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arXiv:1509.05350 · Physical Review A

Simulations of the bichromatic force in multilevel systems

Leland Aldridge, Scott Galica, Edward E. Eyler

Published Jan 20, 2016• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.93.013419

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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 $B leftrightarrow X$ 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 $B leftrightarrow X$, (0-0) transition, still at an early stage, include studies of both the $P_{11}(1.5)/^PQ_{12}(0.5)$ branch, a quasi-cycling configuration with extensive hfs, and the $R_{11}(0.5)/^RQ_{21}(0.5)$ branch, which has a much simpler hfs but requires rotational repumping.

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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↔XB\ensuremath{\leftrightarrow}XB\ensuremath↔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.
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.
Abstract We present a theoretical study of the bichromatic force exerted on magnesium monofluoride (MgF), in which we have considered the complex vibrational and rotational levels and the effects of small internal splittings and degeneracies, including fine and hyperfine structures and the magnetic quantum numbers. We calculate some parameters used in the MgF molecular transitions between X 2 Σ + , A 2 Π and B 2 Σ + states. It is the first time that the radiative lifetimes of B 2 Σ + → X 2 Σ + and B 2 Σ + → A 2 Π have been derived by ab initio calculations. The detailed numerical modeling of bichromatic forces by direct numerical solution for the time-dependent density matrix is presented. Here, we propose a simplified numerical model to study the dynamic process of MgF slowing by neglecting the effect of the high vibrational levels, in which a skewed magnetic field is applied to destabilize the dark state. We deduce the relation between per-bichromatic-component irradiance I and the total Rabi frequency amplitude. We also compare our proposed simplified model with two other theoretical ones (Aldridge et al 2016 Phys. Rev. A 93 013419 ). Monte Carlo simulations show that a buffer-gas-cooled MgF beam with a forward velocity of 120 m s −1 can be decelerated nearly to several m/s within a distance of ∼0.5 cm. Comparing with the B → X transition, we find that the A → X transition in MgF is more suitable for the bichromatic force cooling and slowing.
We examine the prospects for utilizing the optical bichromatic force (BCF) to greatly enhance laser deceleration and cooling for near-cycling transitions in small molecules. We discuss the expected behavior of the BCF in near-cycling transitions with internal degeneracies, then consider the specific example of decelerating a beam of calcium monofluoride molecules. We have selected CaF as a prototype molecule both because it has an easily accessible near-cycling transition and because it is well suited to studies of ultracold molecular physics and chemistry. We also report experimental verification of one of the key requirements, the production of large bichromatic forces in a multilevel system with significant energy level splittings, by performing tests in an atomic beam of metastable helium.
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.
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.}