Quantum Simulation of (non-)abelian gauge theories Enrique Rico Ortega 13 February 2013 miércoles 13 de febrero de 13 1 The team • Albert Einstein Center - Bern University D. Banerjee M. Bögli P. Stebler P. Widmer U.-J. Wiese • Complutense University • Technical University Madrid Vienna M. Müller P. Rabl • IQOQI - Innsbruck University M. Dalmonte D. Marcos P. Zoller miércoles 13 de febrero de 13 2 The references Atomic Quantum Simulation of Dynamical Gauge Fields Coupled to Fermionic Matter: From String breaking to Evolution after a Quench Phys. Rev. Lett. 109, 175302 (2012) Atomic Quantum Simulation of U(N) and SU(N) non-abelian Gauge Theories arXiv:1211.2242 (2012) Quantum Simulation of Dynamical Lattice Gauge Field Theories with Superconducting Q-bits miércoles 13 de febrero de 13 3 Recent related works on dynamical gauge fields H. Büchler, M. Hermele, S. Huber, M.P.A. Fisher, P. Zoller, Atomic quantum simulator for lattice gauge theories and ring exchange models, Phys. Rev. Lett. 95, 40402 (2005). H. Weimer, M. Müller, I. Lesanovsky, P. Zoller, H.P. Büchler, A [digital] open system Rydberg quantum simulator, Nat. Phys. 6, 382 (2010). J.I. Cirac, P. Maraner, J.K. Pachos, Cold Atom Simulation of Interacting Relativistic Quantum Field Theories, Phys. Rev. Lett. 105, 190403 (2010). E. Kapit, E. Mueller, Optical-lattice Hamiltonians for relativistic quantum electrodynamics, Phys. Rev. A 83, (2011). E. Zohar, J.I. Cirac, B. Reznik, Simulating Compact Quantum Electrodynamics with ultracold atoms: Probing confinement and nonperturbative effects, Phys. Rev. Lett. 109, 125302 (2012). L. Tagliacozzo, A. Celi, A. Zamora, M. Lewenstein, Optical Abelian Lattice Gauge Theories, Ann. Phys. 330, 160-191 (2013). Barcelona, Bern, Innsbruck, Leeds, Madrid, Munich, New York, Stuttgart, Tel Aviv, ... miércoles 13 de febrero de 13 4 … and on dynamical non-abelian gauge fields E. Zohar, J.I. Cirac, B. Reznik, A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory, arXiv:1211.2241 (2012). L. Tagliacozzo, A. Celi, P. Orland, M. Lewenstein, Simulations of non- Abelian gauge theories with optical lattices, arXiv:1211.2704 (2012). Barcelona, Bern, Innsbruck, Leeds, Madrid, Munich, New York, Stuttgart, Tel Aviv, ... miércoles 13 de febrero de 13 5 Why quantum simulate Gauge theories? The study of Gauge theories is the study of Nature. miércoles 13 de febrero de 13 6 Why quantum simulate Gauge theories? The study of Gauge theories is the study of Nature. Gauge symmetry as a fundamental principle miércoles 13 de febrero de 13 6 Why quantum simulate Gauge theories? The study of Gauge theories is the study of Nature. Gauge symmetry as a fundamental principle Gauge symmetry as an emergent phenomenon miércoles 13 de febrero de 13 6 Why quantum simulate Gauge theories? The study of Gauge theories is the study of Nature. Gauge symmetry as a fundamental principle Gauge symmetry as an emergent phenomenon Gauge symmetry as a resource miércoles 13 de febrero de 13 6 Gauge symmetry as a fundamental principle Standard model: for every force there is a gauge boson, miércoles 13 de febrero de 13 7 Gauge symmetry as a fundamental principle atoms Standard model: for every force there is a gauge boson, • The photon is the “carrier” of the electromagnetic force. miércoles 13 de febrero de 13 7 Gauge symmetry as a fundamental