simulations and results: Munich 1972

simulations and results: Munich 1972 Boulder 2040: “stuff ion trapper‘s dreams are made of”

experimental quantum simulations

outline: experimental Quantum Simulations (QS) • different implementations of QS (luxury?) • different classes (intentions) of QS +incomplete list of examples • play through one example for QS (quantum magnet) • discuss differences between QS and QC • after successful exp. proof of principle • outperform classical computation • deeper insight in complex quantum dynamics • suggesting 3 objectives • #1: decoherence = error • #2: scaling radio-frequency (Penning) traps • + minimizing effort • #3: new prospects: • ions (and atoms) in optical lattices vision

more than one quantum simulator? testing the “non-testable” quantum simulator = universal quantum computer ions: +individual addressability (not only detection) +large interaction strength (kHz not Hz) @ small decoherence rates +outstanding initialization /preparation however1: -scalability -intrinsically (+bosons/ -fermions) however2: +dream to combine advantages … Didi’s (a)addressing different questions (b)addressing identical questions NJP-special issue on quantum simulations (04.2011) Tillman Esslinger, Chris Monroe, Tobias Schaetz

different classes of quantum simulations class 2 class 1 outperform classical computation address the classically non-trackabkle explore new physics in the laboratory (perhaps even trackable classically) simulating analogues: nonlinear interferometers Dirac equation Solitons early universe (quantum walks) (Duffing oscillator-Roee) Frenkel Kontorova model Kibble-Zureck mechanism D. Leibfried, DJ.Wineland et al. PRL (2002) L.Lamata, T.Schaetz et al. PRL (2007) R.Blatt’s group Nature (2010) + HT on Klein paradox H.Landa, A.Retzker, B.Reznik et al. PRL (2010) + Poster #22 Milburn PRL 2005 R.Schuetzhold, T.Schaetz et al. PRL (2007) Milburn PRA 2002 Ch.Schneider, T.Schaetz et al. PRL (2009) + Poster #39 C.Sanders, D.Leibfried et al. PRL (2009) R.Blatt’s group PRL (2010) R.Ozeri et al., arXiv (2010) Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it W.H.Zurek, P.Zoller et al. PRL (2005)

class 1: why simulating and not computing it ? January 1670

class 1: can not compute it? – find an analog and simulate January 1670

January 1670 March 2006 class 1: can not compute it? – find an analog and simulate

different classes of quantum simulations Blatt group (2010) class 2 class 1 outperform classical computation address the classically non-trackabkle explore new physics in the laboratory (perhaps even trackable classically) simulating analogues: nonlinear interferometers Dirac equation Solitons early universe (quantum walks) (Duffing oscillator-Roee) Frenkel Kontorova model Kibble-Zureck mechanism D. Leibfried, DJ.Wineland et al. PRL (2002) L.Lamata, E.Solano, T.Schaetz et al. PRL (2007) R.Blatt’s group Nature (2010) + HT on Klein paradox H.Landa, A.Retzker et al. PRL (2010) + Poster #22 Milburn PRL 2005 R.Schuetzhold, T.Schaetz et al. PRL (2007) Milburn PRA 2002 Ch.Schneider, T.Schaetz et al. PRL (2009) + Poster #39 C.Sanders, D.Leibfried et al. PRL (2009) R.Blatt’s group PRL (2010) R.Ozeri et al., arXiv (2010) Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it W.H.Zurek, P.Zoller et al. PRL (2005)

different classes of quantum simulations Schaetz group (2010) class 2 class 1 outperform classical computation address the classically non-trackabkle explore new physics in the laboratory (perhaps even trackable classically) simulating analogues: nonlinear interferometers Dirac equation Solitons early universe (quantum walks) (Duffing oscillator-Roee) Frenkel Kontorova model Kibble-Zureck mechanism D. Leibfried, DJ.Wineland et al. PRL (2002) L.Lamata, T.Schaetz et al. PRL (2007) R.Blatt’s group Nature (2010) + HT on Klein paradox H.Landa, A.Retzker, B.Rezniket al. PRL (2010) + Poster #22 Milburn PRL 2005 R.Schuetzhold, T.Schaetz et al. PRL (2007) Milburn PRA 2002 Ch.Schneider, T.Schaetz et al. PRL (2009) + Poster #39 C.Sanders, D.Leibfried et al. PRL (2009) R.Blatt’s group PRL (2010) R.Ozeri et al., arXiv (2010) Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it W.H.Zurek, P.Zoller et al. PRL (2005)

