Microwave photonics with superconducting quantum circuits

In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons. This emerging field of superconducting quantum microwave circuits has been driven by many new interesting phenomena in microwave photonics and quantum information processing. For instance, the interaction between superconducting quantum circuits and single microwave photons can reach the regimes of strong, ultra-strong, and even deep-strong coupling. Many higher-order effects, unusual and less familiar in traditional cavity quantum electrodynamics with natural atoms, have been experimentally observed, e.g., giant Kerr effects, multi-photon processes, and single-atom induced bistability of microwave photons. These developments may lead to improved understanding of the counterintuitive properties of quantum mechanics, and speed up applications ranging from microwave photonics to superconducting quantum information processing. In this article, we review experimental and theoretical progress in microwave photonics with superconducting quantum circuits. We hope that this global review can provide a useful roadmap for this rapidly developing field.

Charge transport layers (CTLs) are key components of diffusion controlled perovskite solar cells, however, they can induce additional non-radiative recombination pathways which limit the open circuit voltage (VOC) of the cell. In order to realize the full thermodynamic potential of the perovskite absorber, both the electron and hole transport layer (ETL/HTL) need to be as selective as possible. By measuring the photoluminescence yield of perovskite/CTL heterojunctions, we quantify the non-radiative interfacial recombination currents in pin- and nip-type cells including high efficiency devices (21.4%). Our study comprises a wide range of commonly used CTLs, including various hole-transporting polymers, spiro-OMeTAD, metal oxides and fullerenes. We find that all studied CTLs limit the VOC by inducing an additional non-radiative recombination current that is in most cases substantially larger than the loss in the neat perovskite and that the least-selective interface sets the upper limit for the VOC of the device. Importantly, the VOC equals the internal quasi-Fermi level splitting (QFLS) in the absorber layer only in high efficiency cells, while in poor performing devices, the VOC is substantially lower than the QFLS. Using ultraviolet photoelectron spectroscopy and differential charging capacitance experiments we show that this is due to an energy level mis-alignment at the p-interface. The findings are corroborated by rigorous device simulations which outline important considerations to maximize the VOC. This work highlights that the challenge to suppress non-radiative recombination losses in perovskite cells on their way to the radiative limit lies in proper energy level alignment and in suppression of defect recombination at the interfaces.

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The impact of energy alignment and interfacial recombination on the internal and external open-circuit voltage of perovskite solar cells

Electronic circuits operating at sub-kelvin temperatures are attractive candidates for studying classical and quantum thermodynamics: their temperature can be controlled and measured locally with exquisite precision, and they allow experiments with large statistical samples. The availability and rapid development of devices such as quantum dots, single-electron boxes and superconducting qubits only enhance their appeal. But although these systems provide fertile ground for studying heat transport, entropy production and work in the context of quantum mechanics, the field remains in its infancy experimentally. Here, we review some recent experiments on quantum heat transport, fluctuation relations and implementations of Maxwell’s demon, revealing the rich physics yet to be fully probed in these systems. Experiments probing non-equilibrium processes have so far been tailored largely to classical systems. The endeavour to extend our understanding into the quantum realm is finding traction in studies of electronic circuits at sub-kelvin temperatures.

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Towards quantum thermodynamics in electronic circuits

We study stochastic energetic exchanges in quantum heat engines. Due to microreversibility, these obey a fluctuation relation, called the heat engine fluctuation relation, which implies the Carnot bound: no machine can have an efficiency greater than Carnot?s efficiency. The stochastic thermodynamics of a quantum heat engine (including the joint statistics of heat and work and the statistics of efficiency) are illustrated by means of an optimal two-qubit heat engine, where each qubit is coupled to a thermal bath and a two-qubit gate determines energy exchanges between the two qubits. We discuss possible solid-state implementations with Cooper-pair boxes and flux qubits, quantum gate operations, and fast calorimetric on-chip measurements of single stochastic events.

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Nonequilibrium fluctuations in quantum heat engines: theory, example, and possible solid state experiments

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.

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Fast Electron Thermometry for Ultrasensitive Calorimetric Detection

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.

Fast electron thermometry towards ultra-sensitive calorimetric detection

We have embedded a small Josephson junction in a microwave resonator that allows simultaneous dc biasing and dispersive readout. Thermal fluctuations drive the junction into phase diffusion and induce a temperature-dependent shift in the resonance frequency. By sensing the thermal noise of a remote resistor in this manner, we demonstrate primary thermometry in the range from 300 mK to below 100 mK, and high-bandwidth (7.5 MHz) operation with a noise-equivalent temperature of better than 10 $\mathrm{\mu K/\sqrt{Hz}}$. At a finite bias voltage close to a Fiske resonance, amplification of the microwave probe signal is observed. We develop an accurate theoretical model of our device based on the theory of dynamical Coulomb blockade.

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Dispersive Thermometry with a Josephson Junction Coupled to a Resonator

We discuss work performed on a quantum two-level system coupled to multiple thermal baths. To evaluate the work, a measurement of photon exchange between the system and the baths is envisioned. In a realistic scenario, some photons remain unrecorded as they are exchanged with baths that are not accessible to the measurement, and thus only partial information on work and heat is available. The incompleteness of the measurement leads to substantial deviations from standard fluctuation relations. We propose a recovery of these relations, based on including the mutual information given by the counting efficiency of the partial measurement. We further present the experimental status of a possible implementation of the proposed scheme, i.e. a calorimetric measurement of work, currently with nearly single-photon sensitivity.

https://iopscience.iop.org/article/10.1088/1367-2630/17/5/055014/pdf

Incomplete measurement of work in a dissipative two level system

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K. L. Viisanen

Papers

Fast Electron Thermometry for Ultrasensitive Calorimetric Detection

Fast electron thermometry towards ultra-sensitive calorimetric detection

Dispersive Thermometry with a Josephson Junction Coupled to a Resonator

Incomplete measurement of work in a dissipative two level system

Dispersive thermometry with a Josephson junction coupled to a resonator