Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2104.14894 · Journal of Physics A Mathematical and Theoretical

Apparent heating due to imperfect calorimetric measurements

Brecht Donvil, Joachim Ankerhold

Published Apr 14, 2022• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1751-8121/ac677d

Related papers

Model for calorimetric measurements in an open quantum system

Brecht Donvil, Paolo Muratore-Ginanneschi, Jukka P Pekola +1 more

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.

arXiv:1803.11015•Physical Review A•May 8, 2018•13 citations

Hybrid master equation for calorimetric measurements

Brecht Donvil, Paolo Muratore-Ginanneschi, Jukka P Pekola

Ongoing experimental activity aims at calorimetric measurements of thermodynamic indicators of quantum integrated systems. We study a model of a driven qubit in contact with a finite-size thermal electron reservoir. The temperature of the reservoir changes due to energy exchanges with the qubit and an infinite-size phonon bath. Under the assumption of weak coupling and weak driving, we model the evolution of the qubit-electron temperature as a hybrid master equation for the density matrix of the qubit at different temperatures of the calorimeter. We compare the temperature evolution with an earlier treatment of the qubit-electron model, where the dynamics were modeled by a Floquet master equation under the assumption of drive intensity much larger than the qubit-electron coupling squared. We numerically and analytically investigate the predictions of the two mathematical models of dynamics in the weak-drive parametric region. We numerically determine the parametric regions where the two models of dynamics give distinct temperature predictions and those where their predictions match.

arXiv:1811.12832•Physical Review A•Apr 29, 2019•9 citations

Theoretical Study of Calorimetric Measurements in Quantum Integrated Circuits

Brecht Donvil

Recent developments in experimental methods allow for the study of thermodynamic properties of quantum systems. In quantum integrated circuits, quantum systems are elements in an electric circuit that can straightforwardly be coupled to other elements. This manipulability allows one to construct quantum heat engines, Maxwell demons etc. Quantum integrated circuits also are one of the main potential settings to realise a working quantum computer. Calorimetric measurements in integrated circuits serve as a promising technique to probe thermodynamic laws of the quantum regime and to study the inner workings of quantum devices. Due to this experimental accessibility, the theoretical study of open quantum systems in the context of quantum integrated circuits is highly relevant. Open quantum systems are typically small systems, e.g. qubits or oscillators, in contact with one or more reservoirs. The research on which this thesis is based can roughly be divided into two parts. The first part is concerned with the thermodynamics of a driven qubit in contact with a thermal bath. This system is the archetype of a quantum out-ofequilibrium system. In one case the qubit is strongly driven by a semiclassical driving field. Building on earlier works, the thermodynamic relations of the system are found by proving the equivalence with an easier to study qubit-oscillator system. In the other, case the qubit is driven by being in contact with two baths with a temperature gradient. The full generating function is derived in a proper approximative scheme and a fluctuation-dissipation relation is found. The second part focusses on a specific experimental scheme to perform calorimetric measurements. The scheme relies on coupling a quantum system to a finite reservoir and performing fast temperature measurements on the reservoir. Doing so allows one to infer energy changes in the reservoir and therefore to obtain the heat exchanged with the system. The dynamics of this system are modelled for weak system-reservoir coupling and concrete experimental predictions are made. In new work, the dynamics for a toy model of a system interacting with a finite reservoir are derived from first principles for a specific model. The first principle derivation matches with the earlier modelled dynamics in the weak coupling and allows to consider strong system-reservoir coupling as well.

Työväentutkimus Vuosikirja•Oct 1, 2020•0 citations

Reaching the ultimate energy resolution of a quantum detector

Bayan Karimi, Fredrik Brange, Peter Samuelsson +1 more

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.

Nature Communications•Jan 17, 2020•79 citations

Ultrasensitive Calorimetric Detection of Single Photons from Qubit Decay

Jukka P Pekola, Bayan Karimi

We describe a qubit linearly coupled to a heat bath, either directly or via a cavity.The main focus of the paper is on calorimetric detection in a realistic circuit, specifically a solid-state qubit coupled to a resistor as an absorber.The bath in the model is formed of oscillators initially in the ground state with a distribution of energies and coupling strengths.A direct numerical solution of the Schrödinger equation for the full system including up to 10 6 oscillators in the bath verifies the expected decay process.We address quantitatively the question of separation of the qubit and bath by adding a cavity in between which by detuning allows one to adjust the decay rate into a convenient regime for detection purposes.Most importantly, we propose splitting a quantum to two uncoupled baths and performing a cross-correlation measurement of their temperatures.This technique enhances significantly the signal-to-noise ratio of the calorimeter.

