Magneto-rotation and magnetic circular dichroism of cesium atoms near a dielectric surface

HAL Id: jpa-00247829

https://hal.archives-ouvertes.fr/jpa-00247829

Submitted on 1 Jan 1993

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Magneto-rotation and magnetic circular dichroism of cesium atoms near a dielectric surface

A. Weis, V. Sautenkov, T. Hänsch

To cite this version:

A. Weis, V. Sautenkov, T. Hänsch. Magneto-rotation and magnetic circular dichroism of cesium atoms near a dielectric surface. Journal de Physique II, EDP Sciences, 1993, 3 (3), pp.263-270.

�10.1051/jp2:1993128�. �jpa-00247829�

Classification Physics Abstracts

32.70 42.50 32.60

Short Commuuication

Magneto-rotation and magnetic circular dichroism of cesium atoms

_{near a}

dielectric surface

A.

Weis,

V-A- Sautenkov

(*)

and T-W- H£nsch

Max-Planck-Institut fir Quantenoptik, W-8046 Garching, Germany

(Received

_on 29 December 1992, accepted _on 20 January

1993)

Rdsumd. Nous _avons dtudid les propridtds magndto-optiques ^d'une _vapeur de cdsium prbs d'une interface de _{verre en} utilisant la technique de rdflexion sdlective. Nous _avons observd des structures sons-dopp16riennes dans les spectres ^de rotation magndtique et de dichroisme

circulaire. L'amincissement spectral pent 4tre expliqu6 _par le comportement transitoire de la

polarisation des _atomes de cdsium due _aux collisions _avec la paroi. Un modble simple qui tient compte des collisions des atomes _avec la paroi et du m41ange des niveaux hyperfins _par le champ

magndtique

donne _une bonne description qualitative des spectres observ4s. Un lager d4saccord est probablement du h des interactions de tongue portde entre les atomes et la paroi.

Abstract. The magneto-optical properties of cesium _{vapor near a} glass surface have been studied by using selective reflection. We have observed sub-Doppler structures in the magneto-

rotation and magnetic circular dichroism spectra. The spectral narrowing _can be explained by the transient polarization behavior of cesium atoms due to wall collisions. A simple model, which takes atom-wall collisions and the mixing of hyperfine levels by the magnetic ^{field into} account, gives _a good qualitative description of the observed spectra. Small

discrepancies

_are likely to be due to long-range atom-surface interactions.

1. Introduction.

The resonant

optical properties

of _a dilute gas near a dielectric surface differ

dramatically

from the

properties

of the vapor. This effect _was discovered

by Cojan ill,

and its theoritical

descrip-

tion _was

subsequently developed

for weak [2] and

strong

_[3]

optical

fields. Atom-wall collisions

modify

the internal and external

degrees

of freedom of the _vapor atoms, ^and

pronounced

effects

(*)

On leave from Lebedev Physics Institute, 117924, Moscow.

264 JOURNAL DE PHYSIQUE II N°3

due to the transient

polarization

behavior of atoms

departing

from the surface _can be observed in reflection

experiments:

the selective reflection

(SR)

spectra from _a

dielectric-gas

interface at

near normal incidence show

high-contrast sub-Doppler

structures

[1-4].

The

spectral shapes

of these

sub-Doppler

reflection _resonances contain information about both atomic collisions

[5-I]

and

long-range

atom-wall interactions

ii,

_8].

The

polarization technique

_can extend the

possible applications

of

SR-spectroscopy

_as it has for transmission and fluorescence spectroscopy.

Magnetc-optical

measurements _are

expected

to

yield complementary

information _on the influence of _a

magnetic

field _on the

spectral

behavior of

absorptive

and

dispersive properties

of _a resonant gas near a dielectric surface.

Magnetic

_resonance and level

crossing experiment

in SR _were first

proposed by

Series in 1967 [9]. ^Excited state

magnetic

level

crossing

_was observed in SR

by

Hanle and Stanzel

[10, iii

and decribed

theoretically by

Schuurmans [12].

