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Next application of quantum computers
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1. Diamond based quantum registers at room temperature Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond, L. Childress, M.V. Gurudev Dutt, J.M. Taylor, A.S. Zibrov, F. Jelezko, J. Wrachtrup, P.R. Hemmer, M.D. Lukin. SCIENCE 314 (5797): 281-285 OCT 13 2006
Quantum register based on individual electronic and nuclear spin qubits in diamond, Gurudev Dutt, M. V., Childress, L., Jiang, L., Togan, E., Maze, J., Jelezko, F., Zibrov, A. S., Hemmer, P. R., Lukin, M. D., SCIENCE 316 (5829): 1312-1316 JUN 1 2007
2. Next application of quantum computers Long distance secure quantum communication Fidelity of photons degrades exponentially with distance
Quantum entanglement can convert into polynomial distance penalty
Quantum repeaters
Entangle adjacent nodes
Local quantum operations in nodes extend range of entanglement
3. Key requirements of quantum repeaters Nodes
Few qubit quantum computers
Optical initialization and readout
Long term storage
Stored qubits isolated from optical I/O
Entanglement between nodes
High fidelity coherent photon capture
Single-photon generation
4. Nitrogen-vacancy (NV) diamond Vacancy with one adjacent carbon replaced by nitrogen
Can have two charge states NV0 and NV-
Natural or HPHT diamond, NV- usually (not always) stable
CVD both stable
Laser excitation can interconvert
NV- has 6-electrons (2 holes)
Ground state triplet
Create NVs by irradiation followed by anneal at ~750 C
Nitrogen-rich Type Ib diamond
electron, neutron, ion irradiation
Pure Type IIa diamond nitrogen implant
Optical zero-phonon line 637 nm
Laser diode
Optical absorption sideband
DPSS laser, ex: 532 YAG
5. Room temperature spin initialization Shine flashlight on NV diamond at room temperature
~ 80 % electron spin orientation in bulk
Near 100% orientation for selected single NVs
6. Room temperature spin readout Meta-stable singlet
~30% suppressed fluorescence for Sx and Sy states
Single-shot readout fidelity ~95% requires SNR ~ 10 = sqrt(100)
100 photons needed
Sz cycling transition gives ~ 1000 photons before spin flip
Fluorescence collection efficiency > 10 % needed
Currently have 2% -- need cavity or waveguide
7. Readout fidelity improvement by selective detection Both excited spin states decay exponentially with time
Therefore ratio becomes large with time
Idea: Wait before detection
Discrimination improved
Disadvantage: Most photons are lost
8. Single crystal diamond waveguides 3-D waveguides undercut in single crystal diamond
2 MeV He implant followed by wet etch and anneal
Damaged diamond layer below surface removed by acid etching
Focused ion beam milling for lateral structures
9. Room temperature solid state optical cavities Purcell factor neglects atom lifetime
Assumed long compared to cavity photon lifetime
Room temp, solid state replace cavity linewidth w/ atom linewidth
Example: NV sidebands ~ 20 nm
Cavity volume ~ l3, max Q ~ 700/20 = 35
Room temperature -- need small mode volume
Minimum mode volume ~ l3
11. Room temp spin lifetime of NV diamond Long spin lifetime
weak dependence on temperature
even up to room temperature
Recent data (Stuttgart) 0.3 msec
12. Processing nodes for quantum repeaters Few qubit quantum computers
Optical initialization -- works at room temperature
Optical readout expected to work at room temperature
Fast single-qubit gates
Scalable nonlinear multi-qubit coupling
Long term storage
Minimum ~ milliseconds, prefer minutes
Stored qubits isolated from optical I/O
Long range entanglement between nodes
13. Single NVs at room temperature Ultra-pure diamond, single NVs easily resolved confocal microscope
14. NV with RF and optical excitation Scan RF frequency monitor fluorescence
When RF matches spin resonance fluorescence decreases
15. NV under pulsed optical excitation Illuminate NV with green laser monitor fluorescence
Exponential rise as spin polarizes
Spin readout possible only before complete polarization
High intensities ionization of NV complicates
16. NV with both optical and RF pulses RF manipulates electron spin, optical readout perturbs spin
Solution -- Apply RF in dark, polarize before & readout afterward
Same-pulse noise suppression
Compare counts at leading & trailing edge of detection pulse
17. Single qubit gate speed Electron spin Rabi flops 7 ns
50 W RF stripline with 4 micron gap
Recently increased to 2 ns
10 micron gap but thicker metal layer
Limitation is 1 ns electronics clock
18. Ramsey fringes in NV spin coherence RF power broadens spin coherence
Apply two p/2 pulses pump & probe
Phase shifts accumulate between pulses
Can scan detuning for fixed delay time
Can scan time for fixed detuning
Nitrogen hyperfine is like fixed detuning
Three transition frequencies give beating
Decay is due to fluctuations in spin bath
