Observation of a Discrete Time Crystal in a

Observation of a Discrete Time Crystal in a Trapped-ion Quantum Simulator Guido Pagano Joint Quantum Institute University of Maryland NIST NCTS, December 2016

Non-Equilibrium Studies with Trapped Ions Systems of trapped ions can exhibit tunable long range interactions Long-Range Transverse Field Ising Model Ø Breaks Integrability Ø Theoretically Challenging Ø Model for quantum systems in nature Excited States and Out-Of-Equilibrium Phenomena • • • Propagation of correlations after a global quench [1] Dynamics of excited state quasiparticles [2, 3] Excited state many-body spectroscopy [4] Many Body Localization [5] and Prethermalization [6] Floquet Systems and Discrete Time Crystals [7] [1] Richerme et al. , (Nature 2014) [2] Jurcevic et al. , (Nature 2014); [3] Jurcevic et al. , (PRL 2015) [4] Senko et al. , (Science 2015); [5] Smith et al. , (Nphys 2016) [6] Neyenhuis et al. , (ar. Xiv: 1608. 00681); [7] Zhang, Hess, et al. (ar. Xiv: 1609. 08684)

Outline • Introduction: how is life in many body excited states? • Our toolbox: Trapped-ion quantum simulator 171 Yb+ • Intermezzo: Many body localization and thermalization • Discrete Time Crystal: What is it and how to observe one

Excited states and out of equilibrium physics . . . Excited States Hot . . . Ground States Cold Life in the Excited States: • How and whether the system M BL thermalizes? • Can we observe spontaneous symmetry breaking or DT topological phases in these C states as well?

Thermalization of closed quantum systems Fundamental question: How and whether a closed quantum many body system thermalizes? ? Classical system Classical Ergodic Hypothesis Closed quantum system Subsystem Bath Subsystem Long Time Average Bath Thermal Ensemble

Thermalization of closed quantum systems Fundamental question: How and whether a closed quantum many body system thermalizes? ? Quantum thermalization Closed quantum system Bath Information hidden by spreading of quantum entanglement Subsystem

Thermalization in static and driven systems Bath Subsystem Static Systems Eigenstate Thermalization Hypothesis (ETH) System acts as its own bath Deutsch ’ 93, Srednicki ’ 94 Rigol ‘ 08 The system heats up at Floquet Systems Many-body localization (MBL) No Thermalization M BL Basko et al. ’ 06; Huse and Oganesyan ’ 07 Znidaric et al. ’ 08; Bardardson et al. ’ 12 Vosk and Altman ’ 13; Serbyn et al. ’ 13 Huse and Oganesyan ’ 13; Iyer et al. ‘ 12 Pekker et al. ’ 13; Bauer and Nayak ’ 13 … The system does not up at D TC Khemani et al. ’ 16: non-trivial phases

Outline • Introduction: how is life in many body excited states? • Our toolbox: Trapped-ion quantum simulator 171 Yb+ • Intermezzo: Many body localization and thermalization • Time Crystal: What is it and how to observe one

200 m

171 Yb+ 2 m 200 m

|1, -1 2 S 1/2 | z = |1, 0 |1, 1 n. HF = 12 642 812 118 Hz + 311 Hz/G 2 (B G)2 171 Yb+ 2 m | z = |0, 0 Quantum Operations from “Global Laser Beams” 1) State Preparation via Optical Pumping 2) Single Shot State Readout via state dependent fluorescence 3) Single Site Imaging Resolution 4) Coherent Rotations with Optical Raman Transitions 200 m

Flipping Spins with Raman transitions Carrier w w+w. HF Beatnote frequency 33 THz 2 P 1/2 w w+w. HF | z 2 S =12. 6 GHz 1/2 | z

Generating Spin Hamiltonians Carrier w Transverse modes w+w. HF-w. TM Beatnote frequency N coupled charges 33 THz 2 P 3 N independent collective modes 1/2 w+w. HF-w. TM w | z 2 S 1/2 | z

Generating Spin Hamiltonians Carrier w Transverse modes -μ w+w. HF± μ Beatnote frequency 33 THz 2 P 1/2 w+w. HF ± w | z 2 S 1/2 | z K. Mølmer and A. Sørensen, PRL 82, 1835 (1999) D. Porras and J. I. Cirac, PRL 92, 207901 (2004) K. Kim et. al. , PRL 103, 120502 (2009)

Extending the Spin Hamiltonian Carrier w Transverse modes -μ -Bz w+w. HF± μ -Bz Beatnote frequency 33 THz 2 P 1/2 w+w. HF ± w | z 2 S 1/2 | z AOM

Outline • Introduction: how is life in many body excited states? • Our toolbox: Trapped-ion quantum simulator 171 Yb+ • Intermezzo: Many body localization and thermalization • Time Crystal: What is it and how to observe one

Searching for Thermalization 1. Initialize along x or z a Neel state 2. Apply Hamiltonian 3. Measure along x or z J. Smith et al. , Nature Physics, doi: 10. 1038/nphys 3783

