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Journal of Physics B Atomic and Molecular Physics

Optical spectrum of strongly coupled dressed atomic states

William Graham Greenwood, Peter R. Fontana

Published Sep 4, 1982• 1 citation
Publisher

Abstract

A strong radio-frequency field couples two excited atomic states which also interact with the virtual radiation field. The radio-frequency field dresses the atomic states and the virtual radiation field causes them to decay spontaneously. The spectrum of the emitted radiation is calculated by Fourier transforming the differential equations for the amplitudes. The solutions are given in terms of recurrence relationships which can be evaluated to any desired accuracy. The optical radiation field acts as a probe on the dressed atomic states. The spectrum shows all the radio-frequency induced resonances. The frequencies of the states and the Bloch-Siegert shifts of the multi-photon resonances can be deduced from this spectrum.

DOI
10.1088/0022-3700/15/17/019

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A strong radio-frequency field couples two excited atomic states which also interact with the virtual radiation field. The radio-frequency field dresses the atomic states and the virtual radiation field causes them to decay spontaneously. The spectrum of the emitted radiation is calculated by Fourier transforming the differential equations for the amplitudes. The solutions are given in terms of recurrence relationships which can be evaluated to any desired accuracy. The optical radiation field acts as a probe on the dressed atomic states. The spectrum shows all the radio-frequency induced resonances. The frequencies of the states and the Bloch-Siegert shifts of the multi-photon resonances can be deduced from this spectrum.
The time evolution of a two-level system interacting with a classical monochromatic radiation field is calculated by Fourier transforming the equations of motion. This can be done exactly if one uses the convolution of the product of two Fourier transformations. The method produces recurrence relationships for the transforms. The time-dependent amplitudes of the states and the transition probability are evaluated by using two such recurrence relationships. The time-averaged probability shows characteristic resonances at odd multiples of the ratio of the natural frequency of the system to the frequency of the radiation field. The peaks of the resonances are displaced by the Bloch-Siegert shift. At these resonances the system is completely saturated with the flipping frequency dependent on the strength of the radiation field. The time dependence and the frequency spectrum of the dipole moment is determined at the main resonance and at the three-quantum resonance. The spectrum contains the zero-frequency terms which are responsible for the coherence resonances.
We study the dynamics of a system consisting of a two-level atom and a quantum oscillator coupled by the vacuum radiation field. The oscillator and the atom are assumed to have the same resonance frequency. In contrast to the two-atom or two-oscillator case, the atom-oscillator system leads to an unclosed hierarchy of equations for the operators that determine the radiation pattern emitted by the atom-oscillator system. Instead of using the operator equations, we formulate the problem in terms of density-matrix equations which can be solved once the initial conditions are specified. As an example, we looked at the radiation pattern, the decay dynamics, and the spectrum for an initial condition in which the oscillator is in its n=1n=1n=1 state and the atom is in its excited state. Dressed states (dressed by the static interaction between the atom and oscillator) prove to be especially useful for interpreting the results and comparing them with the two-atom and two-oscillator systems. All calculations are carried out using the resonance or rotating-wave approximation. The relationship of our work to damped Jaynes-Cummings models is noted.
The spontaneous radiative decay to the ground state of an atomic system initially in the higher of two excited states, coupled in a radiationless fashion by an external field, is investigated by the method of multiple-time-scale perturbation theory. The coupled differential equations of motion for the probability amplitudes are solved to second order, while the usual secular behavior of conventional time-dependent perturbation theory is eliminated in terms of two natural time scales: a fast time scale corresponding to the reciprocal of the level transition frequency and a slower time scale associated with the inverse of the radiation linewidth. Expressions are obtained to this order for the energy shifts and decay characteristics of the excited states and the energy distribution of the final-state photons, quantities previously determined by Fourier analysis and contour integration and by the phenomenological approach of Weisskopf and Wigner. A detailed comparison of these various methods of solution includes conditions under which the present results agree to second order with the previous calculations.
Recent developments on intense laser sources is opening a new field of optical sciences. An intense coherent light beam strongly interacting with the matter causes a coherent motion of a particle, forming a strongly dressed excited particle. A photon emission from this dressed excited particle is a strong nonlinear process causing high-harmonic generation (HHG), where the perturbation analysis is broken down. In this work, we study a coherent photon emission from a strongly dressed excited atom in terms of complex spectral analysis in the extended Floquet-Hilbert-space. We have obtained the eigenstates of the total Hamiltonian with use of Feshbach-Brilloiun-Wigner projection method. In this extended space, the eigenstates of the total Hamiltonian consisting of the radiation field and the atom system have complex eigenvalues whose imaginary part represents the decay rate. Time evolution of the system is represented by the complex eigenvector expansion so that the correlation dynamics between the photon and the atom is fully taken into account. The HHG is interpreted as the irreversible spontaneous photon emission due to the resonance singularity in terms of the multiple Floquet states that are generated by periodic external field. We have found that the interference between the emitted photons over the different Floquet states causes spatial pulse emission correlated with the decay process of the excited atom.
Resonance fluorescence consists of photon absorption and photon reemission by an atom interacting with a monochromatic, resonant and intense laser wave. The aim of this paper is to show that all fluorescence signals can be quantitatively calculated through the dressed atom method and that simple physical pictures can be associated to the results obtained in this manner. In such a method, the compound system «atom plus laser photons interacting together» (atom dressed by the laser photons) is first considered and the emission of fluorescence photons is then included as a radiative relaxation of this new quantum system. Emission frequencies thus appear as allowed Bohr frequencies of the dressed atom and Rabi nutation appears as a quantum beat signal between dressed states. Photon correlation and photon counting signals are well understood when fluorescence is considered as a radiative cascade of the dressed atom downwards its energy diagram. Mixed analysis time-frequency, for example study of temporal correlations between photons emitted in some sidebands of the fluorescence spectrum, is suggested by the dressed atom approach. Finally, when compared with the well known optical Bloch equations method, the dressed atom is shown to have a larger validity domain for the Markov approximation On montre que la methode de l'atome habille permet un calcul quantitatif de tous les signaux de fluorescence et associe les resultats a des interpretations physiques simples. Discussion des resultats et presentation des avantages de cette methode