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

摘要

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 ∈_0 is connected to three superconductors S-a, S_b, and S_c with gap Δ, 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 ∈_0/Δ ＞＞ 1, which is demonstrated with a semianalytical 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 ∈-0/Δ approx＜ 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_φ 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_φ are of order unity in the resonant dot regime ∈_0/Δ approx＜ 1, and they are vanishingly small in the nonresonant dot regime ∈_0/Δ ＞＞ 1.