We study the effects of phase fluctuations of a laser on the dynamics of a two-level atom. We assume that the atom is in a cavity and consider two cases in which the atom is either sandwiched between two parallel metal plates or placed inside a rectangular metallic waveguide. We use the well-known master equation and utilize the phase diffusion model for our analysis. We derive expressions for the dipolar and dissipative forces acting on the atom. We then show that the laser fluctuations produce an increase in the magnitude of the dissipative force and a reduction in the dipolar force. We illustrate that the atom-laser interaction gives rise to a potential, which binds the atom to the central part of the cavity. We also show that the atomic velocity produces significant changes on the potential and on the force acting on the atom. The combined effects of the velocity and laser fluctuations on the atomic motion are discussed.
We study the effects of phase fluctuations of a laser on the dynamics of a two-level atom. We assume that the atom is in a cavity and consider two cases in which the atom is either sandwiched between two parallel metal plates or placed inside a rectangular metallic waveguide. We use the well-known master equation and utilize the phase diffusion model for our analysis. We derive expressions for the dipolar and dissipative forces acting on the atom. We then show that the laser fluctuations produce an increase in the magnitude of the dissipative force and a reduction in the dipolar force. We illustrate that the atom-laser interaction gives rise to a potential, which binds the atom to the central part of the cavity. We also show that the atomic velocity produces significant changes on the potential and on the force acting on the atom. The combined effects of the velocity and laser fluctuations on the atomic motion are discussed.
An effect of phase fluctuations of a driving laser field on dissipative and dipolar forces of two-level atom is considered. The phase fluctuations are treated by a phase diffusion model where phase fluctuations follow Wiener–Levy process. An exact master equation for the relevant density operator is obtained and solved in the steady state. Optical forces are calculated. The effect of phase fluctuations on angular momentum imparted by a Laguerre–Gaussian beam and an ideal Bessel beam to the atom is investigated.
The effect of field fluctuations on the motion of a two-level atom in resonant laser radiation is investigated theoretically. The internal motion of the atom is treated quantum mechanically (optical Bloch equations); the translational motion, which is coupled to the internal motion, is treated classically (Ehrenfest's theorem); and the fluctuating radiation is treated as a classical electromagnetic wave with stochastic phase (phase-diffusion model). An expression for the radiation force and equations of motion for the ensemble-averaged Bloch vector are derived and used to calculate (i) the radiation force in a plane running wave, (ii) the steady-state radiation force in a general standing wave, and (iii) the dissipative force in a plane standing wave in the limit of strong phase fluctuations. In case (iii) it is found that the atomic velocity is damped when the radiation is tuned above resonance, which is opposite to the case of a weak coherent standing wave, in which damping occurs for radiation tuned below resonance. It is shown that fluctuations have a substantial effect on the radiation force only when the spectral width of the radiation approaches or exceeds the spontaneous emission rate.
The dynamics of atoms subject to laser light propagating between perfectly conducting parallel plates is investigated. In the semiclassical approximation the motion of atoms in this context is governed by a van der Waals--type potential, together with a dynamic dipole potential that comes into play as soon as a cavity mode is excited. In addition, the atoms become subject to an average dissipative (spontaneous) force associated with the cavity mode that always acts parallel to the plates. We show that, by a suitable choice of field intensity and detuning, the total transverse potential can be used to confine atoms in transverse vibrational states, while their motion in the parallel direction is controlled by the dissipative force. Significant variations of the characteristics of the system with atom velocity, dipole orientation, and type of excited cavity mode are emphasized. These features are illustrated using typical parameters for the case of sodium atoms between parallel plates with subwavelength separations.
A semiclassical model of the force and momentum diffusion on a point particle is used to describe the motion of a two-level atom strongly coupled to a single Gaussian cavity mode. The effects of the momentum diffusion on the motion of an atom in a cavity are investigated in a regime similar to that of the experiment performed by Mabuchi et al. [Opt. Lett. 21, 1393 (1996)]. It is found that a slow atom quickly develops significant velocities along the cavity axis. The limited bandwidth in the experiment of Mabuchi et al. means that the full intensity signal due to atomic motion in the standing wave is filtered leading to the apparently smaller velocities observed. It is shown that a negative detuning of the laser and cavity from the atomic resonance would lead to nonzero dipole forces and significantly reduced velocities along the standing wave. An analysis of the intensity signal with a larger bandwidth is proposed, which would track the velocity of the atom along the cavity axis. These results are compared with a Monte Carlo wave-function simulation similar to that used to treat Doppler cooling.
This work discusses the effect of a high-intensity standing wave laser field on the motion of neutral atoms moving with a relatively high velocity. The analysis involves a detailed calculation of the force acting on the atoms and the calculation of the diffusion tensor associated with the fluctuations of the quantum force operator. The high-intensity laser field limit corresponds to a Rabi frequency much greater than the natural rate of the atom. The general results are valid for any atomic velocity. Results are then specialized to the case of slow and fast atoms where the Doppler shift of the laser frequency due to the atomic motion is either smaller or larger than the natural decay rate of the atom. The results obtained for the force and diffusion tensor are applied to a particular ideal experiment that studies the evolution of a fast atomic beam crossing a high-intensity laser beam. The theories developed previously, for a similar laser configuration, discuss only the low atomic velocities case and not the more realistic case of fast atoms. Here, an approximate solution of the equation for the distribution is obtained. Starting from the approximate distribution function, the deflection angle and dispersion angle for themore » atomic beam with respect to the free motion are calculated.« less
Two recent experiments have reported the trapping of individual atoms inside optical resonators by the mechanical forces associated with single photons [Hood et al., Science 287, 1447 (2000); Pinkse et al., Nature (London) 404, 365 (2000)]. Here we analyze the trapping dynamics in these settings, focusing on two points of interest. First, we investigate the extent to which light-induced forces in these experiments are distinct from their free-space counterparts, and whether or not there are qualitatively different effects of optical forces at the single-photon level within the setting of cavity QED. Second, we explore the quantitative features of the resulting atomic motion, and how these dynamics are mapped onto experimentally observable variations of the intracavity field. Toward these ends, we present results from extensive numerical simulations of the relevant forces and their fluctuations, as well as a detailed derivation of our numerical simulation method, based on the full quantum-mechanical master equation. Not surprisingly, qualitatively distinct atomic dynamics arise as the coupling and dissipative rates are varied. For the experiment of Hood et al., we show that atomic motion is largely conservative and is predominantly in radial orbits transverse to the cavity axis. A comparison with the free-space theory demonstrates that the fluctuations of the dipole force are suppressed by an order of magnitude. This effect is based upon the Jaynes-Cummings eigenstates of the atom-cavity system and represents distinct physics for optical forces at the single-photon level within the context of cavity QED. By contrast, even in a regime of strong coupling in the experiment of Pinkse et al., there are only small quantitative distinctions between the potentials and heating rates in the free-space theory and the quantum theory, so it is not clear that a description of this experiment as a novel single-quantum trapping effect is necessary. The atomic motion is strongly diffusive, leading to an average localization time comparable to the time for an atom to transit freely through the cavity, and to a reduction in the ability to infer aspects of the atomic motion from the intracavity photon number.