18976 Phys. Chem. Chem. Phys., 2011, 13, 18976–18985 This journal is
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Cite this:
Phys. Chem. Chem. Phys
., 2011, 13, 18976–18985
A cryogenic beam of refractory, chemically reactive molecules with
expansion cooling
Nicholas R. Hutzler,*
a
Maxwell F. Parsons,
a
Yulia V. Gurevich,
a
Paul W. Hess,
a
Elizabeth Petrik,
a
Ben Spaun,
a
Amar C. Vutha,
b
David DeMille,
b
Gerald Gabrielse
a
and John M. Doyle
a
Received 24th March 2011, Accepted 27th May 2011
DOI: 10.1039/c1cp20901a
Cryogenically cooled buffer gas beam sources of the molecule thorium monoxide (ThO) are
optimized and characterized. Both helium and neon buffer gas sources are shown to produce ThO
beams with high flux, low divergence, low forward velocity, and cold internal temperature for a
variety of stagnation densities and nozzle diameters. The beam operates with a buffer gas
stagnation density of B10
15
–10
16
cm
3
(Reynolds number B1–100), resulting in expansion
cooling of the internal temperature of the ThO to as low as 2 K. For the neon (helium) based
source, this represents cooling by a factor of about 10 (2) from the initial nozzle temperature of
about 20 K (4 K). These sources deliver B10
11
ThO molecules in a single quantum state within a
1–3 ms long pulse at 10 Hz repetition rate. Under conditions optimized for a future precision
spectroscopy application [A. C. Vutha et al., J. Phys. B: At., Mol. Opt. Phys., 2010, 43, 074007],
the neon-based beam has the following characteristics: forward velocity of 170 m s
1
, internal
temperature of 3.4 K, and brightness of 3 10
11
ground state molecules per steradian per pulse.
Compared to typical supersonic sources, the relatively low stagnation density of this source and
the fact that the cooling mechanism relies only on collisions with an inert buffer gas make it
widely applicable to many atomic and molecular species, including those which are chemically
reactive, such as ThO.
1 Introduction
Atomic and molecular beams are important tools for precision
spectroscopy and collision studies.
1,2
The most commonly
used beam methods are effusive and supersonic (typically
pulsed in the latter case). Effusive beams of certain species
have very large fluxes, especially metal atoms or low-reactivity
molecules with high vapor pressure. Often, however, these
beams have large velocity spreads and broad distributions
over internal states, reducing the useful signal for many
spectroscopy experiments. Supersonic beams, on the other
hand, are cold translationally and internally, but have a large
forward velocity. Typically, for spectroscopy, it is desirable to
have a beam that is both cold (to narrow spectral features,
and, in the case of molecules, concentrate population in a
small number of rotational levels) and slow (to increase the
interaction time and decrease time-of-flight broadening) while
maintaining high flux. There is a range of techniques to achieve
such a beam. For example, beams of many atomic species can
be laser-cooled and slowed using dissipative optical forces,
3
through techniques such as frequency chirping,
4
Zeeman
slowing,
5
and white-light slowing.
6
There is growing interest
7
in extending such slowing and cooling methods to molecules,
especially polar molecules, whose rich internal structure and
strong dipolar interactions make them candidates for quantum
computing,
8
cold chemistry,
9
precision measurement,
10–13
and
observation of novel quantum phases.
14
Laser cooling
of a molecule has recently been demonstrated,
15,16
and other
existing techniques to produce cold and slow beams of polar
molecules include using time-varying electric fields to decelerate a
supersonic expansion,
17
filtering slow molecules from a
cold source,
18
and buffer gas cooling
19
of both pulsed
20
and
continuous
21
beams.
