PBG CAVITY IN NV-DIAMOND FOR QUANTUM COMPUTING

1. PBG CAVITY IN NV-DIAMOND FOR QUANTUM COMPUTING Team: John-Kwong Lee (Grad Student) Dr. Renu Tripathi (Post-Doc) Dr. Gaur Pati (Post-Doc) Supported By: DARPA, AFOSR

2. OPERATIONS NEEDED FOR A QUANTUM COMPUTER STATE PREPARATION: e.g. OPTICAL PUMPING SINGLE BIT OPERATION: e.g. -PULSE TWO-BIT OPERATIONS: e.g. CNOT METHOD: LASER CONTROLLED SPIN EXCITATION (DARK RESONANCE) MEDIUM: SHB CRYSTAL, e.g. NV-DIAMOND

3. QUANTUM COMPUTING IN NV-DIAMOND: BASIC IDEA KEY FEATURES: BOTTOM LINES: SOLID STATE SCALABLE TO >1000 PARALLEL POSSIBLE (1 cm)3 (5 mm)3 SPIN AS QUBIT OPTICAL OPERATION & READOUT OPTICAL INTERCONNECT POSSIBLE >5000 OPS BEFORE DECOHERENCE NATURALLY SUITED TO TYPE 2 QC

4. ADIABATIC TRANSFER VIA THE DARK STATE |-> = (2|a> - 1|b>)/ |+> = (1|a> + 2|b>)/ |e |e |+> - |e> |a> - |e> |b> - |e> |->=|b> |->=|a> |- |+ |b |a |a> + |e> |b> + |e> |+> + |e> 1 EQUIVALENT TO A -PULSE AMPLITUDE TOPOLGICALLY ROBUST 0 TIME

5. METHOD 1: CAVITY ENHANCED COUPLING STEP 1: COHERENCE TRANSFER VIA CAVITY QED ATOM A ATOM B g 1 2 1 2 g g   0 0  1 1  A B A B

6. STEP 2: ENTANGLEMENT (CNOT) VIA CAVITY QED COHERENCE TRANSFER VIA RAMAN INITIAL CONDITIONS: ATOM A -- ELECTRON COHERENCE ATOM B -- NUCLEAR COHERENCE AFTER ADIABATIC TRANSFER: ATOM A -- PURE STATE ATOM B -- PRODUCT STATE “CNOT” WITH RAMAN p PULSE ATOM A ATOM B ATOM A ATOM B  1 2     1 2    PURE STATE PRODUCT STATE 1 2 RAMAN C-“NOT” e n e n 1 2 1  0 1 2 0 0 1 2 0 g g g g 1 2 1 2  2 0 0 1 2

7. ADIABATIC COHERENCE TRANSFER VIA CAVITY-QED DARK STATE ADIABATIC COHERENCE TRANSFER CAVITY VACUUM COUPLING g ATOM 1 ATOM 2 1 2 g INTENSITY 1 0 1 2 TIME RAMAN DARK STATES INITIAL ONE CAVITY PHOTON ATOM 1 ATOM 2 |e1> |e1 b2 0> |b1 e2 0> |e2> NO CAVITY PHOTONS 1 2 2 1 g g g g a b |b1> |a1> |a2> |b2> |a1 b2 0> |b1 b2 1> |b1 a2 0> |b1 b2 0> a b 0 1 2 g 12 1 g

8. DARK STATE QUANTUM COMPUTING IN NV-DIAMOND: NECESSARY ENERGY LEVELS g h g h c d a b c d e f a2 b2 a b e f a1 b1 QUBIT 1 QUBIT 2

9. DARK STATE QUANTUM COMPUTING IN NV-DIAMOND: ROLE OF STORAGE LEVELS c d a b e f a b c d c d b a b a b c d e f e f a a b e f

10. EXPLICIT CONSTRUCT FOR ENTANGLEMENT a c b b c a c a a a c b b a c b c b a a a

11. 2mI Df Df IZ DARK STATE QUANTUM COMPUTING IN SHB CRYSTAL: CANDIDATE MATERIALS IZ 5 g h 1 -1 g h 4.6 MHz 1D2 P 3 1 -1 4.8MHz 3E 1 Q 0 0 Pr:YSO NV-DIAMOND 1 e f c d -1 1 10.2 MHz 3H4 3 c d 4.6 MHz 3A1 17.3 MHz 1 -1 a b 2.8 MHz a b e 5 f 0 0 - Sgn(mI) SZ + 1 -1 [A] [B]

