Fig. 1. Optics pictorial showing production of a TEM₀₁ from an input Gaussian. (a) An input Gaussian passes the phase plate (PP) giving a relative π phase shift between the halves of the beam. (b) The aperture (A) is in the far field of the output beam from PP. This produces the Fourier transform at A. (c) Higher spatial modes are truncated by A. (d) Lens L1 produces the Fourier transform of the output of A resulting in a near TEM₀₁ mode profile. (e) A true TEM₀₁ beam, the profile in (d) only deviates in small fringes outside the main lobes. The images are numerically calculated beam profiles shown as $\sqrt{I(q,p)}$ .

Fig. 2. Profile of TEM₀₁ mode beam. (a) A CCD picture of a TEM₀₁ trapping beam imaged as seen by the atoms. The image extends only 100µm in the z direction. (b) The profile along the narrow axis, the boxes are points integrated along the z axis for the center 10µm and the solid line is a fit to an ideal TEM₀₁ mode profile in Equation 1, giving a waist size of W_x =1.8µm.

Fig. 3. Optical trap beam input ports and imaging ports in the science chamber are shown in this schematic. The setup has the capacity to accept vertical and horizontal visible beams as well as a vertical infrared beam. There are 780 nm absorption imaging beams for both vertical and horizontal diagnostics. L1 and L2 are the final lenses in the vertical and horizontal beam paths, DM1 and DM2 are dichroic mirrors, AgM is a silver mirror. Gravity in the figure is in the -y direction.

Fig. 4. Loading sequence of hTEM₀₁ trap. The pair of lobes for each hTEM₀₁ beam are represented in gray; the lower hTEM₀₁ is the ligher shade. The vertical infrared beam is not shown, but present in all (b) to (d). (a) Combined optical and magnetic trap. (b) Combined gravito-optical trap where the lower hTEM₀₁ beam acts as a sheet supporting against gravity. This trap has vertical trap frequency ω_y ≅850Hz. (c) Transfer step into hTEM₀₁ beam. (d) Final optical trap inside hTEM₀₁ beam. This trap has vertical trap frequency ω_y ≅21kHz.

Fig. 5. BEC Expansion from hTEM₀₁ trap. The black squares give data points for σ _y as a function of time for condensates released at time zero. The data is consistent with the 21 kHz expected trap frequency for this TEM₀₁ trap. The images to the right are absorption images of one of the shots of the indicated data point. The upper picture is of a condensate released from the inside the TEM₀₁ trap, and the lower was released from above the sheet (the gravito-optical trap) as in Figure 4(b). This is the red circle data point on the plot. The lower picture is a 3-D condenstate and does not obey Equation 6.