Electron spin decoherence due to interaction with a nuclear spin bath

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1 Electron spin decoherence due to interaction with a nuclear spin bath Center for Quantum Device Technology Clarkson University Presenter: Dr. Semion Saikin saikin@clarkson.edu

NSF-DMR-121146, ITR/SY: Center for Modeling of Quantum Dynamics, Relaxation and Decoherence in Solid-State Physics for Information-Technology pplications PI: Vladimir Privman, Institution: Clarkson

components of atomic dimensions. These include quantum computers, spintronic devices, and nanometer-scale logic gates. pproach Our approach has been truly interdisciplinary.

2 NSF-DMR , ITR/SY: Center for Modeling of Quantum Dynamics, Relaxation and Decoherence in Solid-State Physics for Information-Technology pplications PI: Vladimir Privman, Institution: Clarkson University Research Objectives The main objectives of our program have been to explore coherent quantum mechanical processes in novel solid-state semiconductor information processing devices with components of atomic dimensions. These include quantum computers, spintronic devices, and nanometer-scale logic gates. pproach Our approach has been truly interdisciplinary. For example, in developing new measures of decoherence for quantum computing, we have employed concepts from many-body quantum physics, computer error-correction algorithms, and nonequilibrium statistical mechanics. In our description of spintronic devices, we have utilized large-scale Monte Carlo simulations, knowledge from solid-state physics of semiconductors and from the microelectronics area of electrical engineering, as well as novel ideas of coherent control of quantum dynamics. Our approach has been to design and evaluate architectures that allow implementation of many gate cycles during the relaxation and decoherence times. This requires development of techniques to evaluate all the relevant time scales: single- and two-quantum-bit gate clock times, as well as time scales of relaxation processes owing to the quantum bit (e.g., spin) interactions with environment, such as phonons or surrounding spins. We have also studied spincontrol and charge carrier transport for spintronics and quantum measurement. gnificant Results Our achievements to date include: new measures of initial decoherence, and evaluation of decoherence for spins in semiconductors; evaluation of solid-state quantum computing designs; studies of transport associated with quantum measurement; investigation of spin-polarized devices and role of nuclear spins in spintronics and quantum computing; general contributions to quantum computing algorithms and to time-dependent and phase-related properties of open many-body quantum mechanical systems; novel analytical and numerical Monte Carlo approaches to studying spin-polarization control for spintronic device modeling; investigation of spin relaxation dynamics in two-dimensional semiconductor heterostructures. Broader Impact We have extensive research collaborations with leading experimental and theoretical groups. The educational impact has included training undergraduate and graduate students, postdoctoral researchers, and development of three new courses to introduce quantum device and quantum algorithmic concepts to graduate and undergraduate students. Our program has contributed to homeland security and received funding from the National Security gency. Our outreach program has included sponsoring presentation events, and an international workshop series Quantum Device Technology, held in May of 22 and May 24, and sponsored by the Nanotechnology Council of IEEE and NS (via RO). We have worked with the REU site for students at SUNY Potsdam to guide several undergraduate research projects in the topics of quantum computing and quantum algorithms.

3 Collaboration Experiment: Sean Barrett, Yale ong Wen Jiang, UCL Marco Fanciulli, MDM Laboratory, Milan, Italy Theory: Leonid Fedichkin, Clarkson University Boris Malkin, Kazan State University, Russia Dima Mozyrsky, LNL Vladimir Privman, Clarkson University Israel Vagner, olon Institute of technology, Israel 3

4 Structure Natural licon: atom (group-iv) 28 92% % I=1/ % 5.43Å Diamond crystal structure 31 P electron spin (T=4.2K) T 1 ~ min T 2 ~ msecs P atom (group-v) + = b 15 Å a 25 Å Natural Phosphorus: 31 P 1% I=1/2 In the effective mass approximation the electron wave function is s-like: F( r) 1 = π ab e ( x y ) / a + z 2 / b 4 2

5 n application for QC -gate J -gate Bohr Radius: : a 25 Å b 15 Å x Ge 1-x 1-x Ge x Ge: a 64 Å b 24 Å B.E.Kane, Nature (1998) 31 P donor Qubit nuclear spin Qubit-qubit interaction electron spin Ex S 1 J -gate S 2 R.Vrijen, E.Yablonovitch, K.Wang,.W.Jiang,.Balandin, V.Roychowdhury, T.Mor, D.DiVincenzo, Phys. Rev. 62, 1236 (2) 31 P donor Qubit electron spin Qubit-qubit interaction electron spin f -gate S 1 Ex S 2 I 1 I 2 Qubit 1 Qubit 2 Qubit 1 Qubit 2 5

