Matter Wave Lensing to Picokelvin Temperatures

Using a matter wave lens and a long time of flight, we cool an ensemble of ${}^{87}\mathrm{Rb}$ atoms in two dimensions to an effective temperature of less than $50_{-30}^{+50}\mathrm{pK}$. A short pulse of red-detuned light generates an optical dipole force that collimates the ensemble. We also report a three-dimensional magnetic lens that substantially reduces the chemical potential of evaporatively cooled ensembles with a high atom number. By observing such low temperatures, we set limits on proposed modifications to quantum mechanics in the macroscopic regime. These cooling techniques yield bright, collimated sources for precision atom interferometry.

Figure 1

(a) Schematic of the apparatus (including vertically oriented quadrupole trap, horizontal TOP coil pairs, and blue-detuned launching lattice). (b) A 3 W laser, $1/e^2$ radial waist $\sigma =3.4\mathrm{mm}$, 1.0 THz red detuned from the ${}^{87}\mathrm{Rb}$ $D_2$ line, acts on the atom cloud as a dipole lens (the $\sim 1\mathrm{mrad}$ beam angle is exaggerated for clarity). (c) Fluorescence image of a 1.6 nK cloud after 2.8 s of free fall. (d) The distribution in (c) refocused using the dipole lens. There is no observed axial heating. (e) Optical analogy showing the object, lens, and image, with object distance $t_o$ and image distance $t_i$.

Figure 2

Comparison of the dipole lens beam intensity profile after numerical paraxial wave propagation of the measured profile by (a) 0.25 m and (b) 16.25 m. The residuals of fitting a 2D Gaussian are shown above each beam profile. The beam is initially spatially filtered by propagation through an optical fiber.

Figure 3

(a) Filled black (open red) points denote measured rms cloud widths on the $x$-axis ($y$-axis) camera. Each point is the weighted mean of Gaussian fits to six experimental shots. The dashed gray curve is a simultaneous fit to the measurements from both cameras and reports a minimum size of $70\mu \mathrm{m}$ at a lens duration of 34 ms. (b) Vertically binned images comparing the transverse size of a $90\pm 10\mu \mathrm{m}$ cloud used to characterize the PSF [solid red (gray) line] to a cloud refocused 2.8 s later (solid black line). The good overlap indicates high-fidelity refocusing. Dotted black: Gaussian profile extracted from a fit of the refocused cloud. The fit accounts for the broadening and distorting effects of the PSF (dashed blue line).

Figure 4

(a) Minimum rms width of the cloud as a function of the fractional object time. (b) The lens duration required to refocus the atom cloud ($\delta t_{\min }$) as a function of the fractional object time. The filled black (open red) points represent measurements on the $x$-axis ($y$-axis) camera. Solid blue line: Expected behavior for a cloud of finite initial size ($56\mu \mathrm{m}$) and no initial $x–v$ correlations in an optical beam with a Gaussian profile. The blue shaded regions represent the corresponding ranges possible with correlations. The curve in (a) has no free parameters. For (b), the optical power is a free parameter that fits to 2.8 W. Dashed gray line: Expected behavior for an ideal harmonic potential of the same strength as at the center of the beam [33]. Dotted black line: Expected behavior for a cloud with zero initial size subject to Gaussian aberrations.

Figure 5

Magnetic lensing in the TOP trap. (a) Absorption images of the ensemble oscillating in the trap. (b) Radial (filled blue circles) and vertical (open black circles) rms cloud widths. Theory curves are based on numerical solutions for trajectories of noninteracting particles in the exact TOP potential. The solid grey curves are simultaneous fits to the center-of-mass trajectory and the vertical width, with free parameters for the TOP potential (radial quadrupole gradient $\nabla B$, spinning bias field $B_0$, and vertical position) as well as initial first and second moments of the vertical distribution. The dashed blue curve results from a 2D Monte Carlo simulation of the atom distribution using the fitted parameters (including $\nabla B=20.9\pm 0.1\mathrm{G}/\mathrm{cm}$, $B_0=6.9\pm 0.3\mathrm{G}$) but no free parameters. The initial radial size is scaled from the fitted vertical size by the ratio of the measured initial cloud widths.