Matthias Meschke

Single-mode heat conduction by photons.

The thermal conductance of a single channel is limited by its unique quantum value GQ, as was shown theoretically in 1983. This result closely resembles the well-known quantization of electrical conductance in ballistic one-dimensional conductors. Interestingly, all particles—irrespective of whether they are bosons or fermions—have the same quantized thermal conductance when they are confined within dimensions that are small compared to their characteristic wavelength. The single-mode heat conductance is particularly relevant in nanostructures. Quantized heat transport through submicrometre dielectric wires by phonons has been observed, and it has been predicted to influence cooling of electrons in metals at very low temperatures due to electromagnetic radiation. Here we report experimental results showing that at low temperatures heat is transferred by photon radiation, when electron–phonon as well as normal electronic heat conduction is frozen out. We study heat exchange between two small pieces of normal metal, connected to each other only via superconducting leads, which are ideal insulators against conventional thermal conduction. Each superconducting lead is interrupted by a switch of electromagnetic (photon) radiation in the form of a DC-SQUID (a superconducting loop with two Josephson tunnel junctions). We find that the thermal conductance between the two metal islands mediated by photons indeed approaches the expected quantum limit of GQ at low temperatures. Our observation has practical implications—for example, for the performance and design of ultra-sensitive bolometers (detectors of far-infrared light) and electronic micro-refrigerators, whose operation is largely dependent on weak thermal coupling between the device and its environment.

Micrometre-scale refrigerators

A superconductor with a gap in the density of states or a quantum dot with discrete energy levels is a central building block in realizing an electronic on-chip cooler. They can work as energy filters, allowing only hot quasiparticles to tunnel out from the electrode to be cooled. This principle has been employed experimentally since the early 1990s in investigations and demonstrations of micrometre-scale coolers at sub-kelvin temperatures. In this paper, we review the basic experimental conditions in realizing the coolers and the main practical issues that are known to limit their performance. We give an update of experiments performed on cryogenic micrometre-scale coolers in the past five years.

Origin of Hysteresis in a Proximity Josephson Junction

We investigate hysteresis in the transport properties of superconductor-normal-metal-superconductor (S-N-S) junctions at low temperatures by measuring directly the electron temperature in the normal metal. Our results demonstrate unambiguously that the hysteresis results from an increase of the normal-metal electron temperature once the junction switches to the resistive state. In our geometry, the electron temperature increase is governed by the thermal resistance of the superconducting electrodes of the junction.

Heat transistor: Demonstration of gate-controlled electronic refrigeration

We present experiments on a superconductor-normal-metal electron refrigerator in a regime where single-electron charging effects are significant. The system functions as a heat transistor; i.e., the heat flux out from the normal-metal island can be controlled with a gate voltage. A theoretical model developed within the framework of single-electron tunneling provides a full quantitative agreement with the experiment. This work serves as the first experimental observation of Coulombic control of heat transfer and, in particular, of refrigeration in a mesoscopic system.

Recombination-limited energy relaxation in a Bardeen-Cooper-Schrieffer superconductor

We study quasiparticle energy relaxation at subkelvin temperatures by injecting hot electrons into an Al island and measuring the energy flux from quasiparticles into phonons both in the superconducting and in the normal state. The data show strong reduction of the flux at low temperatures in the superconducting state, in qualitative agreement with the theory for clean superconductors. However, quantitatively the energy flux exceeds the theoretical predictions both in the superconducting and in the normal state, suggesting an enhanced or additional relaxation process.

Electronic refrigeration at the quantum limit

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 microm 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.

Superconducting quantum interference proximity transistor

The development of superconducting quantum interference devices based on the Josephson effect has led to significant improvements in our ability to measure magnetic fields. A similar device, dubbed the superconducting quantum interference transistor, which exploits the proximity effect, could allow similar significant further improvements. When a superconductor is placed close to a non-superconducting metal, it can induce superconducting correlations in the metal 1,2,3,4,5,6,7,8,9,10, known as the ‘proximity effect’11. Such behaviour modifies the density of states (DOS) in the normal metal12,13,14,15 and opens a minigap12,13,16 with an amplitude that can be controlled by changing the phase of the superconducting order parameter12,15. Here, we exploit such behaviour to realize a new type of interferometer, the superconducting quantum interference proximity transistor (SQUIPT), for which the operation relies on the modulation with the magnetic field of the DOS of a proximized metal embedded in a superconducting loop. Even without optimizing its design, this device shows extremely low flux noise, down to ∼10−5 Φ0Hz−1/2 (Φ0≃2×10−15 Wb is the flux quantum) and dissipation several orders of magnitude smaller than in conventional superconducting interferometers17,18,19. With optimization, the SQUIPT could significantly increase the sensitivity with which small magnetic moments are detected.

Fast Electron Thermometry for Ultrasensitive Calorimetric Detection

We demonstrate radio-frequency 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/root Hz 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.

Trapping hot quasi-particles in a high-power superconducting electronic cooler

The performance of hybrid superconducting electronic coolers is usually limited by the accumulation of hot quasi-particles in their superconducting leads. This issue is all the more stringent in large-scale and high-power devices, as required by the applications. Introducing a metallic drain connected to the superconducting electrodes via a fine-tuned tunnel barrier, we efficiently remove quasi-particles and obtain electronic cooling from 300mK down to 130mK with a 400pW cooling power. A simple thermal model accounts for the experimental observations.

Tunnel spectroscopy of a proximity Josephson junction

We present tunnel spectroscopy experiments on the proximity effect in lateral superconductor\char21{}normal-metal\char21{}superconductor Josephson junctions. Our weak link is embedded into a superconducting ring allowing phase biasing of the Josephson junction by an external magnetic field. We explore the temperature and phase dependence of both the induced minigap and the modification of the density of states in the normal metal. Our results agree with a model based on the quasiclassical theory in the diffusive limit. The device presents an advanced version of the superconducting quantum interference proximity transistor, now reaching flux sensitivities of 3 nA