Shaping Cold Atom Clouds with a Vortex Beam

Abstract

We introduce a method for shaping a cold atom cloud using a vortex laser beam with a polarization singularity at its center, which creates a point of vanishing intensity. Exploiting this feature we experimentally demonstrate two different schemes to create micron-scaled line- and sheet-like atomic density distributions. In the dynamic scheme, atoms in the bright beam regions are accelerated and therefore effectively removed from the cloud. In the dark-state scheme, these atoms are pumped into a state that does not interact with the shaping light. In both cases, an atomic distribution remains, either as a thin line or as a sheet when an additional polarizer is used. We find good agreement between the experimental results and our theoretical model, which predicts the method to be in principle not diffraction-limited, paving the way for studies of phenomena arising in unconfined atomic ensembles on the micrometer scale.

Figures (9)

• Figure 1: Vortex beam. Intensity profiles of a vortex beam generated from a Gaussian beam (TEM$_{00}$) using a $m=1$ vortex retarder placed at the position of the beam waist ($z'=0$). The profiles are calculated at positions (a) $z=0$, (b) $z=0.05\,z_0$, (c) $z=0.5\,z_0$, and (d) $z=0.5\,z_0$ with additional polarization filter. The 2D profiles are shown together with 1D line-scans through the beam center ($y=0$), with the line-scan positions marked in the 2D profiles (white dashed lines). The line-scans in (b)-(d) are approximated by parabolas around the beam center (black dash-dotted line), with curvatures calculated from Eq. \ref{['eq:curvatureSimple']}. All intensities are normalized to the maximum intensity and all lengths are in units of the initial beam waist $w_0$. The white arrows in the 2D profiles indicate the direction of the local light field polarization.
• Figure 2: Shaping schemes. Atomic level schemes for the theoretical description of (a) the dynamic- and (b) the dark-state shaping methods.
• Figure 3: Experimental realization. (a) Experimental setup for the generation and shaping of an atomic cloud. A six-beam magneto-optical trap (MOT) is operated inside a vacuum chamber, whose lateral view-ports allow optical access with the lasers required for MOT operation, cloud imaging and shaping. The Gaussian intensity profile of the shaping beam coming out of the fiber is transformed into a vortex via the vortex retarder (VR) or into a double-lobed structure via the additional polarizer. The beam power during the shaping pulse is monitored via a photodiode (PD). Gravity is pointing in negative y-direction. (b) Level scheme of the $^{87}$Rb D2-line and transition frequencies for the lasers used in the experiment. The shaping light is tuned to different transitions, depending on the shaping method used. (c) Measurement procedure for the shaping of an atomic cloud released from a MOT. After the MOT loading, the cloud is left free to thermally expand during $\tau_1$, after which it is illuminated by the shaping light during $\tau_\text{ill}$ and then freely expands again during $\tau_2$, before being imaged.
• Figure 4: Dynamic shaping with double-lobed beam. Absorption images as simulated (upper rows) and measured (lower rows) for a series of increasing (a) shaping beam power $P$, with $\tau_1=1.2\,$ms, $\tau_\text{ill}=35\,\upmu$s, $\tau_2=565\,\upmu$s, (b) illumination time $\tau_\text{ill}$, with $\tau_1=1.2\,$ms, $\tau_2=565\,\upmu$s, $P=1.45\,$mW, and (c) free expansion time after the shaping $\tau_2$, with $\tau_1=200\,\upmu$s, $\tau_\text{ill}=300\,\upmu$s, $P=1.45\,$mW. All images are shown in the $\tilde{\text{x}}$-$\tilde{\text{y}}$ plane, with the shaping beam tuned to resonance and irradiated from the left. In the simulated images, we set $\beta_0=2.2\cdot10^{4}\, \text{mW}^{-1}\text{cm}^{-2}$ and the visibility of the atoms is adjusted depending on their final velocity to account for the Doppler shift with respect to the imaging beam. All images are normalized to the maximum atom density within the first image of each individual row, both for simulations and experiments.
• Figure 5: Dark-state shaping with vortex beam. Absorption images for a measurement series of increasing vortex beam power $P$, with fixed timings for the shaping sequence $\tau_1=4.5\,$ms, $\tau_\text{ill}=10\,\upmu$s, $\tau_2=0$. All images result from the average of 20 pictures and are shown in the $\tilde{\text{x}}$-$\tilde{\text{y}}$ plane, normalized to the maximum atom density in each image. Between the first and the last picture, the atomic column density is reduced by more than three orders of magnitude.