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TRANSCRIPT
Shanxi University July 2018
Luis A. Orozco www.jqi.umd.edu
Atoms around Optical Nanofibers, modifications on the spontaneous emission
Graduate Students and Postdoctoral associates: J. E. Hoffman, J. A. Grover, J. Lee, S. Ravets (I. d’Optique), P. Solano.
Undergraduate Students: U. Chukwu, C. Ebongue, E. Fenton, B. Friedman, X. Gutierrez, D. Hemmer,
A. Khan, P. Kordell, E. Magnan, D. Ornelas, A. Preciado, J. E. Uruñuela, J. D. Wong-Campos, A. Wood.
Professors and Researchers:
P. Barberis Blostein, G. Beadie, F. K. Fatemi, L. A. Orozco, S. L. Rolston.
University of Maryland, Institute D’Optique, National Institute of Standards and
Technology, Naval Research Laboratory, Army Research Laboratory.
Support from Atomtronics MURI from ARO, DARPA, the Fulbright Foundation, NSF through PFC@JQI, ONR.
Optical Nanofibers
Waist 480 nm, 7 mm long
Taper lenght 28 mm
Angle 2 mrad
Core diameter 5 μmCladding diameter 125 μm
Unmodified fiber
(not to scale)
(a)
Very large radial gradients of E • Div E=0 implies large
longitudinal components.
• The evanescent field can have a longitudinal component of the
polarization! €
∂Er
∂r+∂Ez
∂z= 0
Proportional to the electric field of the guided mode.
Density of modes
Decay into the nanofiber mode
Cooperativity
C1 =β
(1−β)=γ1Dγ rad
Not to scale
γ rad
γ1D
C1 is the ratio of what goes into the selected mode to what goes into all the rest
ONF Optical Density
OD1(!r ) = σ 0
A(!r )
50nm away from the surface
1 atom can block 10% of the light!!
Not to scale
ONF Optical Density
Not to scale
0 50 100 150 200 2500.00
0.05
0.10
0.15
r (nm)
σ 0/Aeff
OD1(!r ) = σ 0
A(!r )
50nm away from the surface
1 atom can block 10% of the light!!
Super- and Sub-radiance (a classical explanation)
“When two organ pipes of the same pitch stand side by side, complications ensue which not infrequently give trouble in practice. In extreme cases the pipes may almost reduce one another to silence. Even when the mutual influence is more moderate, it may still go so far as to cause the pipes to speak in absolute unison, in spite of inevitable small differences.
Lord Rayleigh (1877) in "The Theory of Sound".
Super- and Sub-radiance (a classical explanation)
We need the response of one oscillator due to a nearby oscillator:
!!a1 +γ0 !a1 +ω02a1 =
32ω0γ0d̂1 ⋅
!E 2!r( )a1,
γ = γ0 +32γ0Im d̂1 ⋅
!E 2!r( ){ }, with d̂1 ⋅
!E 2 0( ) = 2
3
ω =ω0 −34γ0 Re d̂1 ⋅
!E 2!r( ){ }
I = E02= I0 I = 4I0
Δt = τ 0 Δt = 12τ 0
ℜe{E}
ℑm{E}
Super- and Sub-radiance (a classical explanation)
Normal radiance Super-radiance
ℜe{E}
ℑm{E}
I = E02= I0 I = 4I0 I = 0
Δt = τ 0 Δt = 12τ 0 Δt =∞
ℜe{E}
ℑm{E}
Super- and Sub-radiance (a classical explanation)
Normal radiance Super-radiance Sub-radiance
ℑm{E}
ℜe{E}ℜe{E}
ℑm{E}
Δt = τ 0 Δt = 12τ 0 Δt =∞
ℜe{E}
ℑm{E}
Super- and Sub-radiance (a classical explanation)
Normal radiance Super-radiance Sub-radiance
ℑm{E}
ℜe{E}ℜe{E}
ℑm{E}
ge + eg ge − eg
Δt = 12τ 0 Δt =∞
ℜe{E}
ℑm{E}
Super- and Sub-radiance (a classical explanation)
Super-radiance Sub-radiance
ℑm{E}
ℜe{E}
ge + eg ge − eg
Super- and sub-radiance are interference
effects!
