Four-color stimulated optical forces for atomic and molecular slowing

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 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.

Simulations of the bichromatic force in multilevel systems

“…In each beam the two frequencies ω + δ and ω − δ produce a train of beat notes, as described above. The total on-axis electric field for this arrangement is approximately [18] E BCF (z, t) = 4 E 0 Re[{ǫ(cos(kz) cos(δt) cos(χ/2) + i sin(kz) sin(δt) sin(χ/2)}e…”

“…The bichromatic force in two-level systems has successfully been demonstrated in several atoms and is amply described in prior publications [9][10][11][12][13][14][15][16][17][18]. In brief, the BCF is the coherent force produced by a balanced counterpropagating pair of two-color cw laser beams.…”

Laser Cooling without Spontaneous Emission

“…We use the He 2 3 S → 3 3 P transition at λ = 389 nm where ω r = 2π × 330 kHz so that t c ≈ 380 ns. Since τ ≈ 106 ns and the time averaged excited state population is ∼ 0.4 [13], the average spontaneous emission time is t SE ≈ 260 ns. Thus we expect an average of ≤1.5 SE events during time t c .…”

Continuous all-optical deceleration and single-photon cooling of molecular beams

“…In this mode of operation, it bears some similarity to the bichromatic force [30][31][32]. This unchirped realization may be regarded as being (in some respects) the polychromatic limit of the bichromatic force [33].…”

“…Shot-to-shot pulse energy variation is also a concern, as is beam-pointing stability and a potential imbalance between the co-and counterpropagating laser beams. Circumventing such sources of population transfer infidelity is necessary if large numbers of molecules are to be decelerated with pulses from a mode-locked laser, as pointed out by Galica et al [33].…”