Physics Department, Harvard University

Quantum control of individual electron and nuclearspins in diamond lattice

Mikhail Lukin

Collaborators:L.Childress, M.Gurudev Dutt, J.Taylor, D.Chang, L.Jiang,A.Zibrov (Harvard)A.Sorensen (Niels Bohr Institute)P.Hemmer (Texas A&M)F.Jelezko, J.Wrachtrup (Stuttgart)

$ ARO-MURI, NSF, Sloan and Packard FoundationsQuickTime™ and a

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Today’s talk

• Introduction: quantum control from AMO to solid-state

• Quantum control of single electron spins

System: electron spin in Nitrogen Vacancy (NV) center in diamond

Understanding mesoscopic environment of single electron spin:

13 C nuclei as a leading decoherence source

• Scaling up using quantum opticsNew ideas and new tools

• Quantum control of single nuclear spins

Single nuclear spin addressing via quantum back-action from electron

Coherent coupling of electron and nuclear spin qubits

NMR on a single spin

Quantum control: from AMO to solid state

• Solid-state quantum systemsNew opportunities:

tight confinement, fast operations strong interactions“easy” entanglement

New challenges: understand complex solid-state environmentdevelop quantum control techniques

Promising, stable qubit candidate We show that interaction with lattice nuclei determine coherence

properties and that (nuclear spin) environment can be understood, controlled and utilized as a resource

• Electron spin as quantum bit

Phonon Relaxation

System: NV color center in high-purity diamond

Optical properties• Sharp zero-phonon emission line @ 637 nm

+ phonon sidebands 650-730 nm• Can be excited either by 637 nm or 532 nm

• detectable via state-selective fluorescence

Ground state properties• non-zero electronic spin (S=1)• microwave transition:

zero-field splitting Δ=2.88 GHz

|Sz||=1Sz =0

“Nature’s own trapped molecular ion”

Early work: S.Rand, N.Manson

Scanning confocal microscope image

Single photon source: ~100,000 cts/sec (Paris, Munich,..)

20 μm copper wire

MW

Permanent magnet 3-axis

Hall sensor

N.A. 1.3 oil immersion

objectiveDichroic

532 nm

fluorescence

APD

APD

Experimental probing of single centers

Preparation and probing of single spins

0

1−1

e0e1

e−1

S

Phonon emission

Optical excitation:•State selective fluorescence

•Electron spins polarization (>90%)

…enables• Manipulation spin states using microwave ESR • Detection using spin-dependent fluorescence

at room temperature

2.88 GHz

Contrast limited by competition of optical pumping and shelving effects (improves with efficient collection)

Calibrates measurement efficiency for other data

First experimentsF.Jelezko, J.Wrachtrup (Stuttgart)

Rabi oscillations of single electron spin

8 MHz MW detuning Overall decay on a 1-2 μs scale

“Beating” of modulation components Each center is different!

Single spin coherence via Ramsey spectroscopy

“Classic” probe of coherence properties

Signatures of complex, non-Markovian environment:can we understand, control it?

Mesoscopic environment of NV centerStiff, mostly spinless 12C latticePossible contributors to dephasing:

• Contact hyperfine interaction: single N nuclear spin (I=1)

• Coupling to remote spins, e.g.:C13 nuclear spins (few percent)

N (impurity) electron spins:need pure samples

N

Theory: mesoscopic spin bath

effective “nuclear” fieldlocal (N) non-local

nuc

nuc

Dephasing of electron spin by mesoscopicenvironment

Dephasing: a large number (1000s) of nearby spins contribute

Bnuc

S

Effect of surrounding spins: • Few spins => few modulation frequencies • Many spins => dephasing

High “nuclear temperature” =>random nuclear field

Nuclear spins evolve slowly:long correlation time of the environment

for 1.1% abundance 13C

Probing single electron coherence via spin echo

…results in much longer coherence

Bnuc

Sx

Typical echo decay …

a tool to understand the dynamics of the local environment

E.Hahn 1950s

The spin echo signal is only sensitive to changes in the environment which happen faster than τ

Single spin echo in magnetic field

Echo envelope on longer time scale…

…periodically collapses and revives

Big effect: T2 >200 μs ~ 200 T2*!

