Quantum superposition of massive objects and collapse models

We analyze the requirements to test some of the most paradigmatic collapse models with a protocol that prepares quantum superpositions of massive objects. This consists of coherently expanding the wave function of a ground-state-cooled mechanical resonator, performing a squared position measurement that acts as a double slit, and observing interference after further evolution. The analysis is performed in a general framework and takes into account only unavoidable sources of decoherence: blackbody radiation and scattering of environmental particles. We also discuss the limitations imposed by the experimental implementation of this protocol using cavity quantum optomechanics with levitating dielectric nanospheres.

[1]  Markus Arndt,et al.  Testing spontaneous localization theories with matter-wave interferometry , 2011, 1103.1236.

[2]  Weber,et al.  Unified dynamics for microscopic and macroscopic systems. , 1986, Physical review. D, Particles and fields.

[3]  C. Davisson,et al.  The Scattering of Electrons by a Single Crystal of Nickel , 1927, Nature.

[4]  Erik Lucero,et al.  Quantum ground state and single-phonon control of a mechanical resonator , 2010, Nature.

[5]  John Ellis,et al.  Quantum gravity and the collapse of the wavefunction , 1989 .

[6]  M. N. Shneider,et al.  Cavity cooling of an optically trapped nanoparticle , 2009, 0910.1221.

[7]  Notes on certain Newton gravity mechanisms of wavefunction localization and decoherence , 2006, quant-ph/0607110.

[8]  Diósi,et al.  Models for universal reduction of macroscopic quantum fluctuations. , 1989, Physical review. A, General physics.

[9]  Lajos Diósi,et al.  Gravitation and quantummechanical localization of macroobjects , 1984, 1412.0201.

[10]  A. Frenkel,et al.  Spontaneous localizations of the wave function and classical behavior , 1990 .

[11]  L. Diósi,et al.  Intrinsic time-uncertainties and decoherence: comparison of 4 models , 2004 .

[12]  Fleming,et al.  Environmental and spontaneous localization. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[13]  Angelo Bassi,et al.  Is Quantum Theory Exact? , 2009, Science.

[14]  O. Stern,et al.  Beugung von Molekularstrahlen , 1930 .

[15]  GianCarlo Ghirardi,et al.  Dynamical reduction models , 2003 .

[16]  John Ellis,et al.  String theory modifies quantum mechanics , 1992 .

[17]  T. Kippenberg,et al.  Cavity Optomechanics: Back-Action at the Mesoscale , 2008, Science.

[18]  R Kaltenbaek,et al.  Large quantum superpositions and interference of massive nanometer-sized objects. , 2011, Physical review letters.

[19]  E. Joos,et al.  The emergence of classical properties through interaction with the environment , 1985 .

[20]  N. Gisin.  Stochastic quantum dynamics and relativity , 1989 .

[21]  Irene M. Moroz,et al.  Spherically symmetric solutions of the Schrodinger-Newton equations , 1998 .

[22]  Lajos Diósi,et al.  A universal master equation for the gravitational violation of quantum mechanics , 1987 .

[23]  N. Gisin.  Quantum measurements and stochastic processes , 1984 .

[24]  C. Ross.  Found , 1869, The Dental register.

[25]  P. Pearle.  Reduction of the state vector by a nonlinear Schrödinger equation , 1976 .

[26]  D. E. Chang,et al.  Cavity opto-mechanics using an optically levitated nanosphere , 2009, Proceedings of the National Academy of Sciences.

[27]  Grassi,et al.  Continuous-spontaneous-reduction model involving gravity. , 1989, Physical review. A, Atomic, molecular, and optical physics.

[28]  D. Bouwmeester,et al.  Creating and verifying a quantum superposition in a micro-optomechanical system , 2008, 0807.1834.

[29]  Markus Aspelmeyer,et al.  Quantum optomechanics—throwing a glance [Invited] , 2010, 1005.5518.

[30]  Florian Marquardt,et al.  Quantum theory of cavity-assisted sideband cooling of mechanical motion. , 2007, Physical review letters.

[31]  R. Penrose.  On Gravity's role in Quantum State Reduction , 1996 .

[32]  Pearle,et al.  Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[33]  Stephen L. Adler,et al.  Lower and upper bounds on CSL parameters from latent image formation and IGM heating , 2006, quant-ph/0605072.

[34]  T J Kippenberg,et al.  Theory of ground state cooling of a mechanical oscillator using dynamical backaction. , 2007, Physical review letters.

[35]  Marcel Mayor,et al.  Quantum interference of large organic molecules , 2011, Nature communications.

[36]  Tilo Steinmetz,et al.  A fiber Fabry–Perot cavity with high finesse , 2010, 1005.0067.

[37]  P. Barker,et al.  Doppler cooling a microsphere. , 2010, Physical review letters.

[38]  F. Károlyházy,et al.  Gravitation and quantum mechanics of macroscopic objects , 1966 .

[39]  J. Ignacio Cirac,et al.  Optically Levitating Dielectrics in the Quantum Regime: Theory and Protocols , 2010, 1010.3109.

[40]  Pearle,et al.  Combining stochastic dynamical state-vector reduction with spontaneous localization. , 1989, Physical review. A, General physics.

[41]  Anton Zeilinger,et al.  Wave–particle duality of C60 molecules , 1999, Nature.

[42]  J. Toennies,et al.  Nondestructive Mass Selection of Small van der Waals Clusters , 1994, Science.

[43]  P. Pearle,et al.  Wavefunction Collapse and Random Walk , 2002 .

[44]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[45]  Anthony J Leggett,et al.  Testing the limits of quantum mechanics: motivation, state of play, prospects , 2002 .

[46]  Markus Aspelmeyer,et al.  Focus on Mechanical Systems at the Quantum Limit , 2008 .

[47]  L. Di'osi,et al.  Continuous quantum measurement and itô formalism , 1988, 1812.11591.

[48]  G. J. Milburn,et al.  Pulsed quantum optomechanics , 2010, Proceedings of the National Academy of Sciences.

[49]  Ivan Favero,et al.  Optomechanics of deformable optical cavities , 2009 .

[50]  Christoph Simon,et al.  Towards quantum superpositions of a mirror , 2004 .

[51]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[52]  On the precise connection between the GRW master equation and master equations for the description of decoherence , 2007 .

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

[54]  J. Ignacio Cirac,et al.  Toward quantum superposition of living organisms , 2009, 0909.1469.

[55]  Sylvain Gigan,et al.  Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes , 2007, 0705.1728.