In this paper we report on a newly developed buffer gas
cooled beam source. We study ThO beams from both helium
and neon buffer-gas-based beam sources, and observe cooling
of ThO from the free expansion of the buffer gas. The flux,
divergence, temperature, and velocity of the buffer gas beams
we studied compare favorably (and for the case of chemically
reactive molecules,
22
very favorably) to supersonic or effusive
beams, as discussed further in Section 3.7. Buffer gas beams
have been successfully utilized in the past to create cold and
slow beams of several species,
19,23,24
including (but not limited to)
a
Harvard University Physics Department, 17 Oxford Street,
Cambridge, MA 02138, USA. E-mail: hutzler@physics.harvard.edu;
Tel: +1 617 495 2713
b
Yale University Physics Department, 217 Prospect Street,
New Haven, CT 06511-8499, USA
PCCP
Dynamic Article Links
www.rsc.org/pccp PAPER
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ND
3
,O
2
, PbO, SrF, SrO, ThO, Na, Rb, and Yb. The beams
presented in the current work operate at a much higher
Reynolds number than previously demonstrated buffer gas
beams, and we observe new and advantageous features, in
particular expansion cooling, not seen in previous work
(though similar results were observed concurrently by a
collaborating group
24
).
Both helium and neon cooled beams were studied. Helium
gas can be used at lower temperatures, and can therefore be
used to lower the initial ThO temperature below that of neon-
based sources. However, neon has much simpler pumping
requirements to maintain good vacuum in the beam region,
and a neon-based source operates at a higher temperature
which allows for larger heat loads for molecule production.
We find that due to expansion cooling in neon, the final,
optimized beam temperatures for both helium- and neon-
based beams are very similar. For a planned precision spectro-
scopy experiment with ThO,
10
the neon-based source is
superior in certain aspects (particularly technical ones) to that
of the helium-based source. Further comparison of helium-
and neon-based sources can be found in Section 3.6.
2 Apparatus
The heart of our cold beam apparatus (see Fig. 1) is similar to
that which is described in earlier buffer gas cooled beam
publications,
20,21,23
to which the reader is referred for
additional technical details. It is a cryogenically cooled,
cylindrical copper cell with internal dimensions of 13 mm
diameter and 75 mm length. A 2 mm inner diameter tube
entering on one end of the cylinder flows buffer gas into the
cell. A 150 mm length of the fill line is thermally anchored to
the cell, ensuring that the buffer gas is cold before it flows into
the cell volume. An open aperture (or nozzle) on the other end
of the cell lets the buffer gas spray out as a beam, as shown in
Fig. 1. ThO molecules are injected into the cell via ablation of
a ceramic target of ThO
2
, located approximately 50 mm from
the exit aperture. A pulsed Nd : YAG laser
25
is fired at the
ThO
2
target, creating an initially hot plume of gas-phase ThO
molecules (along with other detritus of the ablation process).
Hot ThO molecules mix with the buffer gas in the cell, and
cool to near the cell temperature, typically between 4 and
20 K. The buffer gas is flowed continuously through the cell at
a rate f
0
= 1–100 SCCM.w This both maintains a buffer gas
stagnation density of n
0
E 10
15
–10
16
cm
3
(B10
3
–10
2
torr)
and extracts the molecules out of the aperture into a beam.
21
The result, due to the pulsed introduction of ThO into the cell,
is a pulsed beam of ThO molecules (embedded in a continuous
flow of buffer gas) over a 1–3 ms period, as shown in Fig. 2.
We have achieved stable operation of the neon-based beam
with up to a 200 Hz repetition rate; however, the data
presented in this paper are at a repetition rate of 10 Hz. The
cell aperture is a square hole of adjustable side length
d
a
= 0–4.5 mm that can be varied in situ and continuously
while the beam runs.
Either helium or neon is used as the buffer gas (typically
called the carrier gas in most beam literature). The cell
temperature T
0
is maintained at 5 1 K for helium, or
18 1 K for neon, and is controlled by the use of resistive
heaters thermally anchored to the cell. The cell is surrounded
by a radiation shield at 4 K, which is partially covered in
activated charcoal
26
to form a cryopump that keeps the helium
background pressure low. A second radiation shield at
temperature B50 K surrounds the 4 K radiation shield, and
both shields have glass windows to allow the transmission of
spectroscopy lasers, and holes to allow passage of the molecular
beam. The radiation shields and cell are connected by flexible
copper braid heat links to a pulse tube refrigerator.
