Estimation of temperature in micromaser-type systems

Abstract

We address the estimation of the number of photons and temperature in a micromaser-type system with Fock state and thermal fields. We analyze the behavior of the quantum Fisher information (QFI) for both fields. In particular, we show that in the Fock state field model, the QFI for non-entangled initial state of the atoms increases monotonously with time, while for entangled initial state of the atoms, it shows oscillatory behavior, leading to non-Markovian dynamics. Moreover, it is observed that the QFI, entropy of entanglement and fidelity have collapse and revival behavior. Focusing on each period that the collapses and revivals occur, we see that the optimal points of the QFI and entanglement coincide. In addition, when one of the subsystems evolved state fidelity becomes maximum, the QFI also achieves its maximum. We also address the evolved fidelity versus the initial state as a good witness of non-Markovianity. Moreover, we interestingly find that the entropy of the composite system can be used as a witness of non-Markovian evolution of the subsystems. For the thermal field model, we similarly investigate the relation among the QFI associated with the temperature, von Neumann entropy, and fidelity. In particular, it is found that at the instants when the maximum values of the QFI are achieved, the entanglement between the two-qubit system and the environment is maximized while the entanglement between the probe and its environment is minimized. Moreover, we show that the thermometry may lead to optimal estimation of practical temperatures. Besides, extending our computation to the two-qubit system, we find that using a two-qubit probe generally leads to more effective estimation than the one-qubit scenario. Finally, we show that initial state entanglement plays a key role in the advent of non-Markovianity and determination of its strength in the composite system and its subsystems.