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Nature Communications

Reaching the ultimate energy resolution of a quantum detector

Bayan Karimi, Fredrik Brange, Peter Samuelsson, Jukka P Pekola

Published Jan 17, 2020• 79 citations
Publisher

Abstract

Quantum calorimetry, the thermal measurement of quanta, is a method of choice for ultrasensitive radiation detection ranging from microwaves to gamma rays. The fundamental temperature fluctuations of the calorimeter, dictated by the coupling of it to the heat bath, set the ultimate lower bound of its energy resolution. Here we reach this limit of fundamental equilibrium fluctuations of temperature in a nanoscale electron calorimeter, exchanging energy with the phonon bath at very low temperatures. The approach allows noninvasive measurement of energy transport in superconducting quantum circuits in the microwave regime with high efficiency, opening the way, for instance, to observe quantum jumps, detecting their energy to tackle central questions in quantum thermodynamics.

DOI
10.1038/s41467-019-14247-2

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cond-mat.mes-hallCross-listedarXiv:2610.33414•Oct 27, 2026
Quantum calorimetry, the thermal measurement of quanta, is a method of choice for ultrasensitive radiation detection ranging from microwaves to gamma rays. The fundamental temperature fluctuations of the calorimeter, dictated by the coupling of it to the heat bath, set the ultimate lower bound of its energy resolution. Here we reach this limit of fundamental equilibrium fluctuations of temperature in a nanoscale electron calorimeter, exchanging energy with the phonon bath at very low temperatures. The approach allows noninvasive measurement of energy transport in superconducting quantum circuits in the microwave regime with high efficiency, opening the way, for instance, to observe quantum jumps, detecting their energy to tackle central questions in quantum thermodynamics.
Motivated by the recent development of fast and ultrasensitive thermometry in nanoscale systems, we investigate quantum calorimetric detection of individual heat pulses in the sub-meV energy range. We propose a hybrid superconducting injector-calorimeter setup, with the energy of injected pulses carried by tunneling electrons. It is shown that the superconductor constitutes a versatile injector, with tunable tunnel rates and energies. Treating all heat transfer events microscopically, we analyze the statistics of the calorimeter temperature fluctuations and derive conditions for an accurate measurement of the heat pulse energies. Our results pave the way for fundamental quantum thermodynamics experiments, including calorimetric detection of single microwave photons.
We investigate the experimental setup proposed in New J. Phys. 15, 115006 (2013) for calorimetric measurements of thermodynamic indicators in an open quantum system. As a theoretical model we consider a periodically driven qubit coupled with a large yet finite electron reservoir, the calorimeter. The calorimeter is initially at equilibrium with an infinite phonon bath. As time elapses, the temperature of the calorimeter varies in consequence of energy exchanges with the qubit and the phonon bath. We show how under weak-coupling assumptions, the evolution of the qubit-calorimeter system can be described by a generalized quantum jump process including as dynamical variable the temperature of the calorimeter. We study the jump process by numeric and analytic methods. Asymptotically with the duration of the drive, the qubit-calorimeter attains a steady state. In this same limit, we use multiscale perturbation theory to derive a Fokker-Planck equation governing the calorimeter temperature distribution. We inquire the properties of the temperature probability distribution close and at the steady state. In particular, we predict the behavior of measurable statistical indicators versus the qubit-calorimeter coupling constant.
