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

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

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

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

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

22 11 0 1 INTENSITY TIME ADIABATIC COHERENCE TRANSFER ATOM 1 ATOM 2 11 22 g CAVITY VACUUM COUPLING g ATOM 1 ATOM 2 |a 1 > |b 1 > |e 1 > 11 g |a 2 >|b 2 > |e 2 > 22 g INITIAL  RAMAN DARK STATES |a 1 b 2 0> |b 1 a 2 0> 11 g 22 g |b 1 b 2 1> |e 1 b 2 0>|b 1 e 2 0>  2 g  1 g  1  2  |b 1 b 2 0>  NO CAVITY PHOTONS ONE CAVITY PHOTON ADIABATIC COHERENCE TRANSFER VIA CAVITY-QED DARK STATE

DARK STATE QUANTUM COMPUTING IN NV-DIAMOND: NECESSARY ENERGY LEVELS a c QUBIT 1QUBIT 2 b d a c b d ef   ef   gh gh

DARK STATE QUANTUM COMPUTING IN NV-DIAMOND: ROLE OF STORAGE LEVELS a c b d ef a c b d ef   a c b d ef a c b d ef  

DARK STATE QUANTUM COMPUTING IN SHB CRYSTAL: CANDIDATE MATERIALS gh a c b d e f 4.6 MHz 4.8MHz 10.2 MHz 17.3 MHz 2m I ff H43H4 1D21D2 gh a c b d e f P Q 4.6 MHz 2.8 MHz ff 3A13A1 3E3E IZIZ SZSZ 1 Sgn(m I ) + - [A][B] IZIZ Pr:YSONV-DIAMOND

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 2.88 GHz S= ±1 S= 0 B-FIELD G 120 MHz 638 nm ZERO PHONON LINE PHONON SIDEBAND ABSORPTION WAVELENGTH (nm) ARGON LASER REPUMP DYE LASER

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

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

120 MHz LEVEL DIAGRAM S = 0 S = -1 P C EIT AS EVIDENCE OF EFFICIENT STATE PREPARATION IN NV-DIAMOND MHz Probe Beam Detuning (MHz) EIT amplitude (%) P P C

NDFWM SIGNALS: CENTRAL FREQUENCY 120 MHZ COUPLING 7 W/cm 2 = 1.4 I sat PROBE 1 W/cm 2 = 0.3 I sat (SCANNED) READ 4 mW SPOT SIZE 300  m 120 MHz LEVEL DIAGRAM S = 0 S = MHz P C D R ~638nm DIFF. FREQ. (MHz) INTENSITY (ARB.) ANTI-CROSSING B = 1050 G AOM TUNING LIMIT SPIN ALIGNMENT AMPLITUDE VS. MAGNETIC FIELD STRENGTH

10 CONTROLLED NOT WITH NEAR DIPOLE-DIPOLE INTERACTION APPLY OPTICAL 2  PULSE WITH  1 CONTROL ATOM IN |b 2 >, NOTHING HAPPENS --EXCITED STATE SPLIT,  1 NOT RESONANT CONTROL ATOM IN |c 2 >, SIGN |c 1 > IS REVERSED:     | c 1 c 2 >  -     1 c 2 >  PHASE SHIFT GATE EQUIVALENT TO CONTROLLED-NOT IN ROTATED BASIS Frequency of  1 Absorption of  1 Excites optical transition No excitation g= ( /r) 3  (  A  B ) ATOM 1 TARGET ATOM 2 CONTROL |c 1 > |b 1 > |a 1 > |b 2 > |c 2 > |a 2 > gg          1 |c 1 > |a 1 >  1 |c 1 > |a 1 b 2 >- |b 1 a 2 > |a 1 b 2 >+ |b 1 a 2 >  1 g ATOM IN |b 2 >ATOM IN |c 2 > CONTROL-NOT WITH DIPOLE-DIPOLE INTERACTION METHOD 2: DIPOLE-DIPOLE INTERACTION

300 nm 20 nm Diamond SiO 2 Hole filled with nonlinear-optic glass

SiO 2 Holes filled with nonlinear-optic glass Anomalous hole also filled with nonlinear-optic glass Cavity

PMMA (E-Beam Litho) SiO 2 (CF 4 /CHF 3 RIE) Polyimide (O 2 RIE) Alumina (BCl 3 RIE) SiO 2 (CF 4 /CHF 3 RIE) Diamond (O 2 RIE) SiO 2

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