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Quantum interferences induced by the
subwavelength-confined anisotropic
Purcell factor
State Key Laboratory for Mesoscopic Physics & Department of Physics, Peking University, China
Ying Gu
*email: ygu@pku.edu.cn Dec. 07, 2012
2
Contributors:
Luojia Wang, Pan Ren, Qihuang Gong（Peking Univ.）
Olivier J. F. Martin (EPFL, Switzerland)
Junxiang Zhang, Tiancai Zhang （ShanXi Univ., China）
Jingping Xu （Tong ji Univ., China）
Shiyao Zhu （CRSC, China)
Funding:
NSFC, 973 Project, State Key Lab., Peking Univ.
3 3
Outline:
1. Background
Effects of Spontaneously Generated Coherence :
2. Spontaneous Emission Spectra
3. Electromagnetically Induced Transparency (EIT)
In the anisotropic Purcell factor
4. Summary
1. Background
4
5
Surface plasmon polariton (SPP)
ultrasmall optical mode volume Vm
Localized SP or SPR:
localized oscillation
strong local field
SPP: collective oscillations of free electrons
evanescent EM mode bound to surface
William L. Barnes, Alain Dereux & Thomas W. Ebbesen, nature, 424, 824 (2003);
V. Zayatsa, et al, Phys Rep. 2005, 408:131–314;
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With ultrasmall optical mode Vm
What’s new for quantum emitters?
R. R. Chance, A. Prock, and R. Silbey, J. Chem. Phys.62, 2245 (1975); D. E. Chang et al., Phys.
Rev. Lett. 97, 053002 (2006); Edo Waks and Deepak Sridharan, Phys. Rev. A, 82, 043845 (2010)
Weak coupling: Purcell factor F=/ 0
anisotropic electric mode density of oscillations
anisotropic optical mode density
anisotropic decay rates enhanced (F>1)or
suppressed (F<1) spontaneous emission at
subwavelength scale
Strong coupling: Cavity QED
Vm is extremely small g ( ) is very large
Q is not high due to loss
Low-light level nonlinear optics
m
Q
V
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Main research work in this field:
1. Decay rate modification at subwavelength
scale
2. Near field excitation of quantum emitters
3. Strong coupling between plasmonic
nanostructures and quantum emitters
--------The Case for Plasmonics, Mark L. Brongersma, et al,science, VOL 328,440
(2010).
“By squeezing light into nanoscale volumes, plasmonic
elements allow for fundamental studies of light-matter
interactions at length scales that were otherwise
inaccessible”
8
Decay rate modification of quantum emitter
Features of plasmon structures:
1. large Purcell factor 2. anisotropic decay rates R.R.Chance et al, the journal of cheimical physics, 62,2245 (1975);R. Ruppin, J. Chem.Phys.
76,1681 (1982).
9 Sergei Kuhn et al, PRL 97, 017402 (2006) ; Pascal Anger et al, PRL 96, 113002 (2006)
Molecular fluorescence near plasmonic strucrures ------Near field excitation of quantum emitters
Characteristic:
Change of life time
Fluorescence: from quenching,
via enhancement, to suppressing
10
Strong coupling between plasmons and quantum
emitters
A. V. Akimov et al, NATURE|Vol 450|402| 2007; A. Ridolfo, PRL 105, 263601 (2010)
Generation of single
surface plasmons source
Quantum Plasmonics with
Quantum Dot-Metal Nanoparticle
Cavity QED treatment
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Our work: to pursue intercrossing between
quantum optics and plasmonics in weak coupling
☆ Resonance fluorescence of single molecules
assisted by a plasmonic structure Ying Gu, Lina Huang, Olivier J.F. Martin, and Qihuang Gong, Phys. Rev. B, 81, 193103 (2010).
☆ Intrinsic Quantum Beats of Atomic Populations in
Isotropic and Plasmon-induced anisotropic vacuum Ying Gu, Luojia Wang, et al, Plasmonics, 7, 33－38 (2012).
★ Surface-Plasmon-Induced Modification on the
Spontaneous Emission Spectrum via
Subwavelength-Confined Anisotropic Purcell
Factor Ying Gu, Luojia Wang, et al, Nano Letters,12, 2488-2493 (2012).
★ Effects of Spontaneously Generated Coherence
on Electromagnetically Induced Transparency
in the Anisotropic Purcell Factor Luojia Wang ,Ying Gu, et al, in a preparation.
12 Resonance Fluorescence of Single Molecules Assisted by a Plasmon Structure
Ying Gu, Lina Huang, Olivier J.F. Martin, and Qihuang Gong, Phys. Rev. B, 81, 193103 (2010).
Aim to: realize resonance fluorescence of single
molecules near the plasmonic structure
Resonance wavelength matching (SPR=RT=590 nm)
a balance between near field enhancement
and decay rate modification
Mollow triplet and photon antibunching
4 silver nanostrips, 110*50*40 nm3
DBATT molecules
☆ Resonance fluorescence of single molecules
assisted by a plasmonic structure
13
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),()()(
),()(2
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)()2(*
2
)()1(*
1
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)1(*
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1
)2(21)1(1)1(
21
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212
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Crossing damping terms
between two closing upper
levels lead to several quantum
interference effects, named
Spontaneously Generated
Coherence (SGC)
Two dipoles are acting with the common vacuum.
