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illustrative examples of stimulated emission and polarization spectroscopy for sensitive detection of a

pulsed excited forbidden transition

M. Bouchiat, J. Guéna, Ph. Jacquier, M. Lintz, L. Pottier

To cite this version:

M. Bouchiat, J. Guéna, Ph. Jacquier, M. Lintz, L. Pottier. From linear amplification to triggered

superradiance : illustrative examples of stimulated emission and polarization spectroscopy for sensitive

detection of a pulsed excited forbidden transition. Journal de Physique II, EDP Sciences, 1992, 2 (4),

pp.727-747. �10.1051/jp2:1992162�. �jpa-00247668�

Classification Physics A bstracts

32.70 32.808 42.65G 35.10W

Ikom linear amplification to triggered superradiance: illustrative

examples of stimulated emission and polarization spectroscopy

for sensitive detection of

_a

pulsed excited forbidden transition

M-A-

Bouchiat,

3.

Gudna,

Ph.

3acquier,

M. Lintz and L. Pottier

Laboratoire de Spectroscopie Hertzienne

(*),

D6partenlent de Physique de I'ENS, 24 _rue

Lhonlond, 75231 Paris Cedex 05, France

(Received

27 December 1991, accepted 17 January

1991)

Abstract. This paper presents our exper1nlental _strategy for detecting _an electric-field controlled pulsed-excited highly forbidden transition such

as the 65-75 transition of the Cs

atonl. The anlplification of _a pulsed probe bean1close to _resonance for _one hfs conlponent of

the 75

6P~/~

^{transition is} nlonitored. Furthernlore the polarization nlodification experienced by the probe beanl _{as a} result of its interaction with the _vapor is meticulously analysed. In

convincing exanlples _we point out the high sensitivity and complete selectivity of the method for the angular anisctropy of the 75 state, such _as orientation _or alignment created in the 65- 7S excitation _process. We illustrate the flexibility of the method by varying the pump-probe delay, _or by changing the relative positions of the beams _or the nlagnitude of the Kfield that directly controls the optical gain. A smooth transition from linear amplification to triggered superradiance is observed which necessitates readjustment of the probe intensity for optimal detection. We denlonstrate the vapor-induced enhancenlent of the anlplification anisotropy, expected at high optical density.

Sensitive detection of excited atoms is _a

problem nowadays commonly

solved

by looking

at their interaction with _a radiation field. With the advent of tunable laser _sources there _{are so} many

possibilities

that the best choice is far from obvious. Transmission

techniques using

the

pumping beam,

_or stimulated emission

(or absorption)

from the excited state

using

_a second laser beam _{can now serve as} substitutes for fluorescence detection. Which of these methods deserve the most consideration ?

Looking

backwards to the

early days

of

Optical Pumping

_we learn _an instructive lesson. In the seminal Kastler ideas

[ii

and in the

pioneering experimental

work that followed [2], ^the

ground

state orientation _was detected

through

the

polarization

of the reemitted fluorescence

fight.

However several years

later,

Dehmelt's

proposal

of

directly observing

the

pumping

beam after its transmission

through

the vapor [3]

generated

_a renaissance in the field of

optical

(*) Laboratoire assoc16 _au CNRS

(URA

18), £ l'Ecole Nornlale Sup6rieure et h l'Universit6 Pierre et Marie Curie.

pumping.

With this _new

technique

it became

possible

to observe _a

high degree

of atomic

ground

state orientation in conditions where the fluorescence

light

_was

depolarized

_or

severely quenched by

collisions in the excited state. A _new kind of

pumping mechanism,

Dehmelt

pumping,

_was born [4]. ^This

example

is _a

good

illustration of the

complementarity

between the fluorescence and the transmission detection methods. Each _one

requires

different optimization conditions in the

preparation

stage ^{of the} atoms to be

detected,

and

produces

_a different kind of information. Therefore

they

cannot be substituted to one another

indifferently.

A restriction

on the interest of the transmission

technique

is that _a

single

beam is

given

two roles _:

pumping

and detection. In _{some cases} the roles _may fall into conflict. This kind of

difficulty

_was solved

by making

_use of two beams _{: one} intense

pumping

beam and _one faint

probe

beam observed in transmission [5, 6]. ^{Then either beam could be}

optimized

in

intensity, polarization

and

frequency.

The

versatility

of the

experiments

_as well _as the

clarity

of their

interpretation

_were thus

simultaneously upgraded

_[7].

Sensitive detection of excited atoms is _one of the

major

difficulties encountered in

today's problem

of accurate measurement of

parity

violation in atoms [8]. ^As a definite

example

_we take cesium. The detection

problem

_concerns the 75 atoms excited

through

the

highly

forbidden 65-75 transition. In the first

generation

PV

experiment

fluorescence

light

emitted

directly

in the

7Si/~ 6Pi/~

fine _structure transition _was observed and its

polarization analyzed.

This

method,

reminiscent of the Kastler

approach, although

it has

produced significant

results [9], has the drawback of very low

efficiency.

