In this paper we discuss the effect of scattered radiation generated by a gas of cold atoms on the temperature of the gas. We show that by treating the reradiated field of the atoms as a fluctuating background field we can derive a master equation for a single atom where the effect of the surrounding medium is included in an effective relaxation operator. This relaxation operator is of second order in the interaction with the medium and in the binary-collision approximation can be written as the sum of two-body interactions with a correlation time equal to the natural lifetime of the atomic transition. The effect of the medium on the two most important sub-Doppler cooling mechanisms, Sisyphus and motion-induced orientation cooling, is investigated analytically in a one-dimensional model. In this we restrict ourselves to the limit of low saturation, weak background field and take the rate-equation limit for the collision operator. We find that both mechanisms are very sensitive to such a background field and that the temperature increases approximately as the number of atoms to the one-third power.
In this paper we discuss the effect of scattered radiation generated by a gas of cold atoms on the temperature of the gas. We show that by treating the reradiated field of the atoms as a fluctuating background field we can derive a master equation for a single atom where the effect of the surrounding medium is included in an effective relaxation operator. This relaxation operator is of second order in the interaction with the medium and in the binary-collision approximation can be written as the sum of two-body interactions with a correlation time equal to the natural lifetime of the atomic transition. The effect of the medium on the two most important sub-Doppler cooling mechanisms, Sisyphus and motion-induced orientation cooling, is investigated analytically in a one-dimensional model. In this we restrict ourselves to the limit of low saturation, weak background field and take the rate-equation limit for the collision operator. We find that both mechanisms are very sensitive to such a background field and that the temperature increases approximately as the number of atoms to the one-third power.
Abstract We propose a system of four-level atoms which can generate a sub-Doppler cooling in the presence of quantum interference effects. The atom is modeled as a double -type system where dipole-allowed transitions are correlated through the spontaneously generated coherence (SGC). We will show that the including of such interference effects created by spontaneous emission gives rise to a cooling mechanism in which the lowest achievable temperatures approach the single-photon recoil limit. Indeed, this mechanism benefits from the features generated by the phenomenon of SGC-induced electromagnetically induced transparency; in the regime of weak coupling fields, atoms can be subject to a strong radiation pressure force, allowing them to be cooled to near, and even below, the recoil temperature.
We report the investigation of the influence of atomic motion on the fluorescence dynamics of a dilute atomic ensemble driven by resonance pulse radiation. We show that even for sub-Doppler temperatures, the motion of atoms can significantly affect the nature of both superradiation and subradiation. We also demonstrate that, in the case of an ensemble of moving scatterers, it is possible to observe the nonmonotonic time dependence of the fluorescence rate. This leads to the fact that, in certain time intervals, increasing temperature causes not an decrease but an increase of the fluorescence intensity in the cone of coherent scattering. We analyze the role of the frequency diffusion of secondary radiation as a result of multiple light scattering in an optically dense medium. It is shown that spectrum broadening is the main factor which determines radiation trapping upon resonant excitation. Along with broadening, we found a shift and distortion of the shape of the spectrum over time. At later time, after the trapping stage, the dynamics is dominated by close pairs of atoms (dimers). The dynamics of the excited states of these dimers has been studied in detail. It is shown that the change in the lifetime of the given adiabatic term of the diatomic quasimolecule induced by the change in the interatomic distance as well as possible nonadiabatic transitions between sub- and superradiant states caused by atomic motion can lead not to the anticipated weakening of subradiation effect, but to its enhancement.
