Advanced ERC Grant:QUAGATUA

  AvHSenior

ResearchGrant

+FeodorLynen

HamburgTheoryPrize

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

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)

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)

1. Entanglement in Many Body Systems

1.1 Computational complexity

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)

1.1 What can be simulated classically?

Quantum Monte Carlo

Systematic perturbation theory

Variational methods (mean field, MPS, PEPS MERA, TNS…)

Exact diagonalization

1.1 What is computationally hard?

Fermionic models

Frustrated systems

Quantum dynamics

Disordered systems

1.2 Entanglement of pure states

“Good” entanglement measure for pure states Take reduced density matrix: ρA = TrB(ρAB) = TrB(|ΨAB›‹ΨAB|), and then take von Neumann entropy E(|ΨAB›‹ΨAB|) = S(ρA) = S(ρB), where S(ρ) = -Tr(ρ log ρ). Note that maximally entangled states have E(|ΨAB›‹ΨAB|) = log dANote: For mixed states a super hard

problem…

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

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

1.3 Why there are some hopes? - Area laws

Classical area laws

Thermal area laws

Quantum area laws in 2D?

Quantum area laws in 1D

1.3 Area laws

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(ρA) ~ ∂A (Jacob Beckenstein, Mark Srednicki…)

A

B

1.3 Area laws for thermal states

AB

1.3 Quantum area laws in 1D

1.3 Quantum area laws in 1D

1.3 Quantum area laws in 2D, 3D …

?

One can prove generally S(ρA) ≤ |∂A| log(|∂A|)

1.4 TNS and quantum many-body systems

1... 1| | ,...,Ni i Nc i i

We need coefficients to represent a state.2N

To determine physical quantitites (expectation values) an exponential number of computations is required.

Many-body quantum systems are difficult to describe.

|

1.4 Definition of TNS (MPS in 1D)

1P 2P 3P 4P 5P 6P

2

1

| |kk nn

P n

maps 2D D

as:

|

D-dimensional

| | | | |

are maximally entangled states 1

| | ,D

m

m m

where

GHZ states:

| 0,0 |1,1 | 0,0 |1,1

P

| GHZ | 0,0,0 |1,1,1

1D states:

| 0 0,0 | |1 1,1|P where maps 2 2 2

2) Periodic boundary conditions:

It outperforms DMRG

,

k j k j k jx x y y z z

k j

H

1) Open boundary conditions:

It coincides with DMRG

1P 2P 3P 4P 5P 6P

| | | | |

1P 2P 3P 4P 5P 6P

| | | | |

|

(Verstraete, Porras, Cirac, PRL 2004)

1 2

1

1

1 2 1,..., 0

| Tr ... | ,...,N

N

ii iN N

i i

A A A i i

2D states:

General:

|

|

|

|

,i jP

2

1

| |kk nn

P n

2D D D D

maps

Definition of TNS (MPS in 1D)

2. Non-locality in Many Body Systems

2. Non-locality in Many Body Systems

Courtesy of Ana Belén Sainz

paris.pdf

J. Tura, R. Augusiak, A.B. Sainz, T. Vértesi, M. Lewenstein, and A. Acín, Detecting the non-locality of quantum many body states, arXiv:1306.6860, Science 344, 1256 (2014).

J. Tura, A.B. Sainz, T. Vértesi, A. Acín, M. Lewenstein, R. Augusiak, Translationally invariant Bell inequalities with two-body correlators, 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

Analytic example: Family of many body Bell inequalities

2.3 Physical realizations with ultracold

ions

2.3 Realizations with ultracold ions/atoms

2.3 Realizations with ultracold ions

2.3 Realizations with ultracold ions

2.3 Realizations with ultracold ions

2.3 Realizations with ultracold ions

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)

Quantum Optics Theory ICFO

Hits 2013-2014

Shakin‘ and artificial gauge fields

Shakin‘ and artificial gauge fields

Syntethic gauge fields in syntethic dimensions

For applications to quantum random walks: talk to Sam Mugel

Detection of topological order

In print in

Phys. R

ev. Lett.

Quantum simulators of lattice gauge theories

Submitted to

Physical Review X

Artificial graphene (with Leticia Tarruell)

Spinor dynamics of high spin Fermi gas

The world according to Om

Commissioned by Reports on Progress in

Physics

Toward quantum nanophotonics (with Darrick Chang)

High harmonic generation and atto-nanophysics

Condensation of excitons (with François Dubin, experiment)

+ M. Lewenstein

In print in

EPL

Classical Brownian motion and biophotonics (with Maria García-Parajo)

Submitted to

Nature Physics

Ultracold atoms in optical lattices: Simulating quantum many-body physicsM. Lewenstein, A. Sanpera, and V. Ahufinger, Oxford University Press (2012)Atomic Physics: Precise measurements & ultracold matterM. Inguscio and L. Fallani, Oxford University Press (2013)

Quantum simulators, precise measurements and ultracold matter