different classes of quantum simulations class 2 class 1 outperform classical computation address the classically non-trackabkle explore new physics in the laboratory (perhaps even trackable classically) simulating analogues: nonlinear interferometers Dirac equation Solitons early universe (quantum walks) (Duffing oscillator-Roee) Frenkel Kontorova model Kibble-Zureck mechanism D. Leibfried, DJ.Wineland et al. PRL (2002) L.Lamata, E.Solano,T.Schaetz et al. PRL (2007) R.Blatt’s group Nature (2010) + HT on Klein paradox H.Landa, A.Retzker, B.Reznik et al. PRL (2010) + Poster #22 Milburn PRL 2005 R.Schuetzhold, T.Schaetz et al. PRL (2007) Milburn PRA 2002 Ch.Schneider, T.Schaetz et al. PRL (2009) + Poster #39 C.Sanders, D.Leibfried et al. PRL (2009) R.Blatt’s group PRL (2010) R.Ozeri et al., arXiv (2010) Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it W.H.Zurek, P.Zoller et al. PRL (2005)

from: www.nano-world.org Quantum simulation - H.Haeffner’s @ Berkeley Frenkel-Kontorova model: How does a chain of ions move in a periodic potential ? Ions move collectively • Frenkel-Kontorova model describes: • dislocations in crystals • dry friction • epitaxial growth • transport properties in Josephson Junction arrays • elasticity of DNA Garcia-Mata et al., Eur. Phys. J. D (2007)

different classes of quantum simulations class 2 class 1 outperform classical computation address the classically non-trackabkle explore new physics in the laboratory (perhaps even trackable classically) simulating analogues: nonlinear interferometers Dirac equation Solitons early universe (quantum walks) (Duffing oscillator-Roee) Frenkel Kontorova model Kibble-Zureck mechanism D. Leibfried, DJ.Wineland et al. PRL (2002) D. Leibfried, DJ.Wineland et al. PRL (2002) L.Lamata, T.Schaetz et al. PRL (2007) R.Blatt’s group Nature (2010) + HT on Klein paradox L.Lamata, T.Schaetz et al. PRL (2007) R.Blatt’s group Nature (2010) + HT on Klein paradox H.Landa, A.Retzker et al. PRL (2010) + Poster #22 Milburn PRL 2005 R.Schuetzhold, T.Schaetz et al. PRL (2007) Milburn PRA 2002 Ch.Schneider, T.Schaetz et al. PRL (2009) + Poster #39 C.Sanders, D.Leibfried et al. PRL (2009) R.Blatt’s group PRL (2010) R.Ozeri et al., arXiv (2010) Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it W.H.Zurek, P.Zoller et al. PRL (2005)

Roadrunner –Los Alamos 1.1 Petaflops/s 2000 t 3.9 MW State of the art (Jülich 2010): 42 spins (242x 242) each doubling allows for one more spin 1/2 only

different classes of quantum simulations class 2 class 1 outperform classical computation address the classically non-trackabkle explore new physics in the laboratory (perhaps even trackable classically) simulating analogues: nonlinear interferometers Dirac equation Solitons early universe (quantum walks) (Duffing oscillator-Roee) Frenkel Kontorova model Kibble-Zureck mechanism simulating solid state physics: Bose-Hubbard model Spin boson model quantum spin Hamiltonians (e.g. quantum Ising spin frustration) Anderson localization three particle interaction D.Porras and I.Cirac PRL (2004) D.Porras, I.Cirac et al. PRA (2008) D.Porras and I.Cirac PRL (2004) Schaetz’s group Nature Physics (2008) Monroe’s group Nature (2010) D.Porras +talk on Tuesday

Quantum simulation - Diego’s @ Madrid • Universidad Complutense de Madrid -Diego Porras, Miguel Angel Martín-Delgado, Alejandro ermúdez • Exotic quantum many-body physics of trapped ions – Exotic models 3-spin Ising interactions • Quantum dynamics in the presence of disorder – Anderson localization, phonon transport • Other current interests: Many-body dynamics in the presence of decoherence, disorder, magnetic frustration...