Since _our

goal

is to achieve _a better

experimental

statistics,

_we have addressed the

problem

of active detection of the 75 state

[10]. Namely during

the lifetime of the excited state the atoms interact with another radiation field from

a second tunable laser. In the present _case this laser is tuned to _one hfs component ^of the 75

6P~/2

transition.

Then,

_I) the fluorescence which is induced

by

the pump laser in the 75

6Pi/~

component is reduced whenever the second laser is resonant for _one hfs component

ill,

12] ^and

it)

with

sufficiently

efficient 75

pumping,

^the

probe

radiation _{may even} be

amplified (13].

Obviously

the

problem

of

making

active

optical

detection efficient and sensitive is not _re- stricted _to the _case of atomic PV measurements. This

question

has received _very broad interest in the domains of molecular spectroscopy and chemical

dynamics

for the last ten years. The

method _we call inhibited fluorescence spectroscopy

[iii

has _more than _{one common} feature with Stimulated Emission

Pumping (SEP),

_{now a}

powerful

vibration-rotation spectroscopy ^tool

quite generally

^{used for small}

polyatomics

_[14].

Independently,

active detection _was demon-

strated

quite early

in the

history

of

high

resolution spectroscopy

[15].

For several _{reasons we} believe that the three-level

lambda-type

^65~7S-6P system in cesium

(Fig. I)

is _{a case} of

special interest, regardless

of its connection with the PV

problem

_: I) ^{The two S states connected}

by

the _pump laser _are of the _same

parity,

the oscillator

strength

is

only

4 _x

10~~~,

and the 65-75 transition rate is

easily governed by

_a static electric field E. The excitation

probability

is P _c~ tx~

(E

_e(~ +

fl~(Exe

_{« (~} where

tx and

fl

stand for the scalar and vector transition

polarizabilities,

_e ^{for the} _pump

polarization

and

~r for the Pauli operator

acting

_on the electronic

spin

state [16].

(The

ratio

alp

₌ -9.9 is well determined

[17]). Consequently, varying

the field

magnitude

is _a very convenient _way of

controlling

the 75-6P

population

inversion. With intense

pulsed

^excitation the transition rate _can be made

large enough

so that the excited _vapor becomes

superradiant

for the 75-6P transitions. We thus have _a

unique

situation in which _{one can pass}

continuously

from _a

regime

of weak linear

amplification

to

triggered superradiance, by just changing

at will the oscillator

strength

without any modification in the

damping

rates. This leads _to

simply interpreted

results.

ii)

^{As it is}

^conceived,

our 65-75-6P

experiment simultaneously

demonstrates _many of the

possibilities

of the active detection method. We have tried to take full

advantage

of all the

2184MHz

253 203 152

6 Py~

6Sw

-3

Fig. 1. Scheme of the lower levels of cesium. Straight arrows : laser couplings. Wavy _{arrows :} fluorescence.

parameters which

specify

both the pump and the

probe

beams. In

particular

_we attach

special importance

to

light polarization dependent

effects.

Practically

all

configurations

of pump and

probe polarizations

have been realized. We will

give

several illustrations of the fruitful associ- ation of active detection with

polarization

spectroscopy [6, 19]. ^In

addition,

when the

optical

medium becomes

optically

thick at the

probe frequency,

_we have succeeded in demonstrat-

ing

the additional attractive feature

predicted

before

[10],

an enhancement of the

polarization dependent

effects.

The method

developed by

the Zurich _group also

aiming

at _a sensitive detection of the 65-75 transition [18]

might,

at first

sight,

look

closely

connected _to our's _: it consists in _a twc-laser

experiment

_on the three level 65-7S-15P system. However the Zurich

experiment

does _not involve

optical

detection _at all

(the

Cs 16P atoms _are detected in

a thermionic

diode),

it is

performed

with _cw lasers and all

polarization

effects connected with _an

angular anisotropy

of the 75 _state

are

ignored.

We

prefer

_our

approach

because _we believe in the

importance

of _a direct observation of the 75 atoms which have

completed

the 65-75

one-photon

transition.

It is the _purpose of this _paper to illustrate the

possibilities opened

_up

by

the _use of active detection with the

example

of the 6S-75-6P system

prepared

with intense

pulsed

excitation.

They

_can

conveniently

^be classified

according

to the

typical

effects

generated

in the

probe

beam when the _pump beam is turned _on, and this motivates the division of this _paper into the

following

six sections _:

Demonstrating

active detection with resonant

probe amplification Associating

active detection and

polarization

spectroscopy

Changing

the time

delay

between _pump and

probe

Changing

the

gain

parameter _: three

amplification regimes Enhancing polarization dependent signals

Varying

the relative

position

of the two laser beams.

1.

Demonstrating

active detection with resonant

probe amplification.

The

experiment

uses 10 _ns

long pulses

to excite the 65-75 transition

la

_ci 639

nm).

