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International Symposium on Molecular Spectroscopy (ISMS)

THE BICHROMATIC FORCE ON SMALL MOLECULES

Leland Aldridge, Edward E. Eyler, Donal Sheets, Scott Galica

Published Jun 22, 2016• 0 citations
Publisher

Abstract

The bichromatic force is a coherent optical force that has been demonstrated to exceed the saturated radiative force from a monochromatic cw laser by orders of magnitude in atomic systems. By stimulating photon emission between two states, the bichromatic force allows us to increase the photon scattering rate beyond the spontaneous emission rate while also suppressing decays into dark states. We present studies of the efficacy of the bichromatic force on molecular systems using the test cases of $B$-$X$ (0,0), $P_{11}(1.5)/^PQ_{12}(0.5)$ in CaF and $\tilde{A}$(000)$-\tilde{X}$(000), $P_{11}(1.5)/^PQ_{12}$(0.5) in the linear triatomic molecule SrOH. Computational results from detailed multilevel models indicate that both of these molecular systems are suitable for the use of the bichromatic force, with neither repumping nor magnetic destabilization of dark states interrupting the coherent cycling at the heart of the force. We comment on the applicability of the bichromatic force to arbitrary polyatomic molecules, and present our experimental progress in demonstrating the bichromatic force on CaF and possibly on SrOH.\footnote{Supported by the National Science Foundation.}

DOI
10.15278/isms.2016.wj14

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The bichromatic force is a coherent optical force that has been demonstrated to exceed the saturated radiative force from a monochromatic cw laser by orders of magnitude in atomic systems. By stimulating photon emission between two states, the bichromatic force allows us to increase the photon scattering rate beyond the spontaneous emission rate while also suppressing decays into dark states. We present studies of the efficacy of the bichromatic force on molecular systems using the test cases of BBB-XXX (0,0), P11(1.5)/PQ12(0.5)P_{11}(1.5)/^PQ_{12}(0.5)P11​(1.5)/PQ12​(0.5) in CaF and A~\tilde{A}A~(000)−X~-\tilde{X}−X~(000), P11(1.5)/PQ12P_{11}(1.5)/^PQ_{12}P11​(1.5)/PQ12​(0.5) in the linear triatomic molecule SrOH. Computational results from detailed multilevel models indicate that both of these molecular systems are suitable for the use of the bichromatic force, with neither repumping nor magnetic destabilization of dark states interrupting the coherent cycling at the heart of the force. We comment on the applicability of the bichromatic force to arbitrary polyatomic molecules, and present our experimental progress in demonstrating the bichromatic force on CaF and possibly on SrOH.\footnote{Supported by the National Science Foundation.}
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.
We demonstrate the effect of the coherent optical bichromatic force on a molecule, the polar free radical strontium monohydroxide (SrOH). A dual-frequency retroreflected laser beam addressing the X[over ˜]^{2}Σ^{+}↔A[over ˜]^{2}Π_{1/2} electronic transition coherently imparts momentum onto a cryogenic beam of SrOH. This directional photon exchange creates a bichromatic force that transversely deflects the molecules. By adjusting the relative phase between the forward and counterpropagating laser beams we reverse the direction of the applied force. A momentum transfer of 70ℏk is achieved with minimal loss of molecules to dark states. Modeling of the bichromatic force is performed via direct numerical solution of the time-dependent density matrix and is compared with experimental observations. Our results open the door to further coherent manipulation of molecular motion, including the efficient optical deceleration of diatomic and polyatomic molecules with complex level structures.
This dissertation describes calculations and simulations which extend the optical bichromatic force (BCF), which has previously been examined primarily in the context of two-level systems, to more complex polychromatic fields and to multilevel systems. Through detailed examination of various simple multilevel systems, I develop prescriptions for the application of the BCF to general multilevel systems. I apply these prescriptions to simulations of the molecular systems CaF and SrOH and provide BCF parameters for each that will guide future experiments. The design of an experiment to measure BCF deflection of a molecular beam of CaF is discussed. I close with discussion of prospects for extending this work to a molecular decelerator which can be used as the first stage of a molecular trap.
Coherent optical bichromatic forces have been shown to be effective tools for rapidly slowing and cooling simple atomic systems. While previous estimates suggest that these forces may also be effective for rapidly decelerating molecules or complex atoms, a quantitative treatment for multilevel systems has been lacking. We describe detailed numerical modeling of bichromatic forces by direct numerical solution for the time-dependent density matrix in the rotating-wave approximation. We describe both the general phenomenology of an arbitrary few-level system and the specific requirements for slowing and cooling on a many-level transition in calcium monofluoride (CaF), one of the molecules of greatest current experimental interest. We show that it should be possible to decelerate a cryogenic buffer-gas-cooled beam of CaF nearly to rest without a repumping laser and within a longitudinal distance of about 1 cm. We also compare a full 16-level simulation for the CaF $B\ensuremath{\leftrightarrow}X$ system with a simplified numerical model and with a semiquantitative estimate based on two-level systems. The simplified model performs nearly as well as the complete version, whereas the two-level model is useful for making order-of-magnitude estimates, but nothing more.
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 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.