Recently

_we have studied in SR _a zerc-field

magnetic

resonance in the

ground

state of cesium atoms _{near a}

glass

interface

[13].

In the present

work,

the

spectral dependence

of the

magnetc-optical

rotation and the _mag- netic circular dichroism of _a resonant vapor near a transparent ^dielectric surface have been studied. The

experiments

_were

performed

_near the cesium D2 line (A = 852

nm)

at low

light

intensities _so thant non-linear effects [3,

6,

13] can be

neglected.

2 Theoretical model.

To _our

knowledge

_no

theory

has been

developed

_so far that describes the

magnetic

circular dichroism and the

magnetc-rotation

of the

plane

of

polarization

in selective reflection

experi-

ments.

In references [2, 3] it was shown that

optical properties

of _{a vapor near a} dielectric surface

can not be described

by

convential

dispersion theory.

The SR in the

vicinity

of _an atomic

resonance line has to be decribed

by

_a

complex

interface admittance A. The

reflectivity

R is

given by

~ ~

(no A(~

(no + A(~

where _no is the index of refraction of the transparent dielectric. The admittance A may therefore be

interpreted

_{as an} effective index of refraction.

At low vapour

density,

when (A

ii

« I, the reflected

intensity

is

proportional

to Re

A,

_so that the circular dichroism D, ^{I-e- the difference} of the reflection coefficients for a+

polarized light

will be

given by

Re

(A+ A-).

On the other

hand,

it is easy ^to

show,

the

magnetc-rotation angle

4l is

proportional

to Im

(A+ A-).

In transmission

experiments,

the situation is

just

the

inverse,

I-e- the

magnetic

circular dichroism and the

magnetc-rotation

are

proportional

to the

absorption

and the

dispersion respectively.

According

to [2] ^the

spectral dependence

of the interface admittance A _near the _resonance

frequency

_weg of _a transition _g

- e can be

expressed

_as

~~~

^~

r~~

^{~ ~~}

^~~~~i)

^~

^tY

~~~

where _{tY = 7}

/2

rD is the ratio of the

homogeneous (full)

width _{7 of} the transition to the

Doppler

width rD _{= weg}

(2kT/mc~)~/~ Expression ii)

_was obtained

by using perturbation theory

in

the limit of

vanishing

_vapor

density

and

lignt intensity

and

by assuming

that ₇ «

rD(~).

The constant of

proportionality depends

on the _vapour

density

N and _on the

optical

transition

probability

W.

The truncated

velocity averaging

in

ii)

has its

origin

in the

breaking

of the symmetry intrc- duced

by

the dielectric

interface,

and expresses the remarkable fact that atoms

moving

^toward

the surface and atoms

moving

_away from it

give

^indentical contributions to the _resonance reflec-

tivity.

This leads to the appearance in the reflection spectrum of structures with

sub-Doppler

widths _on the order of

@.

A

longitudinal magnetic

field B has _a twofold effect _on the interface admittance A.