The

frequency

is stabilized and the

spectral

width is

nearly

Fourier limited _so that

tuning

at the center of _one hfs component can be achieved. A _cw monomode tunable laser

beam,

collinear to the _pump,

probes

the 75

6P~/~

^transition at 1.47 _pm. It is driven

by

_a fast

electrooptical

amplification

/~'f _reference

jump

_pro e

fi

j lms

^time

Fig. 2. Typical exper1nlental t1nling for the laser pulses.

switch

(~)

which

gives high flexibility

in the choice of

operating conditions, namely pump-probe delay

and

probe

duration. After the 75 atoms have emitted their

photon, they

accumulate in the

6P~/~

^{state which is made}

long-lived by

_resonance radiation

trapping.

From

previous

observations [12] we know that the lifetime of the 6P

population

reaches several microseconds.

Consequently

it is essential _to observe the

probe only

_as

long

_as stimulated emission dominates

absorption.

In

typical working

conditions the

probe

beam is switched _on at the end ofthe _pump

pulse

for _an

optimized

duration

+w 20 _ns

(see Fig.2).

A second identical

probe pulse,

switched

on I _ms after the first _one, monitors the transmission when _no excited _atoms remain and

provides

the reference S needed to extract the _vapor contribution. In this

'iJipulse" technique

the _vapor

amplification

factor is obtained at each pump

pulse.

4-5 4~ 4-3

;,:.

b i

11

200MXz

~ II, ,,~;

";,.'Q ^' ~

~ f~°~~

Fig. 3. Amplification of the probe beanl, _vs. probe frequency

:

a)

Transmitted probe signal Sout -The oscillations _are due to etalon eTects in _an optical fiber.

b)

Amplification _power

(Sout S) IS.

This quantity is unaffected by probe intensity fluctuations _or drifts. _{ncs Ci} 2.7 _x 10~~

at/cnl~,

_trans-

verse E field 280

V/cnl.

Exc. pulse i mJ, resonant for 65 F

= 4 - 75 F

= 4. Probe nearly saturating.

(~)

We

use an

integrated

LiNb03 directional coupler of 2 GHz bandwidth, operated with typical voltages of only lo V

(generously

provided by A. Carenco from CNET, Bagneux,

France).

4 5

jsz +s,)/S

1

<-4

4-3

o-s

isz s,)/s

o

vpc

-o.s

$~~f

Fig.

4. Top

: Amplification _{power vs.} probe frequency. Bottom _: Optical rotation spectrum.

ncs C~ 2

x10~~

_at

/cm~

lon#tudinal E field _: 2,4

kV/cnl.

Exc. pulse 400 pJ, circularly polarized,

resonant for 65 F

= 3

- 75 F

= 4.

Figure

3 illustrates the spectrum of the

probe amplification

when the

probe frequency

is swept over the hfs

profile

of the 75 F ₌ 4

-

6P3/2

transition.

Comparison

^between

fig-

ures 3a and 3b

clearly

demonstrates the

advantage

of the

"bipulse" technique

for

providing signals

unaffected

by probe intensity

fluctuations. Several features of the recorded spectra are

noteworthy

_:

I)

Despite

the _very weak

optical absorption

at the _pump

wavelength

_cs

10~~)

,

the

ampli-

fication factor reaches cs 100il

(Fig. 4, top),

and _{even more} in the conditions where the _vapor

superradiates (see SectA).

ii)

As

expected

from

velocity

selection

by

the collinear _pump and

probe

beams the

amplifica-

tion

displays sub-Doppler

resolution _:

amplification

_occurs

only

if the _pump and the

probe

_are

resonant for the _same

velocity

class. As shown in

figure

3 this makes it

possible

to

completely

resolve the

6P~/~ hyperfine

^{structure. Note however that such} a result

requires

to simultane-

ously satisfy

two

conflicting

conditions _: the

spectral

resolution of the lasers must of _course be

high,

but _so must also be their

temporal

resolution since _we have _to build _a

high

75

population

in _a time short

compared

to the 75 _state

decay

time. The

pulse

durations which

satisfy

both conditions

actually belong

to _{a narrow}

domain, having

its _center close to the actual conditions.

iii)

The three lines in

figure

3 _{are seen} to appear on a

negative Doppler-broadened profile

of lower

amplitude,

whose relative

height

is observed to increase with the Cs

density.

This

absorption

due _to thermalized

6P3/2

atoms appears unrelated _to 65-75

excitation,

_as shown

by

its

persistence

when the _pump

pulse

is detuned from _resonance

,

in which _case the

amplification peaks disappear.

We have identified this effect _as due to 6P excitation

occuring during

the pump

pulse by

indirect non-resonant processes

(such

_as

photoelectron production

and electron

bombardement of the

ground

state

atoms).

As shown below these _processes do not affect the

polarization dependent

spectra.

2.

Associating

active detection _and

polarization spectroscopy.

