Magnetic Resonance at the quantum limit and beyond

Transcription

1 Magnetic Resonance at the quantum limit and beyond Audrey BIENFAIT, Sebastian PROBST, Xin ZHOU, Denis VION, Daniel ESTEVE, & Patrice BERTET Quantronics Group, SPEC, CEA-Saclay, France Jarryd J. Pla, Cheuk C. Lo & John J.L. Morton London Centre for Nanotechnology, University of College London Brian Julsgaard, Klaus Moelmer Aarhus University, Danemark

2 Motivation : quantum-enhanced magnetic resonance Conventional magnetic resonance spectroscopy Low sensitivity, room-temperature operation, Macroscopic samples, Spin-Field interaction classical Quantum technologies Superconducting circuits and resonators Superconducting amplifiers Quantum-enhanced magnetic resonance High sensitivity, millikelvin operation, nanoscale samples Spin-Field interaction in the quantum regime Towards single-spin detection

3 Pulsed Inductive Detection Electron Spin Resonance (ESR) Excite spins Echo emission B 0 Sensitivity Minimal number of spins NN mmmmmm detected with a SNR = 1 in a single echo? τ τ π/2 π echo time π π/2

4 Sensitivity of an inductive detection spectrometer gg resonator ωω 0, QQ TT EE B 0 τ τ π/2 π echo time L.O. I NN mmmmmm = nnnnnnnnnn SSSSSSSSSSSS ffffffff oooooo ssssssss Q

5 Sensitivity of an inductive detection spectrometer gg resonator ωω 0, QQ TT EE B 0 τ τ π/2 π echo time L.O. I NN mmmmmm = nnnnnnnnnn SSSSSSSSSSSS ffffffff oooooo ssssssss = CC Q Single-spin cooperativity CC = QQQQ2 TT EE ωω 0

6 Sensitivity of an inductive detection spectrometer nn eeee gg resonator ωω 0, QQ T nn aaaaaa TT EE B 0 τ τ π/2 π echo time L.O. I NN mmmmmm = nnnnnnnnnn SSSSSSSSSSSS ffffffff oooooo ssssssss = nn II CC Q Number of noise photons in the detected quadrature bandwidth nn II = SS II(ωω) ħωω = nn eeee,ii + nn aaaaaa,ii Single-spin cooperativity CC = QQQQ2 TT EE ωω 0

7 Sensitivity of an inductive detection spectrometer nn eeee gg resonator ωω 0, QQ T nn aaaaaa TT EE B 0 τ τ π/2 π echo time L.O. I Q NN mmmmmm = nnnnnnnnnn SSSSSSSSSSSS ffffffff oooooo ssssssss = nn II pp CC A.Bienfait et al., Nature Nano (2015) Spin polarization For spin ½ at T pp = tanh ħωω 0 2kkkk Number of noise photons in the detected quadrature bandwidth nn II = SS II(ωω) ħωω = nn eeee,ii + nn aaaaaa,ii Single-spin cooperativity CC = QQQQ2 TT EE ωω 0

8 EPR sensitivity : state-of-the-art 1000 NN mmmmmm Commercial ESR spectrometer (300K) 100 nn II 10 1 NN mmmmmm 10 7 Sigillito et al., APL 2014 (1.7K) 0.1 1E-12 1E-10 1E-8 1E-6 1E pp CC

9 Equilibrium thermal noise and quantum limit nn eeee,ii = ΔII 2 = 1 2 coth ħωω 0 2kkkk nn eeee,ii TT/(ħωω 0 /kk)

10 Equilibrium thermal noise and quantum limit 1.5 nn eeee,ii = ΔII 2 = 1 2 coth ħωω 0 2kkkk 1.0 Q I nn eeee,ii 0.5 ΔII 2 kkkk 2ħωω TT/(ħωω 0 /kk)

11 Equilibrium thermal noise and quantum limit 1.5 nn eeee,ii = ΔII 2 = 1 2 coth ħωω 0 2kkkk 1.0 ΔΔII 22 = Q I nn eeee,ii 0.5 Q I ΔII 2 kkkk 2ħωω 0 QUANTUM LIMIT ωω 0 /2ππ = 7.3GHz TT = 20mmmm TT/(ħωω 0 /kk)

12 Josephson Parametric Amplifier in out Input SQUID array X. Zhou et al., PRB (2014) M. Castellanos-Beltran et al., APL (2007) C. Eichler et al., PRL (2010) N. Bergeal et al., Nature (2010) 12/61

