simulations and results:

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simulations and results Munich 1972
Boulder 2040 stuff ion trappers dreams are
made of
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(No Transcript)
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experimental quantum simulations
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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
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more than one quantum simulator?
(a)addressing different questions
(b)addressing identical questions
NJP-special issue on quantum simulations
(04.2011) Tillman Esslinger, Chris Monroe, Tobias
Schaetz
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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.Blatts
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.Blatts 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)
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class 1
why simulating and not computing it ?
January 1670
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class 1
can not compute it? find an analog and simulate
January 1670
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class 1
can not compute it? find an analog and simulate
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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.Blatts 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.Blatts 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)
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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.Blatts
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.Blatts 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)
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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.Blatts 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.Blatts 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)
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Quantum simulation - H.Haeffners _at_ 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)
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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.Blatts
group Nature (2010) HT on Klein paradox
L.Lamata, T.Schaetz et al. PRL (2007) R.Blatts
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.Blatts 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)
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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
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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) Schaetzs group
Nature Physics (2008) Monroes group Nature (2010)
D.Porras talk on Tuesday
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Quantum simulation - Diegos _at_ 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...

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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
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pick one simulating quantum-spin-systems
how to simulate

• spin s
• magnetic field B
• spin-spin interaction J

quantum Ising model
XY model
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our spin/ion - 25Mg (I5/2)
Mg25 I5/2
(mf-4,.,4)
mf-4
P3/2 (S1/2, L1)
F4,3,2
(mf-3,.,3)
P1/2 (S1/2, L0)
F3,2
mf-2
???
mf-1
F2
mf0
mf1
mf2
S1/2 (s1/2, L0)
mf3
mf2
mf1
F3
mf0
mf-1
???
mf-2
mf-3
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lasers - 25Mg (I5/2)- 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
???
ñ1ñ ñ0ñ
2S1/2
1.79 GHz
???
ñ1ñ ñ0ñ
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e.g. quantum magnetism (B)
proposal Porras and Cirac 2004
e.g. quantum-Ising model
eff. magnetic field (global qubit-rotation)
???
???
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e.g. quantum magnetism (J)
e.g. quantum-Ising model
eff. magnetic field (global qubit-rotation)
F? -1.5 F?
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e.g. quantum magnetism (J)
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 )
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quantum baby phase transition
adiabatic evolution
detect
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summary whats up spins?
adiabatic transition
J

J
simulating a quantum magnet in an ion trap
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beyond the ground state
adiabatic evolution
excited state
energy level system up side down J
-J (simulating -HIsing)
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Simplest case of spin frustration - C.Monroes
J12J13J23 gt 0
K. Kim, et al., Nature 465, 590 (2010)
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Distribution of magnetization for N2,3,..9
spins (Uniform FM couplings) C. Monroes
Ferromagnet (d-function)
1.0 0.8 0.6 0.4 0.2 0.0
Binder Ratio
N9 (theory)
N2 (theory)
N2
N9
Paramagnet (Gaussian)
-N/2 0 N/2
mx
Ratio of transverse field to Ising coupling
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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
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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
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computing versus simulation

• Techniques for minimizing noise in an quantum
  simulation
• (Poster) Q 28.5 Di 1630 Uhr
• Towards two-dimensional quantum simulations with
  trapped ions
• (Talk) Q 21.1 Di 1630 Uhr

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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) -decoher
ence ?nature? -2 dimensional trap-lattice
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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
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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?)

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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
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objective 2
scaling exp. quantum simulations in surface ion
traps
state of the art 1
1group of D.Wineland (USNIST)

• extend into second dimension (arrays of ions)
• optimize architecture for quantum simulations (no
  cryogenics, large Jspin/spin)
• (potentially without lasers)

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R.SchmiedDidi 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 Mølmerphase 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

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Hensingers
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
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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
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Microwave magnetic (gates) interactions
Didis(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 610-9 1 mm trap
size l 1 mm h 2 p/l a0 310-5 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
Trap rf
Trap rf
GND
GND
I
I
I
proposal Christian Ospelkaus et al. PRL 101,
090502 (2008) related work ion molecule M.
Johanning et al., arXiv0801.0078 simulation
J. Chiaverini, W. Lybarger, PRA77, 022324 (2008)
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Magnetic Gradient Induced Coupling MAGIC
minimizing laser efforts DC -Wunderlichs
Schmidt-Kalers
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).)

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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
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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 (gt99)
• long range interaction (Jspin/spingt20kHz)

arrays of traps
I.Bloch
should not compete but complete
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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 lattice1
• (e.g. electron tunnling)
• ions/spins in 2D/3D optical lattice1
• (old QS)
• atoms and ion(s) in common 2D/3D optical
  lattice1
• (new QS)

1priv. com. I.Cirac and P.Zoller

• atom and ion in common optical trap
• (no micromotion)
• universal quantum computing
• pushing gate2 for ions in optical trap array
• hybrid (Coulomb crystal in RF optical lattice2)

( )
ion separation

2Nature Cirac,Zoller (2010)
3NJP Cirac group (2008)
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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) -
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Max-Planck Institute for Quantum Optics Garching
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