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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.

Sylvain

Jonathan Jeff

3 2012

THE TEAM

Eliot

6 2015

Pablo Jeff

Optical Nanofibers

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)

The scale

Optical Nanofibers

λ=780 nm

Lowest order fiber modes Intensities

HE11 TM01 TE01 HE21

Polarization of the lowest order modes

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

Polarization at the fiber waist

Rotates like a bicycle wheel

Atoms interacting with light (decay) near an ONF.

Rate of decay (Fermi’s golden rule)

rad

Phase space density Interaction

Rate of decay free space (Fermi’s golden rule)

γ0 =ω03d 2

πε0!c3

Evanescent Coupling γ rad

γ1D Not to scale

γTot = γ rad +γ1D

γ0 γTot ≠ γ0

Density of modes in 1D

Decay into the nanofiber mode

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!!

Many atoms interacting with light (decay) near an ONF. Super- and sub-radiance.

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".


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( ){ }

P = εΔt

= IA⇒Δt = εIA


For N dipoles ε⇒ Nε

I = E02= I0

Δt = τ 0


Normal radiance

ℜe{E}

ℑm{E}

I = E02= I0 I = 4I0

Δt = τ 0 Δt = 12τ 0

ℜe{E}

ℑm{E}


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}


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}


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-radiance Sub-radiance

ℑm{E}

ℜe{E}

ge + eg ge − eg

Super- and sub-radiance are interference

effects!

Observation of infinite-range interactions

Infinite Range Interactions

Not to scale


Not to scale


Not to scale

γ12 ∝ coskz

The limit is now how many atoms can we put withing the coherence

length associated with the spontaneous emission.


U1D ∝ exp(ikr)

Ω12 ∝ sinkz

Long distance modification of the atomic radiation


Vfree ∝exp(ikr)kr

V1D ∝ exp(ikr)

Experimental idea

Probe Beam

The idea behind the experiment

Probe Beam


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


42

Preparing the atoms

JQI trap

α =γ1Dγ0

Coupling Enhancement

We use untrapped atoms!

Atomic density distribution around the ONF

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

De-pump

Probe

Re-pump

Preparing the 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 )

Measuring the Radiative Lifetime

Measuring the Radiative Lifetime

1 mm

-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

-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


τ ≈ 7.7τ 0

τ ≈ 0.9τ 0

Subradiance versus Radiation Trapping

⋅ ⋅ ⋅N

Subradiance versus Radiation Trapping

τ ∝OD2 Δ( )

Radiation trapping depends on the OD, which depends on the excitation frequency

Decay time vs detunning

It is not radiation trapping. It has to be subradiance!!

Understanding the Signal

Understanding the Signal

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

Polarization dependent signal

Vertically polarized probe Horizontally polarized probe

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


-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


Can we see a collective atomic effect of atoms around the

nanofiber?

Long distance modification of the atomic radiation

nanofiber

Left MOT

Splitting the MOT in two

Right MOT

≈ 400λ

Right MOT

Left MOT

Both MOTs

Evidence of infinite-range interactions

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.

Thanks!

The slope (0.02) is smaller than γ1D (0.10) because it is an average over different realizations,

non all of them superradiant.

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