We analyze the stochastic evolution and dephasing of a qubit within the quantum jump (QJ) approach. It allows one to treat individual realizations of inelastic processes, and in this way it provides solutions, for instance, to problems in quantum the
rmodynamics and distributions in statistical mechanics. As a solvable example, we study a qubit in the weak dissipation limit, and demonstrate that dephasing and relaxation render the Jarzynski and Crooks fluctuation relations (FRs) of non-equilibrium thermodynamics intact. On the contrary, the standard two-measurement protocol, taking into account only the fluctuations of the internal energy $U$, leads to deviations in FRs under the same conditions. We relate the average $langle e^{-beta U} rangle $ (where $beta$ is the inverse temperature) with the qubits relaxation and dephasing rates, and discuss this relationship for different mechanisms of decoherence.
We discuss work performed on a quantum two-level system coupled to multiple thermal baths. To evaluate the work, a measurement of photon exchange between the system and the baths is envisioned. In a realistic scenario, some photons remain unrecorded
as they are exchanged with baths that are not accessible to the measurement, and thus only partial information on work and heat is available. The incompleteness of the measurement leads to substantial deviations from standard fluctuation relations. We propose a recovery of these relations, based on including the mutual information given by the counting efficiency of the partial measurement. We further present the experimental status of a possible implementation of the proposed scheme, i.e. a calorimetric measurement of work, currently with nearly single-photon sensitivity.
We propose a remarkably simple electronic refrigerator based on the Coulomb barrier for single-electron tunneling. A fully normal single-electron transistor is voltage $V$ biased at a gate position such that tunneling through one of the junctions cos
ts an energy of about $k_BT ll eV, E_C$, where $T$ is the temperature and $E_C$ is the transistor charging energy. The tunneling in the junction with positive energy cost cools both the electrodes attached to it. Immediate practical realizations of such a refrigerator make use of Andreev mirrors which suppress heat current while maintaining full electric contact.
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 experim
ents. We find that the common non-equilibrium 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.
We study quasiparticle energy relaxation at sub-kelvin temperatures by injecting hot electrons into an aluminium island and measuring the energy flux from electrons into phonons both in the superconducting and in the normal state. The data show stron
g reduction of the flux at low temperatures in the superconducting state, in qualitative agreement with the presented quasiclassical theory for clean superconductors. Quantitatively, the energy flux exceeds that from the theory both in the superconducting and in the normal state, possibly suggesting an enhanced or additional relaxation process.
