We examine two approaches for significantly extending the velocity range of the optical bichromatic force (BCF), to make it useful for laser deceleration of atomic and molecular beams. First, we present experimental results and calculations for BCF deceleration of metastable helium using very large BCF detunings and discuss the limitations of this approach. We consider in detail the constraints, both inherent and practical, that set the usable upper limit of the BCF. We then show that a more promising approach is to utilize a BCF profile with a relatively small velocity range in conjunction with chirped Doppler shifts, to keep the force resonant with the atoms as they are slowed. In an initial experimental test of this chirped BCF method, helium atoms are slowed by $\ensuremath{\sim}$370 m/s using a BCF profile with a velocity width of $\ensuremath{\lesssim}$125 m/s. Straightforward scaling of the present results indicates that a decelerator for He* capable of loading a magneto-optical trap can yield a brightness comparable to a much larger Zeeman slower.
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.
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 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),
P11(1.5)/PQ12(0.5) in CaF and
A~(000)
−X~(000),
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
BleftrightarrowX 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
BleftrightarrowX, (0-0) transition, still at an early stage, include studies of both the
P11(1.5)/PQ12(0.5) branch, a quasi-cycling configuration with extensive hfs, and the
R11(0.5)/RQ21(0.5) branch, which has a much simpler hfs but requires rotational repumping.