ULTRACOLD METASTABLE HELIUM-4 AND HELIUM-3
GASES
W. VASSEN, T. JELTES, J.M. MCNAMARA, A.S. TYCHKOV,
W. HOGERVORST
Laser Centre Vrije Universiteit Amsterdam, The Netherlands
K.A.H. VAN LEEUWEN
Dept. of Applied Physics, Eindhoven Univ. of Technology, The Netherlands
V. KRACHMALNICOFF, M. SCHELLEKENS, A. PERRIN, H. CHANG,
D. BOIRON, A. ASPECT, C.I. WESTBROOK
Lab. Charles Fabry de l’Institut d’Optique, Univ. Paris-Sud, Palaiseau, France
We discuss our work to obtain a condensate containing more than 107 atoms and the
first degenerate Fermi gas in a metastable state. Sympathetic cooling with Helium-4
is used to cool 106 Helium-3 atoms to a temperature T/TF < 0.5. The ultracold bosonic
and fermionic gases have been used to observe the Hanbury Brown and Twiss effect
for both isotopes, showing bunching for the bosons and antibunching for the
fermions. A proposal for high resolution spectroscopy at 1.557 μm, connecting both
metastable states directly, is discussed at the end.
1. Introduction
Helium in the metastable 2 3S1 state has been Bose condensed in 2001 by
two French groups [1,2]. Since then research on ultracold metastable helium
gases has been concentrated on determining the scattering length, measuring
loss processes, studies of the hydrodynamic regime and producing longrange molecules. In 2005 two other groups realized BEC in metastable
helium [3,4]. Studies of atom-atom correlations in ultracold clouds of 4He
bosons were started around that time as well, exploiting the unique detection
properties of metastable atoms [5]. In this contribution we will discuss
experiments performed in Amsterdam. We will discuss the setup in which a
BEC containing over 107 atoms and a degenerate Fermi gas (DFG) of
metastable 3He containing over 106 atoms was realized. Next we discuss
experiments where the Amsterdam and Orsay/Palaiseau groups joined forces
measuring the Hanbury Brown and Twiss effect both for a gas of ultracold
1
2
bosons and a cloud of ultracold fermions, demonstrating atom bunching for
He and atom antibunching for 3He.
4
2. Helium level structure and relevant parameters
Relevant energy levels are shown in Fig. 1. The helium atom is strongly LScoupled effectively leading to two spectra, that of parahelium, where the
electron spins are antiparallel and that of orthohelium where the spins are
parallel. The ground state of orthohelium (1s2s 3S1 or He*) can be laser
cooled with laser light of 1083 nm exciting the 1s2s 3S1 – 1s2p 3P (2 3S – 2
3
P) transition. The 2 3S1 state, populated in a DC discharge, has a lifetime of
~8000 s which is infinite for all practical purposes. Its 20 eV internal energy
provides the unique detection possibilities: (almost) everything a He* atom
hits gets ionized and the released electron can be counted with high
efficiency using electron multipliers or microchannel plate (MCP) detectors.
metastable state:
1s2s 3S1 (4He*)
F= 1/2,3/2 (3He*)
Figure 1: Level scheme showing the relevant energy levels for laser cooling and trapping of 4He
in the 2 3S1 state (MJ=+1 in a magnetic trap). The 2 3S state is split in a F=3/2 and a F=1/2 state
(ΔE=6740 MHz) in the case of 3He. The F=3/2 state has the lowest energy and is used for
cooling and trapping (MF=+3/2 in the magnetic trap).
3
Losses in ultracold He* gases, either in a magneto optical trap (MOT) or a
magnetic trap, are mainly due to two-body inelastic Penning ionization
where one ion and one ground state atom are produced in a collision. The
loss rate constant for this process in an unpolarized gas is quite large:
~1×10-10 cm3/s in the dark and ~4×10-9 cm3/s in the light of a MOT [6,7].
When the atoms are in a fully stretched state (as in a magnetic trap) these
losses are suppressed in first order and the rate constant drops to ~1×10-14
cm3/s. In the fully stretched state of 4He* (|J,MJ>=|1,+1>) Penning losses are
therefore acceptable and a BEC can be realized. The 4He*-4He* scattering
length a44 that determines many properties of a BEC has recently been
measured with high accuracy: a44(exp)= +7.5105 (25) nm [8]. Recent ab
initio calculations of the molecular potential have allowed an astonishing
accuracy in the calculation of a44 as well and approach the experimental
accuracy: a44(theory)= +7.562 (28) nm [9]. Mass scaling of the potential then
provides a theoretical value of a34(theory)= +27.1 (5) nm for the scattering
length determining the collision rate between spin-polarized 3He* and 4He*
atoms [9].
3. The experimental apparatus
Laser cooling and trapping of He* atoms is performed at a wavelength of
1083 nm. As the isotope shift is 33 GHz we use two separate laser systems,
each laser locked to the cycling transition of the relevant isotope in a DC
discharge cell. The experimental setup is shown in Figs. 2 and 3. We use a
liquid nitrogen cooled DC discharge source, which uses recycling of helium
atoms from the turbo pump exhaust via molecular sieves.
