We present a Floquet scattering theory of electron waiting time distributions in periodically driven quantum conductors. We employ a second-quantized formulation that allows us to relate the waiting time distribution to the Floquet scattering matrix of the system. As an application we evaluate the electron waiting times for a quantum point contact, modulating either the applied voltage (external driving) or the transmission probability (internal driving) periodically in time. Lorentzianshaped voltage pulses are of particular interest as they lead to the emission of clean single-particle excitations as recently demonstrated experimentally. The distributions of waiting times provide us with a detailed characterization of the dynamical properties of the quantum-coherent conductor in addition to what can be obtained from the shot noise or the full counting statistics.Introduction.-A surge of interest in dynamic quantum conductors has recently led to a number of groundbreaking experiments [1][2][3][4][5][6]. An on-demand coherent single-electron source based on a submicron capacitor [1,7] has been experimentally realized and successfully operated in the gigahertz regime [2]. Recently, the fermionic analogue of an optical Hong-Ou-Mandel experiment was performed to demonstrate that two such on-demand sources produce indistinguishable electronic quantum states [3]. Additionally, clean single-particle excitations have been created on top of a Fermi sea by applying a periodic sequence of Lorentzian-shaped voltage pulses to an electrical contact [4,5] following a pioneering theoretical proposal by Levitov and co-workers [8][9][10].These experimental breakthroughs hold promises for future gigahertz quantum electronics with precisely synchronized single-particle operations. One may envision circuit architectures with driven single-electron emitters coupled to the edge states of a quantum Hall conductor (or to the helical edge states in a topological insulator [11,12]) serving as rail tracks for charge and information carriers by guiding them to beam splitters (quantum point contacts) and particle interferometers for further processing. To facilitate progress towards this goal, a detailed understanding of the single-particle emitters and their statistical properties is required.In one approach, the full counting statistics of emitted charge is analyzed [13][14][15][16][17]. The charge fluctuations are typically integrated over many periods of the driving and important short-time physics may be lost. In a complementary approach, one considers the distribution of waiting times between charge carriers [18][19][20][21][22][23][24][25]. This view on quantum transport seems promising as picosecond single-electron detection is now becoming feasible [6]. A quantum theory of electron waiting times has recently been developed for voltage-biased mesoscopic conductors [20], however, so far without an explicit driving. To describe the statistical properties of coherent single-electron emitters, a theory of waiting time distributions (WTD)...

We evaluate the joint distributions of electron waiting times in coherent conductors described by scattering theory. Successive electron waiting times in a single-channel conductor are found to be correlated due to the fermionic statistics encoded in the many-body state. Our formalism allows us also to investigate the waiting times between charge transfer events in different outgoing channels. As an application we consider a quantum point contact in a chiral setup with one or both input channels biased by either a static or a time-dependent periodic voltage described by Floquet theory. The theoretical framework developed here can be applied to a variety of scattering problems and can in a straightforward manner be extended to joint distributions of several electron waiting times.

Motivated by recent progress in electron quantum optics, we revisit the question of single-electron entanglement, specifically whether the state of a single electron in a superposition of two separate spatial modes should be considered entangled. We first discuss a gedanken experiment with singleelectron sources and detectors, and demonstrate deterministic (i. e. without post-selection) Bell inequality violation. This implies that the single-electron state is indeed entangled and, furthermore, nonlocal. We then present an experimental scheme where single-electron entanglement can be observed via measurements of the average currents and zero-frequency current cross-correlators in an electronic Hanbury Brown-Twiss interferometer driven by Lorentzian voltage pulses. We show that single-electron entanglement is detectable under realistic operating conditions. Our work settles the question of single-electron entanglement and opens promising perspectives for future experiments.

The entanglement of coherently split electron-hole pairs in an electronic conductor is typically not considered accessible due to particle number conservation and fermionic superselection rules. We demonstrate here that current cross-correlation measurements at the outputs of an electronic MachZehnder interferometer can nevertheless provide a robust witness of electron-hole entanglement. Specifically, we consider neutral excitations generated by modulating the transmission of an unbiased quantum point contact periodically in time. For an optimized modulation profile, an entangled state with one positively-charged leviton (a hole) and one negatively-charged leviton (an electron) gets delocalized over the two paths of the interferometer and is detected at the output arms. We evaluate the influence of finite electronic temperatures and dephasing corresponding to recent experiments.

We evaluate the distribution of waiting times between electrons emitted by a driven mesoscopic capacitor. Based on a wave packet approach we obtain analytic expressions for the electronic waiting time distribution and the joint distribution of subsequent waiting times. These semi-classical results are compared to a full quantum treatment based on Floquet scattering theory and good agreement is found in the appropriate parameter ranges. Our results provide an intuitive picture of the electronic emissions from the driven mesoscopic capacitor and may be tested in future experiments.