27
Fig. 1 Left: The cold beam apparatus. The features inside the vacuum chamber are described in Section 2, and the features outside the vacuum
chamber are described in Section 3. Right: A detailed view of the cell. (a) A continuous gas flow maintains a stagnation density of buffer gas atoms
(filled blue circles) in thermal equilibrium with a cold cell. A solid piece of ThO
2
is mounted to the cell wall. (b) A YAG pulse vaporizes a portion of
the target and ejects hot ThO molecules (empty red circles). (c) Collisions with the buffer gas cool the molecules, which then flow out of the cell to
form a beam.
w 1 SCCM = 1 cm
3
per minute of gas at standard conditions, or about
4.5 10
17
gas atoms per second.
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The beam exiting the cell is incident on a conical collimator
with a 6 mm diameter orifice located 25 mm from the cell
aperture. There are expected to be few collisions this far from
the cell aperture, so for our work, the features of this
collimator are more akin to those of a simple differentially
pumped aperture. For helium buffer gas, the collimator is at a
temperature of about 8 K. For neon buffer gas the collimator
is heated to 30 K to prevent neon ice formation.
All of the cryogenic apparatus is kept inside a room-
temperature vacuum chamber of internal volume B0.2 m
3
.
During beam operation, vacuum is maintained by cryopumping
of the charcoal and radiation shields, and no external pumping
on the vacuum chamber is required. However, a small
(60 l s
1
) turbomolecular pump continuously pumps on the
chamber, to pump out any gas released should the cryopumps
warm up and stop pumping. The main chamber has a pressure
of o10
5
torr during buffer gas flow, as measured with an
ion gauge.
The ThO
2
target is constructed from ThO
2
powder, pressed
and sintered as described in existing literature.
28
These targets
typically yield >30 000 YAG shots on a single focus site
before the yield per shot drops to 50% of the initial value, at
which time the focus must be moved to a new spot. The large
surface area (B1cm
2
) of the target should allow for >10
7
shots before target replacement is necessary.
2.1 Qualitative features of buffer gas beams
Here we present a brief overview of the features of a
buffer gas cooled beam, which are discussed in detail in the
existing literature.
29
Central to understanding the unique
properties of buffer gas cooled beams is the process of
hydrodynamic entrainment.
21
A ‘‘hydrodynamic’’ buffer gas
cooled beam is designed so that the characteristic pumpout
time (t
pump
) for the molecules to exit the cell is less than the
characteristic diffusion time to the cell walls (t
diff
),
30
both of
which are typically 1–10 ms. These conditions result in many
of the molecules being extracted from the cell before they
diffuse and stick to the cold cell walls. The ratio of these
timescales is given by
g
cell
t
diff
t
pump
f
0
s
v
0;b
L
cell
; ð1Þ
where s is the cross section for collisions between ThO and the
buffer gas,
v
0;b
is the mean thermal velocity of the buffer gas
atoms (the subscript 0 indicates in-cell, stagnation quantities),
and L
cell
is the length of the cell. The parameter g determines
whether the beam system is running with hydrodynamic
entrainment or not. When g
cell
\ 1 the molecules are entrained
in the flow of the buffer gas, which results in an order of unity
fraction of cooled, in-cell molecules being extracted into the
molecular beam. For a hydrodynamic source, during the
initial cooling and through the extraction phase, the molecules
are in a low-density environment colliding only with inert gas
atoms. These aspects of hydrodynamic buffer gas beams make
this method an attractive alternative for species that are reactive,
refractory, or otherwise difficult to obtain in the gas phase.