+ 1° deflection
Figure 2: Schematic of the experimental setup used to trap 3He* and 4He* atoms. The
collimation section (two-dimensional) significantly improves the MOT loading. A deflection
zone (in the horizontal plane) prevents ground state atoms entering the 2 m long Zeeman slower.
4
© J. McNamara
Turbo
Pump 1
Turbo
Pump 2
Figure 3: Schematic of one-dimensional Doppler cooling in the cloverleaf magnetic trap (left)
and UHV chamber (right; the arrow indicates the absorption imaging beam). The coils are
located in plastic boxes positioned inside the re-entrant window flanges.
We typically load 2 × 109 4He* atoms or 1 × 109 3He* atoms in 1 s in a MOT
at a temperature of 1 mK. After a short spin polarization pulse the atoms are
loaded into a spherical cloverleaf trap matching the MOT cloud. The high
(24 G) bias magnetic field in this geometry allows efficient 1-dimensional
Doppler cooling to a temperature of 0.15 mK (in 2 s), shrinking the cloud
considerably and increasing the phase space density about a factor 600 to a
value around 10-4 - 10-5 [3]. In another 2 s the cloud is compressed at small
bias field (~3 G). The trap lifetime is 2 – 3 minutes (either 3He or 4He).
To produce a BEC we perform a 15 s rf evaporative cooling ramp
realizing a BEC containing (1.5–4) × 107 4He* atoms [3]. We monitor the
BEC applying absorption imaging at 1083 nm (not very efficient due to the
low efficiency of CCD cameras at 1083 nm) or on an MCP detector mounted
directly under the trap (see Fig. 4). The latter technique is very sensitive
allowing us to monitor a BEC after up to 75 s trapping inside the magnetic
trap. To monitor the growth of a condensate we use a second MCP detector
that attracts all ions produced by Penning ionization. As soon as the
condensate starts to grow a dense cloud forms and the ion signal suddenly
increases [3]. The lifetime of our condensate is about 1 s. We studied this as
a function of the thermal fraction and found that a large thermal fraction
reduces the lifetime of the condensate considerably. We attribute this to
transfer of condensate atoms to the thermal cloud during condensate decay.
A simple model that assumes thermal equilibrium during the decay confirms
this and allows extraction of the two- and three-body loss rate constants
[3,10].
5
4He*
3He*
3He*+4He*
Figure 4: Time-of-flight pictures of a BEC (upper figure), a DFG (middle figure) and a mixture
(lower figure). The upper figure shows three plots, each with a slightly different end rf
frequency, showing a thermal cloud above the BEC temperature, a mixture of BEC and thermal
cloud, and a pure BEC with the typical inverted parabola shape. In the middle figure a fit to a
Fermi-Dirac distribution is shown from which we extract a temperature T=0.45 TF. In the lower
figure the dashed-dotted line shows the BEC contribution to the signal and the dashed line the
DFG contribution.
6
m=+1
|B|
BEC
m=0
B0
Figure 5: He* atom laser, realized by repeatedly output coupling of a fraction of the BEC in 250
MHz/s ramps. The time-of-flight signal shows the effects of mean-field repulsion.
We can couple out a small fraction of the atoms from a condensate applying
an rf ramp as shown in Fig. 5. We applied repeatedly a 250 MHz/s rf ramp to
couple atoms out of the condensate showing a typical atom laser pulse shape,
revealing mean-field repulsion.
To produce a degenerate Fermi gas a we load a MOT with both isotopes
[3,6,7,11,12]. With an equal number of both isotopes in our gas reservoir we
trap 1 × 109 4He* atoms and 7 × 108 3He* atoms in a MOT. However, we can
not cool so many fermions and therefore reduce the number of fermions to 110% of the number of bosons. The large heteronuclear scattering length
provides almost ideal conditions for sympathetic cooling and we obtain a
DFG containing 2 × 106 3He* atoms at T/TF=0.45 (Fig. 4) as well as a
degenerate mixture (also Fig. 4). Three-body losses probably limit the
lifetime of this mixture to ~10 ms [12].
4. Hanbury Brown and Twiss experiments
In 2005 the atomic analogon of the Hanbury Brown and Twiss (HBT) effect
was demonstrated for metastable 4He* atoms released from a cloverleaf
magnetic trap very similar to the one in Amsterdam [5]. The HBT effect, first
demonstrated for light in the fifties of the 20th century [13], represents the
measurement of the two-body second-order correlation function
g
( 2)
r
r
r
r
r r
E * (r ) E * (r ′) E (r ) E ( r ′)
I (r ) I ( r ′)
r r
=
(r , r ′) =
r 2
r
r 2
I (r )
E * (r ) E (r )
displaying the joint probability of detecting two atoms (or photons) at
locations r and r’. For incoherent sources this function equals 1 for large
separations and will tend to 2 for bosons and 0 for fermions, for detector
7
separations smaller than the correlation length l: bosons bunch and fermions
antibunch. In the Amsterdam experiments we demonstrated bunching for
4
He* and antibunching for 3He* trapped in identical traps at the same
temperature [14]. For this purpose the position sensitive detector (PSD) of
the Orsay (now Palaiseau) group was transported to Amsterdam and
mounted under the Amsterdam UHV chamber (which is shown in Fig. 3).