In the _case of the E-field controlled 6S-75

transition,

the

angular

state of the excited atoms

depends

not

only

_on the _pump

polarization

but also _on the E-field direction. The detection of

angular properties

of _an atomic _state

by polarization analysis

of _a transmitted

probe

beam has

a

long history

in

optical-pumping experiments

[4, 7]. ^{The 6S-75-6P} system

nicely

illustrates here that the

high sensitivity

of this method is not restricted to _cw laser

operation.

our

experimental procedure, specifically

conceived for the _case of

pulsed operation

with

inherently large

_source

instabilities,

is shown to achieve sensitive measurements of the

outgoing probe polarization. Furthermore,

the 65-75-6P system ^{will show the}

following

crucial feature _: the

polarization effects, completely

insensitive to the 6P atoms, _are characteristic of the 75

angular properties.

This detection _appears not

only

selective but also flexible since it allows the choice of

measuring

_any 75 orientation _or

alignement.

In

addition,

because

amplification

factors _as

large

as 100il

can be

reached,

there is _no dilution in the transfer of the 75

angular anisotropy

to the modification of the

probe polarization.

The

polarization

_epr of the

probe

at the output ^{of the cell is}

analyzed by

_a

polarizing beamsplitter

cube with two detection channels

corresponding

to the two

orthogonally polarized

output beams

[20].

With _an

incoming probe

beam chosen

linearly polarized

the _axes of the cube _are oriented _{so as to}

analyze

the two

polarizations

at + 45° from _epr The

amplitude

of each output

signal

is

proportional

to the number of

photons

detected

during

the

pulse.

With the excitation laser off

(second probe pulse

in the

"bipulse" technique,

_see

Fig. 2),

the _two

outputs balance each other

exactly

and their _sum S

serves as a reference. With the excitation

laser _on

(first probe pulse),

subtraction of the reference from each output

provides

the _two

amplification signals

Sz ^and

Sy.

The normalized _sum

(Sz

+

Sy) IS

_measures the

amplification

factor of the _vapor.

Simultaneously

^the normalized differential

signal (Sz Sy) IS gives

the

polarization

rotation

angle

correlated with the

pulsed

excitation. In balanced

operation, taking

the difference of the two channels leads to

high rejection

of the technical _common noise and

brings

down the noise close to the shot noise limit [20].

As _a first illustration of the

polarization dependent effects, figure

4 _concerns the situation where the _pump beam is

circularly polarized,

thus

giving

rise to _a 75 orientation directed

along

the beams. The _pump

frequency

is

kept

resonant for _one hfs component

(6Si

_/~ F ₌ 3 _-

7Si

_j~ F

=

4).

The

amplification

factor and the

polarization dependent signal

_are

plotted

ver- sus the

probe frequency

_{swept across} the

6P~/~

^{hfs. The}

polarization signal

exhibits three

dispersive line-shaped

resonances whose relative

signs

and

heights

_agree with the calculated

optical

rotation spectrum

resulting

from the orientation of the 75 state.

(In

[12] ^similar _agree-

ment _was found for the _cw

spectra).

The small

wiggles

noticeable _on the

wings

of the lines

simply

result from the

(time)

Fourier transform of the

rectangular shaped

detection function.

The spectra ⁱⁿ

figure

5 were recorded in somewhat extreme conditions

(high

Cs

density)

where the

Doppler

free

amplification

lines _are almost dominated

by

the

absorption

due to the thermalized

6P~j~

^{atoms. In such conditions the}

amplification

spectrum looks _messy and is difficult to

interpret.

In marked _contrast the differential

signal (Sz Sy)

is clean. It exhibits

no

Doppler

broadened

contribution,

_an indication that 6P atoms do not contribute. The _same

conclusion is

independently

deduced from records taken either

using

_a non~resonant pump beam _or with _a

probe

laser tuned for the

unpopulated hyperfine

level of 75. The

polarization dependent signal

indeed achieves

complete selectivity

of 75 _atoms alone.

sx+sy

I

08

sx sy

250MHz

iO/

O

u

^v

)robe

4-5

4-4

4-3

Fig.

5. Selectivity of the difference

signal (Bottom)

_even when the _surf

signal (Top)

is overwhe1nled in _a background. Top _: nnnornlalized tran8mitted intensity

(no

reference

subtraction).

Bottom _:

diiserence signal recorded with drcdar analysis

(1/4

plate inserted before'the

polarimeter),

in units of probe intensity, _ncs ~f

9.5x10~~ at/cm~,

_transverse E field _:

65V/cm.

Exc, pulse drcularly polarized, resonant for F ₌ 4 _- F

= 4.

Figure

5 _was taken with _a

circularly polarized

_pump beam _as

previously (in FigA)

but with _a

circularly polarized analysis

of the

probe

beam

(insertion

of _a

1/4 plate just

before the

analyzing cube).

On the other

hand,

the

technique

of the

probe bipulse

_was not yet ⁱⁿ

place.

The

advantages gained

with the bidifferential method _were

appreciated

later _on. Not

only

does this

technique

eliminate fluctuations of the

amplification signal

^{but it} also _proves invaluable for

precise polarization

measurements.

Slight

imbalances of the

polarimeter independent

of the atomic system, ⁱⁿ

particular

the

polarization

defects of all the

optics

which _may evolve in

time,

_are ^detected at each

pulse

^and can be corrected

for, leaving

the

anisotropy

of the _vapor

well

distinguished.

