Quantum control of individual electron and nuclear spins in …jila · 2006-09-20 · Today’s...
Transcript of Quantum control of individual electron and nuclear spins in …jila · 2006-09-20 · Today’s...
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
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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