We demonstrate quantum-limited electronic refrigeration of a metallic island in a low-temperature microcircuit. We show that matching the impedance of the circuit enables refrigeration at a distance, of about 50 m in our case, through superconducting leads with a cooling power determined by the quantum of thermal conductance. In a reference sample with a mismatched circuit this effect is absent. Our results are consistent with the concept of electromagnetic heat transport. We observe and analyze the crossover between electromagnetic and quasiparticle heat flux in a superconductor.

The detection of mechanical vibrations near the quantum limit is a formidable challenge since the displacement becomes vanishingly small when the number of phonon quanta tends towards zero. An interesting setup for on-chip nanomechanical resonators is that of coupling them to electrical microwave cavities for detection and manipulation. Here we show how to achieve a large cavity coupling energy of up to (2π) 1 MHz/nm for metallic beam resonators at tens of MHz. We used focused ion beam (FIB) cutting to produce uniform slits down to 10 nm, separating patterned resonators from their gate electrodes, in suspended aluminum films. We measured the thermomechanical vibrations down to a temperature of 25 mK, and we obtained a low number of about twenty phonons at the equilibrium bath temperature. The mechanical properties of Al were excellent after FIB cutting and we recorded a quality factor of Q ∼ 3 × 10 5 for a 67 MHz resonator at a temperature of 25 mK. Between 0.2K and 2K we find that the dissipation is linearly proportional to the temperature. Keywords nanomechanics, NEMS, quantum limit, detection, dissipationThe measurement of small-amplitude vibrations in mechanical systems is becoming an increasingly interesting problem [1,2]. From the point of view of basic science, the study of mechanical systems close to the quantum limit has attracted a lot of interest recently [3,4]. The endeavor towards the ground state of the harmonic phonon oscillations has been going on in various physical systems such as in optomechanics [5][6][7], or in electrically coupled beam resonators which have been measured using single-electron transistors [4,8], or lately, with on-chip microwave cavities [9][10][11][12].The quantum challenge is posed by several issues, including the relatively low frequency (f 0 ∼ 10 MHz), of the lowest modes in suspended beams. The quantum limit implies stringent requirements on temperature, since hf 0 needs to be small in comparison to k B T . On the other hand, at higher frequencies, the coupling to measuring systems diminishes rapidly. Third, the zero-point vibration amplitudes x ZP = /2mω 0 , where m is the effective mass and ω 0 = 2πf 0 is the angular frequency, are vanishingly small even at the atomic scale. Very recently, O'Connell et al.[13] demonstrated a piezoelectric mechanical mode at the quantum ground state by using a coupling to a superconducting qubit. However, bringing a purely mechanical mode to the quantum limit remains an ongoing quest, with the goal becoming a reality probably in the near future.Micromechanical resonators are also used in applications as detectors. The best devices take advantage of the trend to smaller size and higher frequencies, and will soon approach sensing at the atomic mass unit level [14,15]. They could also be operated as sensors of position, force, or high-frequency electromagnetic fields.For conductive resonators, capacitive coupling to an electrical measuring apparatus is useful for readout. In contrast to magnetomotive or optical detection, one can obtain v...

Laterally coupled quantum dot molecules are studied using exact diagonalization techniques. We examine the two-electron singlet-triplet energy difference as a function of magnetic field strength and investigate the magnetization and vortex formation of two-and four-minima lateral quantum dot molecules. Special attention is paid to the analysis of how the distorted symmetry affects the properties of quantum-dot molecules.

Voltage fluctuations generated in a hot resistor can cause extraction of heat from a colder normal metal electrode of a hybrid tunnel junction between a normal metal and a superconductor. We extend the analysis presented in Phys. Rev. Lett. 98, 210604 (2007) of this heat rectifying system, bearing resemblance to a Maxwell's demon. Explicit analytic calculations show that the entropy of the total system is always increasing. We then consider a single-electron transistor configuration with two hybrid junctions in series, and show how the cooling is influenced by charging effects. We analyze also the cooling effect from nonequilibrium fluctuations instead of thermal noise, focusing on the shot noise generated in another tunnel junction. We conclude by discussing limitations for an experimental observation of the effect.