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Quantum computing with Rydberg atomsKlaus Mølmer
Coherence school
Pisa, September 2012
• Rydberg physics and Rydberg blockade • Rydberg physics and quantum information
- quantum computing
- pure state quantum control of ensembles
- quantum phase transitions
• Rydberg and many-body physics• Rydberg physics and quantum (n.l.) optics
Review paper: M. Saffman et al: Rev. Mod. Phys. 82, 2313–2363 (2010).
Outline
Johannes Robert Rydberg, 1854-1919 Albert Victor Bäcklund, 1845-1922
Rydberg atoms
Large principal quantum numbers
Very large orbitals,
Large dipoles ~n2
Long lifetimes
Rydberg blockade
∆E ~ 1/ R6 van der Waals
∆E ~ 1/ R3 static or resonant dipole
Neutral atoms interact weaklyRydberg states~100 kHz at few μm
~100 MHz at few μm
Rydberg blockade and quantum information
Rydberg blockade gate:Jaksch et al, PRL 85, 2208 (2000)
Saffman et al,
Grangier et al
conditional gates on many targets
Rydberg blockade and quantum information
Long distance gates
Multi-qubit gates in one operation
See also: Rydberg Quantum Simulators, Weimer et al
=
C-NOT
C-NOTk
multi-target
Ck-NOT
multi-control
EASY
L. Isenhower, M. Saffman, K. Mølmer, Multibit Ck-NOT quantum gates via Rydberg blockade, Quantum Inf Process 10, 755 (2011).
2k+3 pulses
5 pulses
Rydberg blockade and quantum information
x
Grover:
1) Σcx |x> Σ (-1) f(x) cx |x> (-1) if x matches the “marked“ x0
2) Inversion of cx about their mean.
Rydberg blockade and quantum information
x1/√N
~3/√N
Repeat √N times
Grover:
1) Σcx |x> Σ (-1) f(x) cx |x> (-1) if x matches the “marked“ x0
2) Inversion of cx about their mean.
1) Is every bit OK?Excite from ”wrong state” change of sign, … and two errors do not cancel.
2) Change of sign of all statesbut the symmetric one |s> = Σ|x> = (|0> +| 1>)k
Excite from ”wrong state” (|0> - |1>).
Rydberg blockade and quantum information
2k π-pulses
2k π-pulses
One Grover step in 4k π-pulses4k < 49k-149 one and two-bit gatesNeed √N Grover steps
Mutual Bss small, ”ancilla” Bsr bigOne Grover step in 8 π-pulses
Klaus Mølmer, Larry Isenhower, Mark Saffman, Efficient Grover search with Rydberg blockade, J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 184016
Rydberg blockade and quantum information
Missing atom = no Rydberg excitation50 % chance: all remaining qubits are correct50 % chance:all remaining qubits are random
Filtering and majority votedetermines all qubits in few trials
Figure: Grover search with 40 atoms 20 atoms are lost in each trialAfter 10 trials, all 40 bits are guessedcorrectly with high probability. D. D. Bhaktavatsala Rao and KM in preparation
Rydberg blockade and quantum information
Symmetric collective excitation of a single atom into
different internal states: encoding bit value 1
… |N>|2>|1>
|0>
…
E. Brion,et al , Phys. Rev. Lett. 99, 260501 (2007)
|r>
Rydberg blockade and ensemble qubits
… |N>|2>|1>
|0>
…
Number of bits ~ number of states (linear scaling)!!!
|r> |r’>
Rydberg blockade and ensemble qubits
A 14 bit computer in a Cs cloud
… and 127 bits (!) in a cloud of holmium.
Rydberg blockade and ensemble qubits
Ho 4I15/2 ground
state contains 128 hyperfine states!!!
Distributed computing on different clouds with flying qubits
Long distance quantum communication
Multi-atom collective effects in light emission
(phase matching and ”superradiance”).
Directional single photon
source (collective em.)
Saffman and Walker, 2005.
Rydberg ensemble qubits and light-matter interface
Rydberg ensemble qubits and light-matter interface
Repeater with on-board distillation
Anne Nielsen and KM, PRA
Line Pedersen and KM, PRA
Combine multi-bit ensembles and
single-photon interfaces:
Entangled pulses on-demand
Quantum (atom) optics
n atoms
0 or 1 atom
N-n atoms
|r>
Quantum state of ground state occupation numbers: |n>
-- second quantization, coupled oscillator, collective spins, …
Spin squeezed states, Schrödinger cat states, NOON states
Ressource states for clocks, magnetometers, navigation,
light emission, quantum computing, QM tests, …
Quantum (atom) optics
n atoms
0 or 1 atom
Rydberg blockade:
blocks state transfer
non-linear coupling strengths Ω√n
Jaynes-Cummings simulator
… many proposals by ”the usual suspects”.
N-n atoms
|r>
Quantum (atom) optics
EIT, STIRAP=100 % transfer
|g> |r>
|gg> |gg>-|ee>
… |g … g> ???
D. Møller et al
Quantum (atom) optics
n or n-1 atoms
0 or 1 atomΩ√n: |n,0> |n-1,1>
Jaynes-Cummings dynamics
Eigenenergies: +/- Ω2√n
N-n atoms
|r>
a+b + b+a = Jx
Eigenenergies : Ω1 mx
|e>
|g>
Adiabatic multi-atom ”dark state”
|0,0>JC = |gN>
↨
|Jx=0> Dicke state
|Jx=0> |r> if N is odd
odd/even: phase Schr. Cat.
Quantum phase transition ?
Rydberg blockade and many body physics
A resonant laser will only excite one atom, further excitation is blocked
Partial suppression of excitation in large clouds
Büchler, Zoller, Pupillo et al.
Pohl, Demler, Lukin
Rydberg dressing
Rydberg blockade and (non-lin.) quantum optics
M. Fleischhauer, et al.,
Lukin et al
C. Adams et al
Saffman and Walker
A. Kuzmich et al
Summary
• Rydberg blockade is one among many proposals for quantum information processing.
• Rydberg blocked ensembles has unique features:
special multi-particle gates, long distance with selectivity• Rydberg blocked ensembles are ”hybrid in a single
system” (unique qubits, collective qubits, interface to light, microwaves, … .)
• Growing control capabilities, new ideas, new physics …