6 Interaction with phonons Donor electron spin in :P Sources of decoherence D. Mozyrsky, Sh. Kogan, V. N. Gorshkov, G. P. Berman Phys. Rev. B 65, (22) Gate errors X. u, S. Das Sarma, cond-mat/27457 Interaction with 29 nuclear spins Theory I.. Merkulov, l. L. Efros, M. Rosen, Phys. Rev. B 65, 2539 (22) S. Saikin, D. Mozyrsky, V. Privman, Nano Letters 2, 651 (22) R. De Sousa, S. Das Sarma, Phys. Rev. B 68, (23) S. Saikin, L. Fedichkin, Phys. Rev. B 67, 16132(R) (23) J. Schliemann,. Khaetskii, D. Loss, J. Phys., Condens. Matter 15, R189 (23) Experiments. M. Tyryshkin, S.. Lyon,. V. stashkin,. M. Raitsimring, Phys. Rev. B 68, (23) M. Fanciulli, P. ofer,. Ponti, Physica B , 895 (23) E. be, K. M. Itoh, J. Isoya S. Yamasaki, cond-mat/42152 (24) 6

Spin amiltonian 28 e = + ( i, j) Spin Z i nucl Z ( i) + f ( i) + Dip i i j e - 29 31 P Effect of external field Electronnuclei interaction Nucleinuclei interaction Effective Bohr radius ~ 2-25 Å

7 Spin amiltonian 28 e = + ( i, j) Spin Z i nucl Z ( i) + f ( i) + Dip i i j e P Effect of external field Electronnuclei interaction Nucleinuclei interaction Effective Bohr radius ~ 2-25 Å Lattice constant = 5.43 Å In a natural crystal the donor electron interacts with ~ 8 nuclei of 29 System of 29 nuclear spins can be considered as a spin bath Electron spin Zeeman term: Nuclear spin Zeeman term: e = Z nulc Z yperfine electron-nuclear spin interaction: gβs ( i) = γ i I f ( i) = S I i i Dipole-dipole nuclear spin interaction: Dip ( i, j) i = I D ij I j 7

8 yperfine interaction e - 29 Contact interaction: = Cont SI Dipole-dipole interaction: Dip µ µ = r e n 3 3( µ e r)( µ 5 r n r) yperfine interaction: f = ( S S S ) x y z xx yx zx xy yy zy xz yz zz I I I x y z Contact interaction only: pproximations: igh magnetic field Contact interaction igh magnetic field = xx yy zz = zx zy zz = zz 8

9 Energy level structure (high magnetic field) e Z = gβ z S z P P Z = γ P z I z - 31 P electron spin = P f P zz S z I P z - 31 P nuclear spin - 29 nuclear spin 1 Z 1 f 9

10 Effects of nuclear spin bath (low field) = xx yy zz gβδ ~ ( S+ I + S I + ) gβ P 2 15 e Z ~ z P = const 42Oe δ = const 3Oe 1/T [µs -1 ] 1 ρ = 1 e t/ T Magnetic field [Oe] S. Saikin, D. Mozyrsiky and V. Privman, Nano Lett. 2, (22) 1

11 (a) S= Donor electron spin in :P Effects of nuclear spin bath (high field) (b) S= = e - zx zy zz π -pulse e - + ~ ( t) x z Electron spin system Nuclear spin system z eff eff 28 I k z I k 31 P 31 P 11

12 yperfine modulations of an electron spin qubit.8.6 ρ ρ.4.2 Threshold value of the magnetic field for a fault tolerant 31 P electron spin qubit: ρ th max ~ 9T 2 S. Saikin and L. Fedichkin, Phys. Rev. B 67, article 16132(R), 1-4 (23) t t (µsec) 3.x x1-5 2.x x1-5 1.x1-5 5.x t (µsec) 4.x1-5 3.x1-5 2.x1-5 1.x t (µsec) 12

13 Spin echo modulations: Experiment x Spin echo: (τ) M x M. Fanciulli, P. ofer,. Ponti Physica B , 895 (23) τ 2τ t E. be, K. M. Itoh, J. Isoya S. Yamasaki, cond-mat/ nat T = 1 K [ 1] 13

14 Conclusions Effects of a nuclear spin bath on the decoherence of an electron spin qubit in a :P system has been studied. new measure of decoherence processes has been applied. In the low field regime the coherence of a qubit decays exponentially with a characteristic time, T ~.1 µsec. In the high magnetic field regime, quantum operations cause the qubit state to deviate from the ideal state. The characteristic time for these processes is on the order of.1 µsec. The threshold value of an external magnetic field required for fault-tolerant quantum computation is ext ~ 9 Tesla. S. Saikin, D. Mozyrsky, V. Privman, Nano Letters 2, 651 (22) S. Saikin, L. Fedichkin, Phys. Rev. B 67, 16132(R) (23) 14

15 Future prospects Spin diffusion Initial drop of spin coherence. M. Tyryshkin, S.. Lyon,. V. stashkin, and. M. Raitsimring Phys. Rev. B 68, (23) M. Fanciulli, P. ofer,. Ponti Physica B , 895 (23) Control for spin-spin coupling in solids S. Barrett s Group, Yale Development of error avoiding methods for spin qubits in solids. M. Fanciulli Group, MDM Laboratory, Italy 15

Lecture2: Quantum Decoherence and Maxwell Angels L. J. Sham, University of California San Diego

Michigan Quantum Summer School Ann Arbor, June 16-27, 2008. Lecture2: Quantum Decoherence and Maxwell Angels L. J. Sham, University of California San Diego 1. Motivation: Quantum superiority in superposition