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

Statistics of energy dissipation of a driven two-level system

Philip Wollfarth

Published Jan 1, 2016• 0 citations
Publisher

Abstract

In this thesis the statistics of energy dissipated by a periodically driven two-level system is studied. A measurement scheme is proposed, where the energy exchange between the system and the bath is monitored. In addition, the system undergoes two strong measurements before and after the driving is applied. Consequently, the statistics of the dissipated energy is strongly affected by the external manipulations. In the context of the well-known fluctuation relations, the proposed measurement scheme allows for a feasible detection of quantum signatures.

DOI
10.5445/ir/1000068451

Related papers

Distribution of energy dissipated by a driven two-level system

Philip Wollfarth, Alexander Shnirman, Yasuhiro Utsumi

In the context of fluctuation relations, we study the distribution of energy dissipated by a driven two-level system. Incorporating an energy counting field into the well-known spin-boson model enables us to calculate the distribution function of the amount of energy exchanged between the system and the bath. We also derive the conditional distribution functions of the energy exchanged with the bath for particular initial and/or final states of the two-level system. We confirm the symmetry of the conditional distribution function expected from the theory of fluctuation relations. We also find that the conditional distribution functions acquire considerable quantum corrections at times shorter or of the order of the dephasing time. Our findings can be tested using solid-state qubits.

arXiv:1407.3223•Physical Review B•Oct 13, 2014•14 citations

Quantum Jump Approach for Work and Dissipation in a Two-Level System

F. W. J. Hekking, Jukka P Pekola

We apply the quantum jump approach to address the statistics of work in a driven two-level system coupled to a heat bath. We demonstrate how this question can be analyzed by counting photons absorbed and emitted by the environment in repeated experiments. We find that the common nonequilibrium fluctuation relations are satisfied identically. The usual fluctuation-dissipation theorem for linear response applies for weak dissipation and/or weak drive. We point out qualitative differences between the classical and quantum regimes.

arXiv:1305.5207•Physical Review Letters•Aug 27, 2013•157 citations

Energy Exchange in Driven Open Quantum Systems at Strong Coupling

Matteo Carrega, Paolo Solinas, Maura Sassetti +1 more

The time-dependent energy transfer in a driven quantum system strongly coupled to a heat bath is studied within an influence functional approach. Exact formal expressions for the statistics of energy dissipation into the different channels are derived. The general method is applied to the driven dissipative two-state system. It is shown that the energy flows obey a balance relation, and that, for strong coupling, the interaction may constitute the major dissipative channel. Results in analytic form are presented for the particular value K=1/2 of strong Ohmic dissipation. The energy flows show interesting behaviors including driving-induced coherences and quantum stochastic resonances. It is found that the general characteristics persists for K near 1/2.

arXiv:1603.06369•Physical Review Letters•Jun 14, 2016•112 citations

Calorimetric measurement of work for a driven harmonic oscillator

Rui Sampaio, Samu Suomela, Tapio Ala-Nissilä

A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.

arXiv:1607.02342•Physical review. E•Dec 15, 2016•4 citations

Influence of the two level approximation on the measurement of work in a driven open harmonic oscillator

Rui Sampaio, Samu Suomela, Tapio Ala-Nissilä

A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This provides a realization of the two measurement protocol in open quantum systems. However, the measurement scheme assumes that only the two lowest levels of the system can be occupied. The possibility of occupying higher levels becomes relevant when the system is driven for a sufficiently long time or the temperature is high enough. This causes a systematic error in the calorimetric measurement. We quantify this by considering a driven quantum harmonic oscillator in contact with an ideal heat bath for which we derive analytic expressions for the average work and its variance. We find that for the average work the two level approximation holds in the limit of small dissipation for short driving time and low temperature. In the limit of strong dissipation it will hold for any driving time, at low temperature. However the approximation is not valid for the variance and the higher moments of work at finite temperature.

