quantum computing with rydberg atoms klaus mølmer coherence school pisa, september 2012

Quantum computing with Rydberg atomsKlaus Mølmer

Coherence school

Pisa, September 2012

http://www.au.dk/da/

• 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


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


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.


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>).


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


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


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’>


A 14 bit computer in a Cs cloud

… and 127 bits (!) in a cloud of holmium.


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, …


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>


EIT, STIRAP=100 % transfer

|g> |r>

|gg> |gg>-|ee>

… |g … g> ???

D. Møller et al


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 …

quantum computing with rydberg atoms klaus mølmer coherence school pisa, september 2012

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