HAL Id: jpa-00247796
https://hal.archives-ouvertes.fr/jpa-00247796
Submitted on 1 Jan 1992
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entic 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 diusion de documents
scientiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Accurate optical measurement of nuclear polarization in
optically pumped 3He gas
N. Bigelow, P. Nacher, M. Leduc
To cite this version:
N. Bigelow, P. Nacher, M. Leduc. Accurate optical measurement of nuclear polarization in op-
tically pumped 3He gas. Journal de Physique II, EDP Sciences, 1992, 2 (12), pp.2159-2179.
�10.1051/jp2:1992258�. �jpa-00247796�
J.
Phys.
II France
2
(1992)
2159-2179
DECEMBER
1992,
PAGE
2159
Classification
Physics Abstracts
32.808 42.60K
67.65
Accurate optical
measurement
of
nuclear
polarization
in
optically
pumped
3He
gas
N. P.
Bigelow (*),
P. J.
Nacher
and M.
Leduc
Laboratoire
de
Spectroscopie
Hertzienne
(**), Ecole Normale Supdrieure,
24
rue
Lhomond, 75231
Paris,
France
(Received IO
June
1992,
accepted
in
final form 8 September 1992)
Rdsumd.
On
peut
maintenant produire
par
pompage
optique de fortes polarisations nucldaires
M
(M
supdrieure h 80 fb)
dans
l'3He
gazeux.
Le
gaz
est
excitd
par une
ddcharge radiofrdquence
et
orientd
h
l'aide d'un laser LNA de forte
intensitd qui
est
pompd
par
des lampes
et
accordd
sur
la
transition 2
35-2 3P
h 1,08
~m.
Dans
cet
article,
nous
ddcrivons
une
expdrience off
nous mesurons
M
avec une
grande prdcision absolue. Notre
mdthode
est
fondde
sur
la
variation
en
fonction
de M
de l'absorption
par
les
atomes
mdtastables
d'un faisceau sonde
de
faible intensitd polarisd
lindairement. Nous
mesurons
le
rapport
des
absorptions
pour
des polarisations
ar
et
«.
Le
faisceau
sonde
est
un
laser LNA pompd
par
diode
qui
se propage
perpendiculairement h la direction de
l'aimantation. Simultan6ment,
nous mesurons
M
par
le degr6 de polarisation circulaire
S
de la raie
h
668
nm
dmise
par
la ddcharge. Nos rdsultats
montrent
une
relation lindaire
entre
M
et
S
dans
toute
la
gamme
des
valeurs de M rdalisdes
et
pour
des conditions expdrimentales varides (pression dans
la cellule, champ magndtique, niveau
de d£charge,
etc.).
Ceci foumit
une
seconde
m£thode
pour
mesurer
la polarisation nucldaire
de
l'3He.
Cette mdthode
est
simple h
mettre
en ~euvre
et
se
trouve
ainsi calibr6e dans
une gamme
de pression
allant de
0,15
h 6,5
tow.
AbstracL
Large nuclear polarizations
M (over
80 fb)
can
now
be
achieved in
gaseous
3He
by
optical pumping. The
gas
is excited by
an
RF discharge and is
oriented
using
a
high
power
LNA
laser which is lamp pumped and
tuned
to
the
2
35-2 3P
transition
at
1.08
~m.
In
this
paper we
describe
an
experiment in which
we measure
M
with high absolute precision. Our method is based
on
a
change
as a
function
of M in the ratio of
«
or
ar
polarized light absorbed from
a
weak probe
beam by
the
2
35
metastable
atoms.
The probe
was
delivered by
a
diode pumped LNA laser
and
propagated perpendicular
to
the direction of the
magnetization. Simultaneous
measurement
of
M
was
made by monitoring
the degree of circular
polarization
S
of the optical line
at
668
nm
emitted
by the discharge. Our
measurements
show
a
linear
relationship between
M
and
S
for all accessible
M values and for
a
wide
range
of experimental
conditions (sample
pressure,
magnetic field,
RF
discharge
level, etc.). This provides
a
second method of
measurement
of the
3He
nuclear
polarization which is simple
to
operate
and
is
calibrated
over a pressure range
of 0.15
to
6.5
tow.
