Probing deformed commutators with macroscopic harmonic oscillators

Abstract

A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated to a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters are roughly extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass $m_{\mathrm{P}}$ ($\approx 22\mu \mathrm{g}$), and compare it with a model of deformed dynamics. Previous limits to the parameters quantifying the commutator deformation are substantially lowered.

11 pages, 3 figures, reference added

References in corpus (10)

• Sideband Cooling Micromechanical Motion to the Quantum Ground State
• Strong dispersive coupling of a high finesse cavity to a micromechanical membrane
• Test of the Equivalence Principle Using a Rotating Torsion Balance
• Universality of Quantum Gravity Corrections
• High quality mechanical and optical properties of commercial silicon nitride membranes
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications
• Minimal Length in Quantum Gravity, Equivalence Principle and Holographic Entropy Bound
• On the Stability of Planetary Circular Orbits in Noncommutative Spaces
• Coherent States in Gravitational Quantum Mechanics
• Precision Measurement of a low-loss Cylindrical Dumbbell-Shaped Sapphire Mechanical Oscillator using Radiation Pressure

Cited by in corpus (110)

• Gravitational tests of the Generalized Uncertainty Principle
• Gravitational Decoherence
• GUP parameter from quantum corrections to the Newtonian potential
• Generalized Uncertainty Principle, Classical Mechanics, and General Relativity
• Constraining the generalized uncertainty principle with the gravitational wave event GW150914
• Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale
• Lorentz violation and generalized uncertainty principle
• Testing of Generalized Uncertainty Principle With Macroscopic Mechanical Oscillators and Pendulums
• Two-membrane cavity optomechanics
• 30 years in: Quo vadis generalized uncertainty principle?
• GUP parameter from Maximal Acceleration
• Massive quantum systems as interfaces of quantum mechanics and gravity
• Tests of Quantum Gravity induced non-locality via opto-mechanical quantum oscillators
• Cosmological Horizons, Uncertainty Principle and Maximum Length Quantum Mechanics
• The deformation parameter of the generalized uncertainty principle
• Experiments testing macroscopic quantum superpositions must be slow
• Amplified transduction of Planck-scale effects using quantum optics
• Sensitivity-bandwidth limit in a multi-mode opto-electro-mechanical transducer
• Noise robustness of synchronization of two nanomechanical resonators coupled to the same cavity field
• Planck scale Corrections to the Harmonic Oscillator, Coherent and Squeezed States
• Microfabrication of large area high-stress silicon nitride membranes for optomechanical devices
• Baryogenesis in non-extensive Tsallis Cosmology
• On Quantum Gravity Tests with Composite Particles
• Generalized uncertainty principle and Asymptotic Safe gravity
• Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy
• A new bound on polymer quantization via an opto-mechanical setup
• Generalized uncertainty principle or curved momentum space?
• Scale--dependent Hayward black hole and the generalized uncertainty principle
• Bounds on GUP parameters from GW150914 and GW190521
• Quantum-optical tests of Planck-scale physics
• Observational Tests of the Generalized Uncertainty Principle: Shapiro Time Delay, Gravitational Redshift, and Geodetic Precession
• The minimal length is physical
• Quantum correlations in optomechanical crystals
• Probing anharmonicity of a quantum oscillator in an optomechanical cavity
• Maximal momentum GUP leads to quadratic gravity
• Optomechanical tests of a Schrödinger-Newton equation for gravitational quantum mechanics
• Black hole thermodynamics in the presence of a maximal length and minimum measurable in momentum
• Primordial Big Bang Nucleosynthesis and Generalized Uncertainty Principle
• Gravitational Effects in Quantum Mechanics
• An optomechanical heat engine with feedback-controlled in-loop light
• Modification of Schrödinger-Newton equation due to braneworld models with minimal length
• Control of Recoil Losses in Nanomechanical SiN Membrane Resonators
• Beyond linear coupling in microwave optomechanics
• Constraining the Generalized Uncertainty Principle with the light twisted by rotating black holes and M87*
• Phonon Josephson Junction with Nanomechanical Resonators
• Testing Generalised Uncertainty Principles through Quantum Noise
• Effective GUP-modified Raychaudhuri equation and black hole singularity: four models
