SELECTIVE REFLECTION SPECTROSCOPY WITH A HIGHLY PARALLEL WINDOW: PHASE TUNABLE HOMODYNE DETECTION OF THE RADIATED ATOMIC FIELD

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Submitted on 27 Aug 2004

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SELECTIVE REFLECTION SPECTROSCOPY WITH A HIGHLY PARALLEL WINDOW: PHASE

TUNABLE HOMODYNE DETECTION OF THE RADIATED ATOMIC FIELD

Aram Papoyan, G. Grigoryan, S. Shmavonyan, David Sarkisyan, Jocelyne Guéna, Michel Lintz, Marie-Anne Bouchiat

To cite this version:

Aram Papoyan, G. Grigoryan, S. Shmavonyan, David Sarkisyan, Jocelyne Guéna, et al.. SELECTIVE

REFLECTION SPECTROSCOPY WITH A HIGHLY PARALLEL WINDOW: PHASE TUNABLE

HOMODYNE DETECTION OF THE RADIATED ATOMIC FIELD. 8th EPS conference on atomic

and molecular physics, 2004, Rennes, France. pp.4-84. �hal-00002633v2�

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ER(nr) non- resonant reflection (resonant)

atomic response

windo w

dilute vapou r

IR =

|

ER(nr) + Eat

|

^² (non-resonnant)

reflection at the interface

Eat atomic response

imaginary part of Eat ... is not detected!!

real part: interferes with non-res. reflected amplitude

detected signal

Observable = reflected intensity:IR =

|

ER(nr) + Eat

|

^²≈≈

|

ER(nr)

|

² . {1+ 2Re(Eat

/

ER(nr))}

How to detect the imaginary part?? Some proposals have been made:

Bre ws ter inci de nce (ER(nr)=0) ? (Akul'shin et al, Soviet J. Q. E. 19(1989), 416)

→

→t he sub-doppler feature of SR spectroscopy is lost;

multi dielectric c oating?(theor. work by Vartanyan and Trager, Opt Commun 110(1994), 315)

→

→t he coating may be da maged by the ato mic vapour

me tallic coating?(Chevrollier et al, Phys Rev E63(046610), 2001)

→

→considerable attenuation of the ato mic signal, due to the requ ired meta l t hic kness amplitude-and- phase diagram

depending on the relative p hase between the t wo NR re flected bea ms, two opposite regi mes are e xpected

-close to a reflection maximum:

No qualitative change :

SR signal still displays real partof the atomic response

-close to a reflection minimum:

t hen:

-Re (Eat)does not interfere with Erefl1 + Ere fl2 not detected -Im(Eat)i nterferes wit h Ere fl1 + Erefl2 DETECTED!

- the Im(Eat)x(Ere fl1+Ere fl2) signal changes sign around refl.

min imu m

! "!#!$$%$

! " !#!$$%$

& '()*&

(qualitative approach)

Irefl =

|

ER(nr)1 + ER(nr)2+ Eat

|

² windo

w dilute vapou r

1 2

1

2

1

2 1

2

1 Eat amplitude-and- phase diagram

How tochange the interferencecondition in the window?

very easily, by changing the window temperature For 0.5 mm sapphire window andλ=852nm:

∆∆T ≈≈30°C ↔↔2ππchangeof the interference (see Jahier et al, Appl Phys B71 (2000), 561 for the use of the

"temperature tuning" of the windows for reflection-loss free vapour cells)

++ ,,-- --..

//--001122 --3344

Twindow190-230° C

Tside- arm=160° C

Cs vapour, 3x1014/cm3

sapphire window diaphrag m (rejects fluorescence)

signal = Iref l , vs Twindow &

ννlaser 852nm

laser diode

F'= 4 F'= 3

F'= 2

-The interference pattern is obvious

-The atomic signal is small...

(dilute vapour) off-resonance

background subtraction

-the atomic signal is more e vi de nt - (still a "wavy" offset pattern: t he subtracted, off-resonance background has a non negligib le dependance on the laser frequency)

55

667789: ;<=>9?