•Jul 8, 2016•0 citations

Numerically exact treatment of dissipation in a driven two-level system

Wallace S. Teixeira, F. L. Semião, Jani Tuorila +1 more

Recent progress in the experimental implementations of controlled quantum systems and especially of tunable dissipation for them provides an ideal starting point for precision studies of open quantum systems and their models. However, typically the standard weak-coupling approximations are very accurate in describing the dynamics of the simplest and most easily experimentally approachable system, the qubit, since it is challenging to engineer dissipation that is strong relative to the qubit frequency while preserving a high level of control. In this paper, we propose to overcome such challenges by studying a driven qubit, for which the weak-coupling approaches may fail at dissipation rates comparable to the Rabi frequency of the drive which is typically much lower than the qubit frequency. Consequently, we observe such failure of the temporally local Lindblad master equation, the induced dynamics of which are compared with a numerically exact method. To this end, we propose a metric that may be used in experiments to verify our predictions. In addition, we study the well-known Mollow triplet and observe its meltdown owing to dissipation in an experimentally feasible parameter regime. Thus we expect our results to inspire future experimental research on open quantum systems and expand the understanding on this intriguing field of physics.

•Nov 11, 2020•0 citations
In this thesis the statistics of energy dissipated by a periodically driven two-level system is studied. A measurement scheme is proposed, where the energy exchange between the system and the bath is monitored. In addition, the system undergoes two strong measurements before and after the driving is applied. Consequently, the statistics of the dissipated energy is strongly affected by the external manipulations. In the context of the well-known fluctuation relations, the proposed measurement scheme allows for a feasible detection of quantum signatures.
In the context of fluctuation relations, we study the distribution of energy dissipated by a driven two-level system. Incorporating an energy counting field into the well-known spin-boson model enables us to calculate the distribution function of the amount of energy exchanged between the system and the bath. We also derive the conditional distribution functions of the energy exchanged with the bath for particular initial and/or final states of the two-level system. We confirm the symmetry of the conditional distribution function expected from the theory of fluctuation relations. We also find that the conditional distribution functions acquire considerable quantum corrections at times shorter or of the order of the dephasing time. Our findings can be tested using solid-state qubits.
We apply the quantum jump approach to address the statistics of work in a driven two-level system coupled to a heat bath. We demonstrate how this question can be analyzed by counting photons absorbed and emitted by the environment in repeated experiments. We find that the common nonequilibrium fluctuation relations are satisfied identically. The usual fluctuation-dissipation theorem for linear response applies for weak dissipation and/or weak drive. We point out qualitative differences between the classical and quantum regimes.
The time-dependent energy transfer in a driven quantum system strongly coupled to a heat bath is studied within an influence functional approach. Exact formal expressions for the statistics of energy dissipation into the different channels are derived. The general method is applied to the driven dissipative two-state system. It is shown that the energy flows obey a balance relation, and that, for strong coupling, the interaction may constitute the major dissipative channel. Results in analytic form are presented for the particular value K=1/2 of strong Ohmic dissipation. The energy flows show interesting behaviors including driving-induced coherences and quantum stochastic resonances. It is found that the general characteristics persists for K near 1/2.
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This provides a realization of the two measurement protocol in open quantum systems. However, the measurement scheme assumes that only the two lowest levels of the system can be occupied. The possibility of occupying higher levels becomes relevant when the system is driven for a sufficiently long time or the temperature is high enough. This causes a systematic error in the calorimetric measurement. We quantify this by considering a driven quantum harmonic oscillator in contact with an ideal heat bath for which we derive analytic expressions for the average work and its variance. We find that for the average work the two level approximation holds in the limit of small dissipation for short driving time and low temperature. In the limit of strong dissipation it will hold for any driving time, at low temperature. However the approximation is not valid for the variance and the higher moments of work at finite temperature.
Recent progress in the experimental implementations of controlled quantum systems and especially of tunable dissipation for them provides an ideal starting point for precision studies of open quantum systems and their models. However, typically the standard weak-coupling approximations are very accurate in describing the dynamics of the simplest and most easily experimentally approachable system, the qubit, since it is challenging to engineer dissipation that is strong relative to the qubit frequency while preserving a high level of control. In this paper, we propose to overcome such challenges by studying a driven qubit, for which the weak-coupling approaches may fail at dissipation rates comparable to the Rabi frequency of the drive which is typically much lower than the qubit frequency. Consequently, we observe such failure of the temporally local Lindblad master equation, the induced dynamics of which are compared with a numerically exact method. To this end, we propose a metric that may be used in experiments to verify our predictions. In addition, we study the well-known Mollow triplet and observe its meltdown owing to dissipation in an experimentally feasible parameter regime. Thus we expect our results to inspire future experimental research on open quantum systems and expand the understanding on this intriguing field of physics.