Large number of spins random alignment
Weighted sum of cosine waves (centered at dc)
Coherence time = T2* = 1.7 msec
19. Spin echoes to suppress nitrogen nuclear effects Spin echo
Unequal wait times gives Ramsey fringe
Standard spin echo
Spin coherence detected with RF coil
NV requires final p/2 pulse
Convert coherence back into populations
20. Spin echo envelope decay Echo cancels both nitrogen nuclear and slow spin bath fluctuations
Spin bath fluctuations faster than echo sequence cause decay
RF pulse creates sudden change in electron spin
13C nuclei in spin bath precess around new B field
21. Spin echo revivals Precession of individual 13C in spin bath periodic
For distant 13C, Beff ~ B for all
Echo revivals at Larmor frequency
mCB = 1.071 kHz/Gauss
Revivals decay: mutual 13C spin flips
T2 = 0.24 msec
22. Frozen core Spins close to electron dominated by electron spin
Isolated from rest = frozen core
But not when electron spin is zero
Conditional evolution ? entangle
Now revivals have slow and fast parts
23. Enhanced Larmor frequency in frozen core For electron spin S+1, 13C hyperfine insensitive to applied B field
For electron spin S0, different Larmor frequencies observed
Much faster than bare Larmor frequencies
Maximum for B0 perpendicular to NV quantization axis
24. Electron nuclear coupling Drive electron-spin transition conditional on nuclear spin
25. Two qubit initialization Optical pumping polarizes electron
Selective RF & DC fields swap two levels
Second optical pumping step initializes both
Problems DC field always on, RF transition barely resolved
Repeat initialization sequence several times
26. Multiple coupled nuclear spins Allow 13C to precess for long time
Coherent oscillations of nuclear spin persist out to 0.5 msec
Well before coherence decay
Ramsey fringes -- Can lengthen with spin echo
Electron spin Ramsey fringes only microseconds
Complex dynamics comes from coupling to second nuclear spin
27. >> 20 msec nuclear spin coherence lifetime Nuclear spin echoes show no decay out to 20 msec
Bulk measurements show T2 ~ fractional seconds, T1 ~ hours
Expected to improve substantially for 13C-free host
28. Transfer of electron coherence to nucleus Use previous swap operation to transfer electron coherence to nucleus
29. Store arbitrary electron spin coherence on nuclear spin Initialize electron and nuclear spins
Create electron spin coherence with RF
Store in nuclear spin then retrieve
Analyze with second RF pulse and readout
30. Robust nuclear storage Optically re-initialize electron spin during nuclear storage
Nuclear spin coherence survives many initialization times
Project much better isolation if DC magnetic field is turned off
31. Arbitrary NV entanglement by optical measurement 2-D NV array imaged onto steering mirror array using microscope
Mirror array elements deflect NV emission to large steering mirrors
Large steering mirrors choose pair of NVs to combine on beamsplitter
Measurement entangles
NVs must be indistinguishable same optical resonance frequency
32. Control of NV optical selection rules C3v symmetry E is doublet -- 6 excited states
Non-axial strain lifts degeneracy
Electric field same effect as strain
Can have both Raman and cycling transitions
Upper Sz state can be 99.9% pure 106 cycles
Room temperature both branches excited
When both Sz states are pure room more cycles
33. OPTICAL RAMAN TRANSITION TEMPERATURE DEPENDENCE OPTICAL RAMAN OBSERVED UP TO 30 K
~ 1 kW/cm2
LINEAR DEPENDENCE
SINGLE NV EXCITATION ~ 1 MW/cm2
PROJECT OBSERVABLE UP TO LIQUID NITROGEN TEMPERATURES
34. Room temperature Raman ESR on single NV Nuclear spin coherence created by Raman on ESR transition
~ 1MHz compared to ~ 10 MHz wide ESR line
ESR broadened by optical read light and RF power
Optically detected ESR Also works with dc magnetic gradients
Works at room temperature, incoherent light
Optical initialization and readout of electron spin
Processing quantum information in diamond, Jorg Wrachtrup and Fedor Jelezko, J. Phys.: Condens. Matter 18 (2006) S807S824
35. Nitrogen-vacancy (NV) diamond advantages Room temperature
All elements for scalable solid-state quantum computer exist
Qubits = nuclear and/or electron spin states
Optical spin polarization = easy initialization
Spin-state selective optical readout (need 20% fluor collection for single shot)
Long coherence time ~ 0.3 msec so far
Many operations ~7 nsec Rabi flops = 50,000 operations
Controllable magnetic coupling of neighboring qubits (requires 1 nm spacing)
Liquid helium temperature All room temperature properties plus:
Long range photonic qubit coupling (needs cavity and/or plasmon structures)
Stark shift controlled optical transitions
Potential to interface w/ trapped ions (entangled photon pairs)
Optical Raman spin manipulation
Optical dipole-dipole coupling (10s of nm spacing)
Longer coherence times T1 ~ minutes