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Atom-Light Interface in Strong

Focusing GeometrySyedAbdullah Aljunid, Jianwei Lee,

Kadir Durak, Brenda Chng,

Martin Paesold, Dao Hoang Lan,Gleb Maslennikov, Christian Kurtsiefer

Theory support: Yimin Wang, Teo Zhi Wei Colin,

Lana Sheridan,Valerio Scarani,

CLEO 2011, Europe, Munich EA 9.2

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Atom-Photon Interface

Quantum Information and Communication protocols

information exchange between flying qubits (photons) and

stationary qubits (atoms)

absorptiontriggered

phase shift

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Strong Coupling

V=deffEA E(x , t)=i g(x )a (t)+g* (x) a(t)

Interaction Electric field operator (single mode)

normalizationmode function

=

20Vm

Vm= dxg(x)mode volume

paraxial beams with

gaussian mode function

Vm=Lw0

2

2

=

w02

L0

Strong coupling in a Jaynes-Cummings model

g0=deff=

32c

w02

L

LOSSES

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Reference

15 1.5 2x105M. Koch et. al.,

Phys. Rev. Lett. 105,173003 (2010)

12 0.4 106T. Kampschulte et.al.,Phys. Rev. Lett.105, 153603 (2010)

215 53 4x104R.Gehr et. al.,

Phys. Rev. Lett. 104,203602 (2010)

Cavities

Cavity to compensate for losses

g0

g0 , State of art values

g0

(2)MHz

(2)MHz Finesse

? can we go for even lower finesse to achieve strong coupling ? =

w0

2L

0

Focusing !?S.E. Morrin et al., Phys.Rev. Lett 73, 1489 (1994)

Confocal cavity with w0

Finesse=4.5,=(2)540MHz

g0=(2)32MHz

Finesse enough to observecavity mediated changes in

spontaneous emission

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Strong Focusing

? what is the maximal coupling one can achieve with strong focusing ?

? what is the maximum field at the focus EA, related to input field EL?

EL

EA

Lw

f

analytical solution for field at the focus gives (M.K.Tey et.al., NJP, 11, 043209 (2011))

( )uRw

uu

ue

u

w

E

Esc

LuL

L

A

2

222

22

2

32

222

3

1,

4

11,

4

1

4

3

3

2

=

+

=

f

wu

L

=

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Strong Focusing

The normalization constant for a

strongly focused mode becomes

=Rsc(u)

32L

0

and the coupling strength for anatom in an antinode of cavity's

standing wave is

g0=

c Rsc(u)

L

=27ns ,L=10mm

Current experiments on strong focusing

u0.35L=6mm,g 0(2)40MHz

Strong coupling expected for

(2)10MHzR0.99

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Cavity lenses

f n

n+1

fn1n+1

longitudinal half-axis

transverse half-axis

I. Sahl, On burning mirrors and lenses(Publisher unknown, Baghdad, 984)

prototype lens turned from PMMA bySYNTEC OPTICS

surface irregularity < 100 angstrom

sag error (spherical surface) 300 nm

wavefront deviations ~/10 PV

Work in progress!

NA = 0.35

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Caveats I

Single-mode optical cavity with small waist --- need to work near stability threshold

testing with a different cavity, L = 10 cm, Rc=- 5 cm, R = 0.97, F = 150

w0

2=

2L(2RcL) w0=7.5 m , g0=(2)5.3 MHz ,=(2)16MHz

Ways to go: decrease L further, make more tests on stability in vacuum

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Caveats II

Atom has to be well localized at the antinode of the standing wave

In our experiments we trap87

Rb atom in a tightly focused optical tweezer

trap frequencies

=55 kHz ,l=7 kHz ,

Raman cooling of an atom to the ground state of the trap can be performed

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Raman Cooling

average motional stateafter cooling

n =0.550.07

atomic delocalization

x200 nm

x

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Conclusions

A model describing optical resonators with a strongly

focused mode is proposed. An analytical expressionis obtained for the coupling strength, beyond paraxial

approximation.

We have designed an anaclastic cavity lens with

NA=0.3 that can be used in cavity QED experiments

with strong focusing

To achieve maximal coupling strength a thermal

Motion of atoms must be minimized.We have performed a Raman sideband cooling of single

87Rb atom in a tightly focusing dipole trap to

n =0.550.07

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Thank you!

Syed Abdullah Aljunid

Jianwei LeeKadir Durak

Martin PaesoldDao Hoang Lan

Brenda ChngGleb Maslennikov

Yimin WangColin Teo

Lana Sheridan

Valerio ScaraniChristian Kurtsiefer

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Single atom

(almost) Hanbury-BrownTwiss experiment on

atomic fluorescence during cooling

Rabioscillation

photon

antibunchingD1

D2