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Modern Physics Letters B

COLLECTIVE EFFECTS IN RESONANCE PROPERTIES OF A SYSTEM OF N TWO-LEVEL ATOMS

Nguyen Nhu Dat

Published Nov 20, 1992• 0 citations
Publisher

Abstract

We consider resonance properties of an assembly of N two-level atoms interacting with an intense photon beam. The atoms are assumed to be noninteracting with each other except via the action of the electromagnetic field. Using the phase representation of the radiation field and the boson description of the atom system we calculate the one-photon resonance frequency for two kinds of the system: a beam of atoms moving with uniform velocity and a Boltzmann atom gas. The resonance frequency shift is found to be dependent on the total number of atoms and the initial preparation of the atom system. Numerical results show that the collective shift is of the same magnitude as the Bloch-Siegert one.

DOI
10.1142/s0217984992001423

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We consider resonance properties of an assembly of N two-level atoms interacting with an intense photon beam. The atoms are assumed to be noninteracting with each other except via the action of the electromagnetic field. Using the phase representation of the radiation field and the boson description of the atom system we calculate the one-photon resonance frequency for two kinds of the system: a beam of atoms moving with uniform velocity and a Boltzmann atom gas. The resonance frequency shift is found to be dependent on the total number of atoms and the initial preparation of the atom system. Numerical results show that the collective shift is of the same magnitude as the Bloch-Siegert one.
The resonance fluorescence of a two-atom system interacting collectively with an intense driving field is studied. The first-order dispersion forces, or dipole-dipole interaction, between the atoms is included as well. The scattered-light spectrum is found to differ considerably from the single-atom spectrum even for very intense driving fields, in direct contrast with the results obtained by Agarwal et al., who studied the two-atom system but neglected the dipole-dipole interaction. The effects of collective scattering are calculated on the fluorescence spectra of idealized beams of atoms moving with uniform velocity, for a number of different number densities 〈N〉〈N〉〈N〉.
The interaction of a two-level atom with two monochromatic electromagnetic fields having arbitrary amplitudes and resonance frequencies is considered. It is shown that the time averaged upper-level population can exceed 0.5 and even reach 0.7. Its dependence on the frequency difference reveals resonance satellite peaks, which are concerned with three- and five-photon combination scattering. The widths and the resonance spectrum shifts of these peaks are found. The frequency spectrum of the spontaneous emission of an atom contains fine structure under some conditions. This structure does not exist in the case of one monochromatic field. An asymmetry in the intensity distribution for the Rabi satellites due to a field non-monochromaticity is predicted.
Based on the vanishing-damping continued-fraction method which I developed previously for the analysis of the resonance behavior of a two-level atom in a two-frequency field with equal intensities in the two field modes [W. M. Ruyten, Phys. Rev. A 40, 1447 (1989)], I analyze here the related problem in which the two field intensities are unequal. Several analytical results are derived, namely, expressions for the lowest-order Bloch-Siegert shifts of all resonances, and an expression for the positions of the resonances in the limit of one strong and one weak field. It is shown that, in this limit, the resonances exhibit level crossings of the field-atom system.
The interaction of a four-level atomic system with two electromagnetic radiations has been studied. The two intermediate levels are closely spaced such that a single radiation frequency can induce transitions from the ground state to both of them. In a cascade-type double resonance, the pump electric-field amplitude is much stronger than the amplitude of the signal field, which can induce transitions from both of the intermediate levels to the upper state. The 15 optical Bloch equations obtained from the Liouville equations are solved analytically to obtain the Doppler-free signal line shape. The computed signals, exhibiting two Lorentzian line profiles, are presented for different pump frequencies. In addition to these one-photon transitions, we obtain a weak two-photon resonance peak. The two-photon resonance becomes weaker when the detuning of the pump frequency from a resonance frequency is increased. When the pump frequency ${\mathrm{\ensuremath{\Omega}}}_{\mathit{p}}$ is intermediate between the pump resonance frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$, the two-photon resonance is very weak and almost vanishes when ${\mathrm{\ensuremath{\Omega}}}_{\mathit{p}}$=(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$)/2. When the pump frequency is on resonance with one of the transition frequencies, the Rabi splitting of the signal shows asymmetry because of the presence of a close-lying transition which is pumped off resonance. The intensity-dependent shifts of the transitions are such that they repel each other more and more as the intensity of the pump field is increased. These shifts arise from the nonresonant interaction between the atom and the field.
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.