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

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

experimental quantum simulations

outline: experimental Quantum Simulations (QS) 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  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

(a)addressing different questions (b)addressing identical questions NJP-special issue on quantum simulations (04.2011) Tillman Esslinger, Chris Monroe, Tobias Schaetz more than one quantum simulator? ions: +individual addressability (not only detection) +large interaction strength (kHz not Hz) @ small decoherence rates +outstanding initialization /preparation however 1 : -scalability -intrinsically (+bosons/ -fermions) however 2 : +dream to combine advantages quantum simulator = universal quantum computer testing the “non-testable” Didi’s …

class 1 class 2 explore new physics in the laboratory (perhaps even trackable classically) outperform classical computation address the classically non-trackabkle different classes of quantum simulations 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) H.Landa, A.Retzker, B.Reznik et al. PRL (2010) + Poster #22 L.Lamata, T.Schaetz et al. PRL (2007) R.Blatt’s group Nature (2010) + HT on Klein paradox 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) Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it R.Ozeri et al., arXiv (2010) W.H.Zurek, P.Zoller et al. PRL (2005)

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

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

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

class 1 class 2 explore new physics in the laboratory (perhaps even trackable classically) outperform classical computation address the classically non-trackabkle different classes of quantum simulations 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) H.Landa, A.Retzker et al. PRL (2010) + Poster #22 L.Lamata, E.Solano, T.Schaetz et al. PRL (2007) R.Blatt’s group Nature (2010) + HT on Klein paradox 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) Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it R.Ozeri et al., arXiv (2010) W.H.Zurek, P.Zoller et al. PRL (2005) Blatt group (2010)

class 1 class 2 explore new physics in the laboratory (perhaps even trackable classically) outperform classical computation address the classically non-trackabkle different classes of quantum simulations 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) H.Landa, A.Retzker, B.Reznik et al. PRL (2010) + Poster #22 L.Lamata, T.Schaetz et al. PRL (2007) R.Blatt’s group Nature (2010) + HT on Klein paradox 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) Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it R.Ozeri et al., arXiv (2010) W.H.Zurek, P.Zoller et al. PRL (2005) Schaetz group (2010)

class 1 class 2 explore new physics in the laboratory (perhaps even trackable classically) outperform classical computation address the classically non-trackabkle different classes of quantum simulations 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) H.Landa, A.Retzker, B.Reznik et al. PRL (2010) + Poster #22 L.Lamata, E.Solano,T.Schaetz et al. PRL (2007) R.Blatt’s group Nature (2010) + HT on Klein paradox 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) Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it R.Ozeri et al., arXiv (2010) W.H.Zurek, P.Zoller et al. PRL (2005)

Ions move collectively Quantum simulation - H.Haeffner’s @ Berkeley Frenkel-Kontorova model: How does a chain of ions move in a periodic potential ? from: www.nano-world.org 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)

class 1 class 2 explore new physics in the laboratory (perhaps even trackable classically) outperform classical computation address the classically non-trackabkle different classes of quantum simulations 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) H.Landa, A.Retzker et al. PRL (2010) + Poster #22 L.Lamata, T.Schaetz et al. PRL (2007) R.Blatt’s group Nature (2010) + HT on Klein paradox 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) Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it R.Ozeri et al., arXiv (2010) W.H.Zurek, P.Zoller et al. PRL (2005) 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

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

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

-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... Quantum simulation - Diego’s @ Madrid

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

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

lasers - 25 Mg + (I=5/2)- transitions 2 P 1/2 2 P 3/2 2 S 1/2  1.79 GHz ~ 200 GHz    F = 3, m F = -3     F = 2, m F = -2   Detection (   ) Raman quantum state of motion (harmonic oscillator) 280 nm     ~ 2750 GHz repump

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

e.g. quantum-Ising model: eff. magnetic field (global qubit-rotation) BxBx P 3/2 P 1/2 S 1/2 eff. spin-spin Interaction J (conditional optical dipole force) F  = -1.5 F  e.g. quantum magnetism (J)

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

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

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

“beyond” the ground state excited state adiabatic evolution ( + ) entanglement 1010 degenerate excited state: energy level system up side down: J -J (simulating -H Ising )

Simplest case of spin frustration - C.Monroe’s AFM J 12 =J 13 =J 23 > 0 ? K. Kim, et al., Nature 465, 590 (2010) |  = |  +|  +|  +|  +|  +|  ground state is entangled B x =0 P 0 P 1 P 2 P 3 |    = |  +|  +|  still entangled! symmetry breaking field B x |    = |  +|  +|  still entangled! Bx0Bx0 P 0 P 1 P 2 P 3 Frustration  Entanglement

0.01 0.1 1 10 Ratio of transverse field to Ising coupling N=2 N=9 (theory) N=2 (theory) Ferromagnet (  -function) Paramagnet (Gaussian) 1.0 0.8 0.6 0.4 0.2 0.0 “Binder Ratio” Distribution of magnetization for N=2,3,..9 spins (Uniform FM couplings) – C. Monroe’s mxmx -N/2 0 +N/2

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

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?) ?+??+?

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

optimized surface electrode trap array optimized current carrying wires to implement interactions (Sørensen Mølmer+phase gates) R.Schmied+Didi: It might look like this… 2D lattice of ions, cooled and optically pumped by lasers 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 Schmied,Wesenberg, Leibfried PRL(2009)

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 Hensinger’s

other ways for scaling: Ion arrays in Penning traps 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 0.5 mm Richard Thompson Dany Segal, (Wini + Ferdiand) Crick et al (Imperial College), Optics Express 2008 B John Bollinger

Microwave magnetic (gates) interactions – Didi’s (Christian Ospelkaus, Ulrich Warring) 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) critical for motional excitation: field gradient over wavepacket size a 0  10 nm (Be +, 5 MHz) plane wave: = 30 cm  =k a 0 = 6×10 -9 1 mm trap size: l= 1 mm  =2  /l a 0 = 3×10 -5 30  m trap size: l= 30  m  =2  /l a 0 = 0.001 729 nm/Ca + : = 729 nm  =k a 0 = 0.03 313 nm/Be + : = 313 nm  =k a 0 = 0.1 Trap rf GND I ~ 30  m BzBz 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

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

objective #3 for 30 years: atoms in optical fields should not compete but complete  individual addressability  operations of high fidelity (>99%)  long range interaction (J spin/spin >20kHz) + I.Bloch arrays of traps for 60 years: ions in radio frequency fields sharing advantages of ions and optical lattices: first step in our lab: trapping an ion in optical dipole trap* -loading and cooling in rf-trap -dipole trap on / rf-trap off - detection in rf-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

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) optical dreaming * 1 priv. 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 ) scaling quantum simulations with ions (atoms) in an optical lattice vision + ( ) ion separation * 3 NJP: Cirac group (2008) * 2 Nature: Cirac,Zoller (2010) ( )

summary: novel physics #1 #2 #3  how to mitigate, how to exploit it (chemistry/biology)  how to investigate (mesoscopic) decoherence  proof of principle on ions (and atoms) for quantum simulations scaling quantum simulations in ion traps 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 T c ) (quantum phase transitions, spin frustration, spin glasses,…) - quantum information processing / quantum metrology - cold chemistry (cold collisions) - … decoherence = error

Max-Planck Institute for Quantum Optics Garching Deutsche Forschungsgemeinschaft IMPRS-APS PhDs: Steffen Kahra Günther Leschhorn GS: Tai Dou 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 news from the 3.8 fs beam line miac post doc position available

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

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

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