These

possibilities

_are

fully exploited

in the

experimental

results

presented

next.

Figure

6a illustrates _a situation in which the

probe frequency

is

kept

resonant for the hfs

7Si

_{/~ F =} 4 _-

6P~/~

^F' = 4

component,

^while

sweeping

the _pump

frequency

_vex

through

the

Doppler

65 F ₌ 3 _- 75 F

= 4

absorption profile.

Atoms with _non~zero

longitudinal

velocities

are thus

brought

to the 75 state in

proportion

to the

ground

state maxwellian distribution.

Since the

probe

is tuned _{at resonance} for the _zero

velocity

class the

amplification

factor exhibits

a narrow

(Doppler-free)

maximum _{at vex resonant} for the _same

velocity

class. In addition two

bumps

_{appear on} each side of the main _resonance.

They correspond

to the 75 atoms whose

non-zero

velocity

makes them resonant for either of the two

adjacent

hfs 4 _- 3 _or 4 _- 5

components of

7Sij.2

-

6P3j2>

^{distant from the 4} - 4 line

by only

203 and -253 MHz

respectively.

(al @

11 ~ Eli s

4-5 4-3

5

$~-s

Vjumj ~fl

5ooMRz

-~

f f

(4-3) (4~4) (4 5) ^{200MHz -}

V

)robe

Fig.

6. Spectra of the linear

birefringence signal: a)

Amplification _power

(top)

and

birefringence Signal (bottom)

vs. excitation frequency swept _across the F

= 3 _- F

= 4 component. ^The resonances

indicated _are those of the probe with the Doppler~shifted excited velocity dosses, _{nc~ ci} io~~

at/cm~, longitudinal

E field

: 2

kV/cm.

Exc. pulse _: i mJ, linear polar. Probe kept resonant for 4-4; circular polar.

b)

^Same

signals

_as in

a)

_vs. probe frequency. Same conditions, except probe circular polarization of opposite

sign.

Pump frequency kept resonnant for 65, F

= 3

- 75, F

= 4 exdtation.

In the conditions of

figure

6 the _pump

polarization

_eex is1inear and the E field is

parallel

_to

the direction

I

_{of both beams.}

Consequently

the excitation _{process possesses a} symmetry with respect to the

plane (E,

_eex

).

Therefore _we expect ^the

principal

axes of the _vapor

anisotropy

to be

iex

and the

orthogonal

direction

I

x

iex.

In

particular

^the

probe

beam should

experience

a linear

birefringence

of the _{same axes,} whenever it

approaches

_resonance. Since this effect

concerns the real part ^{of the refraction} index it is

expected

to have _a

dispersive

line

shape.

This

is well demonstrated in the lower part of

figure

6. The

polarimeter

_axes have been oriented _at 45° from the

anisotropy

_axes. The

polarization

of the

incoming probe beam,

chosen

circular,

becomes

elliptic

^{under the} effect of the _vapor linear

birefringence.

This _causes

an imbalance at the output ^{of the}

polarimeter.

As shown in

figure

6a the observed effect agrees

well,

in size and

sign,

with theoretical

predictions.

For

comparison, figure

fib shows the

corresponding experimental

spectra when the

probe (instead

of the

pump) frequency

is swept across the 75 F ₌ 4 _-

6P~jz ^hfs,

^the pump

frequency

now

being kept

resonant for the

zerc-velocity

class _on 65 F ₌ 3 _- 75 F ₌ 4. The three resonances, now associated with the

same class of 75 atoms, ^have

comparable sizes,

and

angular

factors alone

explain

the

remaining

differences.

(These

factors _can be calculated

using

the formulas

given

in

[12], appendix B).

lsrsyh_~~/S

io-3

~ ~3

Fig.

7. Detection of _a small linear dichroism. The angle between _pump and probe linear polariza- tions is modulated by _a small angle + 9F. The bF-odd difference signal is plotted _vs. probe frequency.

Each point is averaged _over 18 shots. bF

" ii _x io~~ _rod. Longit. E-field _: 2.5

kV/cm.

Probe

amplification factor ci i. Exc. pulse _: 1.i mJ. _ncs ~f io~~

at/cm~.

The

high sensitivity

of the method is illustrated in

figure 7,

where _an

anisotropy

of _a few

10~3

is shown _to be detected well above the noise

despite

_a short

integration

time. In this

experiment,

_a

longitudinal

E field is

applied

and the direction of the _pump linear

polarization

eex is tilted with respect to the direction of the

probe

linear

polarization

_epr

by

_a small

angle

8F

(induced by

a

Faraday glass modulator). Consequently

the

principal

axes of the 75

anisotropy,

and therefore the _axes of the linear dichroism at the

probe frequency,

are also

tilted, by

the

same

angle 8F.

This results in _a

8F-odd

contribution to the differential

signal

of the

polarimeter (whose

_{axes are} at + 45° from

ipr).

The spectrum ^{of the}

bF-odd signal

_vs,

probe frequency,

shown in figJ1re

7,

_agrees with the

prediction.