Suggests periodic dynamics of electron environment

Dynamics of spin environment in B fieldMain reason for echo evolution: changes in Bnuc

Nuclear Larmor evolution leads to⇒ de-correlation of Bnuc⇒ re-phasing after one Larmor period

Beff

Sx

Echo revives when waiting interval matches Larmor period!

L. Childress, M.G.Dutt, J.Taylor et al, Science, in press

A picture of single electron environment: 13C nuclei in diamond lattice

Environment as a resource: can we address and use individual isolated 13C nuclei in diamond lattice?

13C

Coupled electron-nuclear system: more detailed view

S

In weak B field electron dynamics is conditional upon nuclear state and vice versa => entanglement

Larmor

I(j)Hyperfine interaction of electron with single nuclear spin I(j)

Many spins in bath Decoherence!

hyperfine

ms

Echo signal resulting from single nucleus

Sj

0

1

Larmor collapse and revival

…displays coherent electron-nuclear spin dynamics

τFast modulation (hyperfine)

rj

Proximal nuclei are special: back-action from electron

Two effects of electron on proximal nuclei due to hyperfine field:

• larger hyperfine splitting

Hyperfine coupling enhances nuclear magnetic moment

• Hyperfine interaction mixes electronic and nuclear states: response to B-field given by g-tensor

Atomic physics of spin bath

Proximal nuclei are very special: they precess faster

• enhanced Larmor frequency

electron moment

Substantial enhancement even for weak mixing since

hyperfine level mixing

Coherent dynamics involving individual nuclear spins

Most display periodic entanglement and disentanglementwith (some) isolated nuclear spin(s)

L. Childress, M.G.Dutt, J.Taylor et al

Each NV center has its own, specific dynamics

Fast hyperfine modulation

Larmor envelope

Coupling to proximal 13C: nuclei-resolving microscopeEcho modulation frequencies for different centers

Fast component

• level mixing and μ enhancement depend on relative distance

Confirms the model

13 C

Allows to determine coupling constantsfor individual nuclear spins, information on positions

… and B-field orientation relative to S-I axis!

Coherent, deterministic coupling to isolatedsingle nuclear spins in diamond lattice

Addressing of well-defined, isolated nuclear spins possible (up to 3)Coherent, controllable two-qubit (or few qubit!) system

L. Childress, M.G.Dutt, J.Taylor, A.Zibrov, F.Jelezko, J.Wrachtrup, P.Hemmer and M.D.L, Science, in press (2006)

Theory

SI(j)

Watching single nuclear spin precessionPulse sequence to map qubits between electron to nuclear spin

MW

π/2

π/ω j,1

π/2

π/ω j,0

polarize polarize measure

nuclear polarization Larmor precession mapping to electron

M.Gurudev Dutt. L.Childress et al

NV E 20 Gauss

Larmor delay (μs)

Example: single nuclear spin dynamics

• NMR on single, isolated nuclear spin!

Nuclear spin as robust quantum memory

Isolated nuclear qubit: potential for excellent quantum memory

Second long coherence times are expected for isolated nuclear spins!

How well is 13C really isolated (e.g. from nearby electron)?Example: cycling electron with green light during nuclear precession

0.8

0.6

0.4

0.2

0 1 2

green pulse duration, μs

prec

essi

on a

mpl

itude

Preliminary dataB = 20 Gauss

3 4

>200 photonsscattered

Outlook: useful quantum processors from two qubits

Nuclear spinElectron spin

Quantum emitter

Electron entanglement via photon scattering & single photon interference

Operations between any pairs can be performed simultaneously: purely optical scaling for

quantum communication & computationTheory:L.Duan, M.Lukin, I. Cirac, P.Zoller Nature 2001, atomic ensemblesL.Duan, C.Monroe (ions)L.Childress, J.Taylor, A.Sorensen. MDL PRL 06, quantum repeatersL.Jiang et al, (06) deterministic computation

Deterministic quantum gates between remote nuclei via electron-nuclear coupling:high fidelity and rates for modest collection efficiency

Summary: single spin environment can be understood, controlled and utilized

Coherent manipulation of single electronspin using AMO techniques

-

Understanding mesoscopic environment ofsingle electron via spin echo

Coherent manipulation of individual proximal nuclei: single spin NMR

Quantum optical techniques for wiring up multi-qubit systems

A new frontier on the interface of AMO and cond-mat physics