequency. For this reason a random perturbation is also called a ‘broadband’ perturbation. We shall determine in this complement the temporal evolution of the quantum system submitted to such a random perturbation. We shall see that the transition probability between two discrete levels is proportional to T for small interaction time T , and has an exponential behaviour at long times, a result which is very similar to that obtained for a transition between a discrete level and a continuum.
The problems concerning the influence of spectral filters on the quantum properties of light have recently attracted great attention in connection with quantum cryptography and quantum data transmission. In this paper, we consider the influence of a spectral filter on the second-order coherence function of a field of a resonator mode and a two-level atom in the framework of the Jaynes-Cummings model. Since the Heisenberg equations for the operators of the field of the resonator mode and the atom can be solved exactly, it is possible to obtain exact analytical Fourier transformation of the dynamics of operators of the resonator mode and two-level atom. We demonstrate that the second-order coherence function of the resonator mode and the two-level atom is equal to zero for all possible frequencies in the spectrum of operator oscillations. We find the interbeam second-order coherence function between different frequencies of the Fourier spectrum and show that in the limit of a large number of quanta, it can take the values in the range from zero to two. Thus, non-classical correlations are formed between certain frequencies in the Fourier spectrum of emitted light. We demonstrate that in the limit of a large number of quanta in the resonator mode, when the filter sums up the frequencies near the resonator eigenfrequency, the second-order coherence function of the field of the resonator mode is not affected by the interaction with the two-level atom.
Nonlinear phenomena occurring during interaction between an atom and a strong rf field of resonant or nonresonant frequency are reviewed. The account is given in both semiclassical and consistently quantummechanical languages. The concept of an atom "dressed by the radiation field" in which not only the optical-frequency field but also the radio-frequency field is quantized is presented in detail. The results are summarized of theoretical and experimental studies of multiphoton transitions, radiative shifts of normal magnetic resonance lines, parametric resonance, and coherent resonances under the conditions of optical pumping. The influence of nonresonance rf fields on magnetic properties and the rate of magnetic relaxation of atoms is discussed.
The scattering of radiation in the presence of collisions can be described quantum-mechanically in terms of essentially two processes. The first may be thought of as an absorption to the excited state followed subsequently (after propagating in the excited state) by emission. This gives rise to radiation redistributed about the transition frequency. The effects of m-degeneracy are particularly interesting for this first process. As an example a case is considered in which the incident frequency is in the quasi-static line wing, while the scattered frequency is close to the line center. It is found that under these circumstances the dominant contribution from this process in the scattered spectrum is obtained for an absorption of the incident frequency taking place during a strong (close) collision and reemission of the scattered frequency when the atom is essentially unperturbed
We have investigated theoretically the possibility of employing noisy laser fields for spectroscopic purposes. The basis for this spectroscopy is a modification of the statistic of the fluctuations caused by the nonlinear interaction. All atomic resonances within the range of several bandwidths can be observed in the power spectrum, even in case of large inhomogeneous broadening. We have derived analytical, nonperturbative results for a real Gaussian, a complex Gaussian, and a phase-diffusing field. The mean transmitted intensity and its variance as well as the power spectrum have been evaluated in the limit of weak absorption for two-level systems. Without modification, we can apply our results also to other transition schemes. As an example, the power spectrum of the D2{\mathit{D}}_{2}D2​ transition of 133Cs^{133}\mathrm{Cs}133Cs driven by a phase-diffusing field is calculated. For this four-level system we find qualitative agreement with experimental results by Yabuzaki et al. [Phys. Rev. Lett. 67, 2453 (1991)].