12. ISSUES WITH N-V DIAMOND SPIN-ORBIT COUPLING SOMEWHAT INHIBITED • RAMAN TRANSITIONS PARTIALLY FORBIDDEN • WORK NEAR ANTI-CROSSING, LEVELS MIX PERMANENT HOLE BURNING • NO CW SIGNAL, CITE RE-ARRANGEMENT • RE-PUMP ON PHONON SIDEBAND DYE LASER ARGON LASER REPUMP 638 nm ZERO PHONON LINE PHONON SIDEBAND S= ±1 ABSORPTION 2.88 GHz 120 MHz S= 0 514 638 0 1050 G B-FIELD WAVELENGTH (nm)

13. EXPERIMENTAL SETUP FOR DARK RESONANCE IN DIAMOND 18 LO APD 20 MHz D AOM ~638nm R APERTURE AOM R D P DIAMOND P C AOM C S = -1 B-FIELD A SCREEN S = 0 120 MHz DYE ARGON SPOTS ON SCREEN SPOT SIZES: ~ 0.3 mm BRAGG SIGNAL D R MATCHED INTENSITIES: (BEAT W/ LO) ® COUPLING -- 14 mW 13 W/cm 2 PROBE -- 14 mW P C A ARGON READ -- 16 mW REPUMP

14. DETECTION OF OPTICALLY INDUCED SPIN ALIGNMENT IN NV-DIAMOND 20 MHz P C R D S = -1 120 MHz S = 0 CAN BE INTERPRETED AS SPATIALLY VARYING COLLECTIVE SINGLE SPIN OPERATIONS

15. EIT AS EVIDENCE OF EFFICIENT STATE PREPARATION IN NV-DIAMOND P LEVEL DIAGRAM P C 64 56 48 P C 40 8.5 MHz EIT amplitude (%) 120 MHz S = -1 32 24 S = 0 16 8 0 -20 -10 0 10 20 Probe Beam Detuning (MHz)

16. SPIN ALIGNMENT AMPLITUDE VS. MAGNETIC FIELD STRENGTH LEVEL DIAGRAM • NDFWM SIGNALS: • CENTRAL FREQUENCY 120 MHZ • COUPLING 7 W/cm2 = 1.4 Isat • PROBE 1 W/cm2 = 0.3 Isat(SCANNED) • READ 4 mW • SPOT SIZE 300 mm 20 MHz AOM TUNING LIMIT ~638nm R D P C 120 MHz INTENSITY (ARB.) S = -1 S = 0 ANTI-CROSSING B = 1050 G 140 120 100 DIFF. FREQ. (MHz)

17. METHOD 2: DIPOLE-DIPOLE INTERACTION 10 CONTROLLED NOT WITH CONTROL-NOT WITH DIPOLE-DIPOLE INTERACTION NEAR DIPOLE-DIPOLE INTERACTION W p APPLY OPTICAL 2 PULSE WITH 1 W • CONTROL ATOM IN |b >, NOTHING HAPPENS --EXCITED STATE SPLIT, NOT RESONANT 1 2 b b b b ® • CONTROL ATOM IN |c >, SIGN |c > IS REVERSED: | c c > - | c c > 1 2 1 2 2 1 1 2 1 2 p • PHASE SHIFT GATE • EQUIVALENT TO CONTROLLED-NOT IN ROTATED BASIS ATOM IN |b > ATOM IN |c > 2 2 |a > |a > 1 2 |a b >- |b a > g 1 2 1 2 |a > |a b >+ |b a > 1 g g W 1 2 1 2 W 1 W b 1 a a 1 b 2 2 1 1 |c > |b > |b > 2 |c > |c > 1 2 |c > 1 1 1 ATOM 1 ATOM 2 No Excites TARGET CONTROL excitation optical 1 W transition l Ö g g g = 0.006 ( /r) ( ) 3 A B Absorption of W Frequency of 1

18. Diamond SiO2 SiO2 Hole filled with nonlinear-optic glass 300 nm 20 nm

19. Holes filled with nonlinear-optic glass Anomalous hole also filled with nonlinear-optic glass SiO2 SiO2 Cavity

20. PMMA (E-Beam Litho) SiO2 (CF4/CHF3 RIE) Polyimide (O2 RIE) Alumina (BCl3 RIE) SiO2 (CF4/CHF3 RIE) Diamond (O2 RIE) SiO2

21. SIMULATION OF THE TWO-DIMENSIONAL ISING MODEL, ISOMORPHIC TO THE PROBLEM OF THE MAXIMUM INDEPENDENT SET