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Physical Review A

π –superconducting quantum interference device from ultracold fermionic atomic gases

Miodrag L. Kulić

Published Nov 28, 2007• 7 citations
Publisher

Abstract

Ultracold fermionic atomic gas with Bardeen-Cooper-Schrieffer pairing between hyperfine states is studied. It is shown that a $\ensuremath{\pi}$-Josephson contact [superfluid--normal-gas--superfluid $(S∕N∕S)$] can be realized in systems where the left and right banks $S$ are superfluids and the weak link $N$ is a normal gas with the finite mismatch in chemical potentials ${\ensuremath{\delta}}_{{\ensuremath{\mu}}_{N}}\ensuremath{\ne}0$. If such a $\ensuremath{\pi}$-junction is part of a closed superfluid ring the superfluid mass-current flows spontaneously---the ultracold atomic $\ensuremath{\pi}$--superconducting quantum interference device ($\ensuremath{\pi}$-SQUID). This situation is realized if the radius of the ring $R$ is larger than the critical one ${R}_{c}$. The same effect will be realized also for ${\ensuremath{\delta}}_{{\ensuremath{\mu}}_{N}}⪢\ensuremath{\Delta}$, where $\ensuremath{\Delta}$ is the superfluid gap in S. The sensitivity of the $\ensuremath{\pi}$-SQUID to inertial effects is discussed in the case of rotational motion.

