Using timetime correlations to detect entanglement and spreading

Using time-time correlations to detect entanglement and spreading of quantum information Martin Gärttner Kirchhoff-Institut für Physik, Heidelberg QSEC 2019 Heidelberg September 26, 2019 Martin Gärttner - QSEC 2019 1

(Analog) Quantum simulation evolve measure Goal: Characterize the prepared states as a function of t and the parameters of H. Problem: • Often only global measurements possible • Full state tomography not feasible for large N Martin Gärttner - QSEC 2019 2

Quantum simulation extended easy to prepare separable interesting entangled? useful? perturb time reversal measure → Measure time-time correlations, out-of-time-order correlations → extract more information about → only global observables needed Martin Gärttner - QSEC 2019 3

OTOCs quantify operator growth Martin Gärttner - QSEC 2019 4

Operator growth Example: site i site j t=0 t>0 operators grow in in time, quantified by commutator Martin Gärttner - QSEC 2019 “scrambling” 5

OTOC measurement in spin systems prepare evolve rotate evolve back measure time Martin Gärttner - QSEC 2019 6

Collective operator spreading At least m terms Martin Gärttner - QSEC 2019 7

Penning trap quantum simulator Martin Gärttner - QSEC 2019 8

With Justin Bohnet Group of John Bollinger (NIST Boulder) Penning trap experiment ODF Britton et al. Nature 2012 Bohnet et al. Science 2015 Two hyperfine states used as spin ½ system CM at Martin Gärttner - QSEC 2019 9

Experimental results [MG, J. G. Bohnet et al. Nat. Phys. 13 781 (2017)] Martin Gärttner - QSEC 2019 10

Fourier transform of magnetization [MG, J. G. Bohnet et al. Nat. Phys. 13 781 (2017)] • Observe operator spreading • Only global spin measurement Martin Gärttner - QSEC 2019 11

OTOCs quantify coherence Martin Gärttner - QSEC 2019 12

Multiple quantum coherences Example: N=3 0 m=-1 m=-2 -3 1 m=0 m=-1 -2 2 m=1 m=0 -1 3 m=2 m=1 0 Martin Gärttner - QSEC 2019 [NMR: Pines group 1980 s] 13

Multiple quantum coherences prepare evolve rotate evolve back measure time Martin Gärttner - QSEC 2019 14

MQC – experimental results N=48 Lines: Simulation including decoherence [MG, J. G. Bohnet et al. Nat. Phys. 13 781 (2017)] Martin Gärttner - QSEC 2019 15

OTOCs detect entanglement Martin Gärttner - QSEC 2019 16

OTOCs as lower bound on QFI → OTOC witnesses multi-particle entanglement. [MG, P. Hauke, A. M. Rey, Phys. Rev. Lett. 120, 040402 (2018)] Martin Gärttner - QSEC 2019 17

OTOCs detect chaos Martin Gärttner - QSEC 2019 18

OTOCs for quantum chaos Quantum – classical correspondence Truncated Wigner Lyapunov exponent Ion experiment: Two bosonic modes class. integrable no chaos Minimal model showing chaos? Three-mode system with integrability breaking? Martin Gärttner - QSEC 2019 19

Three-mode system Martin Gärttner - QSEC 2019 20

Three-mode chaos 1 M. Rautenberg and MG, ar. Xiv: 1907. 04094 0 Martin Gärttner - QSEC 2019 21

Time reversal in spinor BECs Rb BEC Spin-changing collisions: Martin Gärttner - QSEC 2019 M. Rautenberg and MG, ar. Xiv: 1907. 04094 22

Exponential OTOC growth Using truncated Wigner simulations PRELIMINARY Exact diagonalization only up to N=100 Martin Gärttner - QSEC 2019 23

OTOCs in (Rydberg) spin systems Hamiltonian engineering time Time reversal: pulse sequence 1 → H pulse sequence 2 → -H Martin Gärttner - QSEC 2019 24

Acknowledgements A. M. Rey M. Wall J. Bollinger J. Bohnet A. Safavi-Naini R. Lewis-Swan K. Gilmore Martin Gärttner - QSEC 2019 P. Hauke 25

The Team Stefanie Czischek Linda Shen Michael Rautenberg Jan Philipp Klinger Marcel Neugebauer Sebastian Syrkowski Adrian Breamer Thank you! Martin Gärttner - QSEC 2019 26