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 ↔ X system with a simplified numerical model and with a semiquantitative estimate based on 2-level systems. The simplified model performs nearly as well as the complete version, whereas the 2-level model is useful for making order-of-magnitude estimates, but nothing more.

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 three, 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.

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) → B(v ′ = 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.Radiative forces on atoms have been the major tool enabling laser cooling and trapping [1] and the myriad of applications which have resulted, including precision spectroscopy, quantum degenerate gases, ultracold collisions, and quantum simulations. There are two general types of radiative force: spontaneous force, also known as radiation pressure, and stimulated force, also known as the dipole force. Radiation pressure is the result of absorption/spontaneous emission cycles, while the stimulated force arises from absorption followed by stimulated emission. The latter requires an intensity gradient and can be thought of as a coherent redistribution of photons between various propagation directions. Laser manipulation of atoms is a well-developed field, but recently, these techniques have been increasingly applied to molecules [2]. This extension is nontrivial due to the complicated internal structure of molecules caused by their vibrational and rotational degrees of freedom [3]. Radiation pressure has been used to slow, cool, and trap molecules that fortuitously have near-cycling transitions [4][5][6][7][8][9][10][11][12][13]. Stimulated forces have also been used to manipulate molecules [14-17], but on a more limited scale. Compared to radiation pressure, stimulated forces have two significant advantages for molecules: (1) radiation pressure is limited by the spontaneous emission rate, while stimulated forces can greatly exceed this saturated value; and (2) radiation pressure relies on spontaneous emission which can optically pump the molecules into "dark" states which no longer interact with the laser field.A specific type of stimulated force, the bichromatic force (BCF) [18,19], is particularly promising for manipulating molecules [20]. The BCF involves two frequencies which are tuned symmetrically above and below a resonant frequency ω by ±δ. The two frequencies are both present in oppositely-directed beams, which gives rise to counterpropagating trains of beat notes with a fixed relative phase, χ. In a simplified picture of BCF, if each beat is considered an effective π-pulse which inverts the population, a molecule can be excited by a beat from one direction and rapidly returned to the ground state by a beat from the other direction. Each absorption/stimulated emission cycle imparts an i...

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)/ P Q 12 (0.5) in CaF andÃ(000)−X(000), P 11 (1.5)/ P Q 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. a a Supported by the National Science Foundation.

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