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Physical Review A

Light-induced ground-state coherence, constructive interference, and two-photon laser cooling mechanism in multilevel atoms

Soo Chang, Taeg Yong Kwon, Ho Seong Lee, Vladimir G. Minogin

Published Sep 1, 1999• 25 citations
Publisher

Abstract

It is shown that dipole interaction of multilevel atoms having three or more ground-state sublevels with counterpropagating circular polarized laser waves is strongly influenced by ground-state coherence produced by two-photon processes. In the simplest case of a (3+5)-level atom the ground-state coherence is shown to be responsible for constructive atomic interference that enhances upper atomic populations at small velocities. Ground-state coherence is also responsible for the coherent redistribution of the ground-state atomic populations at small velocities. It is found that a two-photon coherent redistribution of atomic populations enhances considerably the radiation force at small velocities and accordingly the friction produced by the radiation force.

DOI
10.1103/physreva.60.2308

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It is shown that dipole interaction of multilevel atoms having three or more ground-state sublevels with counterpropagating circular polarized laser waves is strongly influenced by ground-state coherence produced by two-photon processes. In the simplest case of a (3+5)-level atom the ground-state coherence is shown to be responsible for constructive atomic interference that enhances upper atomic populations at small velocities. Ground-state coherence is also responsible for the coherent redistribution of the ground-state atomic populations at small velocities. It is found that a two-photon coherent redistribution of atomic populations enhances considerably the radiation force at small velocities and accordingly the friction produced by the radiation force.
A theory of deep laser cooling of atoms by counterpropagating circular polarized laser waves in multilevel interaction schemes is developed. Using a (3+5)-level atom as an example, we show that in multilevel interaction schemes two-photon processes are responsible for creating a narrow structure near zero velocity in the ground-state atomic coherence. This structure is in turn responsible for narrow velocity structures in atomic populations and optical coherences. A Fokker-Planck-type kinetic equation is derived for a model of a (3+5)-level interaction scheme. It is found that two-photon coherent processes considerably enhance the radiation force at low velocities and the friction produced by the force at a negative detuning, and considerably decrease the diffusion coefficient. Two-photon processes in multilevel interaction schemes are identified as the basic physical mechanism responsible for deep laser cooling of atoms. The temperature of laser-cooled atoms is derived for a model (3+5)-level atom, and found to be in good agreement with the experimentally observed temperature for laser-cooled cesium atoms.
We extend the kinetic theory of the laser cooling of atoms to four multilevel atomic schemes: (3+5)-, (5+7)-, (7+9)-, and (9+11)-level atom. In all four atomic schemes the atoms are considered to be excited by two counterpropagating circularly polarized laser waves. A comparison of four multilevel atomic schemes shows that the even-order multiphoton processes are responsible for the narrow structures near zero velocity in the atomic coherences, atomic populations, dipole radiation forces, and the diffusion coefficients. The even-order multiphoton processes in a multilevel atom with a big number of magnetic sublevels are shown to produce the velocity structures, which are much narrower than that produced by the two-photon processes in a (3+5)-level atom. It is found that the multiphoton processes enhance the radiation force at low velocities and the friction produced by the force at a negative detuning. The even-order multiphoton processes caused by the laser waves are identified as the basic physical mechanism responsible for the sub-Doppler laser cooling of atoms. The temperature of laser-cooled atoms is derived for all four models and found to be lower for atomic schemes with a larger number of magnetic sublevels.
We extend the kinetic theory of deep laser cooling of multilevel atoms by counterpropagating laser waves to a case of linearly polarized waves and compare the results with those for circularly polarized waves. Considering the excitation of a $(3+5)\ensuremath{-}\mathrm{level}$ atom by two counterpropagating waves with orthogonal linear polarizations $(\mathrm{lin}\ensuremath{\perp}\mathrm{lin}$ configuration), we show that even-order stepwise processes composed of the two-photon optical processes are responsible for narrow structures near zero velocity in the ground-state atomic coherence, atomic populations, and optical coherences. The stepwise processes composed of the two-photon structures are shown to produce velocity structures much narrower than the two-photon structures produced by a single ${\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}}$ configuration [Phys. Rev. A 60, 3148 (1999)]. A Fokker-Planck type kinetic equation is derived for a model of a $(3+5)\ensuremath{-}\mathrm{level}$ atom interacting with two linearly polarized waves in a $\mathrm{lin}\ensuremath{\perp}\mathrm{lin}$ configuration. It is found that stepwise multiphoton coherent processes enhance considerably the radiation force at low velocities and the friction produced by the force at a negative detuning. Contrary to a case of a ${\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}}$ configuration the stepwise processes are found to increase the diffusion coefficient. The stepwise even-order processes caused by two linearly polarized waves are identified as the basic physical mechanism responsible for deep laser cooling of atoms in a $\mathrm{lin}\ensuremath{\perp}\mathrm{lin}$ configuration. The temperature of laser-cooled atoms is derived for a model of a $(3+5)\ensuremath{-}\mathrm{level}$ atom excited by a $\mathrm{lin}\ensuremath{\perp}\mathrm{lin}$ configuration and found to be asymptotically close to that for a case of ${\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}}$ configuration at large detuning.
We have examined the mechanical effects of light on a three level atom. A single excited state decays to two long-lived ground states. One of the transitions is driven by an intense standing wave, while the other is driven by a traveling wave. We examine this system using analytical and computational techniques, and compare with experimental observations of {sup 7}Li. In the absence of the second ground state and laser field, the atom can be cooled by the familiar two level dipole force. In the three level system, the dipole force cooling mechanism is still present, and can be considerably enhanced. As in the two level system, the cold three level atoms are channeled, or localized in space with respect to the standing wave. In the three level case, the atoms can be channeled in the second ground state, even though that state interacts only with the traveling wave laser, which has no spatial structure. We will discuss applications of the three level cooling force to atomic beam slowing experiments, and the attainment of ultra-cold final temperatures using adiabatic cooling.
Microscopic models based on multilevel atoms are central to optimizing nonlinear optical responses and the coherent control of light. These models are traditionally based on single-atom effects that are parametrically extrapolated to include collective effects, such as an enhanced response or propagation within atomic media. In this work, we present a systematic analysis of the cooperative effects arising in driven systems composed of multilevel atoms coupled via a common electromagnetic environment. The analysis is based on an interplay between dressed states induced by the driving field and photon exchanges, and collective decay channels. This theory is applied to the case of four-wave mixing induced by a pair of lasers acting on an atomic pair with internal levels in the diamond configuration. The effect of interatomic correlations and collective decay over the photons created in this nonlinear process is then explored. We identify three regions of operation: (i) laser-dominated, (ii) intermediate, and (iii) dipole-dominated. The dependence of single- and two-photon correlations is studied in detail for each region by varying atomic orientations and laser parameters consistent with current experiments involving atomic gases. Photonic correlation functions are shown to exhibit a transition from a Lorentz-like dependence on the two-photon detuning—with general features that can be obtained in an isolated atom scheme—to a two-peaked distribution when the dipole-dipole interactions become relevant. For weak Rabi frequencies whose value is smaller than the highest collective decay rate, the atoms are trapped inside their ground state as they approach each other. It is found that the anisotropy of the dipole-dipole interaction and its wave nature are essential to understand the behavior of the photon correlations. Signatures of these processes are identified for existing experimental realizations. The intuition obtained from this connection helps to uncover relevant parameters that could be exploited for quantum control protocols based on dispersive and dissipative cooperative effects in multilevel systems.
A theoretical analysis is given of the interaction of a laser field consisting of two orthogonal, linearly polarized, low-power standing waves, with an ensemble of J=1/2 ground-state atoms. The atoms are assumed to move with velocities below the Doppler limit of laser cooling. The two-dimensional light-induced atomic force is calculated for the specific case when the field polarization directions differ by \ensuremath{\pi}/2. The effective optical-pumping time is shown to increase strongly near the nodes of the laser field, leading to a force that can be much larger than that in the one-dimensional case. The force is not isotropic, and can lead to the bunching of the atoms in velocity space.