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arXiv:2410.13270 · Physical Review Letters

Quantum Coulomb Drag Mediated by Cotunneling of Fluxons and Cooper Pairs

Andrew G. Semenov, A. Latysev, Andrei D. Zaikin

Published Feb 24, 2025• 3 citations
arXivHTMLPDF

Abstract

We predict two novel quantum drag effects which can occur in macroscopically quantum coherent Josephson circuits. We demonstrate that biasing one resistively shunted Josephson junction by an external current one can induce a nonzero voltage drop across another such junction capacitively coupled to the first one. This quantum Coulomb drag is caused by cotunneling of magnetic flux quanta across both junctions which remain in the "superconducting" regime. Likewise, Cooper pair cotunneling across a pair of connected in series Josephson junctions in the "insulating" regime is responsible for another-dual-quantum Coulomb drag effect.

DOI
10.1103/physrevlett.134.086001

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arXiv:cond-mat/0301467•Physical review. B, Condensed matter•Mar 17, 2003•32 citations
We predict two novel quantum drag effects which can occur in macroscopically quantum coherent Josephson circuits. We demonstrate that biasing one resistively shunted Josephson junction by an external current one can induce a nonzero voltage drop across another such junction capacitively coupled to the first one. This quantum Coulomb drag is caused by cotunneling of magnetic flux quanta across both junctions which remain in the "superconducting" regime. Likewise, Cooper pair cotunneling across a pair of connected in series Josephson junctions in the "insulating" regime is responsible for another-dual-quantum Coulomb drag effect.
We demonstrate that the system of two connected in series resistively shunted Josephson nanojunctions may exhibit a novel quantum Coulomb drag effect mediated by cotunneling of Cooper pairs. In the Coulomb blockade regime, one of the junctions can develop a non-vanishing electric current while an external voltage bias is applied to another one. This phenomenon results from a non-trivial interplay between macroscopic quantum coherence, dissipation, and electron–electron interactions and can be directly tested in future experiments.
Fluxons in a superconducting loop can be coherently coupled by quantum phase slips occurring at a weak link such as a Josephson junction. If Cooper pair tunneling at the junction occurs through a resonant level, then $2\ensuremath{\pi}$ quantum phase slips are suppressed, and fluxons are predominantly coupled by $4\ensuremath{\pi}$ quantum phase slips. We analyze this scenario by computing the coupling between fluxons as the level is brought into resonance with the superconducting condensate. The results indicate that the $4\ensuremath{\pi}$-dominated regime can be observed directly in the transition spectrum for circuit parameters typical of a fluxonium qubit. We also show that if the inductive energy of the loop is much smaller than the plasma frequency of the junction, then the low-energy Hamiltonian of the circuit is dual to that of a topological superconducting island. These findings can inform experiments on bifluxon qubits as well as the design of novel types of protected qubits.
In a SQUID tuned away from half-integer flux (in units of the superconducting flux quantum), the concurrence of multiple Josephson harmonics and an asymmetry between the junctions leads to the Josephson diode effect -- a nonreciprocal current-voltage characteristic manifested as an asymmetry of critical currents at opposite polarities. We predict a dual version of this effect in a gate-tunable Cooper pair transistor placed in series with a highly resistive environment. When tuned away from half-integer gate charge (in units of the Cooper pair charge) it shows an asymmetry of critical voltages at opposite polarities -- a dual diode effect we refer to as the Bloch diode effect. It arises from an asymmetry in the dispersion of the transistor's Bloch bands. A highly resistive environment can be realized with a Josephson junction array, suggesting that such a diode could be implemented using conventional superconducting quantum circuits.
We investigate nonequilibrium transport through superconducting nanojunctions using a Liouville space approach. The formalism allows us to study finite-gap effects, and to account for both quasiparticle and Cooper-pair tunneling. With focus on the weak-tunneling limit, we study the stationary dc and ac current up to second order (cotunneling) in the hybridization energy. For the particular case of a strongly interacting quantum dot sandwiched between two superconductors, we identify the characteristic virtual processes that yield the Andreev and Josephson current and obtain the dependence on the gate and bias voltage for the dc current, the critical current, and the phase-dependent dissipative current. In particular, the critical current is characterized by regions in the stability diagram in which its sign changes from positive to negative, resulting in a multitude of $0\ensuremath{-}\ensuremath{\pi}$ transitions. The latter signal the interplay between strong interactions and tunneling at finite bias.
Abstract The non-dissipative nonlinearity of Josephson junctions1 converts macroscopic superconducting circuits into artificial atoms2, enabling some of the best-controlled qubits today3, 4. Three fundamental types of superconducting qubit are known5, each reflecting a distinct behaviour of quantum fluctuations in a Cooper pair condensate: single-charge tunnelling (charge qubit6, 7), single-flux tunnelling (flux qubit8) and phase oscillations (phase qubit9 or transmon10). Yet, the dual nature of charge and flux suggests that circuit atoms must come in pairs. Here we introduce the missing superconducting qubit, ‘blochnium’, which exploits a coherent insulating response of a single Josephson junction that emerges from the extension of phase fluctuations beyond 2π (refs. 11–14). Evidence for such an effect has been found in out-of-equilibrium direct-current transport through junctions connected to high-impedance leads15–19, although a full consensus on the existence of extended phase fluctuations is so far absent20–22. We shunt a weak junction with an extremely high inductance—the key technological innovation in our experiment—and measure the radiofrequency excitation spectrum as a function of external magnetic flux through the resulting loop. The insulating character of the junction is manifested by the vanishing flux sensitivity of the qubit transition between the ground state and the first excited state, which recovers rapidly for transitions to higher-energy states. The spectrum agrees with a duality mapping of blochnium onto a transmon, which replaces the external flux by the offset charge and introduces a new collective quasicharge variable instead of the superconducting phase23, 24. Our findings may motivate the exploration of macroscopic quantum dynamics in ultrahigh-impedance circuits, with potential applications in quantum computing and metrology.
We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02−−0.6K),(T=0.02--0.6\mathrm{K}),(T=0.02−−0.6K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.