In the beam region just outside the cell aperture, the
molecules undergo collisions with buffer gas atoms. Because
the average velocity of the buffer gas atoms is higher than that
of the (typically) heavier molecules, and because the collisions
are primarily in the forward direction, the molecules are
accelerated to a forward velocity, v
f
, which is larger than the
thermal velocity of the molecules (just as with supersonic
beams
2
). As the stagnation density is increased, v
f
increases
until it approaches a maximum value, which is that of the
forward velocity of the buffer gas. In flow regimes considered
in the existing literature, the transverse spread is given
approximately by a Maxwell–Boltzmann distribution with
temperature equal to the cell temperature, since there are
typically not enough collisions outside the cell to increase this
spread. In this model the molecular beam is therefore a
thermal cloud of molecules with a center of mass motion given
approximately by the forward velocity of the buffer gas. The
angular distribution has a characteristic full (apex) angle y
given by tanðy=2Þ¼v
?
=v
k
v
0;mol
=
v
0;b
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m
b
=m
mol
p
, where
the subscripts b and mol represent the buffer gas and molecule,
respectively. Since typically m
mol
c m
b
, we have y { 1
so y 2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m
b
=m
mol
p
. The characteristic solid angle is then
O =2p(1 cos(y/2)) E py
2
/4 = pm
b
/m
mol
. This quantity is
approximately 0.1 and 0.3 for ThO in He and Ne, respectively.
This model accurately describes the results of previous buffer
gas beam experiments.
20,21,23
As will be seen in Section 3, we
have studied beam operation at higher Reynolds numbers
than previous experiments, and therefore additional effects
must be considered.
2.1.1 Flow parameterization. Buffer gas beams typically
operate in the intermediate regime between effusive and
Fig. 2 Top: An absorption signal of the ThO molecular beam in a
1 SCCM flow of helium buffer gas with a 4.5 mm diameter cell
aperture. The laser is fixed spatially, so the time variation of the signal
is a result of the molecular beam pulse passing through the laser.
The different traces show absorption in the cell (dotted) and 1 mm
after the cell aperture (solid). For these data, the laser is locked on the
resonance of the X–C Q(1) line. The width and height of the signals
depend on the buffer gas flow rate, buffer gas species, and cell aperture
size; however, the qualitative features are similar. Bottom: By varying
the laser detuning, we obtain an absorption spectrum. This curve
shows the absorption spectrum of the molecular beam 1 mm after the
cell, with the same experimental parameters as in the top figure.
Optical density (OD) is defined as T = e
OD
, where T is the
transmitted fraction of the probe laser light.
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supersonic, where both molecular kinetics and fluid-like behavior
are important. The parameters determining the operating
regime of the beam dynamics outside the cell are the Reynolds
and Knudsen numbers. The Knudsen number is defined as
Kn ¼ l=d ð
ffiffiffi
2
p
n
0
sdÞ
1
, where l is the mean free path of the
buffer gas and d is a characteristic length scale, in our case the
cell aperture diameter d
a
. The Knudsen number is related to
the Mach number, Ma, and Reynolds number, Re,by
31
1
2
(Kn)(Re) E Ma. (2)
Near the cell aperture, the buffer-gas atoms are traveling at
approximately their thermal velocity
v
0;b
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
8k
B
T
0
=pm
b
p
,
where k
B
is Boltzmann’s constant. For the purposes of our
qualitative estimates, this velocity is near to the speed of sound
c
0;b
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
5k
B
T
0
=3m
b
p
¼ 0:8
v
0;b
. Therefore Ma E 1 near the cell
aperture, and we have the relation
1
2
(Kn)(Re) E 1. (3)
Using the formulas above, we estimate the relationship
between flow and Reynolds number to be
Re E 0.7 (f
0
/1 SCCM) (d
a
/4.5 mm),
where we estimate the collision cross section (from diffusion
measurements) to be s E 3 10
15
cm
2
.
