arXiv:0904.0732v2 [physics.flu-dyn] 9 Apr 2009
Metastable helium molecules as tracers in superfluid liquid4He
W. Guo, J.D. Wright, S.B. Cahn, J.A. Nikkel, and D.N. McKinsey
Physics department, Yale University, New Haven, CT 06515
(Dated: April 9, 2009)
Metastable helium molecules generated in a discharge near a sharp tungsten tip operated in either
pulsed mode or continuous field-emission mode in superfluid liquid4He are imaged using a laser-
induced-fluorescence technique. By pulsing the tip, a small cloud of He∗
At 2.0 K, the molecules in the liquid follow the motion of the normal fluid. We can determine the
normal-fluid velocity in a heat-induced counterflow by tracing the position of a single molecule cloud.
As we run the tip in continuous field-emission mode, a normal-fluid jet from the tip is generated
and molecules are entrained in the jet. A focused 910 nm pump laser pulse is used to drive a small
group of molecules to the vibrational a(1) state. Subsequent imaging of the tagged a(1) molecules
with an expanded 925 nm probe laser pulse allows us to measure the velocity of the normal fluid.
The techniques we developed demonstrate for the first time the ability to trace the normal-fluid
component in superfluid helium using angstrom-sized particles.
2molecules is produced.
PACS numbers: 47.27.-i, 29.40.Gx, 67.25.dk, 67.25.D-
Visualizing the flow of superfluid4He has long been
of interest to the scientific community [1, 2]. Recently,
particle image velocimetry with polymer micro-spheres
and hydrogen isotopes has been used to study liquid he-
lium flows [3, 4] and solid hydrogen tracers have been
used to visualize the quantized vortices [5, 6]. However,
the dynamics of micron-sized tracers in the presence of
vortices are complex . Kivotides  analyzed the re-
sults of Zhang and Van Sciver  and concluded that
one must account for particle-vortex interactions  in
order to extract an accurate measurement of the local
normal-fluid velocity from experimental data obtained
using micron-sized tracer particles. Furthermore, if the
vortex-line density is too high then the possibility to use
micron-sized particles to measure the normal-fluid veloc-
ity is lost. On the other hand, it has been shown that
2triplet molecules can be imaged using
a laser-induced-fluorescence technique [9, 10]. The He∗
molecules are much smaller in size (7˚ A radius ) and
should follow the motion of the normal fluid without be-
ing affected by vortices at temperatures above 1 K .
Although so far the sensitivity in imaging the molecules
is not high enough to track the motions of individual
molecules, useful studies can still be performed by track-
ing a group of molecules.  In this Letter we shall show
in two demonstration experiments the methods we devel-
oped in tracing the true normal-fluid flow. In the first
demonstration experiment, a cloud of He∗
used as a single tracer. In the second experiment, a small
group of He∗
2molecules was tagged and imaged using
their internal vibrational levels.
Both experiments were conducted at 2.0 K. A sharp
tungsten tip, made via a standard chemical etching tech-
nique , was used to produce the He∗
liquid helium. It is known that He∗
spin singlet and triplet states are produced near the tip
apex when a negative voltage with amplitude higher than
the field-emission threshold is applied to the tip [15, 16].
2molecules in both
FIG. 1: Schematic diagram showing the cycling transitions
for imaging the He∗
The singlet molecules radiatively decay in a few nanosec-
onds , while the triplet molecules are metastable with
a radiative lifetime of about 13 s in liquid4He . The
widths of the He∗
2molecule absorption spectral lines in
liquid helium (120 cm−1) are considerably larger
than the spacings of the rotational levels (∼7 cm−1).
A single pulsed laser at 905 nm is able to drive triplet
molecules out of the a3Σ+
ustate to produce fluorescence
through a cycling transition (see Fig. 1) . However,
the vibrational levels are separated by about 1500 cm−1
, and the vibrational-relaxation time is on the order
of 1 s . Therefore, molecules falling to excited vibra-
tional levels of the a3Σ+
ustate are trapped in off-resonant
levels. Continuous fiber lasers at 1073 nm and 1099 nm
were used to repump the molecules from the a(1) to the
c(0) states and from the a(2) to the c(1) states respec-
tively. Molecules in the c states have a chance to decay
back to the a(0) state and can be used again.
FIG. 2: (a) Schematic diagram showing the setup for the
molecule cloud experiment. (b) Fluorescence images for He∗
molecule clouds created with (1) 10 ms, (2) 30 ms and
(3) 90 ms pulse on the tip, respectively. The grey bars in-
dicate the tip. The images are a sum of 50 camera exposures.