13 Josephson Parametric Amplifier in out ωω 0 (Φ) DC bias SQUID array ΦΦ ΦΦ ΦΦ ΦΦ X. Zhou et al., PRB (2014) 13/61

14 Josephson Parametric Amplifier in out ωω 0 (Φ) Working ΦΦ DC bias AC pump tone ωω pp 2ωω 0 X. Zhou et al., PRB (2014) 14/61

15 JPA in non-degenerate mode signal ωω in DC bias AC pump tone ωω pp 2ωω in Quantum-limited (ωω iiii ωω pp /22)/2222 (MHz) nn aaaaaa = 1/4 X. Zhou et al., PRB (2014) 15/61

16 JPA in degenerate mode signal ωω in Pump phase DC bias AC pump tone ωω pp = 2ωω in Noiseless amplifier X. Zhou et al., PRB (2014) 16/61

17 Quantum limited ESR with Parametric Amplifier ωω 0 π/2 π B 0 φφ ππ/2 φφ LLLL φφ pppppppp π/2

18 Quantum limited ESR with Parametric Amplifier 2D lumped element Superconducting Al resonator ω 0 /2π = 7.24 GHz, Q =

19 Quantum limited ESR with Parametric Amplifier B 0 Q = µm Spins 100 nm B 0 28 Si 2D lumped element Superconducting Al resonator

20 Quantum limited ESR with Parametric Amplifier B 0 Q = µm Spins 100 nm B 0 28 Si 2D lumped element Superconducting Al resonator Spin-resonator coupling gg 2222 =

21 The Spins: bismuth donors in silicon e Bi Bi +

22 The Spins: bismuth donors in silicon e Bi e - Bi + HH ħ = AAII SS + BB 00 ( γγ ee SS γγ nn II) HYPERFINE ZEEMAN EFFECT Electronic spin = 1/2 20 electro-nuclear states! Nuclear spin I=9/2 Large hyperfine coupling AA = GHz 2ππ

23 The Spins: Bi donors in 28 Si At low-field B 0 =0 B 0 0 F = 5 m F 5 5 A/2π 7.37 GHz F = 4 m F -5 m F 4 m F Bi HH ħ = AAII SS + BB 00 ( γγ ee SS γγ nn II) HYPERFINE ZEEMAN EFFECT Nuclear spin I=9/2 Electronic spin S=1/2 Large hyperfine coupling AA 2ππ = 1.48 GHz RE George et al., Phys Rev Lett (2010); GW Morley et al. Nature Materials (2010)

24 The Spins: bismuth donors in silicon 10 allowed ESR-like low B 0 28 Si Magnetic field B 0 (mt) Implanted Bismuth mf = 4 mf = mt

25 Sensitivity of the setup? How many spins? SNR? JPA off : SNR = 0.7 JPA on : SNR = 7 A. Bienfait et al., Nature Nanotechnology 11, (2016)

26 Spectrometer single-shot sensitivity ΔSS zz = SNR = 7 Estimated sensitivity per echo : NN mmmmmm = = spins Quantitative agreement with expected sensitivity A. Bienfait et al., Nature Nanotechnology 11, (2016)

27 Absolute sensitivity and spin relaxation time TT 1 Repetition rate?? Limited by time TT 1 needed for spins to reach thermal equilibrium TT = 0 TT T 1 = 0.35 s A Q Spectrometer absolute sensitivity : 1700 spin/ HHHH «Short» T 1 due to spontaneous emission in the cavity (Purcell effect)

28 Spin relaxation dependence on detuning ωω 0, QQ gg γγ PP 11 TT 11 = γγ PP + ΓΓ NNNN γγ PP = 4QQgg2 ωω QQ 2 ωω ss ωω 0 ωω 0 2 A. Bienfait et al., Nature (2016)

29 EPR sensitivity : summary 1000 NN mmmmmm Commercial ESR spectrometer (300K) nn II QUANTUM LIMIT NN mmmmmm 10 7 Sigillito et al., APL 2014 (1.7K) NN mmmmmm = improvement over state-of-the-art A.Bienfait et al., Nature Nano (2015) 0.1 1E-12 1E-10 1E-8 1E-6 1E pp CC C. Eichler et al., arxiv(2016)

30 Increasing sensitivity with narrower wire B 0 1 mm 100 um width: 500nm π π/2 π T 1 = 21 ms gg/2ππ = 440 Hz

31 EPR sensitivity : summary 1000 NN mmmmmm Commercial ESR spectrometer (300K) B 0 nn II QUANTUM LIMIT NN mmmmmm 10 7 Sigillito et al., APL 2014 (1.7K) C. Eichler et al., arxiv(2016) A.Bienfait et al., Nature Nano (2015) NN mmmmmm = E-12 1E-10 1E-8 1E-6 1E pp CC 10 4 improvement over state-of-the-art Below QL?? NN mmmmmm = S. Probst (2016)