(*)
Permanent Address
:
Department
of
Physics
and Astronomy and Laboratory
for
Laser
Energetics,
University of
Rochester, Rochester,
N-Y-14627,
U-S-A-
(**) Laboratoire
assoc16
au
CNRS URA 18.
2160 JOURNAL
DE
PHYSIQUE
II
N° 12
Introduction.
Optical pumping
is
an
efficient method for creating
nuclear
polarization in
a gas
of
3He.
Polarized
3He
has applications
in
different fields of
physics ranging
from
quantum
fluids Ii
to
nuclear physics
[2].
Optical pumping
of
3He
was
first
demonstrated in
1963
[3]. More
recently
there has
been
a
renewed interest in
this technique
because
of
the increasingly high values of
nuclear
polarization M
which
have been achieved. Much of the
recent
progress
has resulted
from
the development
of efficient solid
state
IR
lasers
capable of exciting
the
2
35-2
3P
3He
transition
at
1.08
~m.
In particular,
using
a
lamp pumped
LNA
laser
which delivers
a
few
watts
of CW
power
[4-6],
it is possible
to
achieve
values
of
M
in
excess
of 80 fb.
As
a
direct
result
of
these
improvements in M values,
accurate
techniques
for
measuring M
are
increasingly
in
demand.
For
example, consider nuclear physics scattering
experiments [7]
which
use
polarized helium
targets.
In these
experiments asymmetries
are
measured
in
scattering
cross
sections
for
reversal
of
target
polarization and hence the experiments
require
that M be both
large and
precisely known.
In general,
one
can
distinguish several methods for measuring
M
in optically pumped
3He.
The first
group
relies
on a
direct magnetic
measurement.
Such
a
measurement
can
be made
either
by
measuring
the
magnetic field
created
by
the sample
using
an
absolute
magnetometer
[8]
or
by
magnetic
resonance
(NMR). NMR techniques
were
used in the
early experiments [3]
with
pure
3He
and also
for
3He
polarized
by
spin exchange with optically
pumped
rubidium
vapor
[9].
The
3He
NMR signals
must
be calibrated
against
a
known
reference sample of
identical
geometry
such
as
the
proton
reference provided by
a
sample
cell of
pure
water.
This
method, already
used
in
earlier experiments [3], is currently
being examined
with
increased
accuracy
[10].
The
second
group
of
measurements
is
optical and
relatively simple
to operate
as
compared
to
magnetic
measurements
and
the
measurement apparatus
can
be
more
easily isolated from
the
polarized sample. M
is determined
by
analysis
of
the
absorption of the 2 3Si
metastable
atoms
or
of the
polarization of
the
light emitted
by the
discharge.
The
absorption method
has
been
demonstrated by several
groups
using He
lamps
as
the probe
source
[3, II, 12]
and
requires
a
model
of
the
optical pumping
process
to extract
absolute M values. The analysis
of
the
polarization distribution
of the
emission
spectra
was
introduced by
LaloB
II
3, 14].
This
method
relies
on
the
conservation
of
nuclear spin during collisions which excite
atoms
from
the ground
state
to
an
upper
state
;
in
the
excited
state
the
hyperfine interaction
couples
the nuclear
and
electronic
degrees
of freedom such that
the electronic polarization, and hence the polarization
of the
light emitted
as
the excited
state
decays through
spontaneous
emission, both reflect
the
state
of
nuclear
polarization. This method provides
a
practical technique for monitoring
M, but
is
too
complex
to
directly provide absolute values for M,
so
it
must
be calibrated
against
an
other
method
[15].
The precision of
previous absorption
measurements
has
been
limited by
the
lack
of detailed knowledge of
the
coincidence of
the lamp
profile
with the atomic absorption
spectrum.
The
same
limitations
arose
in early studies of
polarization
distribution
of
the
emitted
light, because they
were
calibrated through absorption methods.
