Cooper quartets are aggregates of four electrons that generalize the concept of Cooper pairs, and their study can unfold unexplored perspectives in correlated matter and many-body physics. We propose a method to isolate them in a double-quantum-dot system coupled to conventional superconducting and normal leads. By driving the system out of equilibrium, we show that a resonance between the vacuum
∣0⟩ and the four-electron state
∣4e⟩ emerges in the high bias voltage regime, which involves a two-Cooper pair exchange process and is characterized by finite quartet correlations. We study the transport properties of the system and show that a peak in the Andreev current at high bias voltage has a width that scales with the magnitude of the quartet coupling
Γ4e, which can be tuned by the phase of additional superconducting leads, yielding distinctive signatures. By further studying the current-current correlations and the Fano factor, we establish a regime characterized by equal auto- and cross-correlations, which we interpret as a definitive signature of fast coherent two-Cooper-pair oscillations between the dots and the superconducting leads. The proposed platform, experimentally accessible in a quantum solid-state laboratory, enables exploration of quartet correlations and multifermion-correlated states of matter.
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 ${\ensuremath{\epsilon}}_{0}$ is connected to three superconductors
Sa,Sb, and
Sc with gap $\mathrm{\ensuremath{\Delta}}$, biased at ${V}_{a}=V,\phantom{\rule{0.16em}{0ex}}{V}_{b}=\ensuremath{-}V$, and
Vc=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 ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\gg}1$, which is demonstrated with a semianalytical perturbative expansion of the cross correlations. Noise reveals the absence of granularity of the superflow splitting from
Sc towards
(Sa,Sb) in the nonresonant dot regime, in spite of finite voltage. In the resonant dot regime ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\lesssim}1$, cross correlations measured in the
(Va,Vb) plane should reveal an ``anomaly'' in the vicinity of the quartet line
Va+Vb=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 ${F}_{\ensuremath{\varphi}}$ are introduced, defined as the ratio between the amplitudes of phase modulations of the noise and the currents. At low bias, the Fano factors ${F}_{\ensuremath{\varphi}}$ are of order unity in the resonant dot regime ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\lesssim}1$, and they are vanishingly small in the nonresonant dot regime ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\gg}1$.