In the first experiment, the tungsten tip was mounted
at the center of a polytetrafluoroethene (PTFE) plate
(see Fig. 2 (a)).The PTFE plate had a diameter of
21 mm and a thickness of 1 mm. To make a heater, four
100 Ω metal-film resistors were attached to the PTFE
plate symmetrically around the tip. A nickel mesh plate
was placed 3 cm away from the PTFE plate and was
grounded. The whole device was held at the center of a
helium cell with total volume of about 250 cm3. The in-
tensities of the fiber lasers at 1073 nm and 1099 nm were
chosen to be 3 W/cm2and 1.5 W/cm2respectively. The
intensity of the pulsed laser at 905 nm was 500 µJ/cm2
per pulse, and the repetition rate was 500 Hz. To cre-
ate a small cloud of He∗
2molecules, a −400 V pulse is
delivered to the tungsten tip through a 0.1 µF capacitor
in addition to a constant voltage of −450 V. Electrons
are emitted from the tungsten tip when the total voltage
crosses the field-emission threshold (around −550 V) dur-
ing the pulse. A small cloud of molecules is created near
the apex of the tip as the electrons move a short distance,
lose their energy, and form bubbles in the liquid . At
2.0 K, a He∗
2molecule diffuses less than 1 mm during its
lifetime . Thus the molecule cloud stays together and
serves as a single tracer. The size of the molecule cloud is
of the order of 1 mm but becomes larger for longer pulse
durations. Typical images of a molecule cloud generated
with 10 ms, 30 ms and 90 ms wide pulses are shown in
Fig. 2 (b). These images were taken with an intensified
CCD camera just after application of the voltage pulse
to the tip. The camera was synchronized to each laser
pulse and exposed for 6 µs so as to minimize the dark
With the heater off, the molecule cloud was observed to
drift towards the nickel mesh plate. The drift speed de-
pended on the length of the voltage pulse on the tip. This
effect results from a transient pulling force on the normal
fluid created by the moving electron bubbles . In or-
FIG. 3: The motion of a molecule cloud with 15V on the
heater. The images were taken at 0 s, 0.2 s and 0.4 s respec-
tively after the cloud was created. The duration of the pulse
on the tungsten tip was 5 ms. The images are a sum of 25
der to reduce this effect but also create enough molecules
for good image quality, a voltage pulse of 5 ms dura-
tion was used. The corresponding drift velocity of the
molecule cloud was about 1.8 mm/s.
As we turned on the heater, a thermal counterflow was
set up in the liquid. The normal fluid flowed away from
the heater with a speed vngiven in theory as 
where Q and A are the heat power and cross-section for
heat transfer; ρ, S and T are the helium density, entropy
and temperature respectively.
normal-fluid velocity was parallel to the tip due to the
geometry. A typical set of images showing the motion
of a molecule cloud with 15 V on the heater is shown
in Fig. 3. The heater was turned on a few seconds be-
fore the molecule cloud was generated so as to set up
a steady flow of the normal fluid. The three images in
Fig. 3 were taken at 0 s, 0.2 s and 0.4 s respectively after
the cloud was created. The number of camera exposures
for each image was chosen to be 25 in order to obtain
a good signal-to-noise ratio yet reduce image smearing.
To determine the flow velocity, we fit the image of each
molecule cloud with a Gaussian function. The maximum
of the Gaussian gave the center position for each cloud.
For a given drift time, several images were taken and an
averaged center position was determined. In Fig. 4 (a),
we show the data obtained for the averaged vertical posi-
tion of each molecule cloud as a function of its drift time.
The solid lines in Fig. 4 (a) are linear fits to the data.
The slopes of those solid lines give the corresponding flow
velocities. In Fig. 4 (b), we plot the normal-fluid veloc-
ity obtained as a function of the heat power. For low
heat power, the normal fluid was believed to be in the
laminar flow regime. Heat was transferred to all direc-
tions below the PTFE plate. The cross-section for heat
transfer in this case was estimated to be about 6.2 cm2.
Near the tip apex, the
FIG. 4: (a) The average vertical positions of a molecule cloud
as a function of its drift time for different heat powers. (b) The
obtained normal-fluid velocity as a function of the heat power.
The solid line and the dashed line are the theoretical curves
as discussed in the text.