Buffer gas beams typically operate
19
in the regime Kn E
1–10
2
. Effusive beams require Kn > 1 so that the aperture
does not alter the properties of the atoms extracted from the
cell, while supersonic beams typically
2
have Kn t 10
3
.
3 Measured beam properties
We studied the beam with a variety of buffer gas flows,
aperture sizes, and cell temperatures for both helium and neon
buffer gases using continuous wave laser spectroscopy
from the ThO ground electronic state X (v =0,O =0
+
,
B
e
= 0.33 cm
1
) to the excited electronic state C (v =0,
O =1,T
0
= 14489.90 cm
1
, B
e
= 0.32 cm
1
)
32
at 690 nm.
Two diode lasers are each locked to a stabilized frequency
source via a Fabry–Pe
´
rot transfer cavity. The frequency of one
laser is scanned to obtain spectra, while the other is kept at a
fixed frequency and used to normalize against variation in the
ablation yield (typically a few percent from shot-to-shot). The
scanning laser detuning, Nd : YAG pulses, and data acquisition
are all synchronized via a master control computer. The
scanning laser is split into multiple beams and used for
absorption transverse to the molecular beam at several distances
after the cell aperture, and for laser-induced fluorescence (LIF)
parallel to the molecular beam as shown in Fig. 1. Absorption
data are obtained using silicon photodiodes, and laser-induced
fluorescence is collected with either a CCD camera or a
photomultiplier tube (PMT).
3.1 Rotational cooling
The rotational temperature was determined by fitting a
Boltzmann distribution to the lowest six rotational levels
(J =0toJ = 5) of the ground state X. Population was
determined from the optical density (see Fig. 2) of absorption
on the X to C transition. The lines R(0), Q(1), ..., Q(5) were
used to obtain the population in X, J =0,1,..., 5 respec-
tively. Rotational temperatures with both helium and neon
buffer gases are shown in Fig. 3. The minimum measured
rotational temperature, measured 6 cm from the cell, as a
function of buffer gas flow and aperture size, was 2.0 0.8 K
with neon buffer gas, and 1.7 0.5 K with helium buffer gas
(error bars in this paper refer to the 95% confidence interval
of fits). These represent an increase of a factor of 8.2 and
2.8 in the X, J = 0 population with neon and helium buffer
gases, respectively, from the distribution present at the cell
temperature.
With neon buffer gas the rotational temperature decreases
with both increasing flow and increasing distance from the cell
aperture. The rotational temperature does not change after a
distance of 2 cm after the cell, indicating that the cooling
collisions have stopped before this distance. With helium
buffer gas the rotational temperature is largely independent
of flow, distance from the cell, and aperture size as measured
with 14 different flows, three different distances after the cell,
and three different aperture sizes. The temperature of the
molecules just outside of the cell, however, is lower than the
cell temperature, even for the lowest flow and largest aperture.
This behavior is unexpected: At the lowest flow (1 SCCM) and
the largest aperture (4.5 mm side square), the flow regime is
effusive (Kn E 1) and so we should see no additional cooling
below the cell temperature of 5 K. More low-flow helium
phenomena, along with possible explanations, are discussed in
Section 3.5.2.
For both buffer gases, the molecules approach some
minimum rotational temperature that does not decrease with
additional flow. This minimum temperature appears to be
about 2–3 K, and is similar for both helium and neon. In fact,
the rotational temperature just outside a 9 K cell with a
helium buffer gas flow has a similar minimum temperature
of 2.9 1.3 K.
Fig. 3 Rotational temperatures in the buffer gas cooled beam. Top:
Temperatures measured 1 mm from the cell aperture. Bottom: Final
rotational temperatures in the expansion, measured 6 cm after the cell
aperture. The cell temperatures are 5 1 K and 18 1 K for helium
and neon buffer gases, respectively. The data with a helium buffer gas
were taken with a 2.0 mm aperture, while the data with a neon buffer
gas were taken with both 2.0 mm and 6.5 mm apertures.
