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Annual Meeting Optical Society of America

Coherent transient model of laser cooling in standing waves

Ralph G. DeVoe

Published Jan 1, 1990• 0 citations
Publisher

Abstract

Laser cooling in standing waves is related to the study of coherent optical transients. Transients in the u-component of the optical Bloch vector lead to a simple and unified physical picture of cooling at both low saturation parameter (optical molasses) and high saturation parameter (stimulated cooling). Optical molasses is shown to result from a free induction decay transient depending on the coherence relaxation time T2, while stimulated cooling is an incoherent effect of the population relaxation time T1. The sign, tuning, and saturation characteristics of each are attributed to specific transient phenomena. The model offers a bare-state physical picture of laser cooling which complements the dressed-state "Sisyphus" model. Phase-interrupting processes which make T2 < 2T1 reduce the trap potential by a factor of T2/2T1 and lead to a cooling force proportional to T2–2T1 which has not appeared in previous theories. The new term dominates both optical molasses and stimulated cooling when T2 «T1.

DOI
10.1364/oam.1990.ws5

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•Oct 1, 1992•0 citations
Laser cooling in standing waves is related to the study of coherent optical transients. Transients in the u-component of the optical Bloch vector lead to a simple and unified physical picture of cooling at both low saturation parameter (optical molasses) and high saturation parameter (stimulated cooling). Optical molasses is shown to result from a free induction decay transient depending on the coherence relaxation time T2, while stimulated cooling is an incoherent effect of the population relaxation time T1. The sign, tuning, and saturation characteristics of each are attributed to specific transient phenomena. The model offers a bare-state physical picture of laser cooling which complements the dressed-state "Sisyphus" model. Phase-interrupting processes which make T2 < 2T1 reduce the trap potential by a factor of T2/2T1 and lead to a cooling force proportional to T2–2T1 which has not appeared in previous theories. The new term dominates both optical molasses and stimulated cooling when T2 «T1.
We have observed a new type of laser cooling1mainly based on stimulated emission, which can be much more efficient than the usual laser cooling, i.e., the so-called radiation pressure optical molasses. This cooling occurs in a strong laser standing wave, detuned blue with respect to the atomic resonance. The force exerted on the atom results from a coherent redistribution of photons between the two running waves forming the standing wave. The cooling process can also be seen in the dressed atom picture as a microscopic realization of the Sisyphus myth: the atoms in this diagram see more uphill parts than downhill parts.
The process of laser cooling in a quasi resonant standing laser wave is one of the principal techniques of laser cooling of free atoms. It will be shown that the nonlinear interaction between the counter propagating waves in a standing wave have a profound affect on the mechanical manifestations of the light on the atoms. This can be understood simply by noting that in the Two Wave Mixing (TWM) process, a momentum kick of 2ℏk is transferred to the atom, as a photon is absorbed from one wave and emitted into the counter propagating wave. This process is in fact responsible for the so called "Dipole force" Or "Stimulated Molasses" and has been verified experimentally!. However, since the TWM process requires high laser intensity under normal conditions it does not usually lead to lower equilibrium temperatures. Nevertheless, It has been shown that the TWM process can be modified when the normal decay rates of the atom are altered. This modification can give rise to the appearance of the TWM at lower intensity and can even change its lineshape. This in turn have an important implications on the laser cooling process in a standing wave. Among the important effects: (i) The appearance of the stimulated force at lower intensity when the dipole decay rate is increased by dephasing events.(ii) The appearance of a narrow resonance characterized by the ground state decay in an open system. (iii) The modification of the stimulated force when the quantum fluctuations of the vacuum field are modified by quadrature squeezing3. Processes (ii) and (iii) can change the sign of the stimulated force from a heating force to a cooling force at the red side of the atomic resonance and give additional cooling force much larger than the radiation pressure force.
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 optical forces exerted on a slowly moving two-level atom in a standing wave are profoundly modified when the normal decay rates of the atom are altered. The theory presented in this paper shows that the stimulated emission force becomes dominant at a very low laser intensity. Furthermore, it can change sign to provide an additional cooling force instead of a heating force at laser detunings below the atomic resonance. These phenomena can lead to equilibrium temperatures below the Doppler limit.
Transient laser cooling (TLC) can produce cooling and heating, but often with the opposite detuning from that found in steady state. In TLC the time scale is set by the optical pumping (OP) rate to a state not coupled by the laser field. The combination of such OP processes and the conservative light shift potential U{sub o}sin{sup 2}kz leads to TLC. The average PE of atoms entering a standing wave is U{sub o}/2. They experience the optical force until undergoing OP to an uncoupled state, which is more likely to happen at high light intensity, near an antinode. For {delta} > 0 this means higher PE and thus lower KE, and conversely for {delta} < 0. In TLC there is no final {open_quotes}temperature{close_quotes} resulting from competition between a damping force and diffusive heating. Instead the changes in KE are bounded by U{sub o} so that the signal widths decrease with intensity. This can result in sub-Doppler widths. We have made two independent theoretical studies of these experiments. In a semiclassical calculation we evolve the motion for a calculated OP time and calculate the velocity distribution. We have also performed fully quantum mechanical calculations of the motion of atoms in themore » standing wave whose basis set consists of product states of internal and external atomic coordinates.« less
The force acting on a two-level atom in a low-intensity standing laser wave is calculated. On account of this force, atoms can be trapped at the loops (antinodes) of the field. By quantizing the atomic motion near the bottom of the sinusoidal potential, we have studied the atomic behavior when they are trapped in bound states as well as when they are in the free state. Laser cooling of neutral atoms was first suggested by T. Hansh and A. Schawlow in 1975. The principle involves the Doppler effect in a detuned laser beam. The absorption rate of a photon depends on the apparent frequency of the photon that is shifted ωv/c\omega v/cωv/c from ω\omegaω, where ω\omegaω is the frequency of the laser, v is the velocity of the atom, and c is the velocity of light. For a single laser beam detuned slightly below an atomic resonance frequency, the apparent frequency for atoms moving toward the laser is closer to resonance, which causes a higher absorption rate. And these atoms lose momentum when they absorb a photon from the beam. The velocity of atoms can be decreased from 10$\sp5$ cm/sec, the velocity they have when they escape from an oven, to 10$\sp2$ cm/sec (about 1mK) by a laser beam. For further cooling, counterpropagating beams are necessary. In this study we propose a new mechanism for supercooling, that is, cooling well below the Doppler cooling limit. Within a standing laser wave there exists a force called a "dipole force", which has a sinusoidal spatial dependence. Once atoms are trapped by the potential, their motion around the minimum of the potential well is that of a simple harmonic oscillator. Restricting our attention to the two lowest quantized states, we calculate transition rates between free states and bound states, from which the average residence times in the bound states can be obtained. This first quantum treatment of an atom trapped in the sinusoidal potential is restricted to the one-dimensional case. Generalization to higher dimensions is left for future research.