Hybrid Quantum Circuit with a Superconducting Qubit coupled to a Spin Ensemble

Hybrid Quantum Circuit with a Superconducting Qubit coupled to a Spin Ensemble, Cécile GREZES, Andreas DEWES, Denis VION, Daniel ESTEVE, & Patrice BERTET Quantronics Group, SPEC, CEA- Saclay Collaborating with: J. ISOYA (University of Tsukuba, Japan), V. JACQUES, A. DREAU, J.- F. ROCH (ENS- Cachan, France), I. DINIZ, A. AUFFEVES (CNRS- Grenoble, France)

Outline Superconducting quantum circuit: - qubit & resonator Strong coupling of a spin ensemble to a superconducting resonator: - as a ﬁrst step towards superconducting hybrid quantum circuit Hybrid quantum circuit with a qubit coupled to NVs: - storage and retrieval of quantum state from/to qubit to/ from NVs

Quantum electronic (integrated) circuit = Harmonic oscillator k m k m [x,p] = - iħ In circuit 0 1 2 k B T << ħω High Q factor E L = 1 LC LC resonator Φ +Q - Q C [Φ,Q] = - iħ For details, see e.g., Devoret and Martinis, Quantum Inform. Processing 3, 163 (2004) Superconductor 2 DOS Low loss Macroscopic degrees of freedom Superconducting gap (>~ 100 GHz)

Superconducting qubit: Josephson junction Josephson junction(s): non- linear & non- dissipative inductance H q = Q2 2C I 0 2e cos 2 0 1.7 nm Al AlOx Al I = I 0 sin d dt = 2eV DC Josephson AC Josephson I 0 : critical current of Junction : Phase difference Unharmonic potential Lowest 2 states as a qubit Review (e.g.): Clerke and Wilhelm, Nature 453, 1031 (2008)

Coupling qubits to microwave photons Co- planar waveguide GND plane 5 µm GND plane ~1 cm Low loss Large vacuum fluctuation Wallraff et al., Nature 431 162 (2004) Superconducting co- planar waveguide (CPW) Resonator STRONG COUPLING Superconducting Qubit (Artificial atom)

The hybrid way for Quantum Information Superconducting qubits Design flexibility Scalability Tunability large coupling(s) : fast manipulation Irreproducibility Short coherence time (~< 100μs) Microscopic system: atoms, ions, spins Long coherence times µ- waves to optical frequencies Reproducibility Nature given Small couplings: slow Limited scalability 1µ Quantum processor Wallraff et al., 2004 Idea : Take only the best of both worlds Superconducting resonator Quantum memory Kubo et al., PRL 105, 140502 (2010) Quantum Interface (Bus)

Which microscopic system?: NV- centers in diamond Together with SC qubits: technical constraints working on ~mk (in a dilution fridge) Low B (<< kg for Al films) Our choice: e- spin of Nitrogen- Vacancy centers (NV center) 2.88 GHz Spin triplet (S = 1) with Zero- field splitting - No need of high B to obtain ~GHz ESR frequency - Polarization at dilution fridge temperature Long coherence time (T 2 ~ ms @ room T!) Solid: naturally trapped in a crystal - No need of any (difficult) trapping technique

Spin states of NV- centers: Zeeman & Hyperfine V N n-spin e-spin m s = ±1 +1-1 Hyperfine structure due to 14 N n- spin B NV 2.88GHz S = 1 I = 1 m s =0 m I = +1, - 1, 0 H/ = DS 2 z + E(S 2 x S 2 y) g e µ B B NV S +S A I Zero- field spli/ng Zeeman shi5 Hyperfine

Spin states of NV- centers: Zeeman & Hyperfine Ensemble measurement m s = - 1 m s = +1 V N n-spin e-spin B NV Acostaet al,prb 80, 115202 (2009) H/ = DS 2 z + E(S 2 x S 2 y) g e µ B B NV S +S A I Zero- field spli/ng Zeeman shi5 Hyperfine

