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Physical Review A

Power spectrum of light scattered by a strongly driven Morse oscillator

Gautam Gangopadhyay, Deb Shankar Ray

Published Jun 1, 1990• 5 citations
Publisher

Abstract

We evaluate the power spectrum of light scattered by a weakly nonlinear Morse oscillator driven by a strong single-mode classical electromagnetic field, taking radiation damping into account as the only relaxation process. The spectrum is calculated in the small-noise limit under a near-resonant condition (the resonance is considered in terms of an effective detuning parameter). We show that the single-peak structure that appears in the weak-field limit splits into a symmetric doublet centering around the driving field frequency in the presence of an intense field when the Rabi frequency far exceeds the natural damping rate.

DOI
10.1103/physreva.41.6429

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We evaluate the power spectrum of light scattered by a weakly nonlinear Morse oscillator driven by a strong single-mode classical electromagnetic field, taking radiation damping into account as the only relaxation process. The spectrum is calculated in the small-noise limit under a near-resonant condition (the resonance is considered in terms of an effective detuning parameter). We show that the single-peak structure that appears in the weak-field limit splits into a symmetric doublet centering around the driving field frequency in the presence of an intense field when the Rabi frequency far exceeds the natural damping rate.
The power spectrum of the light scattered by a two-level atom driven near resonance by a monochromatic classical electric field is evaluated. The atom is assumed to relax to equilibrium with the driving field via radiation damping, which is treated by explicitly coupling the atom to the quantized electromagnetic field modes. The power spectrum of the scattered field is directly obtainable from the two-time atomic dipole moment correlation function, which is evaluated by a method based on a Markoff-type assumption analogous to that used to evaluate the time evolution of single-time atomic expectation values.
The power spectrum of the radiation emitted by a driven collision-damped two-level system is evaluated. The driving field, which is treated classically, is assumed to oscillate harmonically near the atomic resonance frequency, and its intensity is allowed to assume arbitrary values. The collisions are assumed to be strong, i.e., to instantaneously thermalize the state of the atom. The limiting forms of the power spectrum of the radiated field are discussed for the cases of low and high excitation of the atomic system.
We consider the finite-temperature cavity electrodynamics with a single Morse oscillator and its spectral aspects. It has been shown that the single-peak structure of the emission spectrum in the presence of weak coupling splits up into a doublet in the limit of strong coupling. In the finite-temperature case, for small average number of photons n\ifmmode\bar\else\textasciimacron\fi{} in the cavity, the line shape first shows doublet structure as the coupling increases. However, these merge to a single peak structure with increasing n\ifmmode\bar\else\textasciimacron\fi{} at values as small as 3 to 4 photons.
We study the dissipative Rabi model under deep strong far-off-resonant driving when the driving frequency and strength exceed significantly the qubit transition frequency. We find analytical expressions for the density matrix, the steady-state first-order field correlation function and the multiphoton emission spectrum. This spectrum consists of a series of narrow delta-like lines, caused by coherent processes and of Lorenzian peaks resulted from the incoherent scattering of photons. It is shown that the width of emission lines as well as the decay rate of the time oscillations in the population difference have oscillating dependence on the driving strength. We show how the features of this dependence are controlled by the relative rates of energetic relaxation and pure dephasing.
The power spectrum of the light scattered by a three-level atom driven near resonance between the ground state (|1>) and the second excited state (|3>) by a monochromatic classical electric field is evaluated following the method developed by B. R. Mollow. The incident field is assumed to interact with the dipole moment between the states |1> and |3>, while the emitted light is assumed to interact with that between the state |3> and the first excited state |2> of the atom. The atom is assumed to relax to equilibrium only via radiation damping for the sake of simplicity. The power spectrum of the scattered field is explicitly calculated from the two-time atomic dipole moment correlation function, which is evaluated on a Markoff-type assumption, and various limiting cases are discussed. In Appendix the case is considered in which radiative damping between the higher excited state and the ground state is also present.
We have measured the emission spectrum of two-level-like Ba atoms driven by a continuous-wave bichromatic field containing a strong resonant component and a weaker component detuned from atomic resonance by the strong-field Rabi frequency. With the specified detuning, the weak field resonantly drives a transition of the atom--strong-field dressed states. Observed spectra show that each peak of the normal (single-driving-field) resonance fluorescence triplet is split into three subpeaks separated by one-half the weak-field Rabi frequency. Also seen is another triplet of peaks displaced from the atomic resonance by twice the strong-field Rabi frequency. Splitting of the normal triplet peaks can be explained through weak-field dressing of the strong-field dressed states. The origin of the additional triplet is less transparent. Comparison with theory is made.