Electronic heat flow and thermal shot noise in quantum circuits
E. Sivre, H. Duprez, A. Anthore, A. Aassime, F. D. Parmentier, A. Cavanna, A. Ouerghi, U. Gennser, F. Pierre
备注：
Minor differences with published article: additional reference [29], more explicit identification 'thermal shot noise' - 'delta-T noise', includes the supplementary figures
When assembling individual quantum components into a mesoscopic circuit, the interplay between Coulomb interaction and charge granularity breaks down the classical laws of electrical impedance composition. Here we explore experimentally the thermal consequences, and observe an additional quantum mechanism of electronic heat transport. The investigated, broadly tunable test-bed circuit is composed of a micron-scale metallic node connected to one electronic channel and a resistance. Heating up the node with Joule dissipation, we separately determine, from complementary noise measurements, both its temperature and the thermal shot noise induced by the temperature difference across the channel (`delta-$T$ noise'). The thermal shot noise predictions are thereby directly validated, and the electronic heat flow is revealed. The latter exhibits a contribution from the channel involving the electrons' partitioning together with the Coulomb interaction. Expanding heat current predictions to include the thermal shot noise, we find a quantitative agreement with experiments.
The study of quantum heat transport in superconducting circuits is significant for further understanding the connection between quantum mechanics and thermodynamics, and for possible applications for quantum information. The first experimental realisations of devices demonstrating photonic heat transport mediated by a qubit have already been designed and measured. Motivated by the analysis of such experimental results, and for future experimental designs, we numerically evaluate the photonic heat transport of qubit-resonator devices in the linear circuit regime through electromagnetic simulati…
We discuss the non-zero frequency noise of heat current with the explicit example of energy carried by thermal photons in a circuit. Instead of the standard circuit modelling that gives a convenient way of predicting time-averaged heat current, we describe a setup composed of two resistors forming the heat baths by collections of bosonic oscillators. In terms of average heat transport this model leads to identical results with the conventional one, but besides this, it yields a convenient way of dealing with noise as well. The non-zero frequency heat current noise does not vanish in equilibriu…
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We study photonic heat conduction between two resistors coupled weakly to a single superconducting microwave cavity. At low enough temperature, the dominating part of the heat exchanged between the resistors is transmitted by single-photon excitations of the fundamental mode of the cavity. This manifestation of single-photon heat conduction should be experimentally observable with the current state of the art. Our scheme can possibly be utilized in remote interference-free temperature control of electric components and environment engineering for superconducting qubits coupled to cavities.
Unveiling the impact in thermodynamics of the phenomena specific to quantum mechanics is a crucial step to identify fundamental costs for quantum operations and quantum advantages in heat engines. We propose a two-reservoir setup to detect the quantum component in the heat flow exchanged by a coherently driven atom with its thermal environment. Tuning the driving parameters switches on and off the quantum and classical contributions to the heat flows, enabling their independent characterization. We demonstrate the feasibility of the measurement in a circuit-QED setup. Our results pave the road…
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Photo-assisted transport through a mesoscopic conductor occurs when an oscillatory (AC) voltage is superposed to the constant (DC) bias which is imposed on this conductor. Of particular interest is the photo assisted shot noise, which has been investigated theoretically and experimentally for several types of samples. For DC biased conductors, a detection scheme for finite frequency noise using a dissipative resonant circuit, which is inductively coupled to the mesoscopic device, was developped recently. We argue that the detection of the finite frequency photo-assisted shot noise can be achie…
Superconducting quantum circuits are potential candidates to realize a large-scale quantum computer. The envisioned large density of integrated components, however, requires a proper thermal management and control of dissipation. To this end, it is advantageous to utilize tunable dissipation channels and to exploit the optimized heat flow at exceptional points (EPs). Here, we experimentally realize an EP in a superconducting microwave circuit consisting of two resonators. The EP is a singularity point of the Hamiltonian, and corresponds to the most efficient heat transfer between the resonator…
High-fidelity single-shot readout of spin qubits requires distinguishing states much faster than the T1 time of the spin state. One approach to improving readout fidelity and bandwidth (BW) is cryogenic amplification, where the signal from the qubit is amplified before noise sources are introduced and room-temperature amplifiers can operate at lower gain and higher BW. We compare the performance of two cryogenic amplification circuits: a current-biased heterojunction bipolar transistor circuit (CB-HBT), and an AC-coupled HBT circuit (AC-HBT). Both circuits are mounted on the mixing-chamber sta…
A method to calculate the statistics of energy exchange between quantum systems is presented. The generating function of this statistics is expressed through a Keldysh path integral. The method is first applied to the problem of heat dissipation from a biased mesoscopic conductor into the adjacent reservoirs. We then consider energy dissipation in an electrical circuit around a mesoscopic conductor. We derive the conditions under which measurements of the fluctuations of heat dissipation can be used to investigate higher order cumulants of the charge counting statistics of a mesoscopic conduct…
Quantum heat transport devices are currently intensively studied in theory. Experimental realization of quantum heat transport devices is a challenging task. So far, they have been mostly investigated in experiments with ultra-cold atoms and single atomic traps. Experiments with superconducting qubits have also been carried out and heat transport and heat rectification has been studied in two terminal devices. The structures with three independent terminals offer additional opportunities for realization of heat transistors, heat switches, on-chip masers and even more complicated devices. Here …
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Here, we outline a theory of radiative heat transfer based on an equivalent electrical network representation for the hot material slabs in an arbitrary multilayered environment with arbitrary distribution of temperatures and electromagnetic properties among the layers. Our approach is fully equivalent to the known theories operating with the fluctuating current density, while being significantly simpler in analysis and applications.