Coupling a single NV center to a resonator Coupling constant: g/2 = g NV µ B B 0 h z y x x y z Br single NV - resonator Hamiltonian : x Vacuum magne>c field above the surface y with g/2π 11 Hz Not enough!! y (µm)

Collective enhancement of coupling constant N- Spin- resonator Hamiltonian : 1 1 0 resonator Harmonic oscillator 2 0 with N = 10 12 (10 18 cm - 3 ) ~ 10 MHz Strong coupling regime accessible Need many spins (NVs) dirty diamond Inhomogeneous broadening: Kurucz et al, PRA 83, 053852 (2011) Diniz et al, PRA 84, 063810 (2011)

The quantum bus: frequency tunable resonator SQUID: Superconducting loop interrupted by 2 Josephson junctions δ 1 δ 2 Φ Flux quantization 0 = /2e DC Josephson effect 2 µm Φ B r GND SIS junction (Al/AlO x /Al) I = I c sin I c ( )=2I c0 cos ( / 0 ) I c 2.95 r = 1 CL( ) Linear regime: tunableinductor Φ ω r / 2π (GHz) 2.90 2.85 2.80-1.0-0.5 0 Φ / Φ 0

Tunable Resonator: implementation Nb on SiO 2 /Si chip Br 10#µm# Superconducting quantum interference devices (SQUID) Coupling capacitor

Measurement setup Isolators

Strong coupling of a spin ensemble to µ- w photons 2.95 2.90 Without diamond 40mK ω / 2π (GHz) 2.85 2.80 2.75 0.1 0.2 0.3 0.4 Φ / Φ 0

Strong coupling of a spin ensemble to µ- w photons 2.95 2.90-32 db With diamond 40mK ω / 2π (GHz) 2.85 S 21 (db) B NV 2.80 2.75 0.99 mt 0.2 0.3 0.4-70 db Φ / Φ 0

Strong coupling of a spin ensemble to µ- w photons 2.95 2.90-32 db With diamond 40mK ω / 2π (GHz) 2.85 S 21 (db) B NV 2.80 2.75 0.99 mt 0.20 2 0.3 0 3 0.40 4-70 db Φ / Φ 0

Strong coupling of a spin ensemble to µ- w photons 2.95 2.90-32 db With diamond 40mK ω / 2π (GHz) 2.85 S 21 (db) B NV 2.80 2.75 0.99 mt 0.20 2 0.3 0 3 0.40 4-70 db Kubo et al., PRL 105 140502 (2010) See also Schuster et al., PRL 105 140501 (2010) Amsuss et al, PRL 107 060502 (2011) Bushev et al., PRB(R) 84 060501 (2011) Φ / Φ 0 Reso Spin +1> Spin - 1>

The hybrid quantum circuit Transmon qubit Bus resonator B 1 e Q R single- shot JBA readout Qubit drive & readout resonator NV NV ensemble Frequency- tuning by flux ω r / 2π (GHz) 2.95 2.90 2.85 F g 2.80-1.0-0.5 0 Φ / Φ 0

Device photos 1 mm The diamond 1 2 HPHT e- irradiated [NV- ] ~ 13 ppm, [N] ~ 13 ppm Prof. J. ISOYA (Univ. Tsukuba) F 50 µm m 0.1 mm Transmon qubit SQUID for bus- frequency tuning External coil Printed circuit board 1 2 F BNV // [111] BNV 30 mk

Device characterization: spectroscopy Bus transmission S21 Q 1 B 2 2.95 NV -40 R //[1,1,1] III I 1 isolated bond & 3 degenerated bonds +1-1 2.85-1 2.62 0.5 Qubit 0 2.57 0.30-70 Pe BNV Frequency, ω/2π (GHz) 2.90 S21 (db) ms=+1 0.35 0.42 Flux, Φ/Φ0