+ Heisenberg model pick one: simulating quantum-spin-systems how to simulate • spin s • magnetic field B • spin-spin interaction J quantum Ising model XY model

our spin/ion - 25Mg+ (I=5/2) Mg25: I=5/2 (mf=-4,….,+4) mf=-4 P3/2 (S=1/2, L=1) [F=4,3,2] (mf=-3,….,+3) P1/2 (S=1/2, L=0) [F=3,2] mf=-2  mf=-1 F=2 mf=0 mf=1 mf=2 S1/2 (s=1/2, L=0) mf=3 mf=2 mf=1 F=3 mf=0 mf=-1  mf=-2 mf=-3

lasers - 25Mg+ (I=5/2)- transitions ~ 200 GHz 2P3/2 F = 3, mF = -3 F = 2, mF = -2 ~ 2750 GHz 2P1/2 quantum state of motion (harmonic oscillator) Detection(s-) Raman 280 nm repump  |ñ|1ñ |ñ|0ñ 2S1/2 1.79 GHz  |¯ñ|1ñ |¯ñ|0ñ

e.g. quantum magnetism (B) P pulse duration effective coupling Bx proposal Porras and Cirac 2004 e.g. quantum-Ising model: eff. magnetic field (global qubit-rotation)  

e.g. quantum magnetism (J) eff. spin-spin Interaction J (conditional optical dipole force) P3/2 P1/2 Bx S1/2 e.g. quantum-Ising model: eff. magnetic field (global qubit-rotation) F= -1.5 F

e.g. quantum magnetism (J) Bx e.g. quantum-Ising model: eff. magnetic field (global qubit-rotation) eff. spin-spin Interaction J (conditional optical dipole force) all parameters to be chosen individually: (e.g. amplitude, range, anti- or ferromagnetic phase …)

ground state ground state amplitude + n<0.03 J(t) B duration (analyse) prepare initialize simulate quantum “baby” phase transition adiabatic evolution detect

fidelity( v ) 98%+- 2% Bx=|J(t)| Jmax Bx summary: what’s up spins? adiabatic transition: J + J simulating a quantum magnet in an ion trap

excited state degenerate excited state: (+ ) entanglement 1 0 0 1 “beyond” the ground state adiabatic evolution excited state energy level system up side down: J -J (simulating -HIsing)

Simplest case of spin frustration - C.Monroe’s AFM AFM J12=J13=J23 > 0 ? ground state is entangled |Y = | +|+| +| +|+| Bx=0 AFM symmetry breaking field Bx P0 P1 P2 P3 Bx0 |Y1 = | +|+| still entangled! |Y2 = | +|+| still entangled! P0 P1 P2 P3 Frustration  Entanglement K. Kim, et al., Nature 465, 590 (2010)

Distribution of magnetization for N=2,3,..9 spins (Uniform FM couplings) – C. Monroe’s Ferromagnet (d-function) 1.0 0.8 0.6 0.4 0.2 0.0 “Binder Ratio” N=9 (theory) N=2 (theory) 0.01 0.1 1 10 N=2 N=9 Paramagnet (Gaussian) -N/20 +N/2 mx Ratio of transverse field to Ising coupling

radial modes: two qubit geometrical phase gate gate time 39 ms General formalism by: Milburn, Schneider, James (1999) Sorensen & Molmer (1999,2000) 97%+- 1% fidelity( )~ gate duration down to 5 ms + H.Schmitz et al. 2009

computing versus simulation • Techniques for minimizing noise in an quantum simulation (Poster) Q 28.5 Di 16:30 Uhr • Towards two-dimensional quantum simulations with trapped ions (Talk) Q 21.1 Di 16:30 Uhr

computing versus simulation • stroboscopic pulses (!t!) • non equilibrium (oscillation) • error correction (e.g. spin echo) • decoherence = error • 1.1 dimensional trap network -continuous evolution (J and B) -equilibrium (adiabatic) -robust (inherent correction) -decoherence = ?nature? -2 dimensional trap-lattice

?+? objective #1 investigate/exploit decoherence • robust: reduced impact of decoherence (e.g. quantum phase transitions?) • gadget: engineered decoherence (e.g. simulate “natural” noise?) • necessary: enhanced (quantum) efficiency by decoherence (e.g. in biological systems?)

our “old” trap 1D + !cryogenics!2 h< ~ rf 2I.Chuang (US:MIT); C.Monroe (US:Michigan) Blatt/Roos (EU:Innsbruck); D.Wineland (US:NIST) objective #2 scaling exp. quantum simulations in surface ion traps state of the art 1 1group of D.Wineland (US:NIST) • extend into second dimension (arrays of ions) • optimize architecture for quantum simulations (no cryogenics, large Jspin/spin) • (potentially without lasers)

R.Schmied+Didi: It might look like this… 2D lattice of ions, cooled and optically pumped by lasers Schmied,Wesenberg, Leibfried PRL(2009) optimized surface electrode trap array optimized current carrying wires to implement interactions (Sørensen Mølmer+phase gates) • key steps: •  couple ions in separate wells with interaction time scale  heating rate • demonstrate feasibility of magnetic gradient interactions • demonstrate feasibility of trap arrays and defect free loading

