We demonstrate radiofrequency thermometry on a micrometer-sized metallic island below 100 mK. Our device is based on a normal metal-insulator-superconductor tunnel junction coupled to a resonator with transmission readout. In the first generation of
the device, we achieve 90 {mu}K/Hz^1/2 noise-equivalent temperature with 10 MHz bandwidth. We measure the thermal relaxation time of the electron gas in the island, which we find to be of the order of 100 {mu}s. Such a calorimetric detector, upon optimization, can be seamlessly integrated into superconducting circuits, with immediate applications in quantum-thermodynamics experiments down to single quanta of energy.
We present an indirect two-qubit parity meter in planar circuit quantum electrodynamics, realized by discrete interaction with an ancilla and a subsequent projective ancilla measurement with a dedicated, dispersively coupled resonator. Quantum proces
s tomography and successful entanglement by measurement demonstrate that the meter is intrinsically quantum non-demolition. Separate interaction and measurement steps allow commencing subsequent data qubit operations in parallel with ancilla measurement, offering time savings over continuous schemes.
Recently, the fundamental laws of thermodynamics have been reconsidered for small systems. The discovery of the fluctuation relations has spurred theoretical and experimental studies on thermodynamics of systems with few degrees of freedom. The conce
pt of entropy production has been extended to the microscopic level by considering stochastic trajectories of a system coupled to a heat bath. However, the experimental observation of the microscopic entropy production remains elusive. We measure distributions of the microscopic entropy production in a single-electron box consisting of two islands with a tunnel junction. The islands are coupled to separate heat baths at different temperatures, maintaining a steady thermal non-equilibrium. As Jarzynski equality between work and free energy is not applicable in this case, the entropy production becomes the relevant parameter. We verify experimentally that the integral and detailed fluctuation relations are satisfied. Furthermore, the coarse-grained entropy production from trajectories of electronic transitions is related to the bare entropy production by a universal formula. Our results reveal the fundamental roles of irreversible entropy production in non-equilibrium small systems.
Controlling electrons at the level of elementary charge $e$ has been demonstrated experimentally already in the 1980s. Ever since, producing an electrical current $ef$, or its integer multiple, at a drive frequency $f$ has been in a focus of research
for metrological purposes. In this review we first discuss the generic physical phenomena and technical constraints that influence charge transport. We then present the broad variety of proposed realizations. Some of them have already proven experimentally to nearly fulfill the demanding needs, in terms of transfer errors and transfer rate, of quantum metrology of electrical quantities, whereas some others are currently just wild ideas, still often potentially competitive if technical constraints can be lifted. We also discuss the important issues of read-out of single-electron events and potential error correction schemes based on them. Finally, we give an account of the status of single-electron current sources in the bigger framework of electric quantum standards and of the future international SI system of units, and briefly discuss the applications and uses of single-electron devices outside the metrological context.
Recent progress on micro- and nanometer scale manipulation has opened the possibility to probe systems small enough that thermal fluctuations of energy and coordinate variables can be significant compared with their mean behavior. We present an exper
imental study of nonequilibrium thermodynamics in a classical two-state system, namely a metallic single-electron box. We have measured with high statistical accuracy the distribution of dissipated energy as single electrons are transferred between the box electrodes. The obtained distributions obey Jarzynski and Crooks fluctuation relations. A comprehensive microscopic theory exists for the system, enabling the experimental distributions to be reproduced without fitting parameters.
The hold time $tau$ of a single-electron trap is shown to increase significantly due to suppression of environmentally assisted tunneling events. Using two rf-tight radiation shields instead of a single one, we demonstrate increase of $tau$ by a fact
or exceeding $10^3$, up to about 10 hours, for a trap with only two superconductor (S) -- normal-metal (N) tunnel junctions and an on-chip resistor $R$ (R-SNS structure). In the normal state, the improved shielding made it possible to observe $tausim$ 100 s, which is in reasonable agreement with the quantum-leakage-limited level expected for the two-electron cotunneling process.
We provide a direct proof of two-electron Andreev transitions in a superconductor - normal metal tunnel junction by detecting them in a real-time electron counting experiment. Our results are consistent with ballistic Andreev transport with an order
of magnitude higher rate than expected for a uniform barrier, suggesting that only part of the interface is effectively contributing to the transport. These findings are quantitatively supported by our direct current measurements in single-electron transistors with similar tunnel barriers.
