Coherent Bichromatic Force Deflection of Molecules

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 ${\tilde{X}}^2{\mathrm{\Sigma }}^{+}\leftrightarrow {\tilde{A}}^2{\mathrm{\Pi }}_{1/2}$ 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 $70\hslash k$ 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.

Figure 1

The energy diagram on the left-hand side depicts optimal bichromatic frequency detunings for SrOH addressed on the ${\tilde{X}}^2{\mathrm{\Sigma }}^{+}\to {\tilde{A}}^2{\mathrm{\Pi }}_{1/2}$ $P(N^{\prime \prime }=1)$ transition for $10\mathrm{W}/{\mathrm{cm}}^2$ irradiance per each frequency component with 688 nm laser light. Solid horizontal lines indicate positions of the energy levels. The parameters were estimated using numerical solutions of optical Bloch equations. Amplitude modulated optical pulses seen by SrOH molecules are shown on the right-hand side.

Figure 2

Data demonstrating bichromatic force deflection of the SrOH beam with the $\pi /2$ relative phase shift between the counterpropagating laser beams. Plots (a) and (c) illustrate the effect of purely radiative force on the molecular beam. Plots (b) and (d) compare the beam profiles for unperturbed molecular beam and with BCF applied. The same vertical axis is used for (a) and (b) as well as the (c) and (d) plots.

Figure 3

Summary of the molecular beam centroid shift for various experimental conditions: unperturbed molecular beam, radiative deflection with retroreflected beam blocked and BCF deflection with a $\pi /2$, $\pi$, and $3\pi /2$ relative phase shift. Reversal of the BCF directionality with the relative phase change is observed.

Figure 4

Calculated profile of the bichromatic force exerted on SrOH molecules as a function of velocity under optimal experimental conditions. The force magnitude is normalized to the size of the maximum radiative force in an ideal two-level atomic system ($F_{\mathrm{rad},2\text{−}\text{level}}=\hslash k\gamma /2$). Sharp resonances around 0 and $\pm 45\mathrm{m}/\mathrm{s}$ represent Doppleron resonances and have been previously seen in BCF profiles for atoms [47]. Solid horizontal line shows the average bichromatic force achieved in the experiment. The calculated force profile assumes an irradiance of $10\mathrm{W}/{\mathrm{cm}}^2$, a magnetic field of 27.2 G skewed 33° with respect to the polarization axis and the frequency parameters depicted in Fig. 1.