principle atoms Standard model: for every force there is a gauge boson, • The photon is the “carrier” of the electromagnetic force. nucleons • The W+, W- and Z0 are the “carriers” of the weak force. miércoles 13 de febrero de 13 7 Gauge symmetry as a fundamental principle atoms Standard model: for every force there is a gauge boson, • The photon is the “carrier” of the electromagnetic force. nucleons • The W+, W- and Z0 are the “carriers” of the weak force. • The gluons are the quarks “carriers” of the strong force. miércoles 13 de febrero de 13 7 Gauge symmetry as a fundamental principle Gauge theories on a Non-perturbative approach to fundamental theories of discrete lattice structure. matter, e.g. Q.C.D. K. Wilson, Phys. Rev. D (1974) miércoles 13 de febrero de 13 8 Gauge symmetry as a fundamental principle Gauge theories on a Non-perturbative approach to fundamental theories of discrete lattice structure. matter, e.g. Q.C.D. 1 S[ ,U] O = [ ,U] e− O [ ,U] K. Wilson, Phys. Rev. D h i Z D (1974) Z N 1 S[ ,U ] e− n n O [ ,U ] ⇠ N n n n=1 X 1 O [ ,U ] ⇠ N n n S[ ,U ] P [Un] e− n n Monte Carlo simulation = Classical/ XStatistical Mechanics miércoles 13 de febrero de 13 8 Gauge symmetry as a fundamental principle Achievements by classical Monte-Carlo simulations: • first evidence of quark-gluon plasma • ab-initio estimate of the entire hadronic spectrum S. Dürr, et al., Science (2008) miércoles 13 de febrero de 13 9 Gauge symmetry as an emergent phenomenon Gauge bosons can appear as collective fluctuations of a strongly correlated many-body quantum system F. Wegner, J. Math. Phys. (1971) J.B. Kogut, Rev. Mod. Phys. (1979) A. Kitaev, Ann. Phys. (2003) P.A. Lee, N. Nagaosa, X.G. Wen, Rev. Mod. Phys. (2006) miércoles 13 de febrero de 13 10 Gauge symmetry as an emergent phenomenon Gauge bosons can appear as collective fluctuations of a strongly correlated many-body quantum system F. Wegner, J. Math. Phys. (1971) J.B. Kogut, Rev. Mod. Phys. (1979) A. Kitaev, Ann. Phys. (2003) Ex.- Kitaev model (Z2 gauge theory) P.A. Lee, N. Nagaosa, X.G. Wen, Rev. Mod. Phys. (2006) (1) (1) (2) (2) (3) (3) H =J1 Si Sj + J2 Si Sj + J3 Si Sj 1 i,j 2 i,j 3 i,j Xh i Xh i Xh i J 2J 2 1 2 XXXX + ZZZZ !16 J 3 0 1 3 vertex | | X plaqX @ A J J , J | 3| {| 1| | 2|} miércoles 13 de febrero de 13 10 Gauge symmetry as an emergent phenomenon Some questions: (i) fractionalization, (ii) confinement-deconfinement quantum phase transition, (iii) spin-liquid physics... miércoles 13 de febrero de 13 11 Volume 94B, number 2 PHYSICS LETTERS 28 July 1980 DYNAMICAL STABILITY OF LOCAL GAUGE SYMMETRY Volume 94B, number 2 PHYSICS LETTERS 28 July 1980 Creation of LightGauge From Chaos symmetry as an D. FOERSTERemergent phenomenon Service de Physique Thdorique, CEN Sac&y, [:-91190 Gif-sur-Yvette, France VolumeSome 94B, number questions: 2 PHYSICS LETTERS 28 July 1980 DYNAMICAL STABILITY OF LOCAL GAUGE SYMMETRY H.B.