Pulse sequences Duration t Readout Rabi JBA switching probability Psw Qubit characterization: Rabi, T1, & T2 t 0.8 wait time t T1 Readout π/2 with small detuning T2 evolution time t Q 0.6 0.4 0.2 0 π Readout π π/2 100 200 300 400 Microwave pulse duration t (ns) 500 T1qubit = 1.75 µs T2qubit = 2.2 µs Readout

Coupling qubit to spin ensemble: single photon swap B 1 Q R NV F e> g> Qubit Bus Spins Qubit pump- up Interaction Measurement >? = 1 3 < ; = *@ABC

Single photon swap between qubit and spins BNV -40 Frequency, ω/2π (GHz) 2.90-1 2.85 I - 1 storage/retrieval of a SINGLE microwave photon into/from a spin ensemble Y. Kubo et al., PRL 107, 220501 (2011). See also Zhu et al. Nature 478 221 (2011). S21 (db) III -70 Qubit excited state probability, Pe 2.95 0.4 1B, 0N V 0B, 1N V 1B, 0N V τs,i 0.2 0 Pe(τr)/Pe(0) = 7 % for single bond τr,i 200 400 Interaction time,τ (ns) 600 Theory with 1.6 MHz ESR linewidth (inhomogeneous broadening) by I. Diniz & A. Auﬀeves

Single photon swap between qubit and spins BNV -40 Frequency, ω/2π (GHz) 2.90-1 2.85 I - 1 Low ﬁdelity: oscillation suppressed by beatings due to 14N hyperﬁne structure Y. Kubo et al., PRL 107, 220501 (2011). See also Zhu et al. Nature 478 221 (2011). S21 (db) III -70 Qubit excited state probability, Pe 2.95 Pe(τr)/Pe(0) = 14 % for triple bond 0.4 τs,iii 0.2 0 τr,iii 200 400 Interaction time, τ (ns) 600 Theory with 2.4 MHz ESR linewidth (inhomogeneous broadening) by I. Diniz & A. Auﬀeves

Storage/retrieval of quantum coherence ( + )/ 2 g> e> g> e> State preparation NV X( /2) Qubit Interaction Bus Spins Tomography Measurement I, X,Y R Q B

Quantum state tomography of retrieved state I, X,Y X( /2) Q R aswap B 0.4 State tomography by no pulse (I), π/2(x), π/2(y) No coherence left 0.4 τs,i <σ x> 0.0 180 π/2(x) -0.2 0 π shifts X π/2(y) e> -0.4 0 > -0.2 0 -<σ y> ac 0.2i n0 (n 100 200 300 Interaction time τ (ns) PRL 107, 220501 (2011) 2 ρge g> 0.2 Coherence retrieved! 0.2 τr,i (20%) arg(ρge) NV -180 400

Spin- Photon entanglement Single photon swap >? ; = *@ABC = 1 3 < Qubit excited state probability, P e 0.4 0.2 0 1 B, 0 NV τ π/2 0 B, 1 NV 200 400 600 Interaction time,τ (ns) Spin- photon entanglement at the half- swap time τ π/2 ( 1 B, 0 NV + 0 B, 1 NV )/ 2

Spin- Photon entanglement Excited state probability, Pe 0.5 0.4 0.3 0.2 5 0 NV Q B aswap /2 /2 R Spin- photon entangled state: ( 1 B, 0 NV + e i 0 B, 1 NV )/ 2 Theory with 1.6 MHz ESR linewidth 200 400 Delay time, τ (ns) T 2 * ~ 200 ns: limited by inhomogeneous broadening of the spin ensemble FFT amp (a.u.) 30 35 40 45 Frequency (MHz) 600 Hyperfine structure!

Summary & Perspective Hybrid quantum circuit with a superconducting qubit coherently coupled to an ensemble of NV centers in a diamond (first step towards quantum memory for microwave photons) Low fidelity due to small coupling constant and inhomogeneous broadening of the spins To improve: more spins and narrower linewidth (=less residual nitrogens, i.e., full conversion into NVs) Next step: Refocusing (spin echo) to really benefit the long coherence time of NV centers