The influence of phase fluctuation on fluxoid quantization in a small superconducting ring has been evaluated. In an isolated mesoscopic-sized superconductor, the number of Cooper pairs is fixed and the phase of the order parameter largely fluctuates due to Heisenberg's uncertainty principle. Under such conditions, it is not trivial whether the single-valuedness of the order parameter is kept and the fluxoid is quantized in the superconductor. We examined the problem experimentally using a superconducting single-electron transistor with a ring-shaped Coulomb island. We found that even when the fluctuation in the number of Cooper pairs is very small and a clear Coulomb oscillation is observed, the magnetic flux which goes through the ring is quantized.The influence of phase fluctuation on fluxoid quantization in a small superconducting ring has been evaluated. In an isolated mesoscopic-sized superconductor, the number of Cooper pairs is fixed and the phase of the order parameter largely fluctuates due to Heisenberg's uncertainty principle. Under such conditions, it is not trivial whether the single-valuedness of the order parameter is kept and the fluxoid is quantized in the superconductor. We examined the problem experimentally using a superconducting single-electron transistor with a ring-shaped Coulomb island. We found that even when the fluctuation in the number of Cooper pairs is very small and a clear Coulomb oscillation is observed, the magnetic flux which goes through the ring is quantized.

Japanese Journal of Applied PhysicsJun 1, 19970 citations

Macroscopic Quantum Devices

J. R. Clarke

Springer eBooksJan 1, 19741 citation

Kondo screening cloud and charge staircase in one-dimensional mesoscopic devices

Rodrigo G. Pereira, Nicolas Laflorencie, Ian K. Affleck +1 more

We propose that the finite size of the Kondo screening cloud, ${\ensuremath{\xi}}_{K}$, can be probed by measuring the charge quantization in a one-dimensional system coupled to a small quantum dot. When the chemical potential $\ensuremath{\mu}$ in the system is varied at zero temperature, one should observe charge steps whose locations are at values of $\ensuremath{\mu}$ that are controlled by the Kondo effect when the system size $L$ is comparable to ${\ensuremath{\xi}}_{K}$. We show that, if the standard Kondo model is used, the ratio between the widths of the Coulomb blockade valleys with odd or even number of electrons is a universal scaling function of ${\ensuremath{\xi}}_{K}∕L$. If we take into account electron-electron interactions in a single-channel wire, this ratio also depends on the parameters of the effective Luttinger model; in addition, the scaling is weakly violated by a marginal bulk interaction. For the geometry of a quantum dot embedded in a ring, we show that the dependence of the charge steps on a magnetic flux through the ring is controlled by the size of the Kondo screening cloud.We propose that the finite size of the Kondo screening cloud, ${\ensuremath{\xi}}_{K}$, can be probed by measuring the charge quantization in a one-dimensional system coupled to a small quantum dot. When the chemical potential $\ensuremath{\mu}$ in the system is varied at zero temperature, one should observe charge steps whose locations are at values of $\ensuremath{\mu}$ that are controlled by the Kondo effect when the system size $L$ is comparable to ${\ensuremath{\xi}}_{K}$. We show that, if the standard Kondo model is used, the ratio between the widths of the Coulomb blockade valleys with odd or even number of electrons is a universal scaling function of ${\ensuremath{\xi}}_{K}∕L$. If we take into account electron-electron interactions in a single-channel wire, this ratio also depends on the parameters of the effective Luttinger model; in addition, the scaling is weakly violated by a marginal bulk interaction. For the geometry of a quantum dot embedded in a ring, we show that the dependence of the charge steps on a magnetic flux through the ring is controlled by the size of the Kondo screening cloud.

arXiv:0801.4166Physical Review BMar 19, 200831 citations

Imprinting Persistent Currents in Tunable Fermionic Rings

Giulia Del Pace, Klejdja Xhani, Alessandro Muzi Falconi +7 more

Persistent currents in annular geometries have played an important role in disclosing the quantum phase coherence of superconductors and mesoscopic electronic systems.Ultracold atomic gases in multiply connected traps also exhibit long-lived supercurrents and have attracted much interest both for fundamental studies of superfluid dynamics and as prototypes for atomtronics circuits.Here, we report on the realization of supercurrents in homogeneous, tunable fermionic rings.We gain exquisite, rapid control over quantized persistent currents in all regimes of the BCS-BEC crossover through a universal phase-imprinting technique, attaining on-demand circulations w as high as 9. High-fidelity readout of the superfluid circulation state is achieved by exploiting an interferometric protocol, which also yields local information about the superfluid phase around the ring.In the absence of externally introduced perturbations, we find the induced metastable supercurrents to be as long-lived as the atomic sample.Conversely, we trigger and inspect the supercurrent decay by inserting a single small obstacle within the ring.For circulations higher than a critical value, the quantized current is observed to dissipate via the emission of vortices, i.e., quantized phase slips, which we directly image, in good agreement with numerical simulations.The critical circulation at which the superflow becomes unstable is found to depend starkly on the interaction strength, taking its maximum value for the unitary Fermi gas.Our results demonstrate fast and accurate control of quantized collective excitations in a macroscopic quantum system and establish strongly interacting fermionic superfluids as excellent candidates for atomtronics applications.Persistent currents in annular geometries have played an important role in disclosing the quantum phase coherence of superconductors and mesoscopic electronic systems.Ultracold atomic gases in multiply connected traps also exhibit long-lived supercurrents and have attracted much interest both for fundamental studies of superfluid dynamics and as prototypes for atomtronics circuits.Here, we report on the realization of supercurrents in homogeneous, tunable fermionic rings.We gain exquisite, rapid control over quantized persistent currents in all regimes of the BCS-BEC crossover through a universal phase-imprinting technique, attaining on-demand circulations w as high as 9. High-fidelity readout of the superfluid circulation state is achieved by exploiting an interferometric protocol, which also yields local information about the superfluid phase around the ring.In the absence of externally introduced perturbations, we find the induced metastable supercurrents to be as long-lived as the atomic sample.Conversely, we trigger and inspect the supercurrent decay by inserting a single small obstacle within the ring.For circulations higher than a critical value, the quantized current is observed to dissipate via the emission of vortices, i.e., quantized phase slips, which we directly image, in good agreement with numerical simulations.The critical circulation at which the superflow becomes unstable is found to depend starkly on the interaction strength, taking its maximum value for the unitary Fermi gas.Our results demonstrate fast and accurate control of quantized collective excitations in a macroscopic quantum system and establish strongly interacting fermionic superfluids as excellent candidates for atomtronics applications.

arXiv:2204.06542Physical Review XDec 30, 202283 citations

Quantum effects in a mesoscopic circuit

Bin Chen, You‐Quan Li, Hui Fang +2 more

Physics Letters ASep 1, 199561 citations

L

is comparable to ${\ensuremath{\xi}}_{K}$. We show that, if the standard Kondo model is used, the ratio between the widths of the Coulomb blockade valleys with odd or even number of electrons is a universal scaling function of ${\ensuremath{\xi}}_{K}∕L$. If we take into account electron-electron interactions in a single-channel wire, this ratio also depends on the parameters of the effective Luttinger model; in addition, the scaling is weakly violated by a marginal bulk interaction. For the geometry of a quantum dot embedded in a ring, we show that the dependence of the charge steps on a magnetic flux through the ring is controlled by the size of the Kondo screening cloud.