We investigate theoretically the noise and the full counting statistics of electrons that are emitted from a superconductor into two spatially separated quantum dots by the splitting of Cooper pairs and further on collected in two normal-state electr
odes. With negatively-biased drain electrodes and a large superconducting gap, the dynamics of the Cooper pair splitter can be described by a Markovian quantum master equation. Using techniques from full counting statistics, we evaluate the electrical currents, their noise power spectra, and the power-power correlations in the output leads. The current fluctuations can be attributed to the competition between Cooper pair splitting and elastic cotunneling between the quantum dots via the superconductor. In one regime, these processes can be clearly distinguished in the cross-correlation spectrum with peaks and dips appearing at characteristic frequencies associated with elastic cotunneling and Cooper pair splitting, respectively. We corroborate this interpretation by analyzing the charge transport fluctuations in the time domain, specifically by investigating the $g^{(2)}$-function of the output currents. Our work identifies several experimental signatures of the fundamental transport processes involved in Cooper pair splitting and provides specific means to quantify their relative strengths. As such, our results may help guide and interpret future experiments on current fluctuations in Cooper pair splitters.
A saddle point plus fluctuations analysis of the periodically driven half-filled two-dimensional Hubbard model is performed. For drive frequencies below the equilibrium gap, we find discontinuous transitions to time-dependent solutions. A highly exci
ted, generically non-thermal distribution of magnons occurs even for drive frequencies far above the gap. Above a critical drive amplitude, the low-energy magnon distribution diverges as the frequency tends to zero and antiferromagnetism is destroyed, revealing the generic importance of collective mode excitations arising from a non-equilibrium drive.
Electron waiting times are an important concept in the analysis of quantum transport in nano-scale conductors. Here we show that the statistics of electron waiting times can be used to characterize Cooper pair splitters that create spatially separate
d spin-entangled electrons. A short waiting time between electrons tunneling into different leads is associated with the fast emission of a split Cooper pair, while long waiting times are governed by the slow injection of Cooper pairs from a superconductor. Experimentally, the waiting time distributions can be measured using real-time single-electron detectors in the regime of slow tunneling, where conventional current measurements are demanding. Our work is important for understanding the fundamental transport processes in Cooper pair splitters and the predictions may be verified using current technology.