A robust cryogenic infrastructure in form of a wired, thermally optimized dilution refrigerator is essential for present and future solid-state based quantum processors. Here, we engineer an extensible cryogenic setup, which minimizes passive and active heat loads, while guaranteeing rapid qubit control and readout. We review design criteria for qubit drive lines, flux lines, and output lines used in typical experiments with superconducting circuits and describe each type of line in detail. The passive heat load of stainless steel and NbTi coaxial cables and the active load due to signal dissi…
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Here, we develop a theory of radiative heat transfer based on an equivalent electrical network representation for the hot material slabs in an arbitrary multilayered environment with arbitrary distribution of temperatures and electromagnetic properties among the layers. Our approach is fully equivalent to the known theories operating with the fluctuating current density, while being significantly simpler in analysis and applications. A practical example of the near-infrared heat transfer through the micron gap filled with an indefinite metamaterial is considered using the suggested method. The…
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Quantum mechanics and Coulomb interaction dictate the behavior of small circuits. The thermal implications cover fundamental topics from quantum control of heat to quantum thermodynamics, with prospects of novel thermal machines and an ineluctably growing influence on nanocircuit engineering. Experimentally, the rare observations thus far include the universal thermal conductance quantum and heat interferometry. However, evidences for many-body thermal effects paving the way to markedly different heat and electrical behaviors in quantum circuits remain wanting. Here we report on the observatio…
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In miniaturising electrical devices down to nanoscales, heat transfer has turned into a serious obstacle but also potential resource for future developments, both for conventional and quantum computing architectures. Controlling heat transport in superconducting circuits has thus received increasing attention in engineering microwave environments for circuit quantum electrodynamics (cQED) and circuit quantum thermodynamics experiments (cQTD). While theoretical proposals for cQTD devices are numerous, the experimental situation is much less advanced. There exist only relatively few experimental…
Logical devices based on electrical currents are ubiquitous in modern society. However, digital logic does have some drawbacks such as a relatively high power consumption. It is therefore of great interest to seek alternative means to build logical circuits that can either work as stand-alone devices or in conjunction with more traditional electronic circuits. One direction that holds great promise is the use of heat currents for logical components. In the present paper, we discuss a recent abstract proposal for a quantum thermal transistor and provide a concrete design of such a device using …
In the framework of the Floquet scattering-matrix theory we discuss how electrical and heat currents accessible in mesoscopics are related to the state of excitations injected by a single-electron source into an electron waveguide. We put forward an interpretation of a single-particle heat current, which differs essentially from that of an electrical current. We show that the knowledge of both a time-dependent electrical current and a time-dependent heat current allows the full reconstruction of a single-electron wave function. In addition we compare electrical and heat shot noise caused by sp…
Tunnel-rate controlled local heat distribution in mesoscopic circuits
Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校）；CNR-Consiglio Nazionale Delle Ricerche, Istituto Officina Dei Materiali（意大利国家研究委员会材料研究所）
We have systematically measured the shot noise in a single electron transistor (SET) as a function of bias and gate voltages. By embedding a SET in a resonance circuit we have been able to measure its shot noise at the resonance frequency 464 MHz, where the 1/f noise is negligible. We can extract the Fano factor which varies between 0.5 and 1 depending on the amount of Coulomb blockade in the SET, in very good agreement with the theory.
