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
vision  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
more than one quantum simulator?
(a)addressing different questions
(b)addressing identical questions
testing the “non-testable”
quantum simulator
=
universal quantum computer
NJP-special issue on quantum simulations (04.2011)
Tillman Esslinger, Chris Monroe, Tobias Schaetz
…
Didi’s
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
different classes of quantum simulations
class 2
class 1
explore new physics in the laboratory outperform classical computation
address the classically
(perhaps even trackable classically)
non-trackabkle
simulating analogues:
nonlinear interferometers
D. Leibfried, DJ.Wineland et al. PRL (2002)
Dirac equation
L.Lamata, T.Schaetz et al. PRL (2007)
R.Blatt’s group Nature (2010)
+ HT on Klein paradox
Solitons
H.Landa, A.Retzker, B.Reznik et al. PRL (2010)
+ Poster #22
early universe
Milburn PRL 2005
R.Schuetzhold, T.Schaetz et al. PRL (2007)
(quantum walks)
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)
(Duffing oscillator-Roee)
R.Ozeri et al., arXiv (2010)
Frenkel Kontorova model
Garcia-Mata et al., Eur. Phys. J. D (2007)
+ H.Haeffner working on it
Kibble-Zureck mechanism
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
class 1:
can not compute it? – find an analog and simulate
January 1670
March 2006
different classes of quantum simulations
class 2
class 1
explore new physics in the laboratory outperform classical computation
address the classically
(perhaps even trackable classically)
non-trackabkle
simulating analogues:
nonlinear interferometers
D. Leibfried, DJ.Wineland et al. PRL (2002)
Dirac equation
L.Lamata, E.Solano, T.Schaetz et al. PRL (2007)
R.Blatt’s group Nature (2010)
+ HT on Klein paradox
Solitons
H.Landa, A.Retzker et al. PRL (2010)
+ Poster #22
early universe
Milburn PRL 2005
R.Schuetzhold, T.Schaetz et al. PRL (2007)
(quantum walks)
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)
(Duffing oscillator-Roee)
R.Ozeri et al., arXiv (2010)
Frenkel Kontorova model
Garcia-Mata et al., Eur. Phys. J. D (2007)
+ H.Haeffner working on it
Blatt group (2010)
Kibble-Zureck mechanism
W.H.Zurek, P.Zoller et al. PRL (2005)
different classes of quantum simulations
class 2
class 1
explore new physics in the laboratory outperform classical computation
address the classically
(perhaps even trackable classically)
non-trackabkle
simulating analogues:
nonlinear interferometers
D. Leibfried, DJ.Wineland et al. PRL (2002)
Dirac equation
L.Lamata, T.Schaetz et al. PRL (2007)
R.Blatt’s group Nature (2010)
+ HT on Klein paradox
Solitons
H.Landa, A.Retzker, B.Reznik et al. PRL (2010)
+ Poster #22
early universe
Milburn PRL 2005
R.Schuetzhold, T.Schaetz et al. PRL (2007)
(quantum walks)
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)
(Duffing oscillator-Roee)
R.Ozeri et al., arXiv (2010)
Frenkel Kontorova model
Garcia-Mata et al., Eur. Phys. J. D (2007)
+ H.Haeffner working on it
Kibble-Zureck mechanism
W.H.Zurek, P.Zoller et al. PRL (2005)
Schaetz group (2010)
different classes of quantum simulations
class 2
class 1
explore new physics in the laboratory outperform classical computation
address the classically
(perhaps even trackable classically)
non-trackabkle
simulating analogues:
nonlinear interferometers
D. Leibfried, DJ.Wineland et al. PRL (2002)
Dirac equation
L.Lamata, E.Solano,T.Schaetz et al. PRL (2007)
R.Blatt’s group Nature (2010)
+ HT on Klein paradox
Solitons
H.Landa, A.Retzker, B.Reznik et al. PRL (2010)
+ Poster #22
early universe
Milburn PRL 2005
R.Schuetzhold, T.Schaetz et al. PRL (2007)
(quantum walks)
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)
(Duffing oscillator-Roee)
R.Ozeri et al., arXiv (2010)
Frenkel Kontorova model
Garcia-Mata et al., Eur. Phys. J. D (2007)
+ H.Haeffner working on it
Kibble-Zureck mechanism
W.H.Zurek, P.Zoller et al. PRL (2005)
Quantum simulation - H.Haeffner’s @ Berkeley
Frenkel-Kontorova model:
How does a chain of ions move in a periodic potential ?
Ions move collectively
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)
different classes of quantum simulations
class 2
class 1
explore new physics in the laboratory outperform classical computation
address the classically
(perhaps even trackable classically)
non-trackabkle
simulating analogues:
nonlinear interferometers
D. Leibfried, DJ.Wineland et al. PRL (2002)
Dirac equation
L.Lamata, T.Schaetz et al. PRL (2007)
R.Blatt’s group Nature (2010)
+ HT on Klein paradox
Solitons
H.Landa, A.Retzker et al. PRL (2010)
+ Poster #22
early universe
Milburn PRL 2005
R.Schuetzhold, T.Schaetz et al. PRL (2007)
(quantum walks)
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)
(Duffing oscillator-Roee)
R.Ozeri et al., arXiv (2010)
Frenkel Kontorova model
Garcia-Mata et al., Eur. Phys. J. D (2007)
+ H.Haeffner working on it
Kibble-Zureck mechanism
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
explore new physics in the laboratory outperform classical computation
address the classically
(perhaps even trackable classically)
non-trackabkle
simulating analogues:
simulating solid state physics:
nonlinear interferometers
Dirac equation
D.Porras and I.Cirac PRL (2004)
Bose-Hubbard model
Solitons
D.Porras, I.Cirac et al. PRA (2008)
Spin boson model
D.Porras and I.Cirac PRL (2004)
Schaetz’s group Nature Physics (2008)
Monroe’s group Nature (2010)
quantum spin Hamiltonians
(e.g.
quantum Ising
spin frustration)
early universe
(quantum walks)
Anderson localization
(Duffing oscillator-Roee)
Frenkel Kontorova model
Kibble-Zureck mechanism
D.Porras
+talk on Tuesday
three particle interaction
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
HI[i, j ,l ]  Ji, j ,l  iz zj  lz
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...
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
vision  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
pick one: simulating quantum-spin-systems
+
how to simulate
H  J  iz zj  B x  ix
i, j
spin 
magnetic field B
spin-spin interaction J
quantum Ising model
i
H  J x  ix xj  J y  iy jy
i, j
HJ
x
 
