1. Advanced ERC Grant: QUAGATUA AvH Senior Research Grant + Feodor Lynen Hamburg Theory Prize Chist-Era DIQIP Maciej Lewenstein Detecting Non-Locality in Many Body Systems Enrico Fermi School Course 191 EU IP SIQS EU STREP EQuaM Advanced ERC Grant: OSYRIS John Templeton Foundation ICFO-Cellex-Severo Ochoa Polish Science Foundation

2. ICFO – Quantum Optics Theory PhD ICFO: Ulrich Ebling (Fermions) Alejandro Zamora (MPS,LGT) Piotr Migdał (QI, QNetworks) Jordi Tura (QI, many body) Mussie Beian (Excitons, exp) Samuel Mugel (Art. Graphene) Aniello Lampo (Open Systems) David Raventos (Gauge Fields) Caixa-Manresa-Fellows: Julia Stasińska (QI, Disorder) Polish postoc grants Ravindra Chhajlany (Hubbard Models) MPI Garching postdoc: Andy Ferris (TNS, Frustrated AFM) Postdocs ICFO: Alessio Celi (LGT, Gen. Rel.) Tobias Grass (FQHE, Exact Diag.) Remigiusz Augusiak (QI, Many Body) Pietro Massignan (Fermions, Disorder) G. John Lapeyre (QI, Statphys) Luca Tagliacozzo (LGT, TNS, QDyn) Christine Muschik (TQNP) Alex Streltsov (QI) Arnau Riera (QThermo, QDyn) Pierrick Cheiney (Art. Graphene, exp) Stagiers (en français) Michał Maik (Dipolar gases) Anna Przysiężna (Dipolar gases)

3. Detecting non-locality in many body systems - Outline 2. Non-locality in many body systems 2.1 Correlations – DIQIP approach 2.2 Non-locality in many body systems 2.3 Physical realizations with ultracold ions 1. Entanglement in many body systems 1.1 Computational complexity 1.2 Entanglement of pure states (generic, and not…) 1.3 Area laws 1.4 Tensor network states Many body physics from a quantum information perspective R. Augusiak, F. M. Cucchietti, M. Lewenstein Lect. Notes Phys. 843, 245-294 (2010). Ultracold atoms in optical lattices: Simulating quantum many-body systems M. Lewenstein, A. Sanpera, V. Ahufinger Oxford University Press (2012)

4. 1. Entanglement in Many Body Systems

5. 1.1 Computational complexity CClassical simulators: What can be simulated classically? What is computationally hard (examples)? Ultracold atoms in optical lattices: Simulating quantum many-body physics, M. Lewenstein, A. Sanpera, V. Ahufinger, in print Oxford University Press (2012)

6. 1.1 What can be simulated classically? QQuantum Monte Carlo SSystematic perturbation theory VVariational methods (mean field, MPS, PEPS MERA, TNS…) EExact diagonalization

7. 1.1 What is computationally hard? FFermionic models FFrustrated systems QQuantum dynamics DDisordered systems

8. 1.2 Entanglement of pure states “Good” entanglement measure for pure states Take reduced density matrix: ρ A = Tr B (ρ AB ) = Tr B (|Ψ AB ›‹Ψ AB |), and then take von Neumann entropy E(|Ψ AB ›‹Ψ AB |) = S(ρ A ) = S(ρ B ), where S(ρ) = -Tr(ρ log ρ). Note that maximally entangled states have E(|Ψ AB ›‹Ψ AB |) = log d A Note: For mixed states a super hard problem…

9. 1.2 Why computations may be hard? Entanglement of a generic state

10. 1.2 Why computations may be hard? Entanglement of a generic state

11. 1.3 Why there are some hopes? - Area laws CClassical area laws TThermal area laws QQuantum area laws in 2D? QQuantum area laws in 1D

12. 1.3 Area laws AArea law: Averaged values of correlations, between the regions A and B, scale as the size of the boundary of A. For instance for quantum pure (ground states): S(ρ A ) ~ ∂A (Jacob Beckenstein, Mark Srednicki…) A B

13. 1.3 Area laws for thermal states A B

14. 1.3 Quantum area laws in 1D

16. 1.3 Quantum area laws in 2D, 3D … ? One can prove generally S(ρ A ) ≤ |∂A| log(|∂A|)

17. 1.4 TNS and quantum many-body systems We need coefficients to represent a state.  To determine physical quantitites (expectation values) an exponential number of computations is required. Many-body quantum systems are difficult to describe.

