We study the time dependent electron-electron and electron-hole correlations in a mesoscopic device which is splitting an incident current of free fermions into two spatially separated particle streams. We analyze the appearance of entanglement as manifested in a Bell inequality test and discuss its origin in terms of local spin-singlet correlations already present in the initial channel and the action of post-selection during the Bell type measurement. The time window over which the Bell inequality is violated is determined in the tunneling limit and for the general situation with arbitrary transparencies. We compare our results with alternative Bell inequality tests based on coincidence probabilities.

We present a theoretical analysis of the appearance of entanglement in noninteracting mesoscopic structures. Our setup involves two oppositely polarized sources injecting electrons of opposite spin into the two incoming leads. The mixing of these polarized streams in an ideal four-channel beam splitter produces two outgoing streams with particular tunable correlations. A Bell inequality test involving cross-correlated spin currents in opposite leads signals the presence of spin entanglement between particles propagating in different leads. We identify the role of fermionic statistics and projective measurement in the generation of these spin-entangled electrons.

We analyze the statistics of the electromagnetic radiation emitted from electrons pushed through a quantum point contact. We consider a setup implemented in a two-dimenional electron gas (2DEG) where the radiation manifests itself in terms of 2D plasmons emitted from electrons scattered at the point contact. The bosonic statistics of the plasmons competes with the fermionic statistics of the electrons; as a result, the quantum point contact emits non-classical radiation with a statistics which can be tuned from bunching to anti-bunching by changing the driving voltage. Our perturbative calculation of the irreducible two-plasmon probability correlator provides us with information on the statistical nature of the emitted plasmons and on the underlying electronic current flow.

The non-equilibrium transport properties of a carbon nanotube which is connected to Fermi liquid leads, where electrons are injected in the bulk, are computed. A previous work which considered an infinite nanotube showed that the zero frequency noise correlations, measured at opposite ends of the nanotube, could be used to extract the anomalous charges of the chiral excitations which propagate in the nanotube. Here, the presence of the leads have the effect that such-noise crosscorrelations vanish at zero frequency. Nevertheless, information concerning the anomalous charges can be recovered when considering the spectral density of noise correlations at finite frequencies, which is computed perturbatively in the tunneling amplitude. The spectrum of the noise crosscorrelations is shown to depend crucially on the ratio of the time of flight of quasiparticles traveling in the nanotube to the "voltage" time which defines the width of the quasiparticle wave-packets injected when an electron tunnels. Potential applications toward the measurement of such anomalous charges in non-chiral Luttinger liquids (nanotubes or semiconductor quantum wires) are discussed.

We propose and analyze a mesoscopic device producing on-demand entangled pairs of electrons. The system consists of two capacitively coupled Mach-Zehnder interferometers implemented in a quantum Hall structure. A pair of electron wave-packets is injected into the chiral edge states of two (of the four) incoming arms; scattering on the incoming interferometers splits the wave-packets into four components of which two interact. The resulting interaction phase associated with this component leads to the entanglement of the state; the latter is scattered at the outgoing beam splitter and analyzed in a Bell violation test measuring the presence of particles in the four outgoing leads. We study the two-particle case and determine the conditions to reach and observe full entanglement. We extend our two-particle analysis to include the underlying Fermi seas in the quantum Hall device; the change in shape of the wave-function, the generation of electron-hole pairs in the interaction regime, and a time delay between the pulses all reduce the degree of visible entanglement and the violation of the Bell inequality, effects which we analyze quantitatively. We determine the device settings optimizing the entanglement and the Bell test and find that violation is still possible in the presence of the Fermi seas, with a maximal Bell parameter reaching B = 2.18 > 2 in our setup.

We study a single-electron pulse injected into the chiral edge-state of a quantum Hall device and subject to a capacitive Coulomb interaction. We find that the scattered multi-particle state remains unentangled and hence can be created itself by a suitable classical voltage-pulse V (t). The application of the inverse pulse −V (−t) corrects for the shake-up due to the interaction and resurrects the original injected wave packet. We suggest an experiment with an asymmetric MachZehnder interferometer where the application of such pulses manifests itself in an improved visibility.PACS numbers: 03.65.Yz, 85.35.Ds, 73.43.Lp On demand single-electron sources are an essential building block on the road to a mesoscopic solid state implementation of quantum computing. Single-particle wave packets can be generated with the help of suitable voltage pulses [1] and a first experimental realization of such a source has been recently achieved [2] in a quantum Hall setup. Contrary to their photonic counterparts, such single-electron states are prone to decoherence due to the interaction with the underlying Fermi-sea [3]. Here, we study the influence of a capacitive Coulomb interaction on a single-electron wave-packet injected into the chiral edge state of a quantum Hall device. Due to the interaction, the injected particle transfers energy to the Fermi sea, leading to the shake-up of electron-hole pairs. Analyzing the resulting scattered state, we find that it corresponds to a simple Slater determinant; the underlying product nature of the resulting multi-particle state allows one to undo the decoherence by applying a suitable local voltage-pulse.The resurrection of decohered single-particle wave packets has numerous potential applications; here, we suggest to test this prediction in a Mach-Zehnder interferometer implemented in a quantum Hall setup. Electronic decoherence has become apparent in such devices [4] through the observation of a non-trivial decay of the visibility [5,6] with increasing bias voltage and a satisfactory explanation could be obtained [7] via accounting for strong Coulomb interaction between edge states. The experiments [4][5][6] have been performed with a finite bias voltage where electrons are stochastically injected into the system. We suggest to use an asymmetric setup operating in the ν = 1 quantum Hall regime, where the decoherence is introduced in a controlled manner through a capacitive coupling of one arm to a metallic gate. Applying suitable voltage pulses to the scattered wave function behind the interaction region, the visibility of the interference pattern can be improved considerably though not perfectly, a consequence of our ignorance regarding the path which the electron has taken in traversing the device.In the following, we study a one-dimensional ballistic conductor with chiral spinless electrons propagating to the right. The capacitive Coulomb interaction is described [8] by the HamiltonianĤ int =hω CN 2 /2, wherêis the effective number of excess electrons within the interaction re...

Repeated measurements as typically occurring in two-or multi-time correlators rely on von Neumann's projection postulate, telling how to restart the system after an intermediate measurement.We invoke the principle of deferred measurement to describe an alternative procedure where coevolving quantum memories extract system information through entanglement, combined with a final readout of the memories described by Born's rule. The new approach to repeated quantum measurements respects the unitary evolution of quantum mechanics during intermediate times, unifies the treatment of strong and weak measurements, and reproduces the projected and (anti-) symmetrized correlators in the two limits. As an illustration, we apply our formalism to the calculation of the electron charge correlator in a mesoscopic physics setting, where single electron pulses assume the role of flying memory qubits. We propose an experimental setup which reduces the measurement of the time correlator to the measurement of currents and noise, exploiting the (pulsed) injection of electrons to cope with the challenge of performing short-time measurements.

We present a nonperturbative expression for the scattering matrix of N particles interacting inside a quantum dot. Characterizing the dot by its resonances, we find a compact form for the scattering matrix in a real-time representation. We study the transmission probabilities and interaction-induced orbital entanglement of two electrons incident on the dot in a spin-singlet state.