Hensinger’s Gold Silicon Robin Sterling (Sussex), Prasanna Srinivasan (Southampton), Hwanjit Rattanasonti (Southampton), Michael Kraft (Southampton) and Winfried Hensinger (Sussex) First generation chip, final processing steps currently being carried out

other ways for scaling: Ion arrays in Penning traps B Richard Thompson Dany Segal, (Wini + Ferdiand) John Bollinger Crick et al (Imperial College), Optics Express 2008 0.5 mm Features: + static trapping fields enable large traps to be used; ions are far from electrode surfaces = low heating rates + for a single plane, the minimum energy lattice is triangular = good for magnetically frustrated simulations - ion crystals rotate (~50 kHz) but rotation precisely controlled = individual particle detection still possible

Microwave magnetic (gates) interactions – Didi’s(Christian Ospelkaus, Ulrich Warring) critical for motional excitation: field gradient over wavepacket size a0 10 nm (Be+, 5 MHz) plane wave: l= 30 cm h =k a0 = 6×10-9 1 mm trap size: l= 1 mm h =2 p/l a0 = 3×10-5 30 mm trap size: l= 30 mm h =2 p/l a0 = 0.001 729 nm/Ca+: l= 729 nm h =k a0 = 0.03 313 nm/Be+: l= 313 nm h =k a0 = 0.1 advantages:  “all electronic” control  no spontaneous emission  no ground state cooling required  laser overhead vastly reduced remaining challenges:  cross talk (especially 1-qubit rot.)  anomalous heating Bz 30 mm GND Trap rf I ~ I ~ Trap rf I ~ GND proposal: Christian Ospelkaus et al. PRL 101, 090502 (2008) related work: ion “molecule”; M. Johanning et al., arXiv:0801.0078 simulation; J. Chiaverini, W. Lybarger, PRA77, 022324 (2008)

minimizing laser efforts: DC -Wunderlich’s + Schmidt-Kaler’s B Magnetic Gradient Induced Coupling: MAGIC individual addressing using magnetic field gradient M. Johanning et al., PRL 102 , 073004 (2009) Yb+ • Quantum Simulations (see also Review: M. Johanning et al. J. Phys. B 42, 154009 (2009).)

first step in our lab: trapping an ion in optical dipole trap* • lifetime limited by • recoil heating only • several 100s of oscillations • in optical potential • loading via rf-trap without heating • ion trapped in optical lattice • loading and cooling in rf-trap • dipole trap on / rf-trap off - detection in rf-trap objective #3 sharing advantages of ions and optical lattices: for 30 years: atoms in optical fields for 60 years: ions in radio frequency fields • individual addressability • operations of high fidelity (>99%) • long range interaction (Jspin/spin>20kHz) + arrays of traps I.Bloch should not compete but complete

( ) ( ) vision optical dreaming scaling quantum simulations with ions (atoms) in an optical lattice trapping and cooling ion(s) in (hybrid) optical lattice atoms and ions in common 1D optical lattice*1 • (e.g. electron tunnling) • ions/spins in 2D/3D optical lattice*1 (old QS) • atoms and ion(s) in common 2D/3D optical lattice*1 • (new QS) *1priv. com. I.Cirac and P.Zoller • atom and ion in common optical trap • (no micromotion) • universal quantum computing • pushing gate*2 for ions in optical trap array • hybrid (Coulomb crystal in RF + optical lattice*2) ( ) ion separation + *2Nature: Cirac,Zoller (2010) *3NJP: Cirac group (2008)

summary: novel physics #2 #1 #3 decoherence = error scaling quantum simulations in ion traps • proof of principle on ions (and atoms) for quantum simulations • how to mitigate, how to exploit it • (chemistry/biology) • how to investigate (mesoscopic) decoherence bridging the gap (proof of principle studies and “useful” QS) • outperforming classical computation • deeper understanding of quantum dynamics(10x10 spins) investigate the impact on: - solid state physics (magnets, ferroelectrics, quantum Hall, high Tc) (quantum phase transitions, spin frustration, spin glasses,…) - quantum information processing / quantum metrology - cold chemistry (cold collisions) - …

IMPRS-APS Max-Planck Institute for Quantum OpticsGarching Deutsche Forschungsgemeinschaft PhDs: (Hector Schmitz) (Axel Friedenauer) Christian Schneider Martin Enderlein GS: Thomas Huber (Robert Matjeschk) (Jan Glückert) (Lutz Pedersen) TIAMO Trapped Ions And MOlecules QSim Quantum Simulations PhDs: Steffen Kahra Günther Leschhorn GS: Tai Dou news from the 3.8 fs beam line miac post doc position available

simulations and results: Munich 1972