Electron spin decoherence in solidstate nuclear spin baths

Electron spin decoherence in solid-state nuclear spin baths: Understanding, control, and applications Ren-Bao Liu rbliu@phy. cuhk. edu. hk Department of Physics, The Chinese University of Hong Kong http: //www. phy. cuhk. edu. hk/rbliu Funded by Hong Kong RGC, NSFC, CUHK Focused Investments Scheme ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 1

Thanks to Wen Yang (postdoc, now @UCSD) Nan Zhao (Postdoc) Jian-Liang Hu (Ph. D student) Zhen-Yu Wang (Ph. D student) Sai-Wah Ho (MPhil student) Jones Z. K. Wan (Postdoc) Jiangfeng Du, Xing Rong, Ya Wang, Jiahui Yang, Pu Huang, Xi Kong, Pengfei Wang, Fazhan Shi (experimentalists @ USTC) Lu J. Sham (UCSD) Wang Yao (UCSD, now @ HKU) ASI 08/12/2011 Wen Yang Nan Zhao Z. Y. Wang www. phy. cuhk. edu. hk/rbliu 2

Outline Ø Introduction - Semiclassical theory: Gone can be back Ø Introduction - Quantum theory: Passive can be active Ø A difference between the two: Strong can be weak Ø An application of decoherence: Bad can be good ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 3

I. Spin decoherence & control: Semiclassical theory R. Kubo, J. Phys. Soc. Jpn. 9, 935 (1954). P. W. Anderson, J. Phys. Soc. Jpn. 9, 316 (1954). ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 4

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Coherence of the slow and the swift It works when the snails’ speeds are kept constant (but random). ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 6

Pictorial Spin Dynamics Schrödinger equation The spin precesses about the magnetic field ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 7

Hahn echo y x rotation 180 o about x-axis Works perfectly for static fluctuations. ASI 08/12/2011 Dynamical Fluctuations www. phy. cuhk. edu. hk/rbliu 8

Semiclassical picture of decoherence Decoherence control by spin-flips (rooted in spin echo) ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 9

II. Quantum theory Local magnetic field is a Q-number (quantum field) Classical noise, static inhomogeneous broadening ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 10

Relevant systems: Electron spin in solids for qubits self-assembled dot gate-defined dot ASI 08/12/2011 interface fluctuation islands donor impurity P: Si NV center in diamond www. phy. cuhk. edu. hk/rbliu 11

1 electron spin + N nuclear spins in the bath In Ga. As QD, e. g. , e-N: MHz >> N-N: k. Hz In type-IIa diamond, e. g. , NV--13 C: k. Hz >> 13 C - 13 C: 10 Hz The nuclear spins (bath) within a range and the electron spin (qubit) form a relatively close system. ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 12

Qubit-bath model for pure dephasing Bath spin interaction (dipole, Zeeman energy, etc. ) Overhauser field operator Zeeman energy Old View: Bath imposes (quantum) noise on center spin New view: Center spin imposes interaction on bath ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 13

Decoherence by quantum entanglement Bifurcated bath evolution which-way info known decoherence ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 14

Quantum many-body theory for spin bath dynamics Step stones: 0. Semiclassical spectral diffusion theory, Anderson, Kubo (1956) 1. Cluster expansion, Witzel & Das Sarma (2005) 2. Pair-correlation: Yao, RBL & Sham (2006). Cluster-correlation expansion (a generalization of textbook cluster expansion to finite systems, good for nano-science): W. Yang & RBL, Phys. Rev. B 78, 085315 (2008). ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 15

Experiments vs. theory Phosphorus donor spins in silicon Black: Experiment [Lyon et al, PRB (2003)] Red: CCE calculation (Nan Zhao, unpublished) ASI 08/12/2011 WITHOUT fitting parameters Nitrogen-vacancy center spin in diamond Black: Experiment [Lukin et al Science (06)] Blue: CCE calculation (Nan Zhao, unpublished) www. phy. cuhk. edu. hk/rbliu 16

Recoherence by disentanglement (quantum erasure) Bifurcated bath evolution which-way info known less coherence left qubit flip bath pathways exchange directions pathway intercross which-way info erased recoherence ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 17

Resurrecting from ashes: When disentangled W. Yao, RBL, and L. J. Sham, Phys. Rev. Lett. 98, 077602 (07). Observable if thermal fluctuation suppressed: Duncan Steel, Amir Yacoby, …? ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 18

Dynamical disentanglement and dynamical decoupling Talks in this ASI by Lu Sham, Goetz Uhrig, Jiangfeng Du, Jiangbin Gong, S. Das Sarma, Amir Yacoby, Joerg Wrachtrup Reviews, e. g. , W. Yang, Z. Y. Wang and R. B. Liu, Front. Phys. 6, 2 (2011). Z. Y. Wang and R. B. Liu, Chapter 15 in Quantum Error Correction, eds. D. Lidar et al (Cambridge U Press, in press) ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 19

NV center spins in diamond: Hot qubit Ø Chemical stability Ø Deep level: thermal stability Ø Weak Spin-orbit interaction (light C atoms, coherence @ RT) Ø Low 13 C abundance Ø Transparent (optical access) Ø Non-toxic (medicine) Quantum coherence time is long @ RT in this US$10. 8 M worth type-IIa diamond, good for solid-state quantum computing & magnetometry, http: //news. yahoo. com ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 20

