Eur. Phys. J. D (2014) 68: 321
https://doi.org/10.1140/epjd/e2014-50505-8

Regular Article

Optimal estimation of a classical force with a damped oscillator in the non-Markovian bath

¹ Department of Physics, Xinyang Normal University, Xinyang, Henan 464000, P.R. China
² Hearne Institute for Theoretical Physics and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, 70803 LA, USA

^a e-mail: gaoyangchang@gmail.com

Received: 12 July 2014
Received in final form: 20 August 2014
Published online: 28 October 2014

Abstract

We derive the optimal quantum limit of probing a classical force by a damped harmonic oscillator initially prepared in the factorized squeezed state. The memory effects of the thermal bath on the oscillator evolution are investigated. We show that the optimal force sensitivity obtained by the quantum estimation theory approaches to zero for the non-Markovian bath, whereas approaches to a finite non-zero value for the Markovian bath as the mean energy of the oscillator goes to infinity.