First,

due to the Zeeman effect the _resonance

frequency

of the transition

(FM

_>-

(F'M

+ I > between

Zeeman sublevels excited with

a+-circularly polarized light

is shifted

by [(gF' -gF)M+ gF')wL>

where _wL is the Larmor

frequency. Secondly,

it is well known that the total

angular

momentum F is _no

longer

_a

good

quantum ^number in the _presence of _a

magnetic

^{field. This leads} to a

mixing

of the

hyperfine

_wave functions

[14,

15] ^which are

given

in lowest order

perturbation theory by

(FM

>'=

(FM

> +

~ _fIFFIM(F'M

_>

₍₂₎

Fl=F+i

For _a

P3/2-state

the

mixing

coefficients _are

flpp,M

₌

~

~~~ (-l)~'+~~"+'+~/~@/(2F'+ _{1)(2F +1)}

~ ~

~

F' I F

3/2

F'

1)

^~~~

-M 0 M F

3/2

^'

where

(wF wfl)

is the

hyperfine splitting

between states

(F)

and

(F').

From

(3)

_{one sees} that the

mixing

of _wave functions is of the order

wL/whf.

Because in Cs _whf

(6Si/2)

> _whf

(6P3/~)

[16], we

neglect

the B-field induced

mixing

of

hyperfine

_wave functions in the

ground

state.

The transition

probability W+

for excitation of the Fo> ^M _-

F,

M + I transition with _a+

polarized light

is

proportional

to

W+ "

(< 6P3/2FM +1(

_z+

(6Si/2FoM

> ~

j

_~~

re

T)

₊

_2TiT2>

with

Ti

₌

j-1)~/(2F +1) j2Fo +1) _j/~

~~

/~ ( l< _6P3/~F

II ^r II

6Si/~Fo

>,

(5)

and

T2 ₌

~fIFF,M+il-1)~' _j£~

~~

/~ _~j

<

6P3/2F'

II ^r II

6Si/2Fo

> 16)

p,

'

The

complete

spectra ^{for the}

magnetc-rotation angle

4l _c~

Im(A+ A-)

and the circular dichroism D _c< Re

(A+ A-)

of the cesium

6Si/2

-

6P3/2

transitions _are

readily

obtained

by

(~)

In [2] ^{the interface admittance A} was also calculated for arbitrary ₇ and finite absorption length labs- This extended theory predicts large density dependent shifts of the SR _resonances which _were

not observed experimentally. In _our calculation _we therefore used the results of perturbation theory

which _are in good _agreement with experimental findings

is-?].

266 JOURNAL DE PHYSIQUE II N°3

an

explicit

summation _over all Zeeman components, ^{with line} centers weg

given by

the lowest order Zeeman

shift,

line

strengths given by equations (4)-(6)

and line

profiles given by equation ii).

These calculated spectra are

presented together

with the

experimental

results in

figures 2a,b

and

3a,b.

3.

Experiement

and discussion.

The

experiments

_were

performed using

_a

single-mode

diode laser with external

optical

feedback

[17].

^{The laser}

spectral

linewidth _was less than MH2. The

parallel

laser beam _{was sent} onto

a Cs _vapor cell in which the

reflecting

interface _was formed

by

_a

glass

window and saturated Cs _vapor. The temperature ^{T of the coldest} spot in the cell _was 393

K,

and the

corresponding Doppler

width and atomic

density

_were rD _" 2~r260 MHz and N

= 5

x10~~ cm~~ respectively.

The

angle

of incidence _was 3 mrad and _a

wedged

window _was

used,

_so that the reflections from the

air-glass

and

glass-vapor

interfaces could be

easily distinguished.

A

homogeneous longitudinal magnetic

field B _was

provided by

_a

pair

of Helmholtz coils. A second Cs cell

(N

= 2 _x

10~°cm~~)

at _room temperature served _{as a}

frequency

reference via the detection of

Doppler-free

saturation resonances.

In _a first series of measurements the

magnetc-rotation

of the

plane

of

polarization

_was studied

(Fig. la).

The

spectrc-polarimeter

_was

basically

the _{same as} the _one described in

[13].

The incident

light