• Minimal length effect on the broadening of free wave-packets and its physical implications
• Universality of minimal length
• Quantum estimation in an expanding spacetime
• Optical Levitation of a Mirror for Reaching the Standard Quantum Limit
• Generalized uncertainty principle in resonant detectors of gravitational waves
• Violation of equivalence in an accelerating atom-mirror system in the generalized uncertainty principle framework
• Reconciling a quantum gravity minimal length with lack of photon dispersion
• Probing deformed quantum commutators
• Probing the generalized uncertainty principle through quantum noises in optomechanical systems
• Tests of Quantum Gravity-Induced Non-Locality via Opto-mechanical Experiments
• Quantum-spacetime effects on nonrelativistic Schrödinger evolution
• Silicon-nitride nanosensors toward room temperature quantum optomechanics
• Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics
• Constraining the generalized uncertainty principle with the atomic weak-equivalence-principle test
• Quadrature squeezing enhances Wigner negativity in a mechanical Duffing oscillator
• Probing quantum gravity effects with quantum mechanical oscillators
• Silicon Nitride MOMS Oscillator for Room Temperature Quantum Optomechanics
• Indirect Probe of Quantum Gravity using Molecular Wave-packets
• Quantum gravitational signatures in next-generation gravitational wave detectors
• Investigating bounds on the extended uncertainty principle metric through astrophysical tests
• Generalized Extended Uncertainty Principles, Liouville theorem and density of states: Snyder-de Sitter and Yang models
• Deterministic preparation of highly non-classical macroscopic quantum states
• The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
• Constraining the generalized uncertainty principle with neutron interferometry
• Position-dependent mass in strong quantum gravitational background fields
• Improved constraints on minimum length models with a macroscopic low loss phonon cavity
• Direct measurement of the optical trap-induced decoherence
• Coherent coupling completes an unambiguous optomechanical classification framework
• A framework for nonrelativistic isotropic models based on generalized uncertainty principles
• Deformed Gazeau-Klauder Schrödinger-Cat States with Modified Commutation Relations
• Space and time transformations with a minimal length
• Path integral action for a resonant detector of gravitational waves in the generalized uncertainty principle framework
• Path Integral for Non-Paraxial Optics
• The Mass Gap of the Space-time and its Shape
• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• System of interacting harmonic oscillators in rotationally invariant noncommutative phase space
• Non-Relativistic Anti-Snyder Model and Some Applications
• Quantum gravitational decoherence of a mechanical oscillator from spacetime fluctuations
• Theoretical and Observational Implications of Planck's Constant as a Running Fine Structure Constant
• Generalized Uncertainty Principle and Quantum Gravity Phenomenology
• Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework
• Large amplitude mechanical coherent states and detection of weak nonlinearities in cavity optomechanics
• Reconciling microscopic and macroscopic tests of the Compton-Schwarzschild correspondence
• Quantum Gravity Constraints on Fine Structure Constant from GUP in Braneworlds
• Derivation of the deformed Heisenberg algebra from discrete spacetime
• Generalized Uncertainty Principle from the Regularized Self-Energy
• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• Full dynamics of two-membrane cavity optomechanics
• Bounded compactness from G(E)UP
• Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model
• Macroscopic detection of deformed QM by the harmonic oscillator
• Effect of Quantum Gravity on Specific Heat of Solid
• Effective information bounds in modified quantum mechanics
• Towards quantum Mechanics on the curved cotangent bundle
• Many-body probes for quantum features of spacetime
• Harmonic oscillator chain in noncommutative phase space with rotational symmetry
• Non-Heisenbergian quantum mechanics
• A novel mechanism for probing the Planck scale with wavepackets following general distributions
• Self-adjoint extensions for a $p^4$-corrected Hamiltonian of a particle on a finite interval
• Quantum speed limit as a sensitive probe of Planck-scale effects
• Towards non-invasive cancer diagnostics and treatment based on electromagnetic fields, optomechanics and microtubules
• GUP/BEB correspondence
• Einstein crystals in Snyder and Snyder-de Sitter noncommutative backgrounds