Abstract
The ability to control and measure the temperature of propagating microwave modes down to very low temperatures is indispensable for quantum information processing, and may open opportunities for studies of heat transport at the nanoscale, also in the quantum regime. Here we propose and experimentally demonstrate primary thermometry of propagating microwaves using a transmon-type superconducting circuit. Our device operates continuously, with a sensitivity down to $4\times 10^{-4}$ photons/$\sqrt{\mbox{Hz}}$ and a bandwidth of 40 MHz. We measure the thermal occupation of the modes of a highly attenuated coaxial cable in a range of 0.001 to 0.4 thermal photons, corresponding to a temperature range from 35 mK to 210 mK at a frequency around 5 GHz. To increase the radiation temperature in a controlled fashion, we either inject calibrated, wideband digital noise, or heat the device and its environment. This thermometry scheme can find applications in benchmarking and characterization of cryogenic microwave setups, temperature measurements in hybrid quantum systems, and quantum thermodynamics.
Highlights
Propagating modes of microwave waveguides play a key role in quantum information processing with superconducting circuits, connecting the quantum processor with the classical electronics controlling it [1]
The frequency of the transmon is tuned by the magnetic flux threading its superconducting quantum interference device (SQUID) loop, which we control by applying a dc current to an on-chip flux line
We have demonstrated that a single quantum emitter strongly coupled to the end of a waveguide can be used for sensitive measurement of the thermal occupation of the waveguide, using simple continuous-wave, single-tone spectroscopy
Summary
Propagating modes of microwave waveguides play a key role in quantum information processing with superconducting circuits, connecting the quantum processor with the classical electronics controlling it [1]. Modes with an Ohmic spectral density and smoothly interfacing with superconducting circuits, are natural candidates for realizing heat baths Their use as (ideally) zero-temperature reservoirs has been pioneered in quantum state preparation and stabilization protocols based on dissipation engineering [9,10]. An established method to obtain this estimate at steady state [11,12,13,14,15,16,17,18] relies on Ramsey measurements of the dephasing time of a qubit coupled to a cavity in the dispersive limit of circuit quantum electrodynamics In this setting, the qubit dephasing rate Γφ depends linearly on the average thermal occupation of the cavity, due to the statistics of thermal photon shot noise in the quantum regime [15,19]. We increase the temperature of the base plate of our refrigerator, which heats the waveguide modes and the thermometer itself and its environment
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