A Diamond Quantum Simulator

Transcription

1 A Diamond Quantum Simulator Martin B Plenio Institute of Theoretical Physics & Center for Quantum-BioSciences Ulm University

2 Quantum Simulation for 2-D Systems Why? Offer unusual physics Anyons, Surface codes, Topological phase transitions, Frustration, Difficult to simulate by classical computers For 1-D we have (t)-dmrg S.R. White, PRL 1992 For 2-D they are really hard to simulate!

3 Quantum Simulation for 2-D Systems 2-D Trapped Ion Coulomb Crystal John NIST 2-D Neutral Atom Optical Lattice Immanuel MPQ Garching

4 Diamond

5 Diamond A perfect diamond is transparent! Fotografiert in Sotheby s London October 2016 Some diamond have colour

6 Colour Centers in Diamond Nuclear Spin Crystals are like people, its only the defects that make them interesting F. Franck Wu, Jelezko, Plenio, Weil, MiniReview Angew. Chemie Intl. Ed.2015

7 Creating 2D-Spin Layers Diamond 111-surface F-F (long range dipole) interaction (6.8kHz nearest neighbor) Fluorographene Monolayer hbn See Lovchinsky et al, Science 2017 for MR of hbn on a diamond surface Abdi, Hwang, Aghtar & Plenio. Phys. Rev. Lett. (2017) See Chou et al, Nano Letters 2017 Numerical study of nitrogen spin-1 lattice Diamond 100-surface Theory: Cai, Retzker, Jelezko, Plenio, Nature Phys. 2013

8 Creating Quasi-2D Spin Layers Nitrogen introduced during the growth of the 13 C layer, facilitating NV centers in the vicinity of the spin layer. Unden, Tomek, Weggler, Frank, London, Zopes, Degen, Meijer, Watanabe, Itoh, Plenio, Naydenov & Jelezko. E-print arxiv:

9 A Diamond Surface Simulator Address three main challenges Initialization of the nuclear spin lattice Control of the Hamiltonian of the nuclear spin lattice Readout from the nuclear spin lattice Theory: Cai, Retzker, Jelezko, Plenio, Nature Phys. 2013

10 Coupling Electron Spins to Nuclei r ˆr H NV-S = gs z 3r x r z I x N + 3r y r z I y N + 3r 2 z é ë ( z -1)I N ù û m s 1/ 2 H S = g N B I N H B E S S m s 1/ 2 Cai, Jelezko, Retzker, Plenio, NJP 2013 Cai, Retzker, Jelezko, Plenio, Nature Physics 2013

11 Coupling Electron Spins to Nuclei r ˆr H NV-S = gs z 3r x r z I x N + 3r y r z I y N + 3r 2 z é ë ( z -1)I N ù û m s 1/ 2 H NV = Ws x H B E S S Continuous Resonant Drive W 1/ 2 1/ 2 H S = g N B I N Environment spectral density 1/ 2 1/ 2 m s 1/ 2 Cai, Jelezko, Retzker, Plenio, NJP 2013 Cai, Retzker, Jelezko, Plenio, Nature Physics 2013

12 Coupling Electron Spins to Nuclei r ˆr H NV-S = gs z 3r x r z I x N + 3r y r z I y N + 3r 2 z é ë ( z -1)I N ù û m s 1/ 2 H NV = Ws x H B E S S Continuous Resonant Drive W 1/ 2 1/ 2 H S = g N B I N Environment spectral density 1/ 2 1/ 2 m s 1/ 2 Cai, Jelezko, Retzker, Plenio, NJP 2013 Cai, Retzker, Jelezko, Plenio, Nature Physics 2013

13 Concatenated Noise Protection Robustness Against Driving Field Fluctuations + = + W 1 (w 0 ) - = - Theory & Experiment: Scheuer,, Jelezko, Plenio, NJP 14, (2012).

14 Concatenated Noise Protection Robustness Against Driving Field Fluctuations W 1 (w 0 ) W 2 (w 0 + W 1, j ) + = + j - = - j Theory & Experiment: Scheuer,, Jelezko, Plenio, NJP 14, (2012) Cao, Shu, Yang, Yu, Gong, He, Hu, Retzker, Plenio, Müller, Tomek, Naydenov, McGuinness, Jelezko & Cai. E-print arxiv:

15 Concatenated Noise Protection Robustness Against Driving Field Fluctuations T 2 = 2.5 ms Theory & Experiment: Scheuer,, Jelezko, Plenio, NJP 14, (2012). (W 1 / W 2) 2

16 FWHM [khz] Spin Ensemble Initialisation Polarization of nuclear spin bath reduces linewidth due to T2 time Polarization of nuclear spin bath reduces NV-ESR linewidth Numerical simulation shows >90% polarization after 500 sweeps of closest 10% of nuclear spins randomly placed in 4nm radius from NV Number of polarization sweeps With magnetic field drifts Without magnetic field drifts Theory & Experiment: London,, Plenio, Jelezko, PRL 111, (2013)

17 Spin Lattice Initialisation 12 C layer 13 C layer 12 C layer N times N times Type IIa substrate Spin locking time of Hartmann-Hahn was fixed to 20ms Polarisation Readout by Polarisation Inversion See also Scheuer, Schwartz, Müller, Chen, Dhand, Plenio, Naydenov & Jelezko, PRB 96, (2017) for analysis for spin ensemble around NV in natural abundance diamond. Unden, Tomek, Weggler, Frank, London, Zopes, Degen, Meijer, Watanabe, Itoh, Plenio, Naydenov & Jelezko. E-print arxiv:

