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Physical Review A

Measurement of the bichromatic optical force on Rb atoms

M. R. Williams, F. Chi, M. Cashen, H. Metcalf

Published Sep 1, 1999• 39 citations
Publisher

Abstract

The limit of $\ensuremath{\Elzxh}k\ensuremath{\gamma}/2$ imposed on the magnitude of radiative forces by the spontaneous decay rate $\ensuremath{\gamma}$ of the excited state can be overcome by coherent control of the momentum exchange between atoms and the light field. This can be implemented with two light beams, each containing two frequencies whose phases, amplitudes, and frequency difference are carefully chosen. We have made precise measurements of the extremely large magnitude and velocity range of this bichromatic force, and have shown that its velocity dependence near the edge of its range is suitable for atomic beam slowing and laser cooling. Our measurements have corroborated various models and calculations of this bichromatic force.

DOI
10.1103/physreva.60.r1763

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The limit of \ensuremath\Elzxhk\ensuremathγ/2\ensuremath{\Elzxh}k\ensuremath{\gamma}/2\ensuremath\Elzxhk\ensuremathγ/2 imposed on the magnitude of radiative forces by the spontaneous decay rate \ensuremathγ\ensuremath{\gamma}\ensuremathγ of the excited state can be overcome by coherent control of the momentum exchange between atoms and the light field. This can be implemented with two light beams, each containing two frequencies whose phases, amplitudes, and frequency difference are carefully chosen. We have made precise measurements of the extremely large magnitude and velocity range of this bichromatic force, and have shown that its velocity dependence near the edge of its range is suitable for atomic beam slowing and laser cooling. Our measurements have corroborated various models and calculations of this bichromatic force.
The spontaneous decay rate $\ensuremath{\gamma}$ of excited atomic states limits the radiative force on atoms to $\ensuremath{\Elzxh}k\ensuremath{\gamma}/2.$ This bottleneck in the dissipative exchange of momentum between atoms and light can be overcome by coherent control of the momentum exchange interactions. The bichromatic force provides such control by using stimulated instead of spontaneous emission to produce the force, while at the same time exploiting spontaneous emission to enable a dissipative interaction. It is implemented with two counterpropagating light beams, each containing two frequencies, whose phases, amplitudes, and frequency difference are carefully chosen. We have made precise measurements of the extremely large magnitude and velocity range of this bichromatic force, and have shown that its velocity dependence near the edge of its range is suitable for atomic beam slowing and laser cooling. Our measurements have corroborated various models and calculations of this bichromatic force.
We have demonstrated that coherent control of the momentum exchange between a light field and atoms can be implemented in frequency-modulated light. The optical parameters are chosen to drive the atoms between ground and excited states by adiabatic rapid passage in counterpropagating modulated light beams. We apply the optical force transversely to a thermal atomic beam, and the deflection provides a measure of the force. The modulation period is 2?/?s<<?, and each half-cycle exchanges momentum 2k, so the resulting force is much greater than the ordinary radiative force. Moreover, the velocity range of the force in such a light field is much greater than that of the radiative force. This constitutes another example of the huge range of capabilities of optical forces in non-monochromatic light.
Stimulated optical forces offer a simple and efficient method for providing optical forces far in excess of the saturated radiative force. The bichromatic force, using a counterpropagating pair of two-color beams, has so far been the most effective of these stimulated forces for deflecting and slowing atomic beams. We have numerically studied the evolution of a two-level system under several different bichromatic and polychromatic light fields, while retaining the overall geometry of the bichromatic force. New insights are gained by studying the time-dependent trajectory of the Bloch vector, including a better understanding of the remarkable robustness of bi- and polychromatic forces with imbalanced beam intensities. We show that a four-color polychromatic force exhibits great promise. By adding new frequency components at the third harmonic of the original bichromatic detuning, the force is increased by nearly 50% and its velocity range is extended by a factor of 3, while the required laser power is increased by only 33%. The excited-state fraction, crucial to possible application to molecules, is reduced from 41% to 24%. We also discuss some important differences between polychromatic forces and pulse trains from a high-repetition-rate laser.
Periodic adiabatic rapid passage from counterpropagating light pulses is used in a parameter domain outside of the conventionally expected successful range to produce large optical forces on atoms by coherent control of the momentum exchange between the light and atoms. Both the magnitude and velocity range are much larger than those of the usual radiative force. We observed the force on metastable He atoms by the deflection of the atomic beam with periodic pulse sequences. We have also been able to map out the force magnitude in the two-dimensional parameter space of peak Rabi frequency and sweep range, and we find qualitative agreement with our model.
The bichromatic optical force (BCF), which can greatly exceed radiative forces, seems ideal for laser slowing and cooling of molecules because it minimizes the effects of radiative decay. However, it relies on sustained coherences between optically coupled states, and molecules, with their many sublevels and decay pathways, present new challenges in maintaining these coherences compared with simple atoms. We have conducted extensive numerical simulations of BCFs in model molecular systems based on the BleftrightarrowXB leftrightarrow XBleftrightarrowX transition in CaF, and have begun experimental tests in a molecular beam.\ In our modeling, the effects of fine and hyperfine structure are examined using a simplified level scheme that is still sufficiently complete to include the major pathways leading to loss or decoherence. To circumvent optical pumping into coherent dark states we explore two possible schemes: (1) a skewed dc magnetic field, and (2) rapid optical polarization switching. The effects of repumping to compensate for out-of-system radiative decay are also examined. Our results verify that the BCF is a promising method for creating large forces in molecular beams while minimizing out-of-system radiative losses, and provide detailed guidance for experimental designs. Compared to a two-level atom, the peak force is reduced by about an order of magnitude, but there is little reduction in the velocity range over which the force is effective. Our experiments on deflection and slowing using the CaF BleftrightarrowXB leftrightarrow XBleftrightarrowX, (0-0) transition, still at an early stage, include studies of both the P11(1.5)/PQ12(0.5)P_{11}(1.5)/^PQ_{12}(0.5)P11​(1.5)/PQ12​(0.5) branch, a quasi-cycling configuration with extensive hfs, and the R11(0.5)/RQ21(0.5)R_{11}(0.5)/^RQ_{21}(0.5)R11​(0.5)/RQ21​(0.5) branch, which has a much simpler hfs but requires rotational repumping.
For cold samples of laser-cooled atoms to be useful in emerging technologies such as compact atomic clocks and sensors, it is necessary to achieve small sample sizes while retaining a large number of cold atoms. Achieving large atom numbers in a small system is a major challenge for producing miniaturized laser-cooled atomic clocks, since the number of captured atoms in a vapor-cell magneto-optical trap (MOT) scales as the fourth power of the laser beam diameter. This strong dependence on size is fundamentally set by the maximum spontaneous light force ħkγ/2, where ħk is the photon momentum and γ/2 is the maximum spontaneous photon scatter rate of a saturated transition of linewidth γ. We are attempting to surmount the limit imposed by spontaneous emission by using bichromatic cooling - a technique that uses stimulated emission to slow the atoms. We have built a table-top experiment that uses stimulated-emission bichromatic cooling to pre-cool rubidium atoms and dramatically enhance the trappable atom number in a small MOT. The apparatus lets us test how bichromatic cooling scales with miniaturization. Here we report on our first experimental results of cooling a thermal beam of rubidium atoms down to MOT capture velocities.