Experimental Realization of Josephson Junctions for an Atom SQUID

We report the creation of a pair of Josephson junctions on a toroidal dilute gas Bose-Einstein condensate (BEC), a configuration that is the cold atom analog of the well-known dc superconducting quantum interference device (SQUID). We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. The junctions and toroidal trap are created with the painted potential, a time-averaged optical dipole potential technique which will allow scaling to more complex BEC circuit geometries than the single atom-SQUID case reported here. Since rotation plays the same role in the atom SQUID as magnetic field does in the dc SQUID magnetometer, the device has potential as a compact rotation sensor.

Figure 1

(a) Schematic of the experimental setup. Arbitrary and dynamic potentials for the BEC are created by the superposition of two red-detuned beams making attractive optical dipole potentials. One beam is a horizontal light sheet, the other is a rapidly moving focused beam which paints the potential. (b) Calculated intensity distribution of the $8\mu \mathrm{m}$ diameter painted atom SQUID potential. (c) In situ absorption image of a BEC in the atom SQUID potential.

Figure 2

Initial (a) and final (b) configuration of atom SQUID potential. Images of a BEC where bias current is less (c) or more (d) than critical current. Image (d) shows the BEC compression that occurs when tunneling is not possible.

Figure 3

(a) Lines: computed critical current vs atom number for three trap depths. Points show the measured critical atom numbers determined by the experiment (see text) with respective critical currents and fitted trap depth: $1{\mathrm{s}}^{-1}$ and 71 nK (circle), $2{\mathrm{s}}^{-1}$ and 74.5 nK (triangle), $4{\mathrm{s}}^{-1}$ and 75.6 nK (square). (b)–(d): Measurement of critical currents. Each data point is the mean of several measurements of the final normalized population difference $z$, with the error bar being the standard error of the mean. Systematic calibration uncertainty in atom number is less than 10%. Solid (blue) curves show the best fit solution of the Josephson equations. The JJ rotation frequency $f$, corresponding bias current $\dot{z}$, and duration of JJ movement $T$ are: (b) $f=0.25\mathrm{Hz}$, $\dot{z}=1{\mathrm{s}}^{-1}$, $T=370\mathrm{ms}$. (c) $f=0.5\mathrm{Hz}$, $\dot{z}=2{\mathrm{s}}^{-1}$, $T=185\mathrm{ms}$. (d) $f=1\mathrm{Hz}$, $\dot{z}=4{\mathrm{s}}^{-1}$, $T=92.5\mathrm{ms}$.

Figure 4

(a) Final value of normalized population difference $z$ for $f=1\mathrm{Hz}$ computed using the Josephson equations (solid line) and the 3D GPE (disks). Inset: disks: current-phase relation from GPE simulation for $N=4250$ atoms. Dashed line: ideal current-phase relation $\dot{z}=2E_J/\hslash N\sin \varphi$. (b) Analogous 1D GPE simulations for a torus with radius $20\mu \mathrm{m}$. Barrier FWHM (in units of healing length $\xi$) and height (in units of chemical potential $\mu$) at $N=22000$ atoms: $3.9\xi$ and $1.8\mu$ (disks), $37\xi$ and $0.93\mu$ (squares), and $36\xi$ and $0.51\mu$ (triangles). Barrier rotation frequencies: 0.2 Hz (solid disks and squares), 0.5 Hz (open disks and squares), 5 Hz (solid triangles), and 12.5 Hz (open triangles). Inset: corresponding current-phase relations for $N=22000$ atoms. Dashed line: ideal current-phase relation for the tunnel JJ.