Pure-dephasing model for NV center spin in nuclear spin bath e- 13 C interaction >> 13 C - 13 C interaction About 500 13 C spins form a “close” bath NV spin splitting hyperfine Bath spin interaction (dipole + Zeeman energy) Bath Hamiltonian conditioned on center spin state: ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 21

The stronger, the weaker Anomalous decoherence effect in a quantum bath Theory: N. Zhao, Z. Y. Wang & RBL, PRL 106, 217205 (2011). Experiments: P. Huang et al. Nature Comm. 2, 570 (2011) Can quantum bath be approximated by a classical noise? ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 22

Spin decoherence: The oldwife tale doublecoherence Singlecoherence ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 23

Free-induction decay due to thermal (classical) noises from 13 C spins N. Zhao, Z. Y. Wang & RBL, PRL 106, 217205 (2011). ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 24

FID experiment & theory Single coherence Multi-coherence Time (ms) ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 25

Spin decoherence: When the bath is small (therefore quantum) ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 26

Anomalous decoherence in a quantum bath Stronger “noises” weaker decoherence ! Stronger noises on qubit Stronger control over environment! N. Zhao, Z. Y. Wang & RBL, PRL 106, 217205 (2011) B=0. 3 Tesla ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 27

Conditional bath evolution at high field: Nuclear spin pair-flips NV ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 28

Multi-transition: Pseudo-fields for the two e-spin states are almost anti-parallel slower decoherence ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 29

Single-transition: Pseudo-fields for the two e-spin states are not (anti-)parallel faster decoherence ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 30

Experimental verification At this weak field, decoherence due mainly to single nuclear spin precessing. Insensitive to specific interactions. Observable in other systems, e. g. , singlettriplet transitions? B=5 Gauss. Calculation w/o fitting parameters ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 31

Atomic-scale magnetometry using NV spin coherence 2>>1+1 1 nucleus is featureless; 2 (or more) nuclei have characteristic. N. Zhao, J. L. Hu, S. W. Ho, J. T. K. Wan, & RBL, Nature Nanotech. 6, 242 (2011). ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 32

Decoherence by pairwise flip-flop Hahn echo, B=0. 15 T dimer NV dimer only incl. all 13 C spins Previously noted by Maze et al (PRB 2008) Dimer: interaction strength ~ hyperfine energy cost large-amplitude flip-flop Many incoherent pairs smooth decoherence Rare coherent pairs coherent oscillations ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 33

A dancing couple out of random walkers UDD 1 UDD 2 UDD 3 a dimer @ 1. 2 nm; B=0. 15 T UDD 4 Uhrig DD: UDD 5 ASI 08/12/2011 Coherence time prolonged by DD, oscillations due to the dimer are pronounced. www. phy. cuhk. edu. hk/rbliu 34

Atomic-scale magnetometry of a dimer Azimuth angle f from [1 -10] A dimer @ ~1. 2 nm from NV; B=. 15 T, tilted from [111] by 10° NV center spin decoherence vs. time & B-field direction Contribution by the dimmer only ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 35

Fingerprint screening ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 36

NMR of a 13 C 2 molecule? Even better if NMR of real single molecules outside diamond could be detected. ASI 08/12/2011 13 C NV www. phy. cuhk. edu. hk/rbliu 37

Noise spectrum due to weak coupling to a molecule Weak hyperfine coupling Transition between nuclear spin states Noise spectrum e. g. , transitions in a water molecule under zero field H H O ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 38

Many-pulse DD: Suppressing noises but one @ a certain frequency background noise Dynamical decoupling suppresses noises Noise @ right frequency is enhanced by a factor of N 2 (N: # of pulses) c. f. optical grating effect ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 39

Toward single molecule NMR Spin coherence of an NV center 10 nm below 5 1 H 216 O or 12 C 1 H 4 molecules, under 100 -pulse periodic dynamical decoupling, at zero B-field 13 C NV H 12 C H H H O ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 40

Single-molecule NMR: Cascade amplification of weak signals single photon detection 1015 Hz 1 e. V 103 Kelvin single electron spin resonance coupling to single nuclear spin nearby coupling to distant nuclear spins noises @ fingerprint frequencies amplified by many-pulse dynamical decoupling GHz MHz k. Hz fingerprint oscillation of nuclear spin clusters Features: Ø Full information about nuclear spin interaction (c. . f. liquid-state NMR: dipolar intra-molecule interaction averaged to zero by rapid rotation of molecules under B field) Ø High-resolution of resonances (c. f. , solid-state NMR: inter-molecule interaction causes large broadening) ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 41

Summary Ø quantum theory and hence control schemes; Ø Anomalous effect in quantum bath: Stronger “noises” may cause slower decoherence; Ø Atomic-scale magnetometry of single nuclear spin clusters at distance; Ø Single-molecule NMR by many-pulse DD Perspective: Single center spins as media for detecting physics and manipulating information in a quantum bath (e. g. , nuclear spins) For more, visit http: //www. phy. cuhk. edu. hk/rbliu ASI 08/12/2011 www. phy. cuhk. edu. hk/rbliu 42