Simulating quantum fields with cavity QED.

As the realization of a fully operational quantum computer remains distant, quantum simulation, whereby one quantum system is engineered to simulate another, becomes a key goal of great practical importance. Here we report on a variational method exploiting the natural physics of cavity QED architectures to simulate strongly interacting quantum fields. Our scheme is broadly applicable to any architecture involving tunable and strongly nonlinear interactions with light; as an example, we demonstrate that existing cavity devices could simulate models of strongly interacting bosons. The scheme can be extended to simulate systems of entangled multicomponent fields, beyond the reach of existing classical simulation methods.

[1]  F. Verstraete,et al.  Sequential generation of entangled multiqubit states. , 2005, Physical review letters.

[2]  T. Wilk,et al.  Three-photon correlations in a strongly driven atom-cavity system. , 2011, Physical review letters.

[3]  U. Schollwoeck.  The density-matrix renormalization group , 2004, cond-mat/0409292.

[4]  Frank Verstraete,et al.  Applying the variational principle to (1+1)-dimensional quantum field theories. , 2010, Physical review letters.

[5]  Eliot Kapit,et al.  Optical-lattice Hamiltonians for relativistic quantum electrodynamics , 2010, 1011.4021.

[6]  J I Cirac,et al.  Continuous matrix product states for quantum fields. , 2010, Physical review letters.

[7]  J. Cirac,et al.  Sequential generation of matrix-product states in cavity QED , 2006, quant-ph/0612101.

[8]  C. cohen-tannoudji,et al.  Annual review of cold atoms and molecules , 2013 .

[9]  S. Bose,et al.  Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays , 2006, quant-ph/0606159.

[10]  J. Raimond,et al.  Manipulating quantum entanglement with atoms and photons in a cavity , 2001 .

[11]  Alexandre Blais,et al.  Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors , 2011 .

[12]  C. W. Gardiner.  Input and output in damped quantum systems III: formulation of damped systems driven by Fermion fields , 2004 .

[13]  T. Schaetz,et al.  Simulating a quantum magnet with trapped ions , 2008 .

[14]  R. Blatt,et al.  Intensity-field correlation of single-atom resonance fluorescence. , 2009, Physical review letters.

[15]  R. Glauber.  The Quantum Theory of Optical Coherence , 1963 .

[16]  J. Dowling.  Exploring the Quantum: Atoms, Cavities, and Photons. , 2014 .

[17]  H. Kimble,et al.  Demonstration of a state-insensitive, compensated nanofiber trap. , 2012, Physical review letters.

[18]  B. Lanyon,et al.  Universal Digital Quantum Simulation with Trapped Ions , 2011, Science.

[19]  E. Lieb,et al.  EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE , 1963 .

[20]  Input-output theory for fermions in an atom cavity , 2002, cond-mat/0205360.

[21]  A. D. Boozer,et al.  Trapped atoms in cavity QED: coupling quantized light and matter , 2005 .

[22]  Michael J. Hartmann,et al.  Strongly interacting polaritons in coupled arrays of cavities , 2006, 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference.

[23]  T. Monz,et al.  An open-system quantum simulator with trapped ions , 2011, Nature.

[24]  M. Lewenstein,et al.  Can one trust quantum simulators? , 2011, Reports on progress in physics. Physical Society.

[25]  Mattias Gustavsson,et al.  Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons , 2010, Nature.

[26]  B. Englert,et al.  Cavity quantum electrodynamics , 2006 .

[27]  J. Eisert,et al.  Holographic quantum states. , 2010, Physical review letters.

[28]  U. Schollwoeck.  The density-matrix renormalization group in the age of matrix product states , 2010, 1008.3477.

[29]  R. Blatt,et al.  Quantum simulation of the Dirac equation , 2009, Nature.

[30]  October I.  Physical Review Letters , 2022 .

[31]  Alán Aspuru-Guzik,et al.  Photonic quantum simulators , 2012, Nature Physics.

[32]  J. Cirac,et al.  Cold atom simulation of interacting relativistic quantum field theories. , 2010, Physical review letters.

[33]  M. Johanning,et al.  Quantum simulations with cold trapped ions , 2009, 0905.0118.

[34]  M. Greiner,et al.  Quantum simulation of antiferromagnetic spin chains in an optical lattice , 2011, Nature.

[35]  G. J. Milburn,et al.  Quantum open-systems approach to current noise in resonant tunneling junctions , 1998 .

[36]  S. Dawkins,et al.  Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber. , 2009, Physical review letters.

[37]  F. Verstraete,et al.  Renormalization and tensor product states in spin chains and lattices , 2009, 0910.1130.

[38]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[39]  Tim Byrnes,et al.  Simulating lattice gauge theories on a quantum computer (熱場の量子論とその応用) , 2006 .

[40]  M. Lewenstein,et al.  Wilson fermions and axion electrodynamics in optical lattices. , 2010, Physical review letters.

[41]  L. Mandel,et al.  Optical Coherence and Quantum Optics , 1995 .

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

[43]  Andrew D. Greentree,et al.  Quantum phase transitions of light , 2006, cond-mat/0609050.

[44]  C. Monroe,et al.  Onset of a quantum phase transition with a trapped ion quantum simulator. , 2011, Nature communications.

[45]  A. Trombettoni,et al.  (3+1) massive Dirac fermions with ultracold atoms in frustrated cubic optical lattices , 2010, 1004.4744.

[46]  J. Dalibard,et al.  Quantum simulations with ultracold quantum gases , 2012, Nature Physics.

[47]  Mauro Paternostro,et al.  Quantum circuits for spin and flavor degrees of freedom of quarks forming nucleons , 2010, Quantum Inf. Process..

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

[49]  H. Ramachandran.  Annual Review of Cold Atoms and Molecules , 2014 .

[50]  Lu-Ming Duan,et al.  Quantum simulation of frustrated Ising spins with trapped ions , 2010, Nature.

[51]  M. Fannes,et al.  Finitely correlated states on quantum spin chains , 1992 .

[52]  B. Lanyon,et al.  Towards quantum chemistry on a quantum computer. , 2009, Nature chemistry.

[53]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[54]  R. Blatt,et al.  Quantum to classical transition in a single-ion laser , 2010, 1002.3621.

[55]  R J Schoelkopf,et al.  Circuit QED and engineering charge-based superconducting qubits , 2009, 0912.3902.

[56]  F. Verstraete,et al.  Quantum Metropolis sampling , 2009, Nature.

[57]  C. Gardiner,et al.  Squeezing of intracavity and traveling-wave light fields produced in parametric amplification , 1984 .

[58]  F. Verstraete,et al.  Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems , 2008, 0907.2796.

[59]  R. Feynman.  Simulating physics with computers , 1999 .

[60]  John Preskill,et al.  Quantum Algorithms for Quantum Field Theories , 2011, Science.

[61]  White,et al.  Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.

[62]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[63]  R. Blatt,et al.  Tunable Ion-Photon Entanglement in an Optical Cavity , 2012, Nature.