x
i
i, j
XY model
i, j
x
j
J
y
 
y
i
i, j
y
j
J
z
 
z
i
i, j
z
j
Heisenberg
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=-3
mf=-2
mf=-2
mf=-1
mf=-1
mf=0
mf=0
mf=1
mf=1
F=2
mf=2
mf=2
mf=3
F=3
S1/2 (s=1/2, L=0)
lasers - 25Mg+ (I=5/2)- transitions
~ 200 GHz
2P
3/2
  F = 3, mF = -3
  F = 2, mF = -2
~ 2750 GHz
2P
1/2
quantum state
of motion
(harmonic oscillator)
Detection (-)
Raman
280 nm
repump




1.79 GHz


2S
1/2
e.g. quantum magnetism (B)
proposal Porras and Cirac 2004
e.g. quantum-Ising model: H  J
z z
x
x



B

 i j  i
i, j
i
eff. magnetic field
(global qubit-rotation)
P

pulse duration
effective
coupling

Bx
e.g. quantum magnetism (J)
e.g. quantum-Ising model: H  J
 
z
i
i, j
eff. spin-spin Interaction J
(conditional optical dipole force)
F= -1.5 F
B
x

x
i
i
eff. magnetic field
(global qubit-rotation)
P3/2
P1/2
S1/2
z
j
Bx
e.g. quantum magnetism (J)
e.g. quantum-Ising model:
H  J  iz zj  B x  ix
i, j
eff. spin-spin Interaction J
(conditional optical dipole force)
i
eff. magnetic field
(global qubit-rotation)
all parameters to be chosen individually:Bx
(e.g. amplitude, range, anti- or ferromagnetic phase …)
amplitude
quantum “baby” phase transition
adiabatic evolution
+
n<0.03
J(t)
B
duration
prepare
initialize
simulate
i
detect
ground state
ground state
B x   ix
(analyse)
| J / B | 1
x
J  iz zj
i, j
summary: what’s up spins?
H  - B   J   
x
x
i
z
i
i
Bx
adiabatic transition:
- B x ( x   x )
1
2
z
j
i, j
fidelity(
v
)
Jmax
J
Bx=|J(t)|
+
98%+- 2%
J
z
z
J 
1 2
simulating a quantum magnet in an ion trap
“beyond” the ground state
excited state
B x   ix
adiabatic
evolution
excited state
J  iz zj
B J
x
i
i, j
energy level system up side down: J
(simulating -HIsing)
degenerate excited state:
( 10
+
01
entanglement
)
-J
Simplest case of spin frustration - C.Monroe’s
AFM
AFM
?
AFM
J12=J13=J23 > 0
ground state is entangled
Bx=0
|Y = | +|+| +| +|+|
symmetry
breaking
field Bx
|Y = | +|+|
still entangled!
P0
P1
P2
P3
P2
P3
Bx0
|Y2 = | +|+|
still entangled!
Frustration  Entanglement
P0
P1
K. Kim, et al., Nature 465, 590 (2010)
Distribution of magnetization for N=2,3,..9 spins
(Uniform FM couplings)
– C. Monroe’s
1.2
“Binder Ratio”
3 mx2
2
- mx4
2m
2 2
x
1
1.0
Ferromagnet
(d-function)
N=9
(theory)
0.8
0.8
0.6
0.6
N=2
(theory)
N=2
0.4
0.4
N=9
Paramagnet
(Gaussian)
0.2
0.2
-N/2
0
mx
+N/2
0.0
0
0.01
0.01
-0.2
0.1
0.1
11
Ratio of transverse field to Ising coupling
10
10
By
NJ xx
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
vision  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
normalized fluorescence
radial modes: two qubit geometrical phase gate
1.0
+
0.8
0.6


0.4
0.2
0.0
gate time 39 s
0
20
40
60
80
time (s)
fidelity(
)~ 97%+- 1%
+
gate duration down to 5 s
General formalism by:
Milburn, Schneider, James (1999)
Sorensen & Molmer (1999,2000)
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
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