14
p=0
p=1
Population trapping condition
The populations are trapped in upper
levels due to quantum interferences.
Dressed state analysis
The spontaneous emission from
|0,n> to |c> is zero
Spontaneous emission cancellation
Lee H, Polynkin P, Scully MO,
et al., PHYSICAL REVIEW A,
55, 4454-4465 (1997) .
.)()()(
),()()(
),()(2
)(2
)(
),()(2
)(2
)(
)()2(*
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)()1(*
1
)2(*
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1
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21
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212
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15
decay rates and crossing damping
in terms of Green’s tensor.
In the anisotropic purcell factor what is different?
new trapping conditions
Ying Gu, Luojia Wang, et al. Intrinsic Quantum Beats of Atomic Populations and Their
Nanoscale Realization through Resonant Plasmonic Antenna, Plasmonics, 7, 33－38 (2012)
Anisotropic Purcell factors lead to
the crossing damping of two
orthogonal dipoles is not zero.
Quantum beats of population oscillations
Beat frequency:
Skip the complex formulas
New quantum interferences in
isotropic and anisotropic vacuum.
Beat frequency is determined by
spacing and dipole moment ratio.
16
Rabi frequency:
Ying Gu, Luojia Wang, et al. Intrinsic Quantum Beats of Atomic Populations and Their
Nanoscale Realization through Resonant Plasmonic Antenna, Plasmonics, 7, 33－38 (2012)
However, “particularity” of anisotropic Purcell
factors is not shown in this case.
17
2. Surface-Plasmon-Induced Modification
on the Spontaneous Emission Spectrum via
Subwavelength-Confined Anisotropic
Purcell Factor
The aim:
the Spontaneous emission
spectrum of four level atoms
with crossing damping.
Two dipoles are not parallel and
the anisotropic Purcell Factor works.
18
Theory
decay rates and crossing damping
in anisotropic vacuum
Green’s tensor
Skip the complex formulas of Master equation, dressed
state analysis, quantum regression thereom
Ying Gu et al. Surface-Plasmon-Induced Modification on the Spontaneous Emission Spectrum via
Subwavelength-Confined Anisotropic Purcell Factor, Nano Lett. 12, 2488-2493 (2012).
linewidths of the central peak and sidebands of SE
19
Mechanism of SE linewidth control
Enlarging the anisotropy
increases the variation.
If the polarization angle bisector of two dipole moments lies
along the major/minor axis of the effective decay rate ellipse,
destructive/constructive interference narrows/widens the
center spectral lines associated with fluorescence.
Ying Gu et al. Surface-Plasmon-Induced Modification on the Spontaneous Emission Spectrum via
Subwavelength-Confined Anisotropic Purcell Factor, Nano Lett. 12, 2488-2493 (2012).
Left：Rapid spectral line narrowing of atom approaching a
metallic nanowire, i.e., becomes small.
Right: the linewidth “pulsing” following periodically-varying
decay rates near a periodic metallic nanostructure
In Surface-Plasmon-Induced
Subwavelength-Confined Anisotropic Purcell factor
20 Ying Gu et al. Surface-Plasmon-Induced Modification on the Spontaneous Emission Spectrum via
Subwavelength-Confined Anisotropic Purcell Factor, Nano Lett. 12, 2488-2493 (2012).
21
3. Effects of Spontaneously Generated
Coherence on Electromagnetically Induced
Transparency in the anisotropic Purcell factor
S. E. Harris, Physics Today, 50, 36 (1997)
Two-photon resonance condition:
pc21
Position of ac stark splittings :
dressed state structure.
Electromagnetically induced transparency (EIT)
22
23 Luojia Wang, Ying Gu et al. Effects of Spontaneously Generated Coherence on
Electromagnetically Induced Transparency in Plasmon nanocavity, In a preparation.
New trapping condition: C=C1∪C2
C1: two photon resonance condition
C2: population trapping condition
Corresponding to the transparency points
The condition of “Two parallel dipoles” still can’t be broken.
24
the linewidths of three peaks are determined by Rabi
frequencies, detuning , anisotropic decay rates and
crossing damping, and the spacing between upper levels.
Luojia Wang, Ying Gu et al. Effects of Spontaneously Generated Coherence on
Electromagnetically Induced Transparency in Plasmon nanocavity, In a preparation.
The interaction Hamiltonian
Let probe light is very weak, we have
25
In a vaccum
for two sets of parallel dipoles
1. New transparent points
appear. Y. J. Zhen et al. PHYSICAL REVIEW A 83,
013810 (2011).
2. The positions of peaks are
corresponding to the
eigenvalues of interaction H.
3. linewidths are very sensitive
to the above parameters, here
is the spacing between two
upper levels.
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In anisotropic Purcell factors for two sets of parallel dipoles
Wider
Narrower
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4. Summary
1. Mechanism of spontaneous emission spectrum
control, its proof and demonstration in
subwavelength-confined anisotropic Purcell factor
2. New EIT condition in Double-Λ system, two
transparent points, linewidth of EIT peaks
Next, using this new EIT to realize the quantum memory,
to control the spontaneous emission, to design the
single surface plasmons source on demand …..
Also, strong coupling between plasmon nanostructure
and quantum emitters ……
Experiments！
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