Quantum state purity versus average phonon number for characterization of mechanical oscillators in cavity optomechanics
arXiv:2211.04425 · doi:10.1103/PhysRevA.107.013502
Abstract
Quantum oscillators in Gaussian states are often characterized by average occupation numbers that refer to a basis of eigenstates of the non-interacting 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.
arXiv comment13 pages, 4 figures
References in corpus (32)
- Cavity Optomechanics
- Sideband Cooling Micromechanical Motion to the Quantum Ground State
- Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion
- Theory of ground state cooling of a mechanical oscillator using dynamical back-action
- Motional Quantum Ground State of a Levitated Nanoparticle from Room Temperature
- Phase noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion
- Real-time optimal quantum control of mechanical motion at room temperature
- An all-optical trap for a gram-scale mirror
- Quantum control of a nanoparticle optically levitated in cryogenic free space
- Parametric Normal-Mode Splitting in Cavity Optomechanics
- Cavity cooling of an optically levitated nanoparticle
- Creation and control of multi-phonon Fock states in a bulk acoustic wave resonator
- Symplectic invariants, entropic measures and correlations of Gaussian states
- Arbitrarily large steady-state bosonic squeezing via dissipation
- Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK
- Purity of Gaussian states: measurement schemes and time-evolution in noisy channels
- Cavity cooling of a levitated nanosphere by coherent scattering
- Motional Sideband Asymmetry of a Nanoparticle Optically Levitated in Free Space
- Nonlinear interaction effects in a strongly driven optomechanical cavity
- Cavity-Based 3D Cooling of a Levitated Nanoparticle via Coherent Scattering
- Measurement of the motional sidebands of a nanogram-scale oscillator in the quantum regime
- Bidimensional nano-optomechanics and topological backaction in a non-conservative radiation force field
- Optomechanical Raman-Ratio Thermometry
- Two-dimensional quantum motion of a levitated nanosphere
- Observation and interpretation of motional sideband asymmetry in a quantum electro-mechanical device
- Ultrastrong parametric coupling between a superconducting cavity and a mechanical resonator
- Appearance and disappearance of quantum correlations in measurement-based feedback control of a mechanical oscillator
- Strong Optomechanical Coupling at Room Temperature by Coherent Scattering
- Quantum optomechanics in a liquid
- Distribution of laser shot noise energy delivered to a levitated nanoparticle
- Quantum displacement sensing and cooling in 3D levitated cavity optomechanics
- Coherent scattering 2D cooling in levitated cavity optomechanics