Quantum state purity versus average phonon number for characterization of mechanical oscillators in cavity optomechanics
Year: 2023
Authors: Borkje K., Marin F.
Autors Affiliation: Univ South Eastern Norway, Dept Sci & Ind Syst, N-3603 Kongsberg, Norway; Univ Firenze, Dipartimento Fis & Astron, I-50019 Sesto Fiorentino, FI, Italy; European Lab Nonlinear Spect, I-50019 Sesto Fiorentino, FI, Italy; Ist Nazl Fis Nucl, Sez Firenze, I-50019 Sesto Fiorentino, FI, Italy; CNR INO, I-50125 Florence, Italy.
Abstract: Quantum oscillators in Gaussian states are often characterized by average occupation numbers that refer to a basis of eigenstates of the noninteracting oscillator Hamiltonian. We argue that quantum state purity is a more appropriate characteristic of such states, which can be applied to oscillators of any dimensionality. For a one-dimensional oscillator, the state purity is directly related to a thermal occupation number defined with respect to the number state basis in which the oscillator’s quantum state is thermal. Thus, it naturally introduces a more versatile definition of an average occupation number. We study optomechanical sideband cooling of one- and two-dimensional mechanical oscillators in particular, and derive exact analytical expressions for the maximal mechanical state purity achievable in the quantum backaction limit. In the case of a one-dimensional oscillator, we show that the thermal occupation number related to purity can be well approximated by the average phonon number in the weak-coupling regime, but that the two differ in the regime of ultrastrong optomechanical coupling or in cases where the oscillator’s resonance frequency is strongly renormalized.
Journal/Review: PHYSICAL REVIEW A
Volume: 107 (1) Pages from: 13502-1 to: 13502-12
KeyWords: Motion; NanoparticleDOI: 10.1103/PhysRevA.107.013502Connecting to view paper tab on IsiWeb: Click here