At _resonance the

sensitivity corresponds

to _a

signal/noise

ratio of

unity

in I _s

(or

12

shots)

for 8F #

10~~

Concerning

the

polarization

_spectra shown

above,

_we draw attention to the

large

difference in the relative

weights

and

signs

of the three

6P~j~

^hfs components

according

to whether the

detected dichroism

(or birefringence)

is circular _or linear _: look for instance at the difference between

figure

4

(optical rotation)

and

figure

fib

(linear birefringence)

_or between

figures

5 and 7

(circular

and linear

dichroism).

This is well understood _on theoretical

grounds [12], assuming

that these

anisotropies

result from the atomic orientation _or

alignment

created

by

the pump

beam,

ⁱⁿ the absence of _any

magnetic

field

(a

condition fulfilled

here).

The

spectral shape

of the

polarization dependent signal

is therefore _a reliable _means to confirm the type of _vapor

anisotropy experienced by

the

probe

beam.

In this

section,

_we have illustrated how the balanced

polarimeter

enables _one to _measure different _vapor

anisotropies depending

_on its orientation and _on the

probe polarization.

A formal treatment shows

that,

in

fact,

all kinds of

anisotropy

_can be measured. A classification of small

anisotropies

_can be made

systematic

and

complete

in the formalism of the Stokes

parameters ^{often used} to describe

light polarization _[21].

The

steady

state

propagation through

the excited _{vapor can} be described

by

a

complex

2x2 transfer matrix M which relates the

polarizations

at the

input

and at the

output

of the cell

ej(~

= M

e($.

^We suppose hereafter that

(ej(~ e([(

^{is small and} can be treated _{as a} first order

perturbation. Choosing

two

real, unitary, orthogonal

vectors

(£, f) perpendicular

to the

probe

_wavevector

ipr

as a basis for the

polarizations,

_{we use} the Pauli and

unity

matrices _{as a}

complete

basis to

develop

the matrix M _:

0

¹ 0 -I 0

M = fl +

(7~+itxo)fl

+

(71+itxi)

₊

(7~+itx2)

+

(7~+itx3)

~ l ~ ° l~

where all coefficients _{7;, tx; are} real.

Apart

from _oo and 70

,

rylated to_the ^isotropic

part ^of the index and

gain

of the _{vapor, we} have introduced

(6

_" ^{~ ~ ~}

,

9 =

~

~)

vi vi

al, the

birefringence

with _axes

(6, 9),

tx2, the

optical rotation,

tx3, the

birefringence

with _axes

(£, f),

71, the

plane

^dichroism with _axes

(6, 9)

72, the circular

dichroism,

73, the

plane

dichroism with _axes

(£, §).

txi and ₇₁ arise from _an excited state

alignment

of _axes

(G, 9),

_tx3 and ₇₃ from _an

alignment

of _axes

(£, f)

, tx2 and ₇₂ from _an orientation

along ipr _(~).

_Our

polarimeter

in balanced mode

operation

makes it

possible

to

disentangle

the different

quantities

_tx; and _7;. Measurements have to be

performed

in three

configurations

with

polarimeter eigenvectors conflitu[ing

a

complyte

basis in the 3-dimensional Stokes parameter _{space :} I)

£, f

11) 6

=

~ ~

~,

_Q

=

~ ~

~ ~ ~ ~

vi vi

^'

iii) I

=

~ ~

~~,

^C

=

~ ~~

In each

configuration

the

probe polarization

is oriented

along

vi vi

either of the _two directions that _{ensure exact} balance without _pump beam.

Table I summarizes the

expressions

of the differential

signal

at the

polarimeter

output in

each _case. Indeed, ^{all of the} coefficients _can be

extracted,

_even with

a certain

redundancy

if _a

complete

set of measurements can be realized.

(~) Using a

nlagnetic

field _{to rotate} the

angular

state via the Hanle effect fives _access to the other components of the orientation _or alignnlent.

3.

Cl..urging

the time

delay

between _pump and

probe.

In this section _we illustrate the

possibilities

offered

by varying

the

pump-probe delay

in three

specifiq examples.

Table I.

Expressions

^{for the}

signal (Sz Sy) /25

at the

output

of the

polarimeter

in bal- anced

operation,

for _a

complete

set of orientations.

(ki, k2)eigenaxes

of the

polarimeter; k($

polarization

of

incoming probe; (fi,V)

^and

(#, L)

defined in text,

(kl> ~2) (~>i) (fi,Q)

,

I _71~a2 72+£Y1

I

71+£Y2 72~£YI

fi 73+tY2 _72-"3

0 73~£Y2 72+£Y3

#

_{73 £Yl 71 +}

£Y3

~ 73+al _71~a3

3. I OPTIMIZING _THE VAPOR AMPLIFICATION POWER. As

expected intuitively,

for collect-

ing

_a

large

atomic

signal

it is essential that the

probe

not be established _too late.

Figure

8 shows

that,

in

typical experimental conditions,

^maximum

probe amplification

_occurs ^{when the}

probe pulse

starts close _to the

peak

of the _pump

pulse.

