Comparing resolved-sideband cooling and measurement-based feedback cooling on an equal footing: analytical results in the regime of ground-state cooling
arXiv:1407.4883 · doi:10.1103/PhysRevA.91.043812
Abstract
We show that in the regime of ground-state cooling, simple expressions can be derived for the performance of resolved-sideband cooling --- an example of coherent feedback control --- and optimal linear measurement-based feedback cooling for a harmonic oscillator. These results are valid to leading order in the small parameters that define this regime. They provide insight into the origins of the limitations of coherent and measurement-based feedback for linear systems, and the relationship between them. These limitations are not fundamental bounds imposed by quantum mechanics, but are due to the fact that both cooling methods are restricted to use only a linear interaction with the resonator. We compare the performance of the two methods on an equal footing --- that is, for the same interaction strength --- and confirm that coherent feedback is able to make much better use of the linear interaction than measurement-based feedback. We find that this performance gap is caused not by the back-action noise of the measurement but by the projection noise. We also obtain simple expressions for the maximal cooling that can be obtained by both methods in this regime, optimized over the interaction strength.
14 pages, 2 png figures; v2: revised for publication
References in corpus (27)
- Sideband Cooling Micromechanical Motion to the Quantum Ground State
- Strong dispersive coupling of a high finesse cavity to a micromechanical membrane
- Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion
- Optomechanical Crystals
- Theory of ground state cooling of a mechanical oscillator using dynamical back-action
- Radiation-pressure cooling and optomechanical instability of a micro-mirror
- Self-cooling of a micro-mirror by radiation pressure
- Circuit cavity electromechanics in the strong coupling regime
- Resolved Sideband Cooling of a Micromechanical Oscillator
- Ground-state cooling of a micromechanical oscillator: generalized framework for cold damping and cavity-assisted cooling schemes
- Feedback-control of quantum systems using continuous state-estimation
- Preparation of Nonclassical States in Cavities with a Moving Mirror
- Mechanical systems in the quantum regime
- State Transfer Between a Mechanical Oscillator and Microwave Fields in the Quantum Regime
- Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity
- Coherent quantum LQG control
- Microwave amplification with nanomechanical resonators
- Ponderomotive Control of Quantum Macroscopic Coherence
- Coherent Quantum-Noise Cancellation for Optomechanical Sensors
- Advantages of Coherent Feedback for Cooling Quantum Oscillators
- Pulsed Laser Cooling for Cavity-Optomechanical Resonators
- Ultra-Efficient Cooling of Resonators: Beating Sideband Cooling with Quantum Control
- Coherent versus measurement feedback: Linear systems theory for quantum information
- Parametric coupling between macroscopic quantum resonators
- Tunable coupling to a mechanical oscillator circuit using a coherent feedback network
- Coherent controllers for optical-feedback cooling of quantum oscillators
- Ground state cooling of nanomechanical resonator via parametric linear coupling
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- Cavity optomechanics assisted by optical coherent feedback
- Quantum Langevin equations for optomechanical systems
- Comparison between continuous- and discrete-mode coherent feedback for the Jaynes-Cummings model
- Towards cavity-free ground state cooling of an acoustic-frequency silicon nitride membrane
- The Energy Cost of Controlling Mesoscopic Quantum Systems
- Coherent vs. measurement-based feedback for controlling a single qubit
- External-level assisted cooling by measurement
- Continuous feedback protocols for cooling and trapping a quantum harmonic oscillator
- Ultimate squeezing through coherent quantum feedback: A fair comparison with measurement-based schemes
- The role of quantum measurements in physical processes and protocols
- Deterministic Equations for Feedback Control of Open Quantum Systems II: Properties of the memory function
- Deterministic Equations for Feedback Control of Open Quantum Systems III: Full counting statistics for jump-based feedback
- Tangential Interpolatory Projection for Model Reduction of Linear Quantum Stochastic Systems
- Minimum-Time Cavity Optomechanical Cooling