Hybrid master equation for calorimetric measurements

Abstract

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 modelled by a Floquet master equation under the assumption of drive intensity much larger than the qubit-electron coupling squared. We numerically and analytically inquire 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.

Exactly solvable model of calorimetric measurements

“…In Fig. 3 we have chosen rather weak coupling, 0 = 0.05μ; therefore, the an- The dots are obtained by numerical evaluation of the exact dynamics (5). The temperature is zero, T = 0.…”

“…Indeed, the energy of the reservoir is influenced by interacting with the system, and by measuring it, one can probe the system [1]. This idea has motivated a series of recent theory papers [2][3][4][5][6], investigating temperature variations in a small metallic particle, caused by photon exchange with a qubit. Here we extend these ideas to an exactly solvable model of a resonant level coupled to a finite-size metallic reservoir, which is the simplest of the well-studied quantum impurity models [7].…”

“…3. Average values of the long-time asymptotic energies of the resonant level E as 0 (34), of the reservoir E as R (35), and of the interaction energy E as I (36) plotted versus the energy of the level 0 .The dots are obtained by numerical evaluation of the exact dynamics(5). The temperature is zero, T = 0.…”

Solvable class of non-Markovian quantum multipartite dynamics

“…(B19) we recover the rates defined in Eq. (22). When each (vectorial) rate involves different Pauli channels more complex expressions are obtained.…”

“…For tackling this issue a broad class of phenomenological and theoretical approaches has been formulated [3], dealing with both time-convoluted and convolutionless master equations [11]. Examples include the dynamics induced by stochastic Hamiltonians defined by non-white noises [12], phenomenological single memory kernels [13][14][15][16], interaction with incoherent degrees of freedom [17][18][19][20][21][22] and arbitrary ancilla systems [23,24], related quantum collisional models [25][26][27][28][29][30][31][32], quantum generalizations of semi-Markov processes [33,34], and random (convex) superpositions of unitary and unital maps [35][36][37], together with some exact derivations from underlying (microscopic or effective) unitary dynamics [38][39][40][41][42][43][44][45][46].…”