18. 1.4 Definition of TNS (MPS in 1D) maps as: D-dimensional are maximally entangled states where GHZ states: 1D states: where maps

19. 2) Periodic boundary conditions: It outperforms DMRG 1) Open boundary conditions: It coincides with DMRG (Verstraete, Porras, Cirac, PRL 2004)

20. 2D states: General: maps Definition of TNS (MPS in 1D)

21. 2. Non-locality in Many Body Systems

22. Courtesy of Ana Belén Sainz paris.pdf J. TuraJ. Tura, R. Augusiak, A.B. Sainz, T. Vértesi, M. Lewenstein, and A. Acín,R. AugusiakA.B. SainzT. VértesiM. LewensteinA. Acín Detecting the non-locality of quantum many body states, arXiv:1306.6860, Science 344, 1256 (2014).arXiv:1306.6860 J. TuraJ. Tura, A.B. Sainz, T. Vértesi, A. Acín, M. Lewenstein, R. Augusiak,A.B. SainzT. VértesiA. AcínM. LewensteinR. Augusiak Translationally invariant Bell inequalities with two-body correlators, arXiv:1312.0265,arXiv:1312.0265 in print to special issue of J. Phys. A on “50 years of Bell’s Theorem”. 2.1 Correlations – DIQIP approach 2.2 Non-locality in many body systems

32. Analytic example: Family of many body Bell inequalities

41. 2.3 Physical realizations with ultracold ions

42. 2.3 Realizations with ultracold ions/atoms

43. 2.3 Realizations with ultracold ions

47. Detecting non-locality in many body systems - Conclusions 2. Non-locality in many body systems “Weak” entanglement ≈ Locality with respect to “simple” Bell inequalities. “Strong” non-locality and symmetry ≈ Classical computability? 1.Entanglement in many body systems “Weak” entanglement ≈ Area laws ≈ Classical computability! Many body physics from a quantum information perspective R. Augusiak, F. M. Cucchietti, M. Lewenstein Lect. Notes Phys. 843, 245-294 (2010). Ultracold atoms in optical lattices: Simulating quantum many-body systems M. Lewenstein, A. Sanpera, V. Ahufinger Oxford University Press (2012)

48. Quantum Optics Theory ICFO Hits 2013-2014

49. Shakin‘ and artificial gauge fields

52. Syntethic gauge fields in syntethic dimensions For applications to quantum random walks: talk to Sam Mugel

53. Detection of topological order In print in Phys. Rev. Lett.

54. Quantum simulators of lattice gauge theories Submitted to Physical Review X

55. Artificial graphene (with Leticia Tarruell)

56. Spinor dynamics of high spin Fermi gas

57. The world according to Om Commissioned by Reports on Progress in Physics

58. Toward quantum nanophotonics (with Darrick Chang)

59. High harmonic generation and atto-nanophysics

60. Condensation of excitons (with François Dubin, experiment) + M. Lewenstein In print in EPL

61. Classical Brownian motion and biophotonics (with Maria García-Parajo) Submitted to Nature Physics

62. Ultracold atoms in optical lattices: Simulating quantum many-body physics M. Lewenstein, A. Sanpera, and V. Ahufinger, Oxford University Press (2012) Atomic Physics: Precise measurements & ultracold matter M. Inguscio and L. Fallani, Oxford University Press (2013) Quantum simulators, precise measurements and ultracold matter