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Physical Review A

Canonical transformation for single-atom resonance fluorescence: The strong-driving-field limit

G. Compagno, Franco Persico

Published Nov 1, 1980• 15 citations
Publisher

Abstract

A canonical transformation, which diagonalizes the single-mode radiation Hamiltonian in the rotating wave approximation, is exploited to dress a two-level atom by the strong monochromatic driving field in the resonance fluorescence phenomenon. Langevin equations of motion are obtained for dressed atomic operators, and their solutions yield the amplitude of waves scattered into the fluorescence field. The power spectrum of the scattered field is obtained from the first-order correlation functions between dressed atomic operators. The results of the present treatment are compared with others, and advantages and disadvantages of the present method are discussed.

DOI
10.1103/physreva.22.2108

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A canonical transformation, which diagonalizes the single-mode radiation Hamiltonian in the rotating wave approximation, is exploited to dress a two-level atom by the strong monochromatic driving field in the resonance fluorescence phenomenon. Langevin equations of motion are obtained for dressed atomic operators, and their solutions yield the amplitude of waves scattered into the fluorescence field. The power spectrum of the scattered field is obtained from the first-order correlation functions between dressed atomic operators. The results of the present treatment are compared with others, and advantages and disadvantages of the present method are discussed.
An S-conserving theory of collective resonance fluorescence by NNN two-level atoms driven by a uniform strong field is presented. The detuning between field and atoms can be varied. A canonical transformation to dress the atoms by the driving field and Langevin equations for dressed operators are used to investigate the behavior of the system. For sufficiently large detuning the dressed atoms are shown to reach a steady state after a transient super-radiant-like decay in times short, compared with the long decay time which is attained on resonance and which is the same as the single-atom spontaneous-decay time. In the transient regime the parameters of the quasi-super-radiant decay are shown to vary with detuning and with the driving-field amplitude. Both the amplitude spectrum and the integrated intensity of the fluorescence field, emitted off resonance by the dressed atoms during the transient, are shown to bear pulselike traces of the quasi-super-radiant decay. The elastic components of the off-resonance amplitude spectrum at the end of the super-radiant-like transient are broadened with respect to resonance, and the integrated intensity exhibits a sudden transient decrease in an appropriate range of detuning, which has been given the name "superdarkening" and which disappears on resonance. After the steady-state regime is attained, the resonance intensity spectrum is shown to coincide with that obtained by other authors, while off resonance the inelastic lines are broadened in a super-radiant-like fashion.
The spectral density of resonance fluorescence from a two-level atom in a monochromatic radiation field of arbitrary strength and detuning is calculated by solution of the wave equation. A basis set in which the strong coupling of the atom and the quantised incident field is diagonal is used, and the resulting infinite set of coupled equations is solved by truncating them to a set of N equations and finally proceeding to the N to infinity limit. The resulting spectral densities of the inelastically scattered field for various levels of intensity of the incident field and degree of detuning are found to be identical with those of Kimble and Mandel (1976, 1977) obtained by solution of the coupled equations of motion of the atom and the radiation field in the Heisenberg picture.
Resonance fluorescence from a single two-level atom driven by a beam of squeezed light is studied in the weak-field limit. We consider the situation where the atom is coupled to the ordinary vacuum and only a few field modes corresponding to the driving field are squeezed. The field produced by the degenerate optical parametric oscillator is used as the driving field. Heisenberg equations of motion are solved in the steady-state and analytic expressions for the fluorescent-light intensity and the spectrum of fluorescent light are derived. We also consider photon statistics of fluorescent light. In particular, squeezing, antibunching, and sub-Poissonian statistics of fluorescent photons are discussed, and analytic expressions for the quadrature variance and the two-time intensity correlation function are presented. Contrary to the case of coherent excitation, the second-order intensity correlation function does not factorize. This and other differences are discussed, and curves are presented to illustrate the behavior of various quantities. We also present results for thermal excitation of the atom.
The calculation is given of the spectral distribution of resonance fluorescence from an atom that is driven near a j=12j=\frac{1}{2}j=21​ to j=12j=\frac{1}{2}j=21​ transition by a monochromatic, xxx-polarized electric field and that is subject to radiation damping only. In accordance with Mollow's results for a two-level system, the power spectrum of the scattered radiation corresponding to the xxx component of the dipole moment contains a coherent part for all driving-field intensities. The coherent part is absent in the fluorescence radiation corresponding to the yyy and zzz components of the dipole moment. For weak driving fields all power scattered by these latter components is present in a narrow Lorentzian. Consistent with energy conservation, the width of the Lorentzian corresponds to the probability of excitation of the atom out of its ground level due to the presence of the driving field. For strong driving fields the power spectra corresponding to the xxx component and to the yyy or zzz component mainly differ in the heights and widths of their central incoherent band and their Rabi-precession-frequency-shifted side bands.
Resonance fluorescence from a single two-level atom driven by a beam of squeezed light is studied in the weak field limit. We consider the situation where the atom is coupled to the ordinary vacuum and only a few field modes corresponding to the driving field are squeezed. The field produced by the degenerate optical parametric oscillator is used as the driving field. This driving field can be described in terms of two real independent Gaussian processes. Heisenberg equations of motion are solved in the steady-state, and analytic expressions for the fluorescent light intensity and the spectrum of fluorescent light are derived. We also consider photon statistics of fluorescent light. In particular, squeezing, antibunching, and sub-Poissonian statistics of fluorescent photons are discussed and analytic expressions for the quadrature variance and the two-time intensity correlation function are presented. Contrary to the case of coherent excitation the second-order intensity correlation function does not factorize.
We consider the resonance fluorescence of a two-level atom in a vacuum with a high intensity driving field, such that the Rabi frequency of the field is non-negligible up to frequencies comparable to the transition frequency of the atom. At these high intensities, the conventional rotating wave approximation cannot be applied to the atom-laser Hamiltonian and the modal densities of the vacuum at the dressed transition frequencies differ significantly from each other. On treating the counter-rotating part of the Hamiltonian as a perturbation and carrying out the Weisskopf-Wigner approximation in the dressed states basis, we find that the high driving intensity leads to significant deviations from the traditional Mollow resonance fluorescence spectrum. In particular we find unequally intense Mollow side-bands and that the generation of higher order triplets and harmonics is substantially enhanced by the high vacuum modal density at the corresponding high resonance frequencies.