It then decreases

rapidly

at

increasing delays.

This behaviour cannot

simply

be

explained by

_a loss of 75 excited atoms due to spontaneous emhsion which would involve _a

longer

time scale

(the

natural 75 lifetime is 48.5

ns).

Neither

can it be

explained by

the

spurious absorption

due to _a 6P

population.

Indeed in

figure

8 the

absorption,

_as measured with _non resonant pump

pulses,

increases

smoothly

with the

delay

and remains small. We believe that _a

possible explanation

_may involve

in-phasing

of individual

atomic

dipoles by

the

probe field,

all the _more efficient when spontaneous ^{emission had} not time

enough

to occur, one characteristic feature of the

triggered superradiance

discussed in the next section. We

plan

to

investigate

this

question

with _{a more}

judicious

utilization of the

optical

^switch

gating

the

probe

beam. One _can attempt to search for _a different

interpretation

in terms of _a coherent

twc-photon

_process. We have

previously

discussed this _process

[12], though

in the context of _cw laser

excitation,

and found it

negligible.

3. 2 DEMONSTRATING SMALL LIGHT-SHIFTS- The intense radiation field of the _pump laser needed to create

population

inversion in _a short time is

responsible

for _ac Stark

siifts.

_{At first}

sight

such effects _seem to be of minor

importance

here since _{we are} interested neither in

frequency

measurements nor in

high

resolution spectroscopy. Nevertheless

light~shifts might

start to affect the

polarization

measurements if

they

_{were source} of

signal

loss _or

signal

noise.

For

instance,

whenever the _pump and

probe pulses overlap,

the

probe

radiation field

experiences

an atomic system ^{whose level}

positions adiabatically

shift

during

observation. To evaluate the

practical importance

of the

effect,

its

magnitude

_can be

calculated,

but with _some

complications coming

from

geometrical

and time

averaging.

This is

why

_we found it valuable _to

quickly

obtain

an

experimental

_answer.

~

(sx+syi/s

'

FUI°F

probe

0

--w

w-delay

probe _delay

0 lo 20

_ns

-1

Fig. 8. Anlplification _{power vs.} purlp-probe delay with _punlp laser resonant for 65, F

= 3

- 75,

F = 4

(+)

_{or non} resonant

(o).

In both _cases, the probe is kept resonant for 75, F

= 4

-

6P~j2,

^F = 5.

Longit. E-field 2

kV/cnl.

Exc, pulse I mJ, ncs Ci 2 _x 10~~

at/cnl~.

Right _: definition of the delay, at scale.

As shown in the

preceding

section

(Figs.

4 and

6), optical

rotation and

birefringence

created

by

the _pump beam

provide large dispersive shaped signals.

As is well

known, vanishing

at the line center

accurately

determines the transition

frequency,

here

averaged

_over the

sample

of atoms detected. The

probe frequency

that

corresponds

to _{a 2ero} of this

signal

is found not to be the _same when the

probe

is switched _on

during

_or

ajler

excitation.

Thi

measured difference is the

light-shift

of the 75

6P3j2

^{transition caused}

^by

^the _pump beam

(averaged

_{over space}

and

time).

The observed shift for _a pump energy

density

of £ ^lmJ

/mm~

is

always

_< 5 MHz

,

which is small

enough

not to be the _source of any

special

_concern

presently.

3 3 DETECTING _A SECONDARY RADIATIVE PROCESS INDUCED BY THE PUMP BEAM. Intri-

gued by

the

origin

of the non-resonant process

responsible

for _a 6P _state

population

induced

by

the _pump

pulse,

we have

probed

the 6P

population

time evolution after _{a pump}

pulse.

This

was done without the electric field

so as not to

populate

the 75 state.

Figure

9 shows the measured

absorption

of the

(20

_ns

long) probe pulse

_as it is

delayed

in time with respect to the pump

pulse

_: the 6P

population builds-up

at a microsecond time scale and then

decays

_{on a}

longer

scale. Also shown in

figure

9 is the fit to the

experimental

data

by

the difference of two

exponentials

with time constants 1.25 ps and 3.2 ps

respectively.

The time constant for

decay

agrees well with the value

+w 3 ps

expected

from _our

previous

measurements of the

damp- ing

time of the

6P~j2 ^population

^{in similar conditions of} resonance radiation

trapping (high

atomic

density) _[12].

On the other hand the

rising

time -constant

(1.26

+

0.06)

_w matches well the

6D5j2

^{natural lifetime}

[22]. Indeed, according

to the work of Collins et al. [23] ^the

excitation of the Cs SD state is

expected

to

originate

from the

photolysis

of cesium dimers in the laser

frequency

_range 530-600 _nm

covering

^the 65-75 _resonance

frequency (Fig. 10).

probe relay

(~s)

Fig.

9. Absorption of the 20 _ns

long

probe pulse following _{a pump} pulse in absence of E~field,

vs. pump-probe delay. Lasers resonant for 65, F ₌ 3 _- 75, F

= 4 _-

6P~j2,F

₌ 5. Pump _energy

1.2 mJ. _{nc~ ci} io~~

at/crn~. (+)

Experimental points. ^The _curve ^is a fit by the difference of two

exponentials with rising and

decreasing

time constants 1.3 _ps and 3.2 _ps respectively.

