Counting statistics and detector properties of quantum point contacts

Dephasing by a zero-temperature detector and the Friedel sum rule

Detecting the passage of an interfering particle through one of the interferometer's arms, known as "which path" measurement, gives rise to interference visibility degradation (dephasing). Here, we consider a detector at equilibrium. At finite temperature, dephasing is caused by thermal fluctuations of the detector. More interestingly, in the zero-temperature limit, equilibrium quantum fluctuations of the detector give rise to dephasing of the out-of-equilibrium interferometer. This dephasing is a manifestation of an orthogonality catastrophe, which differs qualitatively from Anderson's. Its magnitude is directly related to the Friedel sum rule.

Counting statistics for mesoscopic conductors with internal degrees of freedom

We consider the transport of electrons passing through a mesoscopic device possessing internal dynamical quantum degrees of freedom. The mutual interaction between the system and the conduction electrons contributes to the current fluctuations, which we describe in terms of full counting statistics. We identify conditions where this discriminates coherent from incoherent internal dynamics and also identify and illustrate conditions under which the device acts to dynamically bunch transmitted or reflected electrons, thereby generating super-Poissonian noise.

Reduced dynamics with renormalization in solid-state charge qubit measurement

Quantum measurement will inevitably cause backaction on the measured system, resulting in the well-known dephasing and relaxation. In this paper, in the context of solid-state qubit measurement by a mesoscopic detector, we show that an alternative backaction known as renormalization is important under some circumstances. This effect is largely overlooked in the theory of quantum measurement.

Universal detector efficiency of a mesoscopic capacitor

We investigate theoretically a novel type of high frequency quantum detector based on the mesoscopic capacitor recently realized by Gabelli et al. [Science 313, 499 (2006)10.1126/science.1126940], which consists of a quantum dot connected via a single channel quantum point contact to a single lead. We show that the state of a double quantum dot charge qubit capacitively coupled to this detector can be readout in the GHz frequency regime with near quantum limited efficiency. To leading order, the quantum efficiency is found to be universal owing to the universality of the charge relaxation resistance of the mesoscopic capacitor.

Weak values of electron spin in a double quantum dot

We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure--weak measurement followed by a strong one (postselection), where the outcome of the first measurement is kept provided a second postselected outcome occurs. The setup consists of a double quantum dot and a weakly coupled quantum point contact to be used as a detector. Anomalously large values of the spin of a two electron system are predicted, as well as negative values of the total spin. We also show how to incorporate the adverse effect of decoherence into this procedure.

Validity and breakdown of Onsager symmetry in mesoscopic conductors interacting with environments

We investigate magnetic-field asymmetries in the linear transport of a mesoscopic conductor interacting with its environment. Interestingly, we find that the interaction between the two systems causes an asymmetry only when the environment is out of equilibrium. We elucidate our general result with the help of a quantum dot capacitively coupled to a quantum Hall conductor and discuss the asymmetry dependence on the environment bias and induced dephasing.

Entanglement, dephasing, and phase recovery via cross-correlation measurements of electrons

Determination of the path taken by a quantum particle leads to a suppression of interference and to a classical behavior. We employ here a quantum "which path" detector to perform accurate path determination in a two-path Mach-Zehnder electron interferometer, leading to full suppression of the interference. Following the dephasing process we recover the interference by measuring the cross correlation between the interferometer and detector currents. Under our measurement conditions every interfering electron is dephased by approximately a single electron in the detector-leading to mutual entanglement of approximately single pairs of electrons.

Leggett-Garg inequality with a kicked quantum pump

A kicked quantum nondemolition measurement is introduced, where a qubit is weakly measured by pumping current. Measurement statistics are derived for weak measurements combined with single-qubit unitary operations. These results are applied to violate a generalization of the Leggett-Garg inequality. The violation is related to the failure of the noninvasive detector assumption, and may be interpreted as either intrinsic detector backaction, or the qubit entangling the microscopic detector excitations. The results are discussed in terms of a quantum point contact kicked by a pulse generator, measuring a double quantum dot.

Using qubits to measure fidelity in mesoscopic systems

We point out the similarities in the definition of the "fidelity" of a quantum system and the generating function determining the full counting statistics of charge transport through a quantum wire and suggest to use flux or charge qubits for their measurement. As an application we use the notion of fidelity within a first-quantized formalism in order to derive new results and insights on the generating function of the full counting statistics.