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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.

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European Physical Journal D