beam is

linearly polarized by

_a Glan

prism. Upon

reflection from

the dielectric-metal _vapour interface

exposed

to _a

longitudinal magnetic

field the

light

beam becomes

elliptically polarized.

A

polarization

modulation

technique

is then used to extract _a

signal proportional

to the orientation 4l of this

polarization ellipse.

magneto-rotation

circular dichroism

~ B

B(t)

lit)

APOR

la) 16)

Fig. I. Optical detection schemes used for the measurement of the magneto-rotation angle 4l

(a)

and the magnetic ^circular dichroism D

(b).

The

experimental

and theoretical results for the

magnetc-rotation angle

4l in

a field of 6.6

G _on the Fo ₌ 4 _- F

=

3,4,5

^and _on ^the

Fo

_" 3 _- F

=

2,3,4 hyperfine

_components

are shown in

figures 2a,b.

The

(calculated)

solid line _was fitted to the data

by

linear scale transformations

adjusted

in _{a way} to minimize the difference between the

experimental

and theoretical

peak

values for _two

sub-Doppler

resonances. We calculated the

lineshapes using 7/2~r

=

10,

15 and 20 MHz and found the agreement ^{to be best for 15 MHz. This value for} the

homogeneous

linewidth _{7 was} confirmed

by

_an

independent

measurement

using

^FM-SR

~

°~

4

~'~

l~

_0.4

loo MHz

f

_0.3 --

$

_0.2

#

£

4-4

4J U-1 ~ ~

~

#

E ^°

-o.i

detuning a)

o.2

~

^3-4

d ^°

# f

_O-1

~ ~

__

~

cd ~ 3

~ ,_,

o

~ l

,

~

O

~ ~'~

n0 cd

E _{loo MHz}

~

-o.i

detuning

b)

Fig.

2. Experimental

(dots)

and theoretical

(solid line)

spectral dependence of the

magnetc-rotation

angle 4l _on the Fo _" 4

(a)

and Fo _" 3

(b)

hyperfine multiplets of the Cs D2 line

(B

₌ 6.6 G, ₇

" 2« Is

MHz, and rD ₌ 2x 260

MHz).

The dashed line shows the calculated spectrum ^{when the} hyperfine mixing is neglected.

spectroscopy [5]. ^The

good agreement

between

experimental

and theoretical results confirms that

magnetc-rotation

in SR _can be attributed _to the

absorptive properties

^of cesium atoms

near the

glass

surface. The dashed lines in

figures 2a,b

show the theoretical results obtained

268 JOURNAL DE PHYSIQUE II N°3

6

E ₄

2 ₄ 4-5

'

.2

2

# i

~

(

4-3 4-4

'~

£ _loo

MHz

~ --

#

E

detuning a)

4

~ 3

~

.

i~

₂ ^ioomHz

' 3-4

G

~

3

~n

?

_o

~ 3-2

'f

3-3

~-2

~n

E

detuning b)

Fig. 3. Experimental

(dots)

and theoretical

(solid line)

spectral dependence of the magnetic circular dichroism D _on the Fo _" 4

(a)

and Fo _" 3

(b)

hyperfine multiplets of the Cs D2 line

(B

= 6.6 G,

7 " 2x is MHz, and rD

" 2x 260

MHz).

The dashed line shows the calculated spectrum when the

hyperfine mixing is neglected.

when the

mixing

of _wave functions is

neglected _{(I.e, by} setting

T2 _" 0 in

Eq. (4)).

In _a second series of measurements the circular dichroism D, I-e- the difference of the SR reflection coefficients for a+ and a~

polar12ed light,

has been studied

(Fig, lb).

The

incident

light

beam _was

circularly polarized by using

a Glan

prism

and _a

A/4 plate.

We measured the circular dichroism D

directly by modulating

the

longitudinal magnetic

field

Bit)

₌ Bo cos wmt

(Bo

_" 6.6

G,

_{wm =} 2« 80

Hz)

and

using phase

sensitive detection.

The

experimental

^and theoretical results for the circular dichroism D of the Fo

" 4 _-

F ₌

3,4,

5 and of the Fo _" 3

- F ₌

2,3,4 hyperfine

_{components are} shown in

figures 3a,b.

Fitting

was done

by using

the _same

approach

_as ^{with the}

magnetc-rotation

spectra. ^Here too 7 = 2~r 15 MHz gave the best fit. If the circular dichroism _were due to Zeeman