32 Quantum squeezed states below the quantum limit nn eeee,ii = 1 2 coth ħωω 0 2kkkk Q I nn eeee,ii Q I Q I TT/(ħωω 0 /kk) QUANTUM LIMIT QUANTUM SQUEEZING

33 Measurements beyond the quantum limit using squeezing Giovanetti, Lloyd, Maccone, Science (2004) Optical domain Squeezed state production Slusher et al., PRL (1985) L. Wu et al., PRL (1986) Phase measurements in an interferometer Caves, PRD (1981) Grangier et al., PRL (1987), Xiao et al., PRL (1987) LIGO, Nature Phys (2011), Nature Photonics (2013) Spectroscopy Polzik et al., PRL (1992) Imaging Treps et al., Science (2003) M.A. Taylor et al., Nature Phot. (2013) Atomic magnetometry F Wolfgramm et al., PRL (2010) Microwave domain Squeezed state production Movshovitch, Yurke, PRL 65, 1419 (1990) Mallet et al., PRL 106, (2011) Quantum physics experiments Gardiner, PRL (1986) Murch et al., Nature (2012) Toyli et al., arxiv (2016) Proposals for qubit state readout N. Didier et al., PRL 115, (2015) N. Didier et al., PRL 115, (2015) Here : squeezing-enhanced pulsed magnetic resonance detection

34 Principle of the experiment B 0 Spin-echo L.O. I Q

35 Principle of the experiment SQUEEZER B 0 Spin-echo L.O. I Q Signal-to-noise ratio on the echo signal quadrature enhanced by vacuum squeezing at spectrometer input

36 How to generate squeezed microwave vacuum? Q amplification phase Josephson Parametric Amplifier GG IN OUT GG 1 I Pump signal in Frequency ωω pp = 2222

37 Squeezed vacuum characterization L.O. SQZ JPA AMP I I quadrature (V) Time (ms) Variance of I quadratue (V²) AMP Occurences AMP 0 ππ/2 ππ Phase ( ) φφ SQZ φφ JPA Voltage (V)

38 Squeezed vacuum characterization Quantum noise L.O. SQZ JPA AMP I Variance of I quadratue (mv²) Quantum noise n JPA AMP Occurences AMP JPA 0 ππ/2 ππ Phase ( ) φφ SQZ φφ JPA Voltage (V)

39 Squeezed vacuum characterization Reduced quantum noise L.O. SQZ JPA AMP I Deamplified phase φφ SQZ φφ JPA Noise reduction: -25% Variance of I quadratue (mv²) HEMT Occurences HEMT JPA SQZ 0 ππ/2 ππ Phase ( ) φφ SQZ φφ JPA Voltage (V) R. Movshovitch et al., PRL (1990) F. Mallet et al., PRL (2011)

40 Spin-echo emitted in squeezed vacuum Reduced quantum noise L.O. SQZ JPA AMP I SQZ ON B 0 Average 2000 Noise reduction: -25% SQZ ON SQZ OFF ECHO, SQZ ON ECHO, SQZ OFF Occurences Voltage (V) 40/61

41 Spin-echo emitted in squeezed vacuum SNR enhancement by 12% Proof of concept! Currently limited by microwave losses Average 2000 SQZ ON SQZ OFF ECHO, SQZ ON ECHO, SQZ OFF Occurences Voltage (V) 41/61

42 Conclusions Magnetic Resonance enhanced by quantum technologies (superconducting circuits) Magnetic resonance detection with unprecedented sensitivity (reaching the quantum limit) Towards single-spin sensitivity Quantum fluctuations of the field affect spin dynamics (Purcell effect) Dynamical control of T 1 by tuning spin frequency Useful for Dynamical Nuclear Polarization? Proof-of-principle that squeezing can improve sensitivity of magnetic resonance beyond quantum limit. Improving amount of squeezing becomes techn. relevant.

43 Quantronics group, CEA Saclay Acknowledgements University College London Aarhus University, Danemark D. ESTEVE D. VION A. BIENFAIT Y. KUBO S. PROBST J. PLA J. MORTON Quantronics Group B. JULSGAARD K. MOELMER POSITIONS OPEN X. ZHOU P. CAMPAGNE P. JAMONNEAU UC Berkeley T. SCHENKEL