Underlying simplicity of atomic population variations induced by a stochastic phase-fluctuating field

Abstract

We have examined the temporal evolution of a two-level atom in response to stochastic phase-fluctuating fields by applying perturbation theory to the optical Bloch equations written in the instantaneous frame. Our results show that the general nature of the atomic population variations is relatively simple, being composed of adiabatic and nonadiabatic components. The adiabatic response results from Fourier components of the phase variation below the system's Rabi frequency and is proportional to the product of the relatively slow phase variation and its first derivative. The nonadiabatic response has its maximum amplitude at the system's Rabi frequency, for which the atom behaves like a simple harmonic oscillator whose resonance frequency is the Rabi frequency. In this sense the atom acts as a tunable narrow-band filter.

Rabi resonances induced by an off-resonant, stochastic field

“…(7a), and we assumed that VA^+wf^öjdia.] Equation (9) indicates that X (1) responds to the PDF like a damped, driven harmonic oscillator, whose resonant frequency is the Rabi nutational frequency, Cl = x/A 2 +o>f. Note that when the detuning is set equal to zero, the resonant frequency is just the Rabi frequency as observed in our previous investigations [2]. Since the driving frequencies in Eq.…”

“…In the absence of resonant microwaves, optical pumping reduced the density of atoms in the absorbing state [i.e., 5 2 S in (F=2)], and consequently increased the amount of light transmitted through the vapor. However, when the microwave field in the cavity was resonant with the 87 Rb 0-0 hyperfine transition, atoms returned to the 5 2 S m (F=2) state from the 5 2 amount of transmitted light. Since the degree of optical pumping was relatively low, microwave-induced changes in the atomic population distribution were proportional to changes in the transmitted laser light.…”

“…As the starting point for our analysis, we employ the twolevel atom Bloch equations in the rotating frame. The equations are the same as those used previously [2], except now the field detuning A is included (i.e., A = £o ficU -w^J,…”

“…In previous work we investigated the response of an atom, in terms of its Bloch-vector components, to a phasefluctuating field (PDF) [1] that was on resonance with an atomic transition [2,3]. In those studies we found that an atom's temporal response to a resonant PDF is essentially composed of just two components.…”

Precision measurements of absorption and refractive-index using an atomic candle

“…Additionally, the long-term intensity stability of the field produced by the candle has the potential for atomic-clock-like performance [5]. The atomic candle's operation derives from the response of a quantum system to a modulated field; specifically, when an atom interacts with a phase-modulated resonant field, the atomic system's population oscillates at twice the phase-modulation frequency 2i/ m [6]. Of importance for the atomic candle is the fact that the amplitude of these population oscillations is a resonant function of field-strength, reaching a maximum when the Rabi frequency associated with the atomic transition matches 2v m .…”