Bichromatic force on metastable argon for atom-trap trace analysis

For an efficient performance of atom-trap trace analysis, it is important to collimate the particles emitted from an effusive source. Their high velocity limits the interaction time with the cooling laser. Therefore, forces beyond the limits of the scattering force are desirable. The bichromatic force is a promising candidate for this purpose which is demonstrated here on metastable argon-40. The precollimated atoms are deflected in one dimension and the acquired Doppler shift is detected by absorption spectroscopy. With the experimentally accessible parameters, it was possible to measure a force three times stronger than the scattering force. Systematic studies on its dependence on Rabi frequency, phase difference, and detuning to atomic resonance are compared to the solution of the optical Bloch equations. We anticipate predictions for a possible application in atom-trap trace analysis of argon-39 and other noble gas experiments, where a high flux of metastable atoms is needed.

Figure 1

Position-dependent energy levels of the system for different phases of the standing waves. The horizontal lines mark the uncoupled ground (solid) and excited (dashed) states. An atom will undergo transitions between the dressed states with a certain probability and will gain or lose kinetic energy in this process. The preferred direction of the bichromatic force is given by the position and the phase difference $\varphi$ of the standing waves. For $\varphi =0$, the coupling to both modes compensate each other and the states remain uncoupled. In the case of $\varphi =\frac{1}{2}\pi$, atoms which start in the shaded area of a state with larger admixture of the ground state (bold curves) will receive a force to the left side. The opposite force acts on atoms starting in the unshaded area, but due to the three-to-one ratio of the shaded area, the mean force is to the left. For $\varphi =\frac{3}{4}\pi$, the sign is reversed and the average force is to the right. For $\varphi =\pi$, the optimal Rabi frequency is $\mathrm{\Omega }=\frac{\pi }{4}\mathrm{\Delta }$, but no direction is favored. Other choices of phase difference yield nonoptimal results, since the level gaps are increased. Spontaneous emission occurs more likely in the states with larger admixture to the excited state (gray curves) and will change the slope direction. However, the force is retained on average as a subsequent spontaneous emission is more likely to happen once the path has changed.

Figure 2

Velocity-dependent force profile. The parameters for argon, $\gamma =2\pi \times 5.87\text{MHz},\mathrm{\Delta }=2\pi \times 65\text{MHz}\approx 11\gamma$, and $\mathrm{\Omega }=\sqrt{\frac{3}{2}}\mathrm{\Delta }\approx 14\gamma$ are used for the numerical calculation (dashed). Accounting for different Rabi frequencies due to the Gaussian laser beam and therefore nonoptimal bichromatic forces yields a corrected calculation (solid). The sharp resonances correspond to Doppleron resonances and the vertical dashed lines mark $|\pm kv|=\mathrm{\Delta }$, where standard optical molasses can be seen as zero crossings of the force.

Figure 3

Frequency generation. The incoming light has a detuning of $-420$ MHz from atomic resonance ${\omega }_A$ and is shifted upwards to $-\mathrm{\Delta }\pm kv$ with the top and bottom AOMs. The two AOMs in between are driven by synchronized frequency generators and are adjusted for equal distribution into zeroth and first order. A relative phase shift $\varphi$ can be added by tuning the relative phase of the driving rf frequencies. This yields the four frequencies ${\nu }_{BC}={\omega }_A\pm kv\pm \mathrm{\Delta }$ which are amplified subsequently by two homebuilt tapered amplifiers.

Figure 4

Measurement and detection setup. The precollimated beam of metastable ${}^{40}\mathrm{Ar}$ is deflected in the interaction region. The powers of the bichromatic beams have been stabilized by photodiodes placed behind the mirrors that are not shown here. The deflected argon beam acquires a Doppler shift that can be measured by an absorption spectroscopy in the detection zone.

Figure 5

Phase dependence of the force. The bichromatic force has been measured with absorption spectroscopy for different relative phases $\varphi$ of the light fields. The optical phase can be controlled arbitrarily by tuning the phases of the sine waves on the acousto-optical modulators. Thereby, the direction and strength of the force is changed in agreement with theoretical predictions which are shown by the solid curve. As expected from the doubly dressed atom model, the force vanishes near phases $\varphi =0,\varphi =\pi$, and $\varphi =2\pi$.

Figure 6

Rabi frequency dependence of the force. The bichromatic force has been measured for different intensities which are mapped to corresponding Rabi frequencies by using $\mathrm{\Omega }=\gamma \sqrt{\frac{I}{2I_S}}$ and $I_S=14.4\text{W}/{\text{m}}^2$ for circularly polarized light. The bandwidth of the setup has allowed Rabi frequencies roughly between $12\gamma$ and $17\gamma$ since the detuning has to be scaled with $\mathrm{\Delta }=\sqrt{\frac{2}{3}}\mathrm{\Omega }$. The measured data points show a gain of the force, as expected from the doubly dressed atom model and the solid curve shows the numerically calculated force. The spontaneous scattering force (dashed) increases faster but saturates eventually.

Figure 7

Detuning width of the force. The bichromatic force profile has been measured for different frequency offsets which correspond to Doppler shifts $\delta =\left|kv\right|$. The data points resemble the rough structure of the force profiles that have been calculated with the optical Bloch equations, shown by the solid curve. These values are further corrected by accounting for the inhomogeneous Gaussian intensity distribution. The dashed line is the expected spontaneous scattering force with the same intensity and is saturated over most of the shown range.

Figure 8

Proposed setup for a bichromatic transverse kicker. The transversal velocity capture range of the existing collimator covers only $\sim 6\%$ of the atoms leaving the effusive source. This can be increased by a transverse kicker, a precollimation stage to decelerate faster atoms below the critical velocity of the collimator (schematic diagram shown left). The gain as a function of laser detuning (right) to compensate the Doppler shift $\delta$ is shown for bichromatic forces with two separate interaction regions of 5 mm length (solid) and spontaneous scattering forces with a 10-mm-long interaction region (dashed). The limited interaction time favors a bichromatic transverse kicker, even if the interaction region is halved for every direction due to independent collimation of the two perpendicular dimensions.