Gate-tunable zero-frequency current cross-correlations of the quartet mode in a voltage-biased three-terminal Josephson junction

TL;DR

This paper investigates the zero-frequency current noise cross-correlations in a voltage-biased three-terminal Josephson junction, revealing phase-sensitive noiseless quartet currents in nonresonant regimes and phase-dependent noise anomalies in resonant regimes.

Contribution

It provides a semi-analytical analysis of noise cross-correlations in a three-terminal Josephson junction, highlighting phase sensitivity and the conditions for noiseless quartet currents.

Findings

Nonlocal quartets are noiseless at subgap voltage in nonresonant regimes.

Noise reveals superflow splitting without granularity despite finite voltage.

Resonant regimes show phase-sensitive noise anomalies near the quartet line.

Abstract

A three-terminal Josephson junction biased at opposite voltages can sustain a phase-sensitive dc-current carrying three-body static phase coherence, known as the "quartet current". We calculate the zero-frequency current noise cross-correlations and answer the question of whether this current is noisy (like a normal current in response to a voltage drop) or noiseless (like an equilibrium supercurrent in response to a phase drop). A quantum dot with a level at energy $\epsilon_0$ is connected to three superconductors $S_a$, $S_b$ and $S_c$ with gap $\Delta$, biased at $V_a=V$, $V_b=-V$ and $V_c=0$, and with intermediate contact transparencies. At zero temperature, nonlocal quartets (in the sense of four-fermion correlations) are noiseless at subgap voltage in the nonresonant dot regime $\epsilon_0/\Delta\gg 1$, which is demonstrated with a semi-analytical perturbative expansion of the cross-correlations. Noise reveals the absence of granularity of the superflow splitting from $S_c$ towards $(S_a,S_b)$ in the nonresonant dot regime, in spite of finite voltage. In the resonant dot regime $\epsilon_0/\Delta< 1$, cross-correlations measured in the $(V_a,V_b)$ plane should reveal an "anomaly" in the vicinity of the quartet line $V_a+V_b=0$, related to an additional contribution to the noise, manifesting the phase sensitivity of cross-correlations under the appearance of a three-body phase variable. Phase-dependent effective Fano factors $F_\varphi$ are introduced, defined as the ratio between the amplitudes of phase modulations of the noise and the currents. At low bias, the Fano factors $F_\varphi$ are of order unity in the resonant dot regime $\epsilon_0/\Delta< 1$, and they are vanishingly small in the nonresonant dot regime $\epsilon_0/\Delta\gg 1$.