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Physical review. B, Condensed matter

Dynamical mass of a quantum vortex in a Josephson junction array

Ulrich Eckern, Giuseppe Gaetano Luciano, A. Tagliacozzo

Published Dec 1, 1997• 1 citation
Publisher

Abstract

The real-time response to a small external perturbation of a vortex in a quantum Josephson junction array, with long-range Coulomb interaction between Cooper pairs, is analyzed. While the static damping is zero for vortex velocities below some threshold value ${v}_{\mathrm{th}}$ (which implies the possibility of ballistic motion), a dynamical friction due to the coupling to the plasma oscillations is always present for frequencies higher than a given threshold ${\ensuremath{\omega}}_{\mathrm{th}}.$ The latter approaches zero when the velocity increases to ${v}_{\mathrm{th}}.$ However, radiative dissipation of the vortex affects the threshold for ballistic motion. We discuss the conditions under which a mass can be defined for the vortex as a quantum particle.

DOI
10.1103/physrevb.56.14686

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The real-time response to a small external perturbation of a vortex in a quantum Josephson junction array, with long-range Coulomb interaction between Cooper pairs, is analyzed. While the static damping is zero for vortex velocities below some threshold value vth{v}_{\mathrm{th}}vth​ (which implies the possibility of ballistic motion), a dynamical friction due to the coupling to the plasma oscillations is always present for frequencies higher than a given threshold \ensuremathωth.{\ensuremath{\omega}}_{\mathrm{th}}.\ensuremathωth​. The latter approaches zero when the velocity increases to vth.{v}_{\mathrm{th}}.vth​. However, radiative dissipation of the vortex affects the threshold for ballistic motion. We discuss the conditions under which a mass can be defined for the vortex as a quantum particle.
© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.We numerically demonstrate and characterize the emergence of distinct dynamical regimes of a finite-temperature bosonic superfluid in an elongated Josephson junction generated by a thin Gaussian barrier over the entire temperature range where a well-formed condensate can be clearly identified. Although the dissipation arising from the coupling of the superfluid to the dynamical thermal cloud increases with increasing temperature as expected, the importance of this mechanism is found to depend on two physical parameters associated (i) with the initial chemical potential difference, compared to some characteristic value, and (ii) the ratio of the thermal energy to the barrier amplitude. The former determines whether the superfluid Josephson dynamics are dominated by gradually damped plasmalike oscillations (for relatively small initial population imbalances), or whether dissipation at early times is instead dominated by vortex- and sound-induced dissipation (for larger initial imbalances). The latter defines the effect of the thermal cloud on the condensate dynamics, with a reversal of roles, i.e., the condensate being driven by the oscillating thermal cloud, being observed when the thermal particles acquire enough energy to overcome the barrier. Our findings are within current experimental reach in ultracold superfluid junctions.
Abstract In Josephson junction arrays, vortices form stable topological excitations. A key step towards the understanding of their properties was the observation made by Eckern and Schmid that in low‐capacitance junction arrays a vortex behaves as a massive particle moving in a periodic potential and subject to dissipation. The mass is low and quantum effects become observable. The present contribution provides a review of these properties together with a discussion of similar scenarios realized in optical lattices.
We numerically demonstrate and characterize the emergence of distinct dynamical regimes of a finite-temperature bosonic superfluid in an elongated Josephson junction generated by a thin Gaussian barrier over the entire temperature range where a well-formed condensate can be clearly identified. Although the dissipation arising from the coupling of the superfluid to the dynamical thermal cloud increases with increasing temperature as expected, the importance of this mechanism is found to depend on two physical parameters associated (i) with the initial chemical potential difference, compared to some characteristic value, and (ii) the ratio of the thermal energy to the barrier amplitude. The former determines whether the superfluid Josephson dynamics are dominated by gradually damped plasmalike oscillations (for relatively small initial population imbalances), or whether dissipation at early times is instead dominated by vortex- and sound-induced dissipation (for larger initial imbalances). The latter defines the effect of the thermal cloud on the condensate dynamics, with a reversal of roles, i.e., the condensate being driven by the oscillating thermal cloud, being observed when the thermal particles acquire enough energy to overcome the barrier. Our findings are within current experimental reach in ultracold superfluid junctions.
Using state-of-the-art numerical techniques, we investigate how quantum phase fluctuations and quasiparticle tunneling shape the behavior of a small-capacitance Josephson junction across Ohmic, sub-Ohmic, and super-Ohmic dissipation regimes. We show that increasing the Ohmic dissipation strength drives a Berezinskii-Kosterlitz-Thouless quantum phase transition at thermodynamic equilibrium. Deviations from Ohmic behavior profoundly alter this scenario: the super-Ohmic regime exhibits no phase transition, whereas the sub-Ohmic regime displays a continuous second-order transition, consistent with the universality classes of the spin-boson model. Within the Ohmic regime, real-frequency linear-response calculations reveal that the phase particle does not undergo the commonly assumed diffusive-to-localized crossover. Instead, finite resistance progressively suppresses the singular zero-frequency response, producing a ballistic-to-localized change in the dynamics. At finite frequencies, coupling to the environment generates a long-lived excitation in the charge response, which evolves into a resonance as the subgap and shunt resistances are reduced.
We have investigated how the transport properties of small-Josephson-junction arrays vary depending on a quantum control parameter (the ratio of the Josephson coupling energy E J to the charging energy E C ), the magnitude of dissipation, and the dimensionality d of the system. We found that the arrays show Coulomb blockade behavior when R S is larger than about d R Q ( R Q ≡ h /4 e 2 =6.45 kΩ) and E J / E C is smaller than a threshold depending on the value of R S and the dimensionality. The result is discussed in terms of quantum phase transition induced by the charging effect and the dissipation.
We discuss the dynamics of two-dimensional arrays of Josephson junctions in the overdamped regime. Our discussion is restricted to “classical” arrays, where the Josephson coupling energy is much larger than the charging energy. Such arrays represent a highly controllable system to study the dynamics of vortices. Furthermore, they are promising for applications like, e.g., a coherent microwave source. The experiments have been performed with arrays of Nb/AlOx/Nb-tunnel junctions allowing a high degree of junction uniformity across the array. The typical array size is 10×10 junctions. We show spatially resolved measurement results obtained by low-temperature scanning electron microscopy, and demonstrate the merit of these investigations for the clarification of complex regimes of vortex dynamics as well as for the optimization of coherent microwave sources. In the case of external microwave irradiation with increasing power, a continuous transition from a non-locked to a completely locked oscillation state is presented. In addition, we report on the quantitative measurement of the emitted microwave power from the arrays.