Diamond based quantum registers at room temperature

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) S807�S824

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 (10�s of nm spacing) Longer coherence times � T1 ~ minutes