The development of single photon detectors (SPD's) in the microwave regime is a fundamental challenge for obtaining a better understanding of the phenomena and components employed in quantum information technologies. Particularly, the field of quantum thermodynamics has until now been mainly theory oriented due to the lack of suitable detectors. In this thesis I present the first steps in developing a high fidelity SPD suitable for detecting itinerant microwave photons in a transmission line. The device is of mesoscopic size and directly integrable into superconducting quantum circuits. Out of the two main approaches in microwave SPD's, atom-like systems and thermal detectors, we pursue the latter. In a thermal detector, the energy of the photon is transferred into the absorber of the detector, causing an abrupt increase in its temperature. This leads to the destruction of the photon, which can be avoided with an atom-like detector. However, an advantage of the thermal approach is that a broadband microwave detector, operated in a continuous manner, can be realized. This is essential for several experiments for example in quantum thermodynamics. The absorber of our micro calorimeter is a normal metal nanowire. The electron gas in the wire is used for the photon absorption, whereas the phonons work as a heat sink. The absorber is connected to a superconducting electrode via a thin tunnel barrier and grounded through a direct normal metal-superconductor contact, which acts as a heat mirror. The temperature of the electron gas is probed via the differential conductance of a tunnel-junction. For realising a sensitive SPD, it is essential to minimize the heat capacity of the absorber. Thermal properties of small metal structures can deviate significantly from the properties of bulk materials due to the large surface-to-volume ratio. We have measured thermal relaxation in Cu and Ag thin-film nanowires at sub-kelvin temperatures and observed an anomalously long relaxation time in the Cu wires. In addition to a large specific heat, these results may also originate from the slow thermalisation in the granular structure observed in the evaporated Cu wires.; Saavuttaaksemme paremman ymmarryksen kvantti-informaatioteknologiassa hyodynnettavista ilmioista ja komponenteista, on yksittaisten fotonien resoluutiolla toimivien mikroaaltofotoni-ilmaisinten kehittaminen olennainen haaste. Sopivien havaintolaitteiden puutteen vuoksi on erityisesti kvanttitermodynamiikka pysynyt vahvasti teoriaan keskittyneena alana. Tassa vaitoskirjassa esitetaan ensimmaiset askeleet herkan, yksittaisia siirtolinjassa kiertavia mikroaaltofotoneja havaitsevan anturin kehittamisessa. Laite on kooltaan mesoskooppinen, ja se voidaan kytkea suprajohtaviin piireihin. Termiset detektorit - joita kehitamme tassa tyossa - ja atomin kaltaiset systeemit ovat yleisimmin kaytettyja, toisiaan taydentavia ilmaisimia. Termisessa anturissa havaitun fotonin energia siirtyy laitteen absorbaattoriin, aiheuttaen siina nopean, havaittavan suuruisen lampotilan nousun.…
Abstract Performing imperfect or noisy measurements on a quantum mechanical system both impacts the measurement outcome and the state of the system after the measurement. In this paper we are concerned with imperfect calorimetric measurements. In calorimetric measurements one typically measures the energy of a thermal environment to extract information about the system. In our setting the measurement is imperfect due to noise directly acting on the detector. Concretely, we consider an additional noise bath such that its energy is measured simultaneously with the calorimeter energy. Under weak coupling assumptions, we derive a hybrid master equation for the state of the system and the detected energy and find that the presence of the noise bath manifests itself by modifying the jump rates of the reduced system dynamics. We study an example of a driven qubit interacting with a resonant boson calorimeter and demonstrate that increasing the additional noise leads to an apparent reduction in the power flowing from qubit to calorimeter and thus to a seemingly detected heating up of the calorimeter.
Graphene calorimeters are predicted to combine extreme energy sensitivity with rapid thermal recovery, yet experiments remain far from ideal estimates. Here, we directly calibrate a graphene Josephson-junction microwave calorimeter using nanosecond pulses and independently determine the thermal parameters of the same operating device. At 110 mK, calibrated pulse measurements yield a characteristic switching-energy scale of 18.1 meV (2.90 zJ), while time-resolved two-pulse thermometry gives an intrinsic relaxation time of 19.5 ns. Pulse-width-dependent calorimetry and bolometric thermometry show that the electronic heat capacity is 12.4 times and the electron-phonon coupling is approximately 50 times larger than ideal estimates. A thermal model using these measured parameters predicts 21.2 meV, quantitatively reproducing the observed switching response. These results identify the microscopic origin of the sensitivity gap in graphene calorimeters and establish a self-consistent calibration framework for ultrafast nanoscale thermal detectors.