vision  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
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?)
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
vision  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
objective #2
scaling exp. quantum simulations
in surface ion traps
our “old” trap
state of the art 1
1D +
!cryogenics!2
h<
~ rf
2I.Chuang
1group
of D.Wineland (US:NIST)
(US:MIT); C.Monroe (US:Michigan)
Blatt/Roos (EU:Innsbruck); 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
optimized surface electrode trap array
optimized current carrying wires to implement interactions
Schmied,Wesenberg, Leibfried PRL(2009)
(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
John Bollinger
Richard Thompson
Dany Segal,
(Wini + Ferdiand)
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:
1 mm trap size:
30 m trap size:
729 nm/Ca+:
313 nm/Be+:
l= 30 cm
l= 1 mm
l= 30 m
l= 729 nm
l= 313 nm
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
proposal:
related work:
h=k a0 = 6×10-9
h=2 p/l a0 = 3×10-5
h=2 p/l a0 = 0.001
h=k a0 = 0.03
h=k a0 = 0.1
Bz
30 m
GND Trap rf
I~
I ~ Trap rf I ~
GND
Christian Ospelkaus et al. PRL 101, 090502 (2008)
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
individual addressing using magnetic field gradient
M. Johanning et al., PRL 102 , 073004 (2009)
Magnetic Gradient Induced Coupling: MAGIC
B
N
J
i j
ij
z,iz , j
Yb+
•
Quantum Simulations
(see also Review: M. Johanning et al. J. Phys. B 42, 154009 (2009).)
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
vision  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
objective #3
sharing advantages of ions and optical lattices:
for 60 years:
ions in radio frequency fields
for 30 years:
atoms in optical fields
individual addressability
+
operations of high fidelity (>99%)
long range interaction (Jspin/spin>20kHz)
arrays
of traps
I.Bloch
should not compete but complete
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
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)
ion separation
universal quantum computing
pushing gate*2 for ions in optical trap array
+
(
hybrid (Coulomb crystal in RF + optical lattice*2)
*2Nature: Cirac,Zoller (2010)
*3NJP: Cirac group (2008)
)
summary: novel physics
#2
#1
decoherence = error
#3
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)
bridging the gap
(proof of principle studies and “useful” QS)
how to investigate
(mesoscopic) decoherence
 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)
-…
Max-Planck Institute for Quantum Optics
Garching
Deutsche Forschungsgemeinschaft
IMPRS-APS
TIAMO
PhDs:
Trapped Ions
And MOlecules
Steffen Kahra
Günther Leschhorn
GS:
Tai Dou
news from the
3.8 fs beam line
PhDs:
(Hector Schmitz)
(Axel Friedenauer)
QSim
Christian
Schneider
Quantum
Simulations
Martin Enderlein
GS:
Thomas Huber
(Robert Matjeschk)
(Jan Glückert)
(Lutz Pedersen)
miac
post doc position
available