In
the
present
work,
we
describe
experiments in which M
is
directly
measured by absorption
of
a
probe beam with
a
greatly increased
absolute
accuracy.
The
improvements
are
achieved
by
using
a
diode pumped tunable
single-mode LNA laser
to create
the probe beam
and by
using
a
revised experimental
geometry
to
eliminate
sources
of systematic
error.
We have used this
absorption
technique
to
recalibrate the M
dependence of
the
optical polarization distribution
of
one
of the
He
emission lines (3
'D-2
lP
at
668
nm), and
to
extend this calibration
to
high
values
of
M.
Measurements
were
carried
out
under
a
large
range
of experimental
conditions
:
discharge
level, sample
pressure,
magnetic field and polarization
rates
were
varied. In this
article
we
first
N° 12
ACCURATE MEASUREMENT OF
3He
NUCLEAR POLARIZATION
2161
discuss
the
principle
of
our
polarization
measurement
via
absorption. We
then
go on
to
describe the
experimental
set-up
and
measurement
procedure, and
finish
the
paper
with
a
presentation
of
our
results
and
a
discussion
of the
estimated
accuracies,
1.
Principle
of
polarization
measurement
used
in this work.
Absorption
measurements
were
performed
using
a
weak
probe
beam
tuned
to
the
C~
transition
of
the
3He
(2
~Si,
F
=
~
~
2
~Po,
F
=
(see
Fig,
I).
The
absorption
A~
of the probe
beam
2
2
was
measured
as a
function
of
its
optical polarization
p.
In
our
experiments,
as
in the early
work
of reference
[12],
we
measured
the
absorption
for
a
linearly
polarized probe.
In the
present
experiment, the
probe
polarization had
components
both
perpendicular
~p
=
«
) and
parallel ~p= gr)
to
the
quantization
axis. The
two
measured
absorption
signals
are
proportional
to
the
metastable
atom
density,
n~(~);
they also
depend
on
the
relative
populations
of
the magnetic
sublevels
(m~
=
),
,
+
of the
2
3Si,
F
=
state
and
thus depend
on
the nuclear
polarization
of
the
metastable
atoms.
For example,
when
the
2
3Si,
2~P~
F='/~
'~(~
~~(~
i
2j
3
2~S~
F=3/~
.3/2
-1/2
+1/2
+3/2
Fig.
1.
-Magnetic sublevels
involved
in
the optical detection using
the C9
component
of
the
3He
transition
(2
~Sj, F
=
~
-
2
~Po).
The solid lines
are
«transitions,
the
dotted lines
are ar
transitions. The
2
numbers
indicated along the
transitions
are
the relative
oscillator
strengths.
F
=
state
is
fully polarized,
only
the
m~
=
~
state
is populated, and
by
conservation of
angular
momentum
(I.e. the angular
momentum
selection rules), if the probe beam is
gr
polarized, the absorption
A~
~
0.
In comparison, the
absorption
A,
of
a
«-
polarized
probe
is enhanced
as
compared
to
the
case
where there
is
no
net
nuclear
polarization
(M
=
0
).
To
relate the
measured
values of absorption
to
the ground
state
polarization M,
we
use
calculations
of the
3He
pumping
process
which explicitly
treat
the coupling of the polarization
between
different atomic levels involved and for
which
a
generalized model
was
derived
previously
II
6]. The
key
point is that the
nuclear
spin polarization of the ground
state
and of
the
23Si
metastable
state
atoms
are
very
strongly
coupled by
metastability
exchange
collisions. The model
of reference [16] allows
a
direct calculation
of
the metastable
atom
populations under
the
joint influence of
such exchange
collisions,
of
the absorption of
the
pump
laser
and
subsequent
reemission,
and of
various
relaxation phenomena.
It introduces
a
parameter
nz/n~
corresponding
to
the fraction
of
the metastable
atoms
directly
interacting with
the
pump
laser. Actually, in the
present
experiment, where the
pump source
is
a
lamp
pumped
(')
This could
become inaccurate if the total
absorption
in
the
cell
were
not
small
;
in
such
a
situation
an
explicit calculation of each
polarization
component
of the
probe
beam
would be
required.
