Electron spin decoherence in solid-state nuclear spin baths: Understanding, control, and applications Ren-Bao Liu Department of Physics, The Chinese University of Hong Kong ASI 08/12/ Funded by Hong Kong RGC, NSFC, CUHK Focused Investments Scheme

Wen Yang (postdoc, Nan Zhao (Postdoc) Jian-Liang Hu (PhD student) Zhen-Yu Wang (PhD 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 USTC) Lu J. Sham (UCSD) Wang Yao (UCSD, HKU) Thanks to Wen Yang Nan Zhao Z. Y. Wang ASI 08/12/

ASI 08/12/ Outline  Introduction - Semiclassical theory: Gone can be back  Introduction - Quantum theory: Passive can be active  A difference between the two: Strong can be weak  An application of decoherence: Bad can be good

ASI 08/12/ 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).

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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/

ASI 08/12/ Pictorial Spin Dynamics The spin precesses about the magnetic field Schrödinger equation

Hahn echo Works perfectly for static fluctuations. Dynamical Fluctuations rotation 180 o about x-axis x y ASI 08/12/

Decoherence control by spin-flips (rooted in spin echo) Semiclassical picture of decoherence ASI 08/12/

II. Quantum theory Local magnetic field is a Q-number (quantum field) ASI 08/12/ Classical noise, static inhomogeneous broadening

Relevant systems: Electron spin in solids for qubits self-assembled dotinterface fluctuation islands gate-defined dot donor impurity P:Si NV center in diamond ASI 08/12/

1 electron spin + N nuclear spins in the bath The nuclear spins (bath) within a range and the electron spin (qubit) form a relatively close system. In type-IIa diamond, e.g., NV C: kHz >> 13 C - 13 C: 10 Hz ASI 08/12/ In GaAs QD, e.g., e-N: MHz >> N-N: kHz

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

Decoherence by quantum entanglement Bifurcated bath evolution  which-way info known  decoherence ASI 08/12/

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

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

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/

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

ASI 08/12/ 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)

NV center spins in diamond: Hot qubit ASI 08/12/ Quantum coherence time is RT in this US$10.8M worth type-IIa diamond, good for for solid-state quantum computing & magnetometry,  Chemical stability  Deep level: thermal stability  Weak Spin-orbit interaction (light C atoms, RT)  Low 13 C abundance  Transparent (optical access)  Non-toxic (medicine)

Pure-dephasing model for NV center spin in nuclear spin bath NV spin splitting hyperfine Bath spin interaction (dipole- dipole + Zeeman energy) Bath Hamiltonian conditioned on center spin state: e- 13 C interaction >> 13 C - 13 C interaction  About C spins form a “close” bath ASI 08/12/

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

Single- coherence double- coherence ASI 08/12/ Spin decoherence: The oldwife tale

Free-induction decay due to thermal (classical) noises from 13 C spins N. Zhao, Z. Y. Wang & RBL, PRL 106, (2011). ASI 08/12/

FID experiment & theory ASI 08/12/ Time (  s) Single coherenceMulti-coherence

ASI 08/12/ Spin decoherence: When the bath is small (therefore quantum)

Anomalous decoherence in a quantum bath Stronger “noises”  weaker decoherence ! N. Zhao, Z. Y. Wang & RBL, PRL 106, (2011) ASI 08/12/ Stronger noises on qubit  Stronger control over environment! B=0.3 Tesla

Conditional bath evolution at high field: Nuclear spin pair-flips NV ASI 08/12/

Multi-transition: Pseudo-fields for the two e-spin states are almost anti-parallel  slower decoherence ASI 08/12/

Single-transition: Pseudo-fields for the two e-spin states are not (anti-)parallel  faster decoherence ASI 08/12/

Experimental verification ASI 08/12/ B=5 Gauss. Calculation w/o fitting parameters At this weak field, decoherence due mainly to single nuclear spin precessing. Insensitive to specific interactions. Observable in other systems, e.g., singlet- triplet transitions?

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

Decoherence by pairwise flip-flop B=0.15 THahn echo, incl. all 13 C spins Rare coherent pairs  coherent oscillations dimer NV Many incoherent pairs  smooth decoherence Dimer: interaction strength ~ hyperfine energy cost  large-amplitude flip-flop dimer only ASI 08/12/ Previously noted by Maze et al (PRB 2008)

A dancing couple out of random walkers UDD1 UDD2 UDD3 UDD4 UDD5 Coherence time prolonged by DD, oscillations due to the dimer are pronounced. Uhrig DD: a 1.2nm; B  0.15 T ASI 08/12/

Atomic-scale magnetometry of a dimer ASI 08/12/ Azimuth angle  from [1-10] Contribution by the dimmer only A ~1.2nm from NV; B=.15 T, tilted from [111] by 10° NV center spin decoherence vs. time & B-field direction

Fingerprint screening ASI 08/12/

ASI 08/12/ NMR of a 13 C 2 molecule? Even better if NMR of real single molecules outside diamond could be detected. NV 13 C

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 O H H ASI 08/12/

is enhanced by a factor of N 2 (N: # of pulses) right frequency Many-pulse DD: Suppressing noises but a certain frequency ASI 08/12/ Dynamical decoupling suppresses noises c.f. optical grating effect background noise

Toward single molecule NMR NV 13 C Spin coherence of an NV center 10 nm below 5 1 H 2 16 O or 12 C 1 H 4 molecules, under 100-pulse periodic dynamical decoupling, at zero B-field O H H H H H H 12 C ASI 08/12/

Single-molecule NMR: Cascade amplification of weak signals Hz 1 eV 10 3 Kelvin single photon detection coupling to distant nuclear spins GHz single electron spin resonance MHz kHz coupling to single nuclear spin nearby fingerprint frequencies amplified by many-pulse dynamical decoupling fingerprint oscillation of nuclear spin clusters Features:  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)  High-resolution of resonances (c.f., solid-state NMR: inter-molecule interaction causes large broadening) ASI 08/12/

Summary  quantum theory and hence control schemes;  Anomalous effect in quantum bath: Stronger “noises” may cause slower decoherence;  Atomic-scale magnetometry of single nuclear spin clusters at distance;  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) ASI 08/12/ For more, visit