γ12 ∝ coskz
The limit is now how many atoms can we put withing the coherence
length associated with the spontaneous emission.
Infinite Range Interactions
U1D ∝ exp(ikr)
Ω12 ∝ sinkz
Probe Beam
The idea behind the experiment
We look for modifications of the radiative lifetime of an ensemble of atoms around
the ONF.
Probe Beam
The sub- and super-radiant behavior depend on the phase relation of the
atomic dipoles along the common mode
The idea behind the experiment
ρ(r
), p ab
s(r), α
(r)
(arb
.uni
ts)
Atom-surface distance (nm)0 50 100 150 200 250
0.0
0.2
0.4
0.6
0.8
1.0
Density of atoms
ONF mode
Van der Walls shift
Atomic distribution
Distribution of atoms
F=1
F=2
F’=2F’=3
F’=1F’=0
De-pump Re-pump Probe
Preparing the Atoms
20 30 40 50 60 70-30
-25
-20
-15
-10
-5
0
Atom-surface position [nm]
Frecuencyshift
[MHz] Δ
Δ
ρ(r
), p ab
s(r), α
(r)
(arb
.uni
ts)
Atom-surface distance (nm)0 50 100 150 200 250
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 2500.0
0.2
0.4
0.6
0.8
1.0
Atom-surface distance (nm)
Densitydistribution(arb.unit)
Atomic distribution with optical pumping
Density of atoms
ONF mode
Van der Walls shift
Distribution of atoms
Atomic distribution with optical pumping
0 50 100 150 200 2500.0
0.2
0.4
0.6
0.8
1.0
Atom-surface distance (nm)
Densitydistribution(arb.unit)
Measurment of N
-20 -10 0 10 200.6
0.7
0.8
0.9
1.0
frequency (MHz)
Transmission
Probe
OD = N ⋅OD1(!r0 )
Two distinct lifetimes
τ ≈ 7.7τ 0
τ ≈ 0.9τ 0
-4
-3
-2
-1
0
Log 10
cou
nt r
ate
0 5 10 15 20 25 30t/τ
0
-4
-3
-2
-1
0
Log 10
cou
nt r
ate
0 5 10 15 20 25 30t/τ
0
Two distinct lifetimes
τ ≈ 7.7τ 0
τ ≈ 0.9τ 0
Subradiance versus Radiation Trapping
τ ∝OD2 Δ( )
Radiation trapping depends on the OD, which depends on the excitation frequency
Fitting the Simulation
-4
-3
-2
-1
0
Log 10
nor
mal
ized
cou
nt ra
te
-4-2024
Nor
mal
ized
Res
idua
ls
(a)
(b)
0
-1
-2
-3
-4
t/τ0
0 5 10 15 20 25 30
0 5 10 15 20
t/τ0
Log 10
nor
mal
ized
cou
nt ra
te
0
-1
-2
-3
-4Log 10
cou
nt r
ate
t/τ0
0 5 10 15 20
Polarization dependent signal
Vertically polarized probe Horizontally polarized probe
Fitting the Simulation
-4
-3
-2
-1
0
Log 10
cou
nt r
ate
-4-2024
Nor
mal
ized
Res
idua
ls
(a)
(b)
0
-1
-2
-3
-4Log 10
cou
nt r
ate
t/τ0
0 5 10 15 20 25 30
0 5 10 15 20
t/τ0
Observations:
The limit is less than the natural decay rate due to geometry (Purcell effect). About one in 100 of the decays is superadiant. Quantitative agreement with simulations.
Summary
We have seen collective atomic effects (sub and superadiance) induced by the presence of the nanofiber. Superadiance shows long-range dipole-dipole interactions (many times the wavelength) scaling with the optical density (number of atoms). Sub-radiance is more fragile but persists for long enough to observe it.