arXiv:2010.11122•Physical Review X•Feb 8, 2022•13 citations

The information about the state of a qubit gained by a weakly coupled detector

Sahel Ashhab, J Q You, Franco Nori

We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. In particular, we focus on the case when the qubit Hamiltonian and the qubit's operator being probed by the detector do not commute. Because the qubit's state keeps evolving while being probed and because the measurement data is mixed with detector-related background noise, one might expect the detector to fail in this case. We show, however, that under suitable conditions and by proper analysis of the measurement data useful information about the state of the qubit can be extracted. It turns out that the measurement basis is stochastically determined every time the experiment is repeated. We analyze in detail the probability distributions that govern the choice of measurement bases. We also analyze the information acquisition rate and show that it is largely unaffected by the apparent conflict between the measurement and intrinsic qubit dynamics. We discuss the relation between our analysis and the stochastic master equation that describes the evolution of the qubit's state under the influence of measurement and decoherence. In particular, we write down a stochastic equation that encompasses the usual stochastic master equation for the evolution of the qubit's density matrix and additionally contains the measurement information that can be extracted from the observed signal.

arXiv:0904.3258•New Journal of Physics•Aug 13, 2009•37 citations
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.
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.
Ongoing experimental activity aims at calorimetric measurements of thermodynamic indicators of quantum integrated systems. We study a model of a driven qubit in contact with a finite-size thermal electron reservoir. The temperature of the reservoir changes due to energy exchanges with the qubit and an infinite-size phonon bath. Under the assumption of weak coupling and weak driving, we model the evolution of the qubit-electron temperature as a hybrid master equation for the density matrix of the qubit at different temperatures of the calorimeter. We compare the temperature evolution with an earlier treatment of the qubit-electron model, where the dynamics were modeled by a Floquet master equation under the assumption of drive intensity much larger than the qubit-electron coupling squared. We numerically and analytically investigate the predictions of the two mathematical models of dynamics in the weak-drive parametric region. We numerically determine the parametric regions where the two models of dynamics give distinct temperature predictions and those where their predictions match.
Recent developments in experimental methods allow for the study of thermodynamic properties of quantum systems. In quantum integrated circuits, quantum systems are elements in an electric circuit that can straightforwardly be coupled to other elements. This manipulability allows one to construct quantum heat engines, Maxwell demons etc. Quantum integrated circuits also are one of the main potential settings to realise a working quantum computer. Calorimetric measurements in integrated circuits serve as a promising technique to probe thermodynamic laws of the quantum regime and to study the inner workings of quantum devices. Due to this experimental accessibility, the theoretical study of open quantum systems in the context of quantum integrated circuits is highly relevant. Open quantum systems are typically small systems, e.g. qubits or oscillators, in contact with one or more reservoirs. The research on which this thesis is based can roughly be divided into two parts. The first part is concerned with the thermodynamics of a driven qubit in contact with a thermal bath. This system is the archetype of a quantum out-ofequilibrium system. In one case the qubit is strongly driven by a semiclassical driving field. Building on earlier works, the thermodynamic relations of the system are found by proving the equivalence with an easier to study qubit-oscillator system. In the other, case the qubit is driven by being in contact with two baths with a temperature gradient. The full generating function is derived in a proper approximative scheme and a fluctuation-dissipation relation is found. The second part focusses on a specific experimental scheme to perform calorimetric measurements. The scheme relies on coupling a quantum system to a finite reservoir and performing fast temperature measurements on the reservoir. Doing so allows one to infer energy changes in the reservoir and therefore to obtain the heat exchanged with the system. The dynamics of this system are modelled for weak system-reservoir coupling and concrete experimental predictions are made. In new work, the dynamics for a toy model of a system interacting with a finite reservoir are derived from first principles for a specific model. The first principle derivation matches with the earlier modelled dynamics in the weak coupling and allows to consider strong system-reservoir coupling as well.
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.
We describe a qubit linearly coupled to a heat bath, either directly or via a cavity.The main focus of the paper is on calorimetric detection in a realistic circuit, specifically a solid-state qubit coupled to a resistor as an absorber.The bath in the model is formed of oscillators initially in the ground state with a distribution of energies and coupling strengths.A direct numerical solution of the Schrödinger equation for the full system including up to 10 6 oscillators in the bath verifies the expected decay process.We address quantitatively the question of separation of the qubit and bath by adding a cavity in between which by detuning allows one to adjust the decay rate into a convenient regime for detection purposes.Most importantly, we propose splitting a quantum to two uncoupled baths and performing a cross-correlation measurement of their temperatures.This technique enhances significantly the signal-to-noise ratio of the calorimeter.
We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. In particular, we focus on the case when the qubit Hamiltonian and the qubit's operator being probed by the detector do not commute. Because the qubit's state keeps evolving while being probed and because the measurement data is mixed with detector-related background noise, one might expect the detector to fail in this case. We show, however, that under suitable conditions and by proper analysis of the measurement data useful information about the state of the qubit can be extracted. It turns out that the measurement basis is stochastically determined every time the experiment is repeated. We analyze in detail the probability distributions that govern the choice of measurement bases. We also analyze the information acquisition rate and show that it is largely unaffected by the apparent conflict between the measurement and intrinsic qubit dynamics. We discuss the relation between our analysis and the stochastic master equation that describes the evolution of the qubit's state under the influence of measurement and decoherence. In particular, we write down a stochastic equation that encompasses the usual stochastic master equation for the evolution of the qubit's density matrix and additionally contains the measurement information that can be extracted from the observed signal.