Persistent Currents in Rings of Ultracold Fermionic Atoms

We have produced persistent currents of ultracold fermionic atoms trapped in a ring, with lifetimes greater than 10 sec in the strongly interacting regime. These currents remain stable well into the BCS regime at sufficiently low temperature. We drive a circulating BCS superfluid into the normal phase and back by changing the interaction strength and find that the probability for quantized superflow to reappear is remarkably insensitive to the time spent in the normal phase and the minimum interaction strength. After ruling out spontaneous current formation for our experimental conditions, we argue that the reappearance of superflow is due to weak damping of normal currents in this limit. These results establish that ultracold fermionic atoms with tunable interactions can be used to create matter-wave circuits similar to those previously created with weakly interacting bosonic atoms.

Figure 1

Cross sections of an idealized model of the potential experienced by a ${}^6\mathrm{Li}$ atom in our “ring-dimple” optical trap in its final configuration (the potential is twice as deep for molecules). (a) Black line is the potential along a horizontal line through the center of symmetry, transverse to the direction of propagation of the sheet beam. The radial trap frequency for atoms away from the ring minimum is $37(5){\mathrm{s}}^{-1}$. (b) Vertical cross section of the trap potential at $r=0$ (dashed line, blue online) and $r=12.0\mu \mathrm{m}$ (dotted line, red online), as indicated by corresponding vertical lines in (a). The vertical trap frequency is $1.5(1)\times {10}^3{\mathrm{s}}^{-1}$ for atoms near the ring potential minimum, and $1.4(1)\times {10}^3{\mathrm{s}}^{-1}$ away from the ring beam. The plot vertical range is from $U_{\mathrm{trap}}=0$ at the ring minimum to the “trap-off” potential in the midplane of the ring ($1.32\mu \mathrm{K}$).

Figure 2

(a) Absorption image (10 averaged) of an equal spin mixture of ${}^6\mathrm{Li}$ atoms in the trap potential of Fig. 1, with $1\times {10}^4$ atoms in each spin state. A magnetic field of 107.4 mT has been used to tune the scattering length to $-179\mathrm{nm}$. The density peak is at $r=12.0(2)\mu \mathrm{m}$. This is a $50\times 50\mu \mathrm{m}$ region cropped from a $215\times 215\mu \mathrm{m}$ image. (b) Radial column density obtained by azimuthal averaging over the full field of view. The plot is shown vertically rescaled $\times 10$ for $r>20\mu \mathrm{m}$ to emphasize the broad halo extending to $r=100\mu \mathrm{m}$. The black dotted line is the expected density profile ($\times 10$) for an ideal Fermi gas in our trap at $T=25\mathrm{nK}$. In region I the system is 3D degenerate, II is quasi-2D degenerate, and III is quasi-2D thermal. Gray band: $2\sigma$ variation of $n_{2\mathrm{D}}(r)$ when calculated separately for each image in the set.

Figure 3

Evolution of a molecular BEC during the last part of the procedure for measuring the current state of the ring. (a) Absorption image showing the vertical column density after relaxing the ring confinement and sweeping the magnetic field from 82.0 to 68.3 mT to lower the interaction energy. (b)–(d) Evolution of the density profile after the optical trap is shut off, for 1.5, 3.5, and 5.5 ms time of flight. Radial magnetic lensing improves the signal-to-noise ratio in detecting the vortex core associated with the persistent current. Each image is from a separate realization of the experiment.

Figure 4

Probability of detecting an $\ell =1$ current after preparing the superfluid ring in that state near resonance (82 mT) then ramping the interactions into the BCS regime and back. The horizontal axis is the maximum magnetic field ($B_{\max }$) used in the ramp (lower scale) and the interaction parameter $-1/k_F^{\prime }a$ (upper scale) where $a$ is the scattering length and $2\pi /k_F^{\prime }=1.49\mu \mathrm{m}$ is the local Fermi wavelength at the “weak point” of the ring. Black squares represent 16 runs averaged, where $B$ was ramped up and down in 0.2 ms with no hold time at $B_{\max }$. Triangles are data (10 runs each point) obtained when holding at $B_{\max }$ for 0.1 s (upright, blue online) and 0.2 s (inverted, red online), and are horizontally offset (from squares) for clarity. Uncertainties are $1\sigma$ Bayesian binomial confidence intervals [53].