preserving quantum coherence of spins in the presence of noises ren-bao liu department of physics,...

Preserving quantum coherence of spins in the presence of noises

Ren-Bao Liu

Department of Physics, The Chinese University of Hong Kong

http://www.phy.cuhk.edu.hk/rbliu

PRACQSYS 7/8/14 Cambridge 1www.phy.cuhk.edu.hk/

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Funded by Hong Kong RGC, CUHK-FIS, NSFC

Ultrasensitive magnetometryTheory: Nan Zhao, Jian-Liang Hu, S.W. Roy Ho, Jones

T. K. Wan Experiments: Joerg Wrachtrup group (Stuttgart);

Jiangfeng Du group (USTC)

Probe to many-body physcsTheory: Shao-Wen Chen, Zhan-Feng Jiang, Wenlong

Ma (IoS, CAS), Shushen Li (IoS, CAS), Nan Zhao (CSRC)

Experiments: Gary Wolfowicz, John J. L. Morton (UCL)

Collaborators


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Outline

PRACQSYS 7/8/14 Cambridgewww.phy.cuhk.edu.hk/

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I. Introduction– understanding and withstanding qubit decoherence

II. Spin decoherence controlled for ultrasensitive magnetometry – few-body physics in environments

III. Qubit decoherence controlled to detecting many-body physics– quantum criticality at high temperature

IV. Nuclear spin correlations detected by central spin decoherence– first step toward detecting many-body physics in baths


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Spin qubits in solid-state environments

self-assembled dot fluctuation islands

NV center in diamond

gate-defined dot donor impurity P:Si

A model system: 1 electron spin + N nuclear spins

Interaction within bath causing fluctuations and hence qubit decoherence


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Spin decoherence

expt i


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exp

decoherence

x yS i S i

0

noise random field

Random phase: t

B

B t dt

expx yS iS i 0B ( )tB

Dynamical decoupling control of qubit decoherence

Average1 2 1 2

1ˆ ˆ( ) exp2zB t S B t B t dt dt

e S

0exp S d


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R. Kubo, J. Phys. Soc. Jpn. 9, 935 (1954);P. W. Anderson, ibid. 9, 316 (1954).

Quantum fluctuation vs thermal noise

Quantum fluctu a 0tion: ,H B

ˆ

ˆ ˆdynamical quantum fluctuation

but ,

ˆso 0,

iHtI I

iHt i

I

Ht

HB I B I e I C t I

B B

I E I

t e eB


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ˆ Thermal fluctuation: and I IP I I B I B I static inhomogeneous broadening DB0

Cˆ ˆ ˆ ˆ2 II

S P I B I I B I B B

ˆ ˆ2Q I JII JS P I B J J B I E

Characteristic noise spectrum of a molecule

2k kk

S b

e.g., transitions in a water molecule under zero field

O

HH


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Average1 2 1 2 1 2

1ˆ ˆ( ) exp2zF t B t S B t B t F t F t dt dt

e S

Dynamical decoupling control of qubit decoherence

2

0exp ,S F dt

F t 1

1 N t1 3 4 1N 2


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spin decoherence & beyond


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Understanding central spin decoherence (nuclear spin baths)Microscopic quantum theories: Das Sarma, Sham, Liu, Loss, etc)

Protecting spin coherence (by dynamical decoupling)Viola, Lidar, Uhrig, Biercuk, Du, and many other groups

The new stage:Using spin decoherence as a resource of detectionS(w) related to thermodynamics & excitations in environment.

Cˆ ˆ ˆ ˆ2 II

S P I B I I B I B B

Outline


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NV13C

Atomic-scale magnetometry & single-molecule NMRN. Zhao et al, Nat. Nanotech. 6, 242 (2011).

B Laser

MW

Central spin decoherence for ultrasensitive sensing


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NV 10 nm below 5 1H216O, 100-pulse DD

O

HH

2k kk

S b 2

0,exp F tS d


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A single 13C nuclear spin 3 nm away, Nature Nano 7, 657 (2012)

34 kHz

Similar experiments done in Harvard & TU Delft

CSRC-QOQI 2014/7/4www.phy.cuhk.edu.hk/

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Nature Physics 10, 21 (2014)

7 kHz

Central spin decoherence for single-molecule NMR

How about detection of transitions (fluctuations) in many-body systems?


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Summary of Part II

Schneide, Porras & Schaetz, Rep Prog. Phys (2011)

Outline


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1D transverse field Ising model


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1x x zj j j

j

H

1c FM PM

gap

No finite-temperature phase transition

QC at zero temperature

Excitation is gapless @ QC

Detection of quantum criticality by a probe spin


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H.T. Quan, Z. Song, X. F. Liu, P. Zarnardi & C. P. Sun, PRL 96, 140604 (06)

QC at zero temperature

Diverging fluctuation at critical point rapid probe spin decoherence

At high temperature, feature at QC vanishes


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S. W. Chen, Z. F. Jiang & RBL, New J Phys (2013)

high T (small b), thermal fluctuation conceals quantum criticality

To observe quantum criticality: temperature << interaction

nano-Kelvin or pico-Kelvin needed for nuclear spins or cold atoms!