We study drag effect in a system of two electrically isolated quantum point contacts (QPC), coupled by Coulomb interactions. Drag current exhibits maxima as a function of QPC gate voltages when the latter are tuned to the transitions between quantized conductance plateaus. In the linear regime this behavior is due to enhanced electron-hole asymmetry near an opening of a new conductance channel. In the non-linear regime the drag current is proportional to the shot noise of the driving circuit, suggesting that the Coulomb drag experiments may be a convenient way to measure the quantum shot noise…
Superconducting microwave circuits show great potential for practical quantum technological applications such as quantum information processing. However, fast and on-demand initialization of the quantum degrees of freedom in these devices remains a challenge. Here, we experimentally implement a tunable heat sink that is potentially suitable for the initialization of superconducting qubits. Our device consists of two coupled resonators. The first resonator has a high quality factor and a fixed frequency whereas the second resonator is designed to have a low quality factor and a tunable resonanc…
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We report low-temperature shot noise measurements of short diffusive Au wires attached to electron reservoirs of varying sizes. The measured noise suppression factor compared to the classical noise value $2e\left| I\right| $ strongly depends on the electric heat conductance of the reservoirs. For small reservoirs injection of hot electrons increases the measured noise and hence the suppression factor. The universal 1/3-suppression factor can only asymptotically be reached for macroscopically large and thick electron reservoirs. A heating model based on the Wiedemann-Franz law is used to explai…
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The field of thermotronics aims to develop thermal circuits that operate with temperature biases and heat currents just as how electronic circuits are based on voltages and electric currents. Here, we investigate a thermal half-wave rectifier based on a quantum two-level system (a qubit) that is driven by a periodically modulated temperature difference across it. To this end, we present a non-equilibrium Green's function technique, which we extend to the time domain to account for the time-dependent temperature in one of two thermal reservoirs connected to the qubit. We find that the qubit act…
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We have developed a broadband scanning tunnelling microscope capable of conventional, low frequency (<10 kHz), microscopy as well spectroscopy and shot-noise detection at 1 MHz. After calibrating our AC circuit on a gold surface, we illustrate our capability to detect shot-noise at the atomic scale and at low currents (<1 nA) by simultaneously measuring the atomically resolved differential conductance and shot-noise on the high temperature superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$. We further show our direct sensitivity to the temperature of the tunnelling electrons at low voltages. O…
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Superconducting electrical circuits can be used to study the physics of cavity quantum electrodynamics (QED) in new regimes, therefore realizing circuit QED. For quantum information processing and quantum optics, an interesting regime of circuit QED is the dispersive regime, where the detuning between the qubit transition frequency and the resonator frequency is much larger than the interaction strength. In this paper, we investigate how non-linear corrections to the dispersive regime affect the measurement process. We find that in the presence of pure qubit dephasing, photon population of the…
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Quantum thermodynamics is emerging both as a topic of fundamental research and as means to understand and potentially improve the performance of quantum devices. A prominent platform for achieving the necessary manipulation of quantum states is superconducting circuit quantum electrodynamics (QED). In this platform, thermalization of a quantum system can be achieved by interfacing the circuit QED subsystem with a thermal reservoir of appropriate Hilbert dimensionality. Here we study heat transport through an assembly consisting of a superconducting qubit capacitively coupled between two nomina…
We demonstrate quantum limited electronic refrigeration of a metallic island in a low temperature micro-circuit. We show that matching the impedance of the circuit enables refrigeration at a distance, of about 50 um 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.
We present a detailed study of photonic heat transport across a Josephson junction coupled to two arbitrary linear circuits having different temperatures. First, we consider the linear approximation, in which a nonlinear Josephson potential is replaced by a quadratic one and the junction acts as an inductor. Afterwards, we discuss the effects of junction anharmonicity. We separately consider the weak-coupling limit, in which the Bloch band structure of the junction energy spectrum plays an important role, and the opposite strong-coupling regime. We apply our general results to two specific mod…
We calculate the low-frequency current noise for AC biased mesoscopic chaotic cavities and diffusive wires. Contrary to what happens for the admittance, the frequency dispersion is not dominated by the electric response time (the "RC" time of the circuit), but by the time that electrons need to diffuse through the structure (dwell time or diffusion time). Frequency dispersion of noise stems from fluctuations of the Fermi distribution function that preserve charge neutrality. Our predictions can be verified with present experimental technology.