(i) NIELSEN fractionalization, The Niels Bohr Institute, University of Copenhagen, and NORDITA,Creation of Light From Chaos DK-2100(ii) Copenhagenconfinement-deconfinement Volume~, Denmark 94B, number 2 quantumPHYSICS LETTERS phase transition, 28 July 1980 (iii) spin-liquid physics...D. FOERSTER and Service de Physique Thdorique, CEN Sac&y, [:-91190 Gif-sur-Yvette, France DYNAMICAL STABILITY OF LOCAL GAUGE SYMMETRY M.Volume NINOMIYA 94B, number 2 CreationPHYSICS of LETTERSLight FromH.B. ChaosNIELSEN 28 July 1980 The Niels Bohr Institute, University of Copenhagen, DK-21 O0 CopenhagenThe Niels ~, Bohr Denmark Institute, University of Copenhagen, and NORDITA, DYNAMICAL STABILITY OF LOCAL GAUGE SYMMETRY D. FOERSTER DK-2100 Copenhagen ~, Denmark Service de Physique Thdorique, CEN Sac&y, [:-91190 Gif-sur-Yvette, France Received 14 May 1980 Creation of Light From Chaos and D. FOERSTER H.B. NIELSEN M. NINOMIYA DYNAMICAL STABILITY OF LOCAL GAUGE SYMMETRY Service de Physique Thdorique,The Niels CEN Bohr Sac&y, Institute, [:-91190The University Niels Gif-sur-Yvette, Bohr of Institute, Copenhagen, France University and NORDITA, of Copenhagen, DK-21 O0 Copenhagen ~, Denmark And GodCreation said "Let of Light there From be Chaoslight", and thereDK-2100 was lightCopenhagen - Genesis ~, Denmark 1-3 H.B. NIELSEN Received 14 May 1980 and D. FOERSTER The Niels Bohr Institute, University of Copenhagen, and NORDITA, We show that the large distanceDK-2100 behavior Copenhagen of gauge~, Denmark theories is stable, within certain limits, with respect to addition of gauge noninvariantService de Physique interactions Thdorique, at small CEN distances. Sac&y, [:-91190M. NINOMIYA Gif-sur-Yvette, France The Niels Bohr Institute, University of Copenhagen, DK-21 O0 Copenhagen ~, Denmark and And God said "Let there be light", and there was light - Genesis 1-3 H.B. NIELSEN PHYSICAL REVIEW B 68, 115413 ͑2003͒ The Niels Bohr Institute,M. University NINOMIYA of Copenhagen, Received and 14 NORDITA, May 1980 We show that the large distance behavior of gauge theories is stable, within certain limits, with respect to addition of DK-2100 Copenhagen ~,The Denmark Niels Bohr Institute, University ofance Copenhagen, has a highDK-21 chance O0 Copenhagen of arising ~, Denmark spontaneously even 1. One of us (H.B.N.)Artificial has suggested light and [1 ] quantumearlier that order ingauge systems noninvariant of screened interactions at dipoles small distances. symmetries and physical laws should arise naturally if nature is not gauge invariant at the fundamental and Received 14 May 1980 from some essentially random dynamics rather thanAnd God saidscale. "Let there be light", and there was light - Genesis 1-3 M. NINOMIYA Xiao-Gang Wen* being postulatedDepartment to be exact of Physics,or adjusted Massachusetts by hand Institute+1. of Technology,1.Iliopoulos One of Cambridge, us and(H.B.N.) Nanopoulos Massachusetts has suggested [7] 02139, [1have ] earlier USAinformed that us ance has a high chance of arising spontaneously even miércoles 13 deThe febrero Niels Bohr de 13 Institute, University of Copenhagen, DK-21 O0 Copenhagen ~, Denmark 11 The idea of postulating͑Received 25 dynamical November 2002;stability revised ,2 manuscriptin theWe show received thatthatsymmetries the 24 theylarge January distance are and calculating 2003;physical behavior published laws of thegauge should 16renormalization theories September arise is naturally stable, 2003 within ͒ group/3- certainif limits,nature with is not respect gauge to invariantaddition of at the fundamental sense that coupling parameters Andshall God not saidbe contrived"Let theregauge benoninvariant light",functionfrom and interactions somethere for essentiallywas variousat lightsmall - distances.