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arXiv:1307.7156 · Physical Review A

Four-color stimulated optical forces for atomic and molecular slowing

Scott Galica, Leland Aldridge, Edward E. Eyler

Published Oct 16, 2013• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.88.043418

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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.
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.
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.
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.
We demonstrate that a bichromatic standing-wave laser field can exert a significantly larger force on a molecule than ordinary radiation pressure. Our experiment measures the deflection of a pulsed supersonic beam of CaF molecules by a two-frequency laser field detuned symmetrically about resonance with the nearly closed $X(v=0)\ensuremath{\rightarrow}B({v}^{\ensuremath{'}}=0)$ transition. The inferred force as a function of relative phase between the two counterpropagating beams is in reasonable agreement with numerical simulations of the bichromatic force in this multilevel system. The large magnitude of the force, coupled with the reduced rate of spontaneous emission, indicates its potential utility in the production and manipulation of ultracold molecules.
This dissertation discusses an experiment to demonstrate the application of the stimulated bichromatic optical force (BCF) on the diatomic molecule calcium monofluoride (CaF). The research demonstrates the deflection of a supersonic beam of CaF through the application of BCF under a variety of conditions, highlighting distinctive characteristics of the force. Results show that the measured deflection of the molecular beam is consistent with the behavior of BCF under the tested conditions. In particular, we have measured a predicted reversal in the direction of the force as well as an applied force which exceeds the radiation pressure force. Detailed modeling of the BCF in multilevel systems corroborates our findings. We discuss the development and application of these models with respect to non-ideal conditions present in the experiment. The construction of the molecular beam source and BCF laser systems are discussed in detail. A brief discussion of further modeled extensions of the BCF through the addition of higher order sidebands is presented as well. Overall, our results demonstrate that the BCF is a potentially useful tool for manipulation of cold molecules.
We have recently begun to explore the very strong optical forces that can be exerted on atoms by polychromatic light. Unlike the radiative force that is limited to be less than ℏkγ/2 in monochromatic light or the dipole force that alternates on a wavelength scale in a monochromatic standing wave, limiting its utility, these new forces have very attractive features. Not only is their strength far greater than Frad, but also their velocity range is far greater than γ/k, so that beam slowing can be accomplished without Doppler compensation in distances measured in millimeters instead of meters. These forces have been implemented by modulation of a single-frequency laser or by combination of the light of two different single-frequency lasers.