Eur. Phys. J. Plus (2014) 129: 206
https://doi.org/10.1140/epjp/i2014-14206-0

Regular Article

Efficient finite-time measurements under thermal regimes

¹ Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, P.O. Box 6165, 13083-970, Campinas, SP, Brazil
² Instituto de Física de São Carlos, Universidade de São Paulo, P.O. Box 369, 13560-970, São Carlos, SP, Brazil

^* e-mail: carlosbrasil.physics@gmail.com

Received: 31 July 2014
Accepted: 3 September 2014
Published online: 1 October 2014

Abstract

Contrary to conventional quantum mechanics, which treats measurement as instantaneous, here we explore a model for finite-time measurement. The main two-level system interacts with the measurement apparatus in a Markovian way described by the Lindblad equation, and with an environment, which does not include the measuring apparatus. To analyse the environmental effects on the final density operator, we use the Redfield approach, allowing us to consider a non-Markovian noise. In the present hybrid theory, to trace out the environmental degrees of freedom, we use a previously developed analytic method based on superoperator algebra and Nakajima-Zwanzig superoperators. Here, we analyse two types of system-environment interaction, phase and amplitude damping, which allows us to conclude that, in general, a finite-time quantum measurement performed during a certain period is more efficient than an instantaneous measurement performed at the end of it, because the rate of change of the populations is attenuated by the system-measurement apparatus interaction.