Evidence of Many body localization 1. Initialize along z a Neel state 2. Apply Hamiltonian 3. Measure along z J. Smith et al. , Nature Physics, doi: 10. 1038/nphys 3783

Localization in State Space Observable: Normalized Hamming Distance between initial and final states Counts number of spin flips J. Smith et al. , Nature Physics, DOI: 10. 1038 (2016)

Quantum Fisher Information as a Witness • Long-time entanglement growth in MBL state • Full tomography scales exponentially • Witness: Quantum Fisher Information easily accessible J. H. Bardarson, PRL 109, 017202 (2012) M. Pino, PRB 90, 174204 (2014) G. Tόth, PRA 85, 022322 (2012)

QFI vs. Entanglement Entropy Simulations by M. Heyl and P. Hauke Quantum Fisher Information Entanglement Entropy N=14 N=12 N=10 N=8 Non-Interacting Theory J. Smith et al. , Nature Physics, DOI: 10. 1038 (2016)

Outline • Introduction: how is life in many body excited states? • Our toolbox: Trapped-ion quantum simulator 171 Yb+ • Intermezzo: Many body localization and thermalization • Time Crystal: What is it and how to observe one

What are Time Crystals? Consider a creating a spatial crystal of H 2 O Cold Hot Water Ice Continuous Discrete Spatial Symmetry Can time translation symmetry be spontaneously broken? “Quantum Time Crystals” Wilczek (PRL 2012) Time Translational Symmetry Breaking (TTSB) ? Time Independent Time Dependent

No Time Crystals in Equilibrium “No-Go Theorem” for Continuous Time Translational Symmetry Breaking (TTSB) Trivial in any eigenstate Watanabe & Oshikawa (2015) No periodic time order in ground states Long Range Correlations in time? No periodic time order in in thermal states What about states where symmetries are already broken? Discrete Symmetry Breaking Charge Density Wave

Discrete Time Crystals Periodically Driven (Floquet) many-body Hamiltonian: Discrete TTSB Khemani et al. (PRL 2016) ; Else, Bauer, Nayak (PRL 2016); N. Yao et al. (ar. Xiv: 1608. 02589) Von Keyserlingk, Khemani, Sondhi (PRB 2016) Requirements for new Time Crystal definition: ü Oscillations stabilized by manybody effects ü Periodic state response at subharmonic frequencies ü Robust to perturbations (no fine tuned parameters) Eliminates most “trivial” Discrete Time Crystals Realize all three in our chain of trapped ions

Trapped Ion Floquet Evolution Perturbed pulses Zhang, et al. ar. Xiv: 1609. 08684

Trapped Ion Floquet Evolution Weak Interactions: Zhang, et al. ar. Xiv: 1609. 08684

Trapped Ion Floquet Evolution Strong Disorder: Deflector Control Zhang, et al. ar. Xiv: 1609. 08684

Trapped Ion Floquet Evolution MBL Stabilizes DTC

Stabilized Sub-Harmonic Response No Interactions ( ) or disorder ( ) MBL Drive Stabilizes Time Crystal

Robustness of Stabilized Response MBL Drive Stabilizes Time Crystal Up to a point. . .

Sub-Harmonic Peak Heights: An Order Parameter Average over 10 ions and 10 disorder instances

Variance: Signature of Cross-Over Order parameter variance blows up at phase boundary

Phase Diagram Theoretical Phase Boundary Our Data Observed Key Signatures of a Discrete Time Crystal: ü Periodic state dependence at sub-harmonic frequencies ü Robust to perturbations up to symmetry breaking phase boundary ü Oscillations stabilized by many-body interactions Zhang, et al. , ar. Xiv: 1609. 08684 Time Crystals with NV centers: Choi, et al. , ar. Xiv: 1610. 08057

Finite Size effects and different initial state Finite size scaling: sharpening of the peak height DTC independent From initial state

Current limitation to large scale quantum simulation Background gas collisions H 2 1 collision every 2 min for 20 ions @ 300 K and 1 x 10 -11 Torr Solution: Cryogenic ion trap Background gas collisions ~ 1 collision per day for 100 ions @ 4. 2 K and 1 x 10 -17 Torr

• • • Our Progress Built a New Lab Assembled Trap Drove Trap at 4 K Set up the experimental control system Set Up Main Laser Systems Cryo Ions! Pre lim ina ry

Acknowledgements PI: Chris Monroe Post-docs: • Paul Hess • Jiehang Zhang • Guido Pagano Graduate Students: • Aaron Lee • Jake Smith • Harvey Kaplan • Antonis Kyprianidis • Patrick Becker Undergraduates: • Micah Hernandez • Eric Brickelbaw Theory: • Zhe-Xuan Gong • Alexey Gorshkov • Philipp Hauke • Markus Heyl • David Huse • • Norm Yao Ashvin Vishwanath Andrew Potter Dragos Potirniche