Observable quantum entanglement due to gravity

No experiment to date has provided evidence for quantum features of the gravitational interaction. Recently proposed tests suggest looking for the generation of quantum entanglement between massive objects as a possible route towards the observation of such features. Motivated by advances in optical cooling of mirrors, here we provide a systematic study of entanglement between two masses that are coupled gravitationally. We first consider the masses trapped at all times in harmonic potentials (optomechanics) and then the masses released from the traps. This leads to the estimate of the experimental parameters required for the observation of gravitationally induced entanglement. The optomechanical setup demands LIGO-like mirrors and squeezing or long coherence times, but the released masses can be light and accumulate detectable entanglement in a timescale shorter than their coherence times. No macroscopic quantum superposition develops during the evolution. We discuss the implications from such thought experiments regarding the nature of the gravitational coupling.

[1]  Mauro Paternostro,et al.  Revealing Nonclassicality of Inaccessible Objects. , 2016, Physical review letters.

[2]  Seth Lloyd,et al.  Gaussian quantum information , 2011, 1110.3234.

[3]  J. C. Hafele,et al.  Around-the-World Atomic Clocks: Observed Relativistic Time Gains , 1972, Science.

[4]  T. Palomaki,et al.  Entangling Mechanical Motion with Microwave Fields , 2013, Science.

[5]  Abdulrahim Al Balushi,et al.  Optomechanical quantum Cavendish experiment , 2018, Physical Review A.

[6]  Ford,et al.  On the quantum langevin equation , 1981, Physical review. A, General physics.

[7]  James Bateman,et al.  Experimental Realization of a Thermal Squeezed State of Levitated Optomechanics. , 2016, Physical review letters.

[8]  Karsten Danzmann,et al.  Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency. , 2016, Physical review letters.

[9]  Maximilian Schlosshauer,et al.  Decoherence and the Quantum-To-Classical Transition , 2008 .

[10]  R. Jaffe,et al.  Casimir forces between arbitrary compact objects , 2007, 0710.5104.

[11]  Mauro Paternostro,et al.  Spin Entanglement Witness for Quantum Gravity. , 2017, Physical review letters.

[12]  Markus Aspelmeyer,et al.  Optomechanical Bell Test. , 2018, Physical review letters.

[13]  M. Wolf,et al.  Bound entangled Gaussian states. , 2000, Physical review letters.

[14]  Von Welch,et al.  Reproducing GW150914: The First Observation of Gravitational Waves From a Binary Black Hole Merger , 2016, Computing in Science & Engineering.

[15]  M. Aspelmeyer,et al.  Quantum superposition of massive objects and the quantization of gravity , 2018, Physical Review D.

[16]  M Kardar,et al.  Casimir forces between arbitrary compact objects , 2007, Physical review letters.

[17]  Florian Blaser,et al.  Cavity cooling of an optically levitated submicron particle , 2013, Proceedings of the National Academy of Sciences.

[18]  Mauro Paternostro,et al.  Parametric feedback cooling of levitated optomechanics in a parabolic mirror trap , 2016, 1603.02917.

[19]  Kerry Vahala,et al.  Cavity opto-mechanics. , 2007, Optics express.

[20]  S. Bose,et al.  Mesoscopic entanglement from central potential interactions , 2018, 1812.09776.

[21]  Karsten Danzmann,et al.  Observation of squeezed light with 10-dB quantum-noise reduction. , 2007, Physical review letters.

[22]  Roman Schnabel,et al.  Squeezed states of light and their applications in laser interferometers , 2016, 1611.03986.

[23]  A. Peters,et al.  Measurement of gravitational acceleration by dropping atoms , 1999, Nature.

[24]  J. Munday,et al.  Measurement of the Casimir Force between Two Spheres. , 2018, Physical review letters.

[25]  T. Kippenberg,et al.  Cavity Optomechanics , 2013, 1303.0733.

[26]  M. Derakhshani,et al.  Probing a gravitational cat state: Experimental Possibilities , 2016, 1603.04430.

[27]  V Vedral,et al.  Gravitationally Induced Entanglement between Two Massive Particles is Sufficient Evidence of Quantum Effects in Gravity. , 2017, Physical review letters.

[28]  Maaneli Derakhshani,et al.  Probing Gravitational Cat States in Canonical Quantum Theory vs Objective Collapse Theories , 2016, 1609.01711.

[29]  V. Giovannetti,et al.  Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion , 2000, quant-ph/0006084.

[30]  R. Pound,et al.  Apparent Weight of Photons , 1960 .

[31]  F. Illuminati,et al.  Extremal entanglement and mixedness in continuous variable systems , 2004, quant-ph/0402124.

[32]  Charis Anastopoulos,et al.  Probing a gravitational cat state , 2015, 1504.03103.

[33]  S. A. Werner,et al.  Observation of Gravitationally Induced Quantum Interference , 1975 .

[34]  Don N. Page,et al.  Indirect Evidence for Quantum Gravity , 1981 .

[35]  M. Paternostro,et al.  Testing the gravitational field generated by a quantum superposition , 2019, New Journal of Physics.

[36]  M. Aspelmeyer,et al.  Laser cooling of a nanomechanical oscillator into its quantum ground state , 2011, Nature.

[37]  E. Merzbacher.  Decoherence and the Quantum-To-Classical Transition , 2008 .

[38]  J. Teufel,et al.  Sideband cooling of micromechanical motion to the quantum ground state , 2011, Nature.

[39]  M. Paternostro,et al.  Is Gravity Quantum , 2015, 1507.05733.

[40]  G. Vidal,et al.  Computable measure of entanglement , 2001, quant-ph/0102117.

[41]  T. Hayler,et al.  Observation of a kilogram-scale oscillator near its quantum ground state , 2009 .

[42]  M. Aspelmeyer,et al.  Cooling-by-measurement and mechanical state tomography via pulsed optomechanics , 2012, Nature Communications.

[43]  Vlatko Vedral,et al.  Witness gravity’s quantum side in the lab , 2017, Nature.

[44]  Quantum Langevin Equation , 1981 .

[45]  M. Aspelmeyer,et al.  Remote quantum entanglement between two micromechanical oscillators , 2017, Nature.