Preserving quantum coherence of spins in the presence of noises
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Transcript of Preserving quantum coherence of spins in the presence of noises
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
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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
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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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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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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
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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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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
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
S. W. Chen, Z. F. Jiang & RBL, New J Phys (2013)
t ~ 1/T
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Susceptibility at different 1/T
and spin echo signal at different t
S. W. Chen, Z. F. Jiang & RBL, New J Phys (2013)
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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I. Introduction– understanding and withstanding qubit decoherence
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?