In sub-Doppler laser cooling of atoms, the lowest temperatures are known to occur at low (but not too low) excitation, and the temperature increases roughly linearly with laser intensity. However, under conditions for which the lowest temperatures are obtained, the small velocity capture range and low optical pumping rate limit the number of atoms that can be collected into the cold sample. In this study, we present measurements for laser cooling of Rb and metastable He atoms for two counterpropagating laser beams with orthogonal linear polarization (lin\ensuremath{\perp}lin) over a wide range of saturation parameters and laser detunings, together with results of semiclassical (Fokker-Planck) and quantum density matrix calculations. We find that at higher laser intensity, a larger number of atoms can be collected into a final velocity distribution that is significantly narrower than that given by a linear extrapolation vs the square root of laser intensity. Two cooling mechanisms are at work: the sub-Doppler Sisyphus mechanism and also Doppler cooling. Under certain conditions that we discuss, Doppler cooling aids Sisyphus cooling by collecting high-velocity atoms beyond the Sisyphus capture range. He∗ presents a rather unusual situation in that the minimum average kinetic energy (Eav) for purely Sisyphus cooling is comparable to the minimum value of Eav with Doppler cooling alone.
The response of a collision-broadened gas sample to driving coherent radiation is studied theoretically, taking into account effects of coherent excitations of two or more atoms (or molecules). In analogy to the Bloch-type master equation for one-atom coherences, describing the motion of a single atom "dressed" by the relevant (incident and detected) field modes, a master equation is derived for two-atom coherences, including an effective interaction of the Bethe-Salpeter---type, accounting for the mutual interaction of the coherently driven pair. The master equation includes also all symmetrization effects owing to resonance exchange between identical atoms, and is limited to nonreactive gas atoms (or molecules) undergoing binary collisions, including otherwise all (internal and translational) relaxation effects. The self-energy kernels are expressed in a nonperturbative fashion, in terms of binary-collision scattering amplitudes, and include renormalization effects due to coincidence of radiative couplings with the collisions (optical and radiative collisions). The concept of two-atom coherences is generalized to higher coherence ranks by constructing a hierarchy of master equations, including vertex operators that upgrade or downgrade the coherence rank, as a prelude to a diagrammatic method for calculating continuous-wave spectra. This hierarchy is compared with prevalent Agarwal-type master equations, based on the Dicke pseudospin method, and used in the study of two-level atoms.
We present two cooling mechanisms that lead to temperatures well below the Doppler limit. These mechanisms are based on laser polarization gradients and work at low laser power when the optical-pumping time between different ground-state sublevels becomes long. There is then a large time lag between the internal atomic response and the atomic motion, which leads to a large cooling force. In the simple case of one-dimensional molasses, we identify two types of polarization gradient that occur when the two counterpropagating waves have either orthogonal linear polarizations or orthogonal circular polarizations. In the first case, the light shifts of the ground-state Zeeman sublevels are spatially modulated, and optical pumping among them leads to dipole forces and to a Sisyphus effect analogous to the one that occurs in stimulated molasses. In the second case (σ+−σ− configuration), the cooling mechanism is radically different. Even at very low velocity, atomic motion produces a population difference among ground-state sublevels, which gives rise to unbalanced radiation pressures. From semiclassical optical Bloch equations, we derive for the two cases quantitative expressions for friction coefficients and velocity capture ranges. The friction coefficients are shown in both cases to be independent of the laser power, which produces an equilibrium temperature proportional to the laser power. The lowest achievable temperatures then approach the one-photon recoil energy. We briefly outline a full quantum treatment of such a limit.
The semiclassical theory of laser cooling is applied for the analysis of cooling of unbound atoms with the values of the ground and exited state angular moments 1/2 in a one-dimensional nondissipative optical lattice. We show that in the low-saturation limit with respect to the pumping field a qualitative interpretation of the cooling mechanisms can be made by the consideration of effective two-level system of the ground-state sublevels. It is clarified that in the limit of weak Raman transitions the cooling mechanism is similar to the Doppler mechanism, which is known in the theory of two-level atom. In the limit of strong Raman transitions the cooling mechanism is similar to the known Sisyphus mechanism. In the slow atom approximation the analytical expressions for the coefficients of friction, spontaneous and induced diffusion are given, and the kinetic temperature is estimated.