7~sw+ds~

(((

_5~o+6~Sg~

3.5fim

IV (lz540nn1)

~312

~2p_~~2s

-1/2 ^l&

6~Si~+6~S,_~

Internuclear _separation

Fig.

lo. Schematic representation of the photolysis of Cs2 by photons of wavelength _~w 540 _nm.

The _process

occurs either by predissociation

(channel a)

_or by direct dissociation

(channel b).

Further consequences ofthis

photolysis

_process in _our

operating

conditions _are

currently being investigated

and will be

published

elsewhere.

4. Three

amplification regimes.

Of all the parameters

(pump

_energy, cesium

density...) affecting

the 75

population,

the electric field turns out to be _a

particularly

convenient tool for its control. Its effect is

simply quadratic,

N7s '~

E~,

and allows _{us to}

explore

three different

amplification regimes

_: linear

amplifica~

tion for low densities of excited atoms,

triggered superradiance

for

high densities,

and then spontaneous

superradiance

when the

probe

beam is masked.

These _are

obviously

not three

completely

exclusive

regimes.

One _{can pass}

continuously

from

a situation in which _atoms contribute

individually

to the

amplification

of the

probe

beam to a situation in which _a

macroscopic dipole,

_sum of all the individual atomic

dipoles,

forms and

accelerates the de-excitation. The latter _case

corresponds

to

superradiance [24-26].

4. I BRIEF STUDY OF THE SPONTANEOUS SUPERRADIANCE. The

intrinsically

random _na-

ture of spontaneous

superradiance deprives

it of the

stability

_necessary for sufficient

sensitivity

in the detection. This is

why

it is essent1al _to know how to prevent

it,

and it is to this end

that _we have masked the

probe

and

briefly

studied this

phenomenon.

Above _a first

threshold,

_a

single superradiant pulse

is

observed,

at 1.47 ~m

(75

_-

_6P~j~

transition).

Above _a second

threshold,

_a second less intense

pulse

is emitted _a few nanoseconds later _on the 75 _-

6Pij2

^transition at 1.36 _~m

(selected by

_a

filter).

The

pulses

at 1.47 ~m and 1.36 _{~m are} both observed _at each shot.

Figure

II shows that the threshold at 1.47 pm is rather

low, corresponding

to _a rather small number of excited atoms _:

~w 6 _x 10~ in _an

emitting

volume 30 _mm

long

and lmm in diameter.

The _reason is the near-absence of

Doppler dephasing

between the

dipoles (due

to the _narrow

spectral

width of the excitation

source).

Indeed in this _{case one can assume} that the threshold

corresponds

to the condition in which the

superradiant pulse

must _occur before the atoms have

spontaneously decayed

from 75.

Using

the well known formulas for the

superradiance delay

_{[26] :}

tD=TsRlogN

8~ a~

~~~

3 N12r

(here

r must be taken _as the

partial

width of the most

probable

of all 75-6P

hyperfine

tran-

sitions,

_a is the diameter of the

pumping beam,

I ₌ 1.47 _pm the

wavelength

and N the number of excited

atoms),

_one finds _a threshold _:

N2

2

x10~.

_Its

compatibility

with the

experimental

value confirms that there _are few

spurious dephasings (~).

^{It is}

noteworthy

that the

superradiant

spontaneous ^emission

gives

rise to _a lower detection

efficiency

than _one would have with either

amplification

_or

triggered superradiance

and that _{one no}

longer

has _a choice of the

hyperfine

transition for detection.

Figure

12 indicates the variation of the time

delay

of the spontaneous

superradiance

with the square of the electric field

(that is,

the number of excited

atoms).

As

expected,

it decreases when this number

increases,

but the

delay

of the emission is

always longer

for emission to

6Pij~

than for that to

6P~j~

^The

limiting

value (~w15

ns)

_seen in the

figure

is due to the response time of the

photodiode. Clearly

_some inhibition _process of the emission towards

6P3j2

prevents

complete depopulation

of the

7Sij2

F ₌ 4 state via the most

probable channel,

and

permits subsequent

emission towards

6Pij~.

^Such an

incomplete

desexcitation of _an ensemble of atoms may be due to destructive interatomic interference called

subradiance,

which has been

observed in _a demonstrative

experiment performed

at Laboratoire Aimd Cotton

[27].

Using

_a faster

photodiode

it has been

possible

to observe situations in which the medium emits

superradiance

at I

= 1,47 pm even before the end of the excitation

pulse.

A second, less intense

pulse

at the _same

wavelength

_may follow the

first,

due to the

re-buildup

of the 75

population (similar phenomena

have been described in Ref.

[25]).

(~)

Introducing ^the field

gain

_per unit time and unit length, calculated in reference [10], we note that gLTSR

" o.3. Consequently the intensity amplification of _a resonant beam _over the total length

is close to unity for _a time interval equal to TSR-