Controlling charge quantization with quantum fluctuations

In 1909, Millikan showed that the charge of electrically isolated systems is quantized in units of the elementary electron charge e. Today, the persistence of charge quantization in small, weakly connected conductors allows for circuits in which single electrons are manipulated, with applications in, for example, metrology, detectors and thermometry. However, as the connection strength is increased, the discreteness of charge is progressively reduced by quantum fluctuations. Here we report the full quantum control and characterization of charge quantization. By using semiconductor-based tunable elemental conduction channels to connect a micrometre-scale metallic island to a circuit, we explore the complete evolution of charge quantization while scanning the entire range of connection strengths, from a very weak (tunnel) to a perfect (ballistic) contact. We observe, when approaching the ballistic limit, that charge quantization is destroyed by quantum fluctuations, and scales as the square root of the residual probability for an electron to be reflected across the quantum channel; this scaling also applies beyond the different regimes of connection strength currently accessible to theory. At increased temperatures, the thermal fluctuations result in an exponential suppression of charge quantization and in a universal square-root scaling, valid for all connection strengths, in agreement with expectations. Besides being pertinent for the improvement of single-electron circuits and their applications, and for the metal-semiconductor hybrids relevant to topological quantum computing, knowledge of the quantum laws of electricity will be essential for the quantum engineering of future nanoelectronic devices.

Detection of non-Gaussian fluctuations in a quantum point contact

An experimental study of current fluctuations through a tunable transmission barrier, a quantum point contact, is reported. We measure the probability distribution function of transmitted charge with precision sufficient to extract the first three cumulants. To obtain the intrinsic quantities, corresponding to voltage-biased barrier, we employ a procedure that accounts for the response of the external circuit and the amplifier. The third cumulant, obtained with a high precision, is found to agree with the prediction for the statistics of transport in the non-Poissonian regime.

Multiparticle interference, Greenberger-Horne-Zeilinger entanglement, and full counting statistics

We investigate the quantum transport in a generalized N-particle Hanbury Brown-Twiss setup enclosing magnetic flux, and demonstrate that the Nth-order cumulant of current cross correlations exhibits Aharonov-Bohm oscillations, while there is no such oscillation in all the lower-order cumulants. The multiparticle interference results from the orbital Greenberger-Horne-Zeilinger entanglement of N indistinguishable particles. For sufficiently strong Aharonov-Bohm oscillations the generalized Bell inequalities may be violated, proving the N-particle quantum nonlocality.

Breakdown of universality in quantum chaotic transport: the two-phase dynamical fluid model

We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic classical dynamics, and result from the separation of the quantum phase space into a stochastic and a deterministic phase. Consequently, sample-to-sample conductance fluctuations lose their universality, while the persistence of a finite stochastic phase protects the universality of conductance fluctuations under variation of a quantum parameter.

Two-particle Aharonov-Bohm effect and entanglement in the electronic Hanbury Brown-Twiss setup

We analyze a Hanbury Brown-Twiss geometry in which particles are injected from two independent sources into a mesoscopic conductor in the quantum Hall regime. All partial waves end in different reservoirs without generating any single-particle interference; in particular, there is no single-particle Aharonov-Bohm effect. However, exchange effects lead to two-particle Aharonov-Bohm oscillations in the zero-frequency current cross correlations. We demonstrate that this is related to two-particle orbital entanglement, detected via violation of a Bell inequality. The transport is along edge states and only adiabatic quantum point contacts and normal reservoirs are employed.

Orbital entanglement and violation of Bell inequalities in mesoscopic conductors

We propose a spin-independent scheme to generate and detect two-particle entanglement in a mesoscopic normal-superconductor system. A superconductor, weakly coupled to the normal conductor, generates an orbitally entangled state by injecting pairs of electrons into different leads of the normal conductor. The entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current cross correlators. It is shown that the Bell inequality can be violated for arbitrary strong dephasing in the normal conductor.

Stochastic path integral formulation of full counting statistics

We derive a stochastic path integral representation of counting statistics in semiclassical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the saddle-point approximation to the path integral, and fluctuations around the saddle point are suppressed in the semiclassical approximation. We use this approach to derive the current cumulants of a chaotic cavity in the hot-electron regime.

Crossover between classical and quantum shot noise in chaotic cavities

The discreteness of charge in units of e led Schottky in 1918 to predict that the electrical current in a vacuum tube fluctuates even if all spurious noise sources are eliminated carefully. This phenomenon is now widely known as shot noise. In recent years, shot noise in mesoscopic conductors, where charge motion is quantum-coherent over distances comparable to the system size, has been studied extensively. In those experiments, charge does not propagate as an isolated entity through free space, as for vacuum tubes, but is part of a degenerate and quantum-coherent Fermi sea of charges. It has been predicted that shot noise in mesoscopic conductors can disappear altogether when the system is tuned to a regime where electron motion becomes classically chaotic. Here we experimentally verify this prediction by using chaotic cavities where the time that electrons dwell inside can be tuned. Shot noise is present for large dwell times, where the electron motion through the cavity is 'smeared' by quantum scattering, and it disappears for short dwell times, when the motion becomes classically deterministic.

Shot noise by quantum scattering in chaotic cavities

We have experimentally studied shot noise of chaotic cavities defined by two quantum point contacts in series. The cavity noise is determined as (1/4)2e/I/ in agreement with theory and can be well distinguished from other contributions to noise generated at the contacts. Subsequently, we have found that cavity noise decreases if one of the contacts is further opened and reaches nearly zero for a highly asymmetric cavity. Heating inside the cavity due to electron-electron interaction can slightly enhance the noise of large cavities and is also discussed quantitatively.

Quantum dot as spin filter and spin memory

We consider a quantum dot in the Coulomb blockade regime weakly coupled to current leads and show that in the presence of a magnetic field it acts as an efficient spin filter (at the single-spin level), producing a spin-polarized current. Conversely, if the leads are fully spin polarized the up or the down state of the spin on the dot results in a large sequential or a small cotunneling current, and, thus, together with ESR techniques, the setup can be operated as a single-spin memory.

Semiclassical theory of conductance and noise in open chaotic cavities

Conductance and shot noise of an open cavity with diffusive boundary scattering are calculated within the Boltzmann-Langevin approach. In particular, conductance contains a nonuniversal geometric contribution, originating from the presence of open contacts. Subsequently, universal expressions for multiterminal conductance and noise, valid for all chaotic cavities, are obtained classically, based on the fact that the distribution function in the cavity depends only on energy, and using the principle of minimal correlations.

Probing entanglement and nonlocality of electrons in a double-dot via transport and noise

Addressing the feasibility of quantum communication with electrons we consider entangled spin states of electrons in a double-dot which is weakly coupled to leads. We show that the entanglement of two electrons in the double-dot can be detected in mesoscopic transport and noise measurements. In the Coulomb blockade and cotunneling regime the singlet and triplet states lead to phase-coherent current and noise contributions of opposite signs and to Aharonov-Bohm and Berry phase oscillations. These oscillations are a genuine two-particle effect and provide a direct measure of nonlocality in entangled states. We show that the ratio of zero-frequency noise to current is equal to the electron charge.