The detection part of the setup is shown in Fig. 6, showing on the left the
PSD and on the right a schematic of the measurement. The correlation
function for a measurement of atoms released from a harmonic trap is given
by [14]
⎛ ⎡⎛ ⎞ 2 ⎛ ⎞ 2 ⎛ ⎞ 2 ⎤ ⎞
Δx
Δy
Δz
⎟
⎜
g (Δx, Δy, Δz ) = 1 ± ηexp⎜ - ⎢⎜⎜ ⎟⎟ + ⎜ ⎟ + ⎜⎜ ⎟⎟ ⎥ ⎟
⎜
⎟
⎜ ⎢⎝ l x ⎠ ⎝ l y ⎠ ⎝ l z ⎠ ⎥ ⎟
⎦⎠
⎝ ⎣
(2)
th
ht
msi
where si = k BT mωi2 , m the mass of the atom, T the temperature, t the
with correlation lengths in each of the three spatial directions li =
drop time and ωi the trap frequency. The contrast η (0 - 1) depends on the
detector resolution in all three spatial dimensions. This two-particle detector
resolution is 6 nm in the vertical (z-) direction and 500 μm in the horizontal
plane of the detector. As the correlation length in the x-direction is much
smaller than the detector resolution in that direction (we have a cigar-shaped
trap with long axis in the x-direction) η is on the order of 1/15.
Figure 6: Position-sensitive MCP detector and schematic of the experiment. The inset of the
figure on the right conceptually shows the two 2-particle amplitudes that interfere to give
bunching or antibunching.
8
As the detector resolution is very good in the vertical plane, we plot the
measured correlation function along the z-direction in Fig. 7. This plot was
obtained by averaging over about 1000 clouds per isotope, with ~104
detector points per shot. The temperature was 0.5 μK. We also measured the
correlation function along the y-direction, however with substantial
broadening along the horizontal axis due the 500 μm resolution in the x-y
plane [14]. Fig. 7 clearly demonstrates antibunching for fermions and
bunching for bosons, over a macroscopic distance of ~1 mm. The measured
ratio of the correlation lengths is 1.3 ± 0.2, which is as expected, realizing
that the cloud sizes of both isotopes in the trap are equal, the drop times are
equal and the mass ratio is 4/3. Also the individual correlations lengths agree
very well with the formula lz =ħt/msz. We observe a small discrepancy in the
amount of contrast for both isotopes. There are two possible experimental
imperfections that affect the bosons and fermions differently and that may
explain this, i.e. the non-sudden trap switch-off and the determination of the
detector resolution function.
4He*
3He*
- boson
- fermion
Figure 7: Normalized correlation functions for 4He* in the upper plot and 3He* in the lower plot,
measured in the same trap at the same temperature of 0.5 μK. Error bars correspond to the square
root of the number of pairs in each time bin. The line is a fit to a Gaussian function. Correlation
lengths of 0.75 ± 0.07 mm and 0.56 ± 0.08 mm for fermions and bosons, respectively, are
extracted.
9
Figure 8: Measured temperature dependence of correlation length and contrast. The curves are
calculations and describe the measurements reasonably well.
We took data for fermions at 0.5 μK, 1.0 μK and 1.4 μK. The fit results for lz
and η are shown in Fig. 8 together with the calculated results.
The limited resolution in the horizontal plane can be circumvented by
using a negative atom lens, reducing the apparent size of the cloud in the
horizontal plane. This does not affect the correlation length in the vertical
plane but does affect the contrast via the correlation length ly, which
increases. To implement this we focused a 300 mW laser beam, with
elliptical waist and 300 GHz blue detuned from the 1083 nm transition, for
0.5 ms through the expanding 3He* cloud after switching off the magnetic
trap. The results are shown in Fig. 9 and qualitatively agree with
expectations.
without lens
with lens
Figure 9: Normalized correlation functions along the z (vertical) axis for 3He*, demonstrating the
effect of a diverging atomic lens in the x-y plane. The light circles are without lens and the dark
squares with lens. The dip is deeper with the lens because the correlation length in the ydirection is increased which affects the contrast (and not the correlation length in the zdirection).
10
Figure 10: Raw data of an atomic lens experiment with fermions. The data show the numbers of
pairs measured for a 25 μs time bin (1 ms corresponds to a vertical separation of 3.5 mm). They
are averaged over 1000 shots.
We wish to emphasize that the antibunching effect in Fig. 7 is big enough
that significant processing of the data is not necessary. Fig. 10 shows the raw
data of one of our runs before normalizing the data. Normalization (to get the
data of Figs. 7 and 9) is done by dividing the raw data by the
autoconvolution of the sum of the 1000 single-particle distributions.