Géraldine Haack

Electron waiting times in mesoscopic conductors.

Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We illustrate our methodology by calculating the waiting time distribution for a quantum point contact and find a crossover from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off. Even when the low-frequency transport is noiseless, the electrons are not equally spaced in time due to their inherent wave nature. We discuss the implications for renewal theory in mesoscopic systems and point out several analogies with level spacing statistics and random matrix theory.

Resonant quantum gates in circuit quantum electrodynamics

We propose the implementation of fast resonant gates in circuit quantum electrodynamics for quantum information processing. We show how a suitable utilization of three-level superconducting qubits inside a resonator constitutes a key tool to perform diverse two-qubit resonant gates, improving the operation speed when compared to slower dispersive techniques. To illustrate the benefit of resonant two-qubit gates in circuit QED, we consider the implementation of a two-dimensional cluster state in an array of N x N superconducting qubits by using resonant controlled-phase (CPHASE) and one-qubit gates, where the generation time grows linearly with N. For N=3, and taking into account decoherence mechanisms, a fidelity over 60% for the generation of this cluster state is obtained.

Glauber coherence of single electron sources

Recently demonstrated solid state single electron sources generate different quantum states depending on their operation condition. For adiabatic and non-adiabatic sources we determine the Glauber correlation function in terms of the Floquet scattering matrix of the source. The correlation function provides full information on the shape of the state, on its time-dependent amplitude and phase, which makes the coherence properties of single electron states essential for the production of quantum multi-particle states.

Markovian master equations for quantum thermal machines: local versus global approach

The study of quantum thermal machines, and more generally of open quantum systems, often relies on master equations. Two approaches are mainly followed. On the one hand, there is the widely used, but often criticized, local approach, where machine sub-systems locally couple to thermal baths. On the other hand, in the more established global approach, thermal baths couple to global degrees of freedom of the machine. There has been debate as to which of these two conceptually different approaches should be used in situations out of thermal equilibrium. Here we compare the local and global approaches against an exact solution for a particular class of thermal machines. We consider thermodynamically relevant observables, such as heat currents, as well as the quantum state of the machine. Our results show that the use of a local master equation is generally well justified. In particular, for weak inter-system coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations. For intermediate coupling, the local and the global approach both agree with the exact solution and for strong coupling, the global approach is preferable. These results are backed by detailed derivations of the regimes of validity for the respective approaches. (Less)

Parity detection and entanglement with a Mach-Zehnder interferometer

United Nations University, Hermann-Ehlers-Str. 10, 53113 Bonn, Germany(Dated: November 12, 2010)A parity meter projects the state of two qubits onto two subspaces with different parities, thestates in each parity class being indistinguishable. It has application in quantum information forits entanglement properties. In our work we consider the electronic Mach-Zehnder interferometer(MZI) coupled capacitively to two double quantum dots (DQDs), one on each arm of the MZI.These charge qubits couple linearly to the charge in the arms of the MZI. A key advantage of anMZI is that the qubits are well separated in distance so that mutual interaction between them isavoided. Assuming equal coupling between both DQDs and the arms and the same bias for eachDQD, this setup usually detects three different currents, one for the odd states and two for eacheven state. Controlling the magnetic flux of the MZI, we can operate the MZI as a parity meter:only two currents are measured at the output, one for each parity class. In this configuration, theMZI acts as an ideal detector, its Heisenberg efficiency being maximal. Initially unentangled DQDsbecome entangled through the parity measurement process with probability one and for a class ofinitial states our parity meter deterministically generates Bell states.

Autonomous quantum thermal machine for generating steady-state entanglement

We discuss a simple quantum thermal machine for the generation of steady-state entanglement between two interacting qubits. The machine is autonomous in the sense that it uses only incoherent interactions with thermal baths, but no source of coherence or external control. By weakly coupling the qubits to thermal baths at different temperatures, inducing a heat current through the system, steady-state entanglement is generated far from thermal equilibrium. Finally, we discuss two possible implementations, using superconducting flux qubits or a semiconductor double quantum dot. Experimental prospects for steady-state entanglement are promising in both systems.

Single-electron coherence: Finite temperature versus pure dephasing

Abstract We analyze a coherent injection of single electrons on top of the Fermi sea in two situations, at finite-temperature and in the presence of pure dephasing. Both finite-temperature and pure dephasing change the property of the injected quantum states from pure to mixed. However, we show that the temperature-induced mixedness does not alter the coherence properties of these single-electron states. In particular two such mixed states exhibit perfect antibunching while colliding at an electronic wave splitter. This is in striking difference with the dephasing-induced mixedness which suppresses antibunching. On the contrary, a single-particle shot noise is suppressed at finite temperatures but is not affected by pure dephasing. This work therefore extends the investigation of the coherence properties of single-electron states to the case of mixed states and clarifies the difference between different types of mixedness.

Distributions of electron waiting times in quantum-coherent conductors

The distribution of electron waiting times is useful to characterize quantum transport in meso-scopic structures. Here we consider a generic quantum-coherent conductor consisting of a mesoscopic scatterer in a two-terminal setup. We extend earlier results for single-channel conductors to setups with several (possibly spin-degenerate) conduction channels and we discuss the effect of a finite electronic temperature. We present detailed investigations of the electron waiting times in a quantum point contact as well as in two mesoscopic interferometers with energy-dependent transmissions: a Fabry-Perot interferometer and a Mach-Zehnder interferometer. We show that the waiting time distributions allow us to determine characteristic features of the scatterers, for instance the number of resonant levels in the Fabry-Perot interferometer that contribute to the electronic transport.

Heat and charge transport measurements to access single-electron quantum characteristics: Transport measurements for single-electron quantum characteristics

In the framework of the Floquet scattering-matrix theory we discuss how electrical and heat currents accessible in mesoscopics are related to the state of excitations injected by a single-electron source into an electron waveguide. We put forward an interpretation of a single-particle heat current, which differs essentially from that of an electrical current. We show that the knowledge of both a time-dependent electrical current and a time-dependent heat current allows the full reconstruction of a single-electron wave function. In addition we compare electrical and heat shot noise caused by splitting of a regular stream of single-electron excitations. If only one stream impinges on a wave splitter, the heat shot noise is proportional to the well-known expression of the charge shot noise, reflecting the partitioning of the incoming single particles. The situation differs when two electronic streams collide at the wave splitter. The shot noise suppression, due to the Pauli exclusion principle, is governed by different overlap integrals in the case of charge and of heat.

On-demand maximally entangled states with a parity meter and continuous feedback

Generating on-demand maximally entangled states is one of the corner stones for quantum information processing. Parity measurements can serve to create Bell states and have been implemented via an electronic Mach-Zehnder interferometer among others. However, the entanglement generation is necessarily harmed by measurement induced dephasing processes in one of the two parity subspace. In this work, we propose two different schemes of continuous feedback for a parity measurement. They enable us to avoid both the measurement-induced dephasing process and the experimentally unavoidable dephasing, e.g. due to fluctuations of the gate voltages controlling the initialization of the qubits. We show that we can generate maximally entangled steady states in both parity subspaces. Importantly, the measurement scheme we propose is valid for implementation of parity measurements with feedback loops in various solid-state environments.