Quantum fluctuation vs thermal noise

Quantum fluctu a 0tion: ,H B

ˆ ˆdynamical quantum fluctuation iHt iHtB t e Be


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ˆ Thermal fluctuation: and I IP I I B I B I static inhomogeneous broadening DB0

At high temperature, thermal noise >> quantum fluctuationSpin echo can remove the static thermal noise effect

What if thermal fluctuation removed?


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Quantum criticality can be seen even @ infinite temperature

Hahn echo at infinite temperature

At time >> inverse interaction energy, critical feature is seen


t ~ 1/T


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Susceptibility at different 1/T

and spin echo signal at different t


1 2 1 2 1 20

1ln

2

tS t C t t F t F t dt dt

Decoherence function & susceptibility


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2 0

1

4x C i d

Ng

Probe spin coherence (time) ~ susceptibility (inverse temperature)

Spin echo removes static thermal fluctuation and reveals quantum fluctuation.

Summary of Part III


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quantum face transition

nanokelvin millisecond picokelvin second

Suppress thermal noise to single out quantum noise by spin echo

Outline


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II. Qubit decoherence for ultrasensitive magnetometry – few-body physics in environments

III. Qubit decoherence controlled to detect many-body physics:– quantum criticality at high temperature

IV. Nuclear spin correlations detected by central spin decoherence– first steps toward detecting many-body physics in noises

Many-body correlations in a nuclear spin bath (Si:P)


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P donor electron spin coupled to 29Si nuclear spins decoherence

( 4 )

ze z z i i

i

z z zn i ij i j i j i j

i i j

H S S A I

I D I I I I I I

V – intra-bath interaction

bz – local field by hf coupling

Qubit-bath model for pure dephasing

z zH b S V

Overhauser field operatorBath spin interaction (dipole-dipole, Zeeman energy, etc.)

New view: Center spin imposes interaction on bath

with 2zH V V H V b

z n nn

b A J


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Old View: Bath imposes (quantum) noise on center spin

Decoherence by quantum entanglement

( )I t ( )I t

I Bifurcated bath evolution which-way info known decoherence

( ) ( )I t I t

( ) iV tI t e I

L S t I t I t


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Many-body correlations in baths built up during decoherence.

Recoherence by disentanglement (quantum erasure)

( )I t ( )I t

I

( )I t

Bifurcated bath evolution which-way info known less coherence left

qubit flip bath pathways exchange directions pathway intercross which-way info erased recoherence


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Many-body correlations manipulated.

Decoherence under DD: Formalism

†

, +( ) ,n n nL T I U T U T I

2 1 1[ ( 1) ]( ) ( )( ) ( )( )n

z n z zn i V b T t i V b t t i V b tU T e e e ，


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exp exp ?L I iV t iV t I

Linked-cluster expansion (LCE)

0( )

( ) , .t

z z zi V t dtib t ib t ib tiHtV t e Ve e e e

Interaction picture (focus on the bath correlations):

0( )

1 2 3 4

1 1 linked0 0

= exp ,

T̂ ( ) ( ) .!

Ti V t dt

lT T

l l l

I e I V V V V

iV dt dt I V t V t I

l

Saikin et al, Phys. Rev B 75.125314 (2007)


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Linked Feynman diagrams up to fourth order:


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Leading 3- & 4-spin correlations

Leading pair-correlation

Pulse number-parity effect

Theorectical results (CCE): B//[110]Bath: 5000 nuclear spins within 8 nm from the P donor.

Odd pulse number:

Even pulse number:

2.5odd, SD( ) exp /L T T

4even, SD( ) exp /L T T


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DD to suppress quantum fluctuation

CPMG eliminates quantum fluctuations (in the leading order) at echo time

RBL, W. Yao & L. J. Sham,Intl. J. Mod. Phys. B 22, 27 (2008)


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4th-order pair correlation: 4th-order 3- or 4-spin correlations:

Underlining many-body processes:

Odd pulse number

Even pulse number


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LCE-V4z contains 3- & 4-spin correlations

4-body correlations dominate


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W. L. Ma et al.arXiv:1404.2717

Experiments vs theory

ID SDexp / /T T

ID 10 ms (due to P donors)

[P] = 3x1014/cm3

1 1sT B 3452 G

Temperature: 6K


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Summary of Part IV


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Many-body correlations built up and manipulated during central spin decoherence (at “high” temperature).

Dynamical decoupling to separate second-order (two-body) and fourth-order (three-body and four-body) correlations in the nanoscale nuclear spin bath.

Precursor of sensing long-range correlations?

preserving quantum coherence of spins in the presence of noises ren-bao liu department of physics,...

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