18 From Continuous to Pulsed Schemes Polarisation in the Dark

19 From Continuous to Pulsed Schemes Polarisation in the Dark m s 1/ 2 H NV = Ws x 1/ 2 1/ 2 H S = g N B I N H B E S S Continuous Resonant Drive W 1/ 2 1/ 2 m s 1/ 2

20 From Continuous to Pulsed Schemes Polarisation in the Dark

21 Pulsed Polarisation Experiment: Robustness Schwartz, Scheuer, Tratzmiller, Müller, Chen, Dhand, Wang, Müller, Maydenov, Jelezko & Plenio, E-print arxiv:

22 Ground State Preparation Polarisation & Adiabatic Transfer Theory: Cai, Retzker, Jelezko, Plenio, Nat. Phys. 9, 168 (2013)

23 Sensing Silicon Nuclear Spins above Diamond Surface Experiment & Theory: Müller, Kong, Cai, Melentijevic, Stacey, Markham, Isoya, Pezzagna, Meijer, Du, Plenio, Naydenov, McGuinness & Jelezko., Nat. Comm. (2014)

24 Sensing Silicon Nuclear Spins above Diamond Surface Experiment & Theory: Müller, Kong, Cai, Melentijevic, Stacey, Markham, Isoya, Pezzagna, Meijer, Du, Plenio, Naydenov, McGuinness & Jelezko., Nat. Comm. (2014)

25 Readout of Nuclear Spin Lattice Measurement with NV: P (t ) - P (t ) = 2t 2 2 z åg i I i i Spin magnetization Magnetic gradient: magnetic tip å S z = I i z i State-of-art: 7 Gauss per Å Spin structure factor: Various tricks Exploit Hartmann-Hahn condition S(Q) = å (i, j) e iq (r i -r j ) I i z I j z + e iq (r j -r i ) I j z I i z Theory: Cai Plenio, Nat. Phys. 9, 168 (2013) Sufficient to lower bound entanglement: Cramer, Plenio, Wunderlich, PRL 2013 Theory: Cai, Retzker, Jelezko, Plenio, Nature Phys. 9, 168 (2013)

26 Hyperpolarised Nanoscale NMR Qdyne, Hyperpolarisation and Signal Processing Fernandez-Acebal, Rosolio, Scheuer, Müller, Müller, Schmitt, McGuinness, Schwarz, Chen, Retzker, Naydenov, Jelezko, Plenio, arxiv: Schmitt, Gefen, Stürmer, Unden, Wolff, Müller, Scheuer, Naydenov, Markham, Pezzagna, Meijer, Schwarz, Plenio, Retzker, McGuinness & Jelezko. Science 356, 832 (2017) NMR/ESR-on-a-chip spectrometer capillary with culture medium cell under observation Schwartz, Rosskopf, Schmitt, Tratzmiller, Chen, McGuinness, Jelezko & Plenio. E-Print arxiv:

27 The Underlying Signal

28 The Measurement Record from a Two-State Detector

29 What the NV-Center Really Records How Not To Analyse The Signal FFT will require very large amount of data, will exhibit artefacts

30 Analysing the NV Measurement Record How To Do It Use all available knowledge You know the shape of the signal You know your nuclei & magnetic field FFT essentially blind to prior knowledge of Larmor. You look for small chemical shifts around known Larmor Schwartz, Rosskopf, Schmitt, Tratzmiller, Chen, McGuinness, Jelezko & Plenio. E-Print arxiv:

31 Extracting Signals from Very Noisy Data How To Do It Schwartz, Rosskopf, Schmitt, Tratzmiller, Chen, McGuinness, Jelezko & Plenio. E-Print arxiv:

32 The Ulm External Collaborators: Jianming Cai, Alex Retzker, Fedor Jelezko, Boris Naydenov, Tanja Weil

33 The Ulm External Collaborators: Jianming Cai, Alex Retzker, Fedor Jelezko, Boris Naydenov, Tanja Weil

34 Institute of Theoretical Physics & Center for Quantum Biosciences Professors Martin Plenio Susana Huelga Postdocs Mehdi Abdi Felipe Caycedo-Soler Qiong Chen Ish Dhand Sandro Donadi Myung-Joong Hwang Jaemin Lim Mark Mitchison Julen Pedernales Andrea Smirne Zhenyu Wang PhD students Dario Egloff Pelayo Fernandez-Acebal Jan Haase Milan Holzäpfel Matthias Kost Andreas Lemmer Oliver Marty Fabio Mascherpa Andrea Mattioni Shreya Prasanna Kumar Joachim Rosskopf Ilai Schwarz Alejandro Somoza Marquez Kirill Streltsov Thomas Theurer Benedikt Tratzmiller Synergy Grant: Diamond Quantum Devices and Biology & Proof of Concept Grant Master students Michael Bösen Matthias Maucher SFB TRR-21 & SPP 1601 Viet Tran Korbinian Kottmann Arne Pick Moritz Lange External Collaborators Jianming Cai, Alex Retzker, Fedor Jelezko, Boris Naydenov, Liam McGuinness, Tanja Weil