89: ;<=>9?@>

@>

ABC

ABC DD

EE FF G HIJC

G HIJ C

KLM KLM

→

^N^NÔÔ ^PP^QQ^R^R^S^ST^T ÛÛ ^V^VW^W^X^X^TT^YYTTZ[ Z[

the hidd

en side of the selec

tive ref lection signal

\\ ]]^ _ `

^ _ `aa^b^b

window

dilute vapour

ER(at) E0

ER(nr )

n2 n1=1

n3 = n1 windo

w

♣

♣Continui ty equations at the two boundariesbetween the three media:

- air, n₁=1 - (sapphire) window, n2=1.76 - vapour, n₃=1

♠

♠Maxwell equations for the propagationof the backward atomic field in the vapour (withoutusing the slowly varying envelope approximation)

field envelope atomic polarisation

) ( ) /

² ) ( 2 (

² ) (

² z k₀Pz

z ikE z

z E + ∂∂ =− ε

∂∂

♦

♦assuming cell length >> absorption length (no backward beam coming from z=∞∞)

then

0 )

(//

1 exp( 2 )

) 2 exp(

21 23

23 21 12

12

E

i r r

i r t r t E

Rwindowvapour

 

  + −

=

+

ϕ ϕ

E

at

i r r

i t t

) 2 exp(

1 ) exp(

21 23

32 12

ϕ ϕ + −

=ER(nr) (ordinary reflection from a parallel window , with ϕ= n2kxthickness)

= ER(at) (the atomic contribution) (where the tij's andrij's are the amplitude transmission and reflection coefficients) and the backward atomic field is generated by the vapour atomic polarisation:

∫

⁼^∞

= ^L

at ik Pz ikzdz

E

0 ()exp(2 )

2

Defining the atomic response by and assuming the

absence of saturation and non-linearity, we get (ΓΓ,ΓΓD: homogeneous and Doppler widths):

b 21 23

0 23 12

) 2 exp(

1 ) exp( ℑ

=− ϕϕ

i r r

i E t E^at t

( )

∑ ∫

∞ Γ + Γ +

− −

= ℑ

HFS

F F F D

b Cs

i x

dx d x N

0

²)

² ωexp(ω π

c

ℑb

d ef ghijkef

d efghijkef

The model and experiment agree very well(no fitted parameter!)on the size and the temperature dependance of the spectra.

By using a "temperature tunable" window, one can detect at will - the real(dispersive) part

- or theimaginary(absorptive) part of the atomic response.

S/N is betternear the reflection minimum.

Changing from one regime to the other is obtained very easily, just by changing the window temperature by a few degree C.

Possible application: temperature-tunable locking of a laser frequency on the zero of the derivative signal

SELECTIVE REFLECTION SPECTROSCOPY WITH A HIGHLY PARALLEL WINDOW:

PHASE TUNABLE HOMODYNE DETECTION OF THE RADIATED ATOMIC FIELD

A. V. Papoyan, G. G. Grigoryan, S. V. Shmavonyan, D. Sarkisyan, Institute for Physical research, NAS of Armenia, Ashtarak-2, 378410, ARMENIA

J. Guéna, M. Lintz , M.-A. Bouchiat,

LKB, Département de Physique de l'ENS 24 rue Lhomond, 75 231 Paris cedex 05, FRANCE (to be published in Eur. Phys. J. D)

raw derivative

194°C

202°C

211°C

220 220°°C

...and experiment

≈≈reflection minimum

≈≈reflection maximum

"ordinary" selective reflection

ll mmn opq pr

n opq prss

tuvwx yzw

tuvwxyzwxxuu{|}~{{|}~ { raw derivative

ϕ ϕ = π= π//22

ϕ ϕ ==33ππ//44

model...

Re(E_at):

dispersive

"ordinary" selective reflection mixed mixed Im(E_at):

absorptive

ϕ ϕ = π= π//44 ϕ ϕ ≈≈ 00

raw derivative

...and experiment

−−44ππ//35 35

−−33ππ//35 35

−−22ππ//35 35

−−ππ//35 35

+π +π//35 35 00

++22ππ//35 35 ++33ππ//35 35

++44ππ//35 35

model...

zoom at...

derivative signal