In
most
of
our
experimental situations the
total attenuation
was
of
order I
fb
(up
to
5 fb
at
the highest)
so
that
a
linear
approximation is
adequate.
2162 JOURNAL DE
PHYSIQUE
II N°
12
LNA laser (see
Sect. 2,I),
the fraction
n$/n~ is
a
relatively
large number [17], ranging
between
0,I
and 1.0,
because the mode
structure
of the laser is relatively broad, and
hence
a
large
range
of atomic velocity
classes absorb.
Using
the complete
formalism of reference
II
6]
it
is thus possible
to
calculate
exactly the
probe absorption signals
A~, A,_
and
Jt,
~
as
a
function
of M for
given
values
of
the
parameters
n$/n~
and
n~.
The
other input
parameters
of
the calculation
are
the
ground
state
density N, the
nuclear
relaxation time
Ti
and the metastable relaxation time
r~.
Note
that
the
ratio A~/A,
is independent
of
n~.
All the experiments
described in this
work
were
performed in
the absence of the
pump
beam
(see
Sect. 3,
I).
In
this
case a
simplified
version of
the
model
can
be used, given that the
rate
of
metastability exchange
collisions [18]
(=106
s-I)
is
much faster than the metastable
relaxation
rate
(r~
is
on
the order of the
diffusion time
across
the cell, typically of order
10-3
s).
As
discussed in references
[3]
and
[12],
one can
thus
assume
that the metastable and
ground
state
atoms
come,
through collisions,
into
a
«
Boltzmann-type
»
distribution
in angular
momentum
(instead of
energy)
in which
the
population
n(m) of the
m~
magnetic
sublevel
of
the 2
3Si
state
is given by
n
(m)
~
e~
fl~
where
fl
is
a
constant.
The value for
fl
(the effective
«
spin
temperature»)
for
the
ground
state
is
the
same
as
for
the
metastable
state.
The
differences
between
the
results of this simplified
model and those
of
the
more
complete model
of reference
[16]
are
discussed
in
appendix I. The
error
introduced by using the simplified
model
are
less
than
0.19b for
pressures
greater
than
0.7
torr.
For lower
pressures
a
small
correction is
evaluated in appendix I and quoted in the table I which is displayed in
section
3.3.
The
predictions for
the
absorption signals
calculated with this simplified model
are
shown in
figure
2a.
It shows
the
normalized absorptions
A,
~,
A,
and A~
as a
function of
nuclear
polarization
M.
The figure also shows
the
absorption
A,
for
a
beam carrying
equal
intensities
of
«
~
and
«_
polarized light. The vertical scale is
proportional
to
the
metastable
atom
density.
For
small M values the absorptions
A~
and
A~
are
relatively
insensitive
to
M.
As pointed
out
in
4.5
1.0
#
4.0
o
~
~
~i
O-B
~
~
.l
3.0
~
c
~
0.6
t 2
5
~
~
20
~
#
c
~
0.4
)
1.5
g
l.0
lo
2
m
g
#
0.5
~
fl
O-O
O-O
O-O 0.2 0
4
0.6
O-B
.0
O-O 0.2 0.4 0.6 O-B
.0
Nuclear Polarization M
NucIear Polarization
M
a)
b)
Fig.
2.-a)
shows
the
absorption
rate
A~
by the
~He2
~Sj
metastables
as a
function
of nuclear
polarization M for
different
polarizations
p
of the probe
beam
~p
=
gr,
«
~
,
«
and
«
where
«
is
an
equal
amplitude superposition
of
«_
and «~). The
probe
beam
is in
resonance
with the
C~
transition. These
theoretical
results
are
calculated
from reference [16] assuming
a
constant
metastable density
n~
for
all
M and
a
small fractional
absorption.
A~
is normalized
to
M
=
0.
b) shows
the ratio
of
absorptions for wand
ar
polarized light,
which is independent of
n~.