INTRIQ. Coherent Manipulation of single nuclear spin

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Ferhat (Inst. Néel) R. Ballou (Inst. Néel) M.

1 INTRIQ Coherent Manipulation of single nuclear spin Clément Godfrin Eva Dupont Ferrier Michel Pioro-Ladrière K. Ferhat (Inst. Néel) R. Ballou (Inst. Néel) M. Ruben (KIT) W. Wernsdorfer (KIT) F. Balestro (Inst. Néel) INTRIQ 18 Bromont 1

2 Introduction Qubit Superconducting circuits Nature 453, 131 Quantum dots + 1/ NV center Nature 491, 46 Nature 4, 766 1/ PRL 9, P in silicon Nature 489, 541 INTRIQ 18 Bromont

3 Introduction Qudit + 3/ + 1/ - Fundamental investigation (Bell inequality, Chaos dynamics ) - Quantum information (error correction, simulation, algorithm, cryptography ) 1/ 3/ INTRIQ 18 Bromont 3

45 GHz Conductance value Direct read-out Conductance jump position Indirect read-out 1

4 Conductance (ns) Introduction Molecular magnet Terbium electronic spin Terbium nuclear spin +6 or 6 Terbium double-decker (TbPc ) transistor GHz 3.13 GHz.45 GHz Conductance value Direct read-out Conductance jump position Indirect read-out 1 4 Time Godfrin et al ACS Nano Vincent et al Nature INTRIQ 18 Bromont 4

5 Outline Two-level coherent manipulation Qudit to probe Berry s phase Quantum gate phase INTRIQ 18 Bromont 5

6 Two-level coherent manipulation + 3/ Qubit + 1/ 1/ 3/ INTRIQ 18 Bromont 6

7 Qubit Pulse Energy : E Population : α β Phase : ρ Coupling : g Amplitude : A Frequency : f Length : τ Phase : Φ E 1 Ψ = α + βe iρ 1 P = A sin ( π f τ + Φ) INTRIQ 18 Bromont 7

+iω y Ω x iω y δ z Ψ τ = e ihτ/h Ψ Pulse Energy : E Population : α β Phase : ρ Coupling : g

8 Qubit State representation: Bloch Sphere Ω y 1 State dynamic: Hamiltonian Ω x = g A cos(φ) μ N /h Ω y = g A sin(φ) μ N /h δ z = f - E/h δ z Ψ = cos(θ/) + sin(θ/) e iρ 1 Ω x H = h δ z Ω x +iω y Ω x iω y δ z Ψ τ = e ihτ/h Ψ Pulse Energy : E Population : α β Phase : ρ Coupling : g Amplitude : A Frequency : f Length : τ Phase : Φ What we measure What we tune INTRIQ 18 Bromont 8

9 Nuclear Qubit spin dynamic Pulse Ψ = cos(θ/) + sin(θ/) e iρ 1 1 (ns) (ns) INTRIQ 18 Bromont 9

Visibility Visibility Visibility Visibility Visibility

5 T 1 = 34 s T =.6 ms 4 τ (ns) 3.79 3.81 3.

10 Visibility Visibility Visibility Visibility Visibility Visibility Nuclear spin dynamic + 3/ T 1 = 34 s T =.6 ms 4 τ (ns) Frequency (GHz) + 1/ 1 1 T 1 = 18 s.5.5 T = 1.6 ms T 1 = 34 s T =.4 ms 1/ 3/ Godfrin et al PRL τ (ns) 4 τ (ns) Frequency (GHz) Frequency (GHz) INTRIQ 18 Bromont 1

11 Outline Two-level coherent manipulation Qudit to probe Berry s phase Quantum gate phase INTRIQ 18 Bromont 11

12 Berry s phase Geometric phase accumulation : 1 ) Pulse π with phase α = ) Pulse π with phase α = π + Ω/ 1 1 e iω 1 Ω / INTRIQ 18 Bromont 1

13 Berry s phase Geometric phase accumulation : 1 1 ) Pulse π with α = ) Pulse π with α = π + Ω/ 1 e iω 1 Ω / Phase measurement : Interferometer π, π, α π/, Ω π/, Φ P= cos ( Φ+ α ) Φ INTRIQ 18 Bromont 13

14 Berry s phase π α π π π Φ π, π, α π/, π/, Φ P= cos ( Φ+ α ) INTRIQ 18 Bromont 14

15 Berry s phase α π Φ α π π π Φ π, πτ, π, α πτ, Φ P = cos ( α + Φ ) INTRIQ 18 Bromont 15

16 Berry s phase α 1 π α 3 α 3 π πτ, π, π,α 3 π Τ, P = cos ( α 1 + α 3 ) π π α π, π,α 1 INTRIQ 18 Bromont 16

17 Berry s phase π, π, α +1 π, π, α 3 π, π, α πτ, π Τ, 1 1 π πτ, πτ, Φ 3 π πτ, π Τ, Φ 3 π π, π, α 1 α π α π α 3 π π π π π π π Φ Φ α 1 Godfrin et al, NPJ quant. inf (18) INTRIQ 18 Bromont 17

18 Outline Two-level coherent manipulation Qudit to probe Berry s phase Quantum gate phase INTRIQ 18 Bromont 18

19 iswap Gate 3/ A B 1/ A 1 B 1/ 1 A B 3/ 1 A 1 B U iswap = 1 i i 1 INTRIQ 18 Bromont 19

20 Visibility iswap Gate i ππ 1 1 i π π 3π INTRIQ 18 Bromont

21 Measure iswap phase First measurement: τ = π Create paths +3 π π/ +1 π/ τ Second measurement: τ = 3π 1 3 Godfrin et al, NPJ quant. inf (18) INTRIQ 18 Bromont 1

22 Conclusion Full coherent control of a 4-level single nuclear spin Qudit interferometry Suitable basic block for quantum computing Quantum phase measurement Fundamental physic Quantum computing Multi-level resonance Thank you for your attention Implementation of a Grover s algorithm INTRIQ 18 Bromont

arxiv: v2 [quant-ph] 28 Nov 2017

arxiv: v2 [quant-ph] 28 Nov 2017 Operating Quantum States in Single Magnetic Molecules: Implementation of Grover s Quantum Algorithm arxiv:1710.11229v2 [quant-ph] 28 ov 2017 C. Godfrin, 1, 2 A. Ferhat, 1, 2 R. Ballou, 1 S. Klyatskaya,