The solid line in Fig. 4 (b) shows the theoretical curve
based on Eq. (1). However, as one can see, the measured
data starts to deviate from the theoretical curve when
the heat power is above roughly 0.25 W. If we take the
typical length scale for the flow to be 1 cm, then the
measured fluid velocity (3 mm/s) gives a Reynolds num-
ber as high as 3000. It is likely that the normal-fluid
flow started to become turbulent and caused a change
in heat transfer pattern. When the heat power is higher
than 0.8 W, the turbulent flow in the normal-fluid may
be fully developed and the dispersion of the measured
flow velocity is large. The dashed line in Fig. 4 (b) shows
the theoretical curve assuming an effective heat transfer
cross-section of 1.3 cm2. A smaller effective heat transfer
cross-section means most of the heat is transferred along
the tip direction, for which no good explanation has yet
In the second experiment, we created a continuous
molecular beam and selectively imaged a small group of
molecules which were tagged using the first excited vi-
brational level of the a3Σ+
uelectronic state. To create
the molecular beam, we ran the tungsten tip in a con-
tinuous mode by applying a DC voltage higher than the
field-emission threshold. The field-emission current was
controlled to be less than 2.5 nA to keep the electric
heating negligible. The emitted electrons moved from
the tip to the nickel mesh plate leading to a continu-
FIG. 5: (a) Schematic diagram showing the lasers used in the
molecule tagging experiment. (b) and (c) show the molecule
fluorescence images taken with pump laser alone and probe
laser alone, respectively. Both the pump and the probe lasers
were tuned to 905 nm in order to show the beam sizes and
positions of the lasers.
FIG. 6: Fluorescence images showing the positions of a small
group of a(1) molecules at different delay time after they were
created. The delay time between the pump and probe laser
pulses is (a) 0 ms, (b) 10 ms, (c) 40 ms and (d) 70 ms. The
DC voltage on the tungsten tip was 805V.
ous pulling force on the normal fluid. A normal fluid jet
was formed from the tip to the nickel mesh plate carry-
ing the He∗
2molecules along . Molecules created by
field-emission initially occupy the a(0), a(1), and a(2) ex-
cited states. To prepare a pure population of a(0)-state
molecules for tagging and eliminate background signal
for selective imaging, the 1073 nm and 1099 nm fiber
lasers were used to illuminate a small volume near the
tip and drive molecules from the a(1) and a(2) excited
vibrational levels into the a(0) state. Then, as shown
in Fig. 5, a focused pump laser at 910 nm was used to
2molecules by driving population from the a(0)
to the c(0) state and relying on redistribution of the c(0)
population into the long-lived a(1) state (see Fig. 1) via
non-radiative transitions which naturally occur in a few
nanoseconds . An expanded probe laser at 925 nm
was then used to selectively image the tagged molecules
by driving the a(1) population into the d state and in-
ducing 640 nm fluorescence via d → b radiative decay.
In Fig. 6, we show images for a group of tagged a(1)
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FIG. 7: (a) The vertical position of the a(1) molecule cloud as
a function of the pump-probe delay time at several different
DC voltages on the tip. (b) Obtained normal-fluid velocity as
a function of the square root of the current measured on the
nickel mesh plate.
molecules taken at pump-probe delay time of 0 ms, 10 ms,
40 ms and 70 ms respectively with 805 V on the tip. Both
the pump laser and probe laser had a pulse energy of 5 mJ
and repetition rate of 10 Hz. At each fixed pump-probe
delay time, the camera was exposed ten times to obtain
a single image with a good signal-to-noise ratio. The
bright image obtained with zero delay time resulted from
a two-photon transition induced by the pump laser alone
at 910 nm . We also tested another way of producing
a(1) molecules by tuning the pump laser to 805 nm to
drive the a(0) molecules to the a(1) state through the
c(1) state. The signal strength obtained this way is com-
parable to the one with the pump laser tuned to 910 nm.
In Fig. 7 (a), we show the vertical position of the tagged
a(1) molecules as a function of the pump-probe delay
time. The solid curves in Fig. 7 (a) are the linear fits
to the data, and their slopes give the corresponding flow
velocity. The total driving force on the normal fluid ex-
erted by the moving electron bubbles is proportional to
the electric current I . In steady state the driving
force on the jet is balanced by the drag force coming
from the neighboring normal fluid. If we take the typi-
cal length for the jet flow to be 1 mm (the width of the
jet), the Reynolds number is estimated to be ∼5 × 103.
The flow should be in the turbulent regime, hence a drag
force proportional to the square of the flow velocity is
expected . In Fig. 7 (b), the obtained flow velocity
is plotted as a function of I1/2. A linear dependence is
A similar result was discussed in Mehrotra’s paper .
In their experiments, a pair of mesh grids were placed
right in front of the tip to block the electric current while
another pair was placed some distance away to detect the
2molecules. They pulsed their tip on for about a sec-
ond and then measured the time of flight of the neutral
molecules to determine the average drift speed. Com-
pared to their method, our technique has many advan-
tages. For example, we can measure the flow velocity in
the steady state with the tip running all the time and
map out the velocity field along the jet.
In conclusion, we have developed practical techniques
to trace the normal-fluid component in superfluid4He us-
ing metastable He∗
2molecules. Interesting hydrodynamic
phenomena in the normal fluid were observed in the two
demonstration experiments using these techniques. The
ability to track the true normal-fluid flow provides direct
understanding of the hydrodynamics of the normal-fluid
component in superfluid4He, which will in turn feed into
a better understanding of this unique two fluid system.
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