Bruno Küng

Irreversibility on the Level of Single-Electron Tunneling

We present a low-temperature experimental test of the fluctuation theorem for electron transport through a double quantum dot. The rare entropy-consuming system trajectories are detected in the form of single charges flowing against the source-drain bias by using time-resolved charge detection with a quantum point contact. We find that these trajectories appear with a frequency that agrees with the theoretical predictions even under strong nonequilibrium conditions, when the finite bandwidth of the charge detection is taken into account. The second law of thermodynamics states that a macroscopic system out of thermal equilibrium will irreversibly move toward equilibrium driven by a steady increase of its entropy. This macroscopic irreversibility occurs despite the time-reversal symmetry of the underlying microscopic equations of motion. Also, a microscopic system will undergo an irreversible evolution on a long time scale, but, over a sufficiently short observation time � , both entropy-producing trajectories as well as their timereversed entropy-consuming counterparts occur. It is only because of the statistics of these occurrences that a longterm irreversible evolution is established. This phenomenon is described by the fluctuation theorem [1,2]. Irrespective of the description of the trajectories being system-specific, the fluctuation theorem (FT) relates the probabilities P� ð� SÞ for processes that change the entropy

Statistical electron excitation in a double quantum dot induced by two independent quantum point contacts

We investigate experimentally the influence of current flow through two independent quantum point contacts to a nearby double quantum dot realized in a GaAs-AlGaAs heterostructure. The observed current through the double quantum dot can be explained in terms of coupling to a bosonic bath. The temperature of the bath depends on the power generated by the current flow through the quantum point contact. We identify the dominant absorption and emission mechanisms in a double quantum dot as an interaction with acoustic phonons. The experiment excludes coupling of a double quantum dot to shot noise generated by quantum point contact as the dominant mechanism.

An in situ tunable radio-frequency quantum point contact

Incorporating a variable capacitance diode into a radio-frequency (rf) matching circuit allows us to in situ tune the resonance frequency of a rf quantum point contact, increasing the versatility of the latter as a fast charge sensor of a proximal quantum circuit. The performance of this method is compared in detail to conventional low-frequency charge detection. The approach is also applicable to other rf-detection schemes, such as rf single electron transistor circuits.

Kerr coefficients of plasma resonances in Josephson junction chains

We present an experimental and theoretical analysis of the self- and cross-Kerr effect of extended plasma resonances in Josephson junction chains. We calculate the Kerr coefficients by deriving and diagonalizing the Hamiltonian of a linear circuit model for the chain and then adding the Josephson non-linearity as a perturbation. The calculated Kerr-coefficients are compared with the measurement data of a chain of 200 junctions. The Kerr effect manifests itself as a frequency shift that depends linearly on the number of photons in a resonant mode. By changing the input power on a low signal level, we are able to measure this shift. The photon number is calibrated using the self-Kerr shift calculated from the sample parameters. We then compare the measured cross-Kerr shift with the theoretical prediction, using the calibrated photon number.

Test of the fluctuation theorem for single-electron transport

Using time-resolved charge detection in a double quantum dot, we present an experimental test of the fluctuation theorem. The fluctuation theorem, a result from nonequilibrium statistical mechanics, quantifies the ratio of occurrence of fluctuations that drive a small system against the direction favored by the second law of thermodynamics. Here, these fluctuations take the form of single electrons flowing against the source–drain bias voltage across the double quantum dot. Our results, covering configurations close to as well as far from equilibrium, agree with the theoretical predictions, when the finite bandwidth of the charge detection is taken into account. In further measurements, we study a fluctuation relation that is a generalization of the Johnson–Nyquist formula and relates the second-order conductance to the voltage dependence of the noise. Current and noise can be determined with the time-resolved charge detection method. Our measurements confirm the fluctuation relation in the nonlinear tran...

Optimization of sample-chip design for stub-matched radio-frequency reflectometry measurements

A radio-frequency (rf) matching circuit with an in situ tunable varactor diode used for rf reflectometry measurements in semiconductor nanostructures is investigated and used to optimize the sample-specific chip design. The samples are integrated in a 2–4 GHz stub-matching circuit consisting of a waveguide stub shunted to the terminated coplanar waveguide. Several quantum point contacts fabricated on a GaAs/AlGaAs heterostructure with different chip designs are compared. We show that the change of the reflection coefficient for a fixed change in the quantum point contact conductance can be enhanced by a factor of 3 compared to conventional designs by a suitable electrode geometry.

Highly tunable hybrid quantum dots with charge detection

In order to employ solid state quantum dots as qubits, both a high degree of control over the confinement potential as well as sensitive charge detection are essential. We demonstrate that by combining local anodic oxidation with local Schottky-gates, these criteria are nicely fulfilled in the resulting hybrid device. To this end, a quantum dot with adjacent charge detector is defined. After tuning the quantum dot to contain only a single electron, we are able to observe the charge detector signal of the quantum dot state for a wide range of tunnel couplings.

Time-resolved charge detection with cross-correlation techniques

We present time-resolved charge-sensing measurements on a GaAs double quantum dot with two proximal quantum point-contact (QPC) detectors. The QPC currents are analyzed with cross-correlation techniques, which enable us to measure dot charging and discharging rates for significantly smaller signal-to-noise ratios than required for charge detection with a single QPC. This allows us to reduce the current level in the detector and therefore the invasiveness of the detection process and may help to increase the available measurement bandwidth in noise-limited setups.

Noise-induced spectral shift measured in a double quantum dot

We measure the shot noise of a quantum point-contact using a capacitively coupled InAs double quantum dot as an on-chip sensor. Our measurement signals are the (bidirectional) interdot electronic tunneling rates which are determined by means of time-resolved charge sensing. The detector frequency is set by the relative detuning of the energy levels in the two dots. For nonzero detuning, the noise in the quantum point contact generates inelastic tunneling in the double dot and thus causes an increase in the interdot tunneling rate. Conservation of spectral weight in the dots implies that this increase must be compensated by a decrease in the rate close to zero detuning, which is quantitatively confirmed in our experiment.

Phonon-mediated back-action of a charge readout on a double quantum dot

Quantum point contacts are in use as an on-chip capacitative readout for the charge state of quantum dot systems. Here we investigate experimentally the back-action of quantum point contacts (QPCs) on a nearby double quantum dot (DQD). Driving current through a QPC influences the DQD state and leads to a measurable current flow in the DQD circuit with no bias voltage applied. The responsible mechanism is an indirect back-action process due to ohmic heating of the phonon bath. The system behaves like a thermoelectric engine, where a temperature gradient between the phonon bath and the electronic bath generates work observable as a measurable current flowing through the DQD.