DOI
10.1103/physreva.76.053625

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Ultracold fermionic atomic gas with Bardeen-Cooper-Schrieffer pairing between hyperfine states is studied. It is shown that a \ensuremathπ\ensuremath{\pi}\ensuremathπ-Josephson contact [superfluid--normal-gas--superfluid (S∕N∕S)(S∕N∕S)(S∕N∕S)] can be realized in systems where the left and right banks SSS are superfluids and the weak link NNN is a normal gas with the finite mismatch in chemical potentials \ensuremathδ\ensuremathμN\ensuremath≠0{\ensuremath{\delta}}_{{\ensuremath{\mu}}_{N}}\ensuremath{\ne}0\ensuremathδ\ensuremathμN​​\ensuremath=0. If such a \ensuremathπ\ensuremath{\pi}\ensuremathπ-junction is part of a closed superfluid ring the superfluid mass-current flows spontaneously---the ultracold atomic \ensuremathπ\ensuremath{\pi}\ensuremathπ--superconducting quantum interference device (\ensuremathπ\ensuremath{\pi}\ensuremathπ-SQUID). This situation is realized if the radius of the ring RRR is larger than the critical one Rc{R}_{c}Rc​. The same effect will be realized also for \ensuremathδ\ensuremathμN⪢\ensuremathΔ{\ensuremath{\delta}}_{{\ensuremath{\mu}}_{N}}⪢\ensuremath{\Delta}\ensuremathδ\ensuremathμN​​⪢\ensuremathΔ, where \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ is the superfluid gap in S. The sensitivity of the \ensuremathπ\ensuremath{\pi}\ensuremathπ-SQUID to inertial effects is discussed in the case of rotational motion.
he BCS-like pairing in ultracold fermionic atomic (UCFAGUCFAGUCFAG) gases is studied in the model of "isotopic-spin" pairing proposed in 1991 \cite% {Ku-Hof-SSC}. This model assumes a mismatch (δδδ) in chemical potentials of pairing fermionic atoms. It is shown that a πππ-Josephson junction can be realized in UCFAGUCFAGUCFAG systems, where the left and right banks % S are the UCFAGUCFAGUCFAG superfluids. The weak link MMM consists from the normal % UCFAG with the finite mismatch δδδ. If the πππ-junction is a part of a closed ring the superfluid mass-current flows spontaneously in the ring, i.e., the time-reversal symmetry is broken spontaneously. This is realized if the radius of the ring RRR is larger than the critical one $% R_{c} $. All these effects exist also in the case when δ≫Δδ\gg Δδ≫Δ, where ΔΔΔ is the superfluid gap, but with the reduced thickness of the weak link. It is also discussed, that if junctions SM1M2SSM_{1}M_{2}SSM1​M2​S and trilayers % M_{1}SM_{2} from UCFAGUCFAGUCFAG are realizable this renders a possibility for a novel electronics - \textit{hypertronics}.
The BCS-like pairing in ultracold fermionic atomic (UCFAGUCFAGUCFAG) gases is studied in the model of "isotopic-spin" pairing proposed in 1991 \cite% {Ku-Hof-SSC}. This model assumes a mismatch (δδδ) in chemical potentials of pairing fermionic atoms. It is shown that a πππ-Josephson junction can be realized in UCFAGUCFAGUCFAG systems, where the left and right banks % S are the UCFAGUCFAGUCFAG superfluids. The weak link MMM consists from the normal % UCFAG with the finite mismatch δδδ. If the πππ-junction is a part of a closed ring the superfluid mass-current flows spontaneously in the ring, i.e., the time-reversal symmetry is broken spontaneously. This is realized if the radius of the ring RRR is larger than the critical one $% R_{c} $. All these effects exist also in the case when δ≫Δδ\gg Δδ≫Δ, where ΔΔΔ is the superfluid gap, but with the reduced thickness of the weak link. It is also discussed, that if junctions SM1M2SSM_{1}M_{2}SSM1​M2​S and trilayers % M_{1}SM_{2} from UCFAGUCFAGUCFAG are realizable this renders a possibility for a novel electronics - \textit{hypertronics}.
We discuss an idea to realize a spontaneous current in a superfluid Fermi gas. When a polarized Fermi superfluid (${N}_{\ensuremath{\uparrow}}>{N}_{\ensuremath{\downarrow}}$, where ${N}_{\ensuremath{\sigma}}$ is the number of atoms in the hyperfine state described by pseudospin $\ensuremath{\sigma}=\ensuremath{\uparrow},\ensuremath{\downarrow}$) is loaded onto a ring-shaped trap with a weak potential barrier, some excess atoms ($\ensuremath{\Delta}N={N}_{\ensuremath{\uparrow}}\ensuremath{-}{N}_{\ensuremath{\downarrow}}$) are localized around the barrier. As shown in our previous paper [T. Kashimura, S. Tsuchiya, and Y. Ohashi, Phys. Rev. A 82, 033617 (2010)], this polarized potential barrier works as a $\ensuremath{\pi}$ junction in the sense that the superfluid order parameter changes its sign across the barrier. Because of this, the phase of the superfluid order parameter outside the junction is shown to be twisted by $\ensuremath{\pi}$ along the ring, which naturally leads to a circulating supercurrent. While the ordinary supercurrent state is obtained as a metastable state, this spontaneous current state is shown to be more stable than the case with no current. Our results indicate that localized excess atoms would be useful for the manipulation of the superfluid order parameter in cold Fermi gases.
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.
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.
Superconductivity and superfluidity of fermions require, within the BCS theory, matching of the Fermi energies of the two interacting Fermion species. Difference in the number densities of the two species leads either to a normal state, to phase separation, or---potentially---to exotic forms of superfluidity such as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, Sarma state, or breached pair state. We consider ultracold Fermi gases with polarization, i.e., spin-density imbalance. We show that, due to the gases being trapped and isolated from the environment in terms of particle exchange, exotic forms of superfluidity appear as a shell around the Bardeen-Cooper-Schrieffer (BCS) superfluid core of the gas and, for large density imbalance, in the core as well. We obtain these results by describing the effect of the trapping potential by using the Bogoliubov-de Gennes equations. For comparison to experiments, we calculate also the condensate fraction, and show that, in the center of the trap, a polarized superfluid leads to a small dip in the central density difference. We compare the results to those given by local density approximation and find qualitatively different behavior.