splittings alone,

one would expect ^the

Doppler-free

_resonances to be

given,

in _a low B-field limit

(I.e.

_wL <

7) by

the

frequency

derivative of the

spectral dependence

of the SR coefficient. Such

lineshapes,

shown in

figures 3a,b by

^dashed

lines,

_are known from FM-SR spectroscopy ^{of cesium} [5,

7].

The observed

lineshapes (Figs. 3a,b)

differ

considerably

from the latter and _are well described

by

the model

including

_wave function

mixing.

4. Conclusions.

We have studied the

magnetc-optical properties

of cesium vapor near a

glass

surface

by using

selective reflection. A theoretical

approach,

which takes the transient

polarization

behavior of cesium atoms and the

mixing

of

hyperfine

levels

by

the

magnetic

field into account,

gives

a

good qualitative description

of the observed spectra. ^{The small}

discrepancies

between the calculated and measured _{curves may} have several

origins.

For the calculation of the circular dichroism and the

magnetc-rotation angle

we have used

pertubation theory

in the limit of low cesium _vapor

density

and low

magnetic

field. We

neglected

the B-field induced

mixing

of

hyperfine

_wave functions in the

6Si/2 ground

state _as well _as

long

_range atom-surface effects

discussed in references [7,

8].

The effective

potential

for _{atoms near}

a surface

depends

_on the orientation of the atomic

dipoles

with respect to the surface [18]. ^This

particular

_property could stimulate future in-

vestigations

of

magnetc-optical

effects

occuring

at _a

dielectric-vapour

interface. In order to

get _a full

understanding

of the

magnetc-optical activity

of atoms _{near a} dielectric

surface,

the

development

of _{a more}

complete theory

_seems therefore to be of fundamental interest.

Acknowledgements.

We

acknowledge

the assistance of J. Cramer

during

the

early

stage ^{of this}

experiment.

One of

us

(V.A.S.) acknowledges

the Alexander-von-Humboldt foundation for _a research

grant.

References

iii

Cojan J.L., Ann. Phys. France 9

(1954)

385.

[2] Schuurmans M.F.H., J.

Phys.

France 37

(1976)

469.

[3] ^Nienhuis G., Schuller F. and Ducloy M., Phys. Rev. A 38

(1988)

5197.

[4] Burgmans A.L.J. and Woerdman J.P., J. Phys. France 37

(1976)

677.

[5] ^Akulshin A.M., Velichansky V.L., Zibrov A.S., Nikitin V-V-, Sautenkov V-A-, Yurkin E-K- and Senkov N.V., JETP Lett. 36

(1982)

303.

[6] ^Akulshin A-M-, Celikov A-A-, Sautenkov V-A-, Vartanjan T-A- and Velichansky VI., Opt. Com-

mun. 85

(1991)

21.

270 JOURNAL DE PHYSIQUE II N°3

[7] Chevrollier M., Fichet M., Oria M., Rahmat G., Bloch D. and Ducloy M., J. Phys. II France 2

(1992)

631.

[8] Ducloy M. and Fichet M., J. Phys. II France1

(1991)

1429.

[9]Sefies

G.W., Proc. Phys. Sac.

91(1967)

432.

[lo]

^{Hanle W. and Stanzel} G., ^Zeit. NaturL A 25

(1970)

309.

[11] ^Stanzel G., Z. Physik A 270

(1974)

361.

[12] ^Schuurmans M.F.H., Z. Phys. A 279

(1976)

243.

[13] ^Web A., ^{Sautenkov V.A.} and H£nsch T.W., Phys. Rev. A 45

(1992)

7991.

[14] ^Roberts G.J., Baird P.E., Brimicombe M.W.S.M., Sandms P.G.H., Selby D.R. and Stacey D.N.

J. Phys. B 13

(1980)

1389.

[15]Chen

X.,

Telegdi

V.L. and Weis A., J.

Phys.

B ₂₀

(1987)

5653.

[16] ^Arimondo E., Inguscio M. and Violino P., Rev. Mod. Phys. 49

(1977)

31.

[17] ^Hemmerich A., Mclntyre D-H-, Schropp D. Jr, Meschede D, and H£nsch T-W-, Opt. Conlnlun.

75

(1990)

l18.

[18]Meschede

D., Phys. Rep. 211

(1992)

201.