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3.2 Forward velocity
The forward velocity of the ThO beam was measured at
distances between about 6 cm and 16 cm from the cell aperture
using laser-induced fluorescence (LIF) imaging. A counter-
propagating, red-detuned pump beam excites the molecules
on the Q(1) or Q(2) line of the X–C transition, and the
fluorescence is collected with either a CCD camera or a PMT.
The camera gives spatial information about the beam, but since
the exposure time is longer than the molecular pulse duration the
camera averages over an entire pulse. To get time-dependent
information, we use the PMT. We measure the first-order
Doppler shift of the molecules by fitting a gaussian shape to
the obtained LIF spectrum and comparing the center to that
of a transverse absorption spectrum. The forward velocity and
velocity distribution are then inferred from the first-order
Doppler shift and width of the spectrum, respectively.
Values for the forward velocity are between 120 and
200 m s
1
, which are slower than typical supersonic expansions.
The final velocity of a supersonic expansion of a monoatomic
carrier gas is given by
33
v
k
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
5
2
2k
B
T
0
m
r
1:6v
p;0
; ð4Þ
where m is the carrier gas particle mass, T
0
is the stagnation
temperature in the source, and v
p,0
is the most probable
thermal velocity of the carrier in the source. From this
equation, the final velocity is about 600 m s
1
for a supersonic
expansion of room-temperature argon, or about 300 m s
1
for
an expansion of 210 K xenon. With neon buffer gas in an 18 K
cell, the forward velocity (see Fig. 5) approaches a value that is
very close to the final velocity of B200 m s
1
predicted by
eqn (4). With helium buffer gas, the mean forward velocity
approaches about 70% of the value 230 m s
1
predicted by
eqn (4) for a 5 K cell. The lower-than-expected value for
the helium-cooled beam is likely due to collisions with the
background helium that accumulates due to the limited pumping
speed of the activated charcoal, which is not a problem with
neon because once it sticks to a 4 K surface, it remains there
nearly indefinitely (i.e. has negligible vapor pressure at 4 K).
Increasing the amount of charcoal and improving its placement
mitigated this problem; however, the issue remained present.
Further discussion is presented in Section 3.6.
Interpretation of the helium forward velocity data is
additionally complicated by the fact that, unlike with the case
of neon buffer gas, it varies in time over the molecule pulse
duration, as shown in Fig. 6. This dependence of beam
properties on time after ablation is perhaps due to the finite
amount of time required to thermalize the ThO molecules in
the buffer gas cell, which is much smaller with neon due to
neon’s smaller mass mismatch with ThO, and the fact that the
heat introduced by ablation results in a smaller fractional
change in temperature at 18 K versus 5 K. Additionally, the
forward velocity with helium buffer gas varies by as much as
B10% if the ablation spot is moved, and as the charcoal
cryopumps become full of helium and the pumping speed
changes, as discussed in Section 3.6. These effects are not
observed with neon buffer gas.
3.2.1 The velocity vs. flow relationship. We can model the
shape of the velocity vs. flow curve with the ‘‘sudden freeze’’
model,
33
in which we assume that the molecules are in
Fig. 4 Rotational level populations with Boltzmann distribution fits
for 30 SCCM neon flow, 4.5 mm aperture. The top, middle, and
bottom plots show the distributions 1 mm, 2 cm, and 6 cm from the
cell aperture, respectively.
Fig. 5 Top: Mean forward velocity vs. flow rate with neon buffer gas.
The solid line is the hydrodynamic limit for the forward velocity of
neon atoms exiting an 18.5 K cell, given by eqn (4). The forward
velocity of the molecules with neon buffer gas cooling varies by no
more than 10% over a pulse. Bottom: Mean forward velocity vs. flow
rate with helium buffer gas.
Fig. 6 Forward velocity vs. time after ablation for several different
flow rates of the helium buffer gas.
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