Classical and quantum mechanical resonance fluorescence

Fritz Haake, Joseph W. Haus, Kazimierz Rza̧żewski

C. Gerald Carrington

The results of a quantum mechanical formulation of resonance fluorescence in the white light approximation are expressed in a cartesian form equivalent to the classical expressions used in a recent publication. Explicit formulae are derived which allow the cartesian equations to be applied to light, both plane and elliptically polarized and to atomic states with arbitrary angular momenta.

R. I. Sokolovskiǐ

Rima Al-Khuzheyri

Yuliya Bilinskaya, Sreenath K. Manikandan

We present an analytically tractable model of a driven quantum harmonic emitter, such as an oscillating charged dipole, emitting radiation via resonance fluorescence. With this model we are able to characterize the quantum mechanical correlations that are built up at early times between the drive, the resonant emitter, and its fluorescence. We describe detection strategies that can reveal these quantum signatures in experiments by performing joint measurements on the quantum emitter and its fluorescence field. In particular, we show that simultaneous quantum measurements of a driven quantum emitter and its fluorescence can be used to probe the quantum noise of the driving field, relative to the maximally classical coherent state of the driving field, in short-time experiments. We conclude by discussing the applications to quantum sensing in quantum optical, quantum acoustic, and quantum gravitational scenarios of interest.

I. R. Senitzky

The resonance fluorescence spectrum of linear and nonlinear oscillators driven by a monochromatic field of frequency ${\ensuremath{\omega}}_{0}$, near the resonant frequency \ensuremath{\omega}, is calculated both classically and quantum mechanically. The result for the linear oscillator is the same in both calculations: a \ensuremath{\delta} function at ${\ensuremath{\omega}}_{0}$. For the nonlinear oscillator, however, the classical and quantum-mechanical spectra near resonance are qualitatively different: Classically, a \ensuremath{\delta} function at ${\ensuremath{\omega}}_{0}$ is obtained; quantum mechanically, a weak-field calculation leads to a \ensuremath{\delta} function at ${\ensuremath{\omega}}_{0}$ together with finite-width peaks nearby. An intuitive explanation for the difference is suggested by the examination of the quantum-mechanical energy-correlation function for the linear oscillator. This function describes energy oscillations with frequencies within a band centered at ${\ensuremath{\omega}}_{0}$-\ensuremath{\omega}. The oscillations can be interpreted as the beating of the driven oscillation with those produced by the vacuum fluctuations (the latter having a frequency spread of the order of the relaxation constant). Because of the nonlinearity, the energy oscillation modulates the effect of the driving field to produce sidebands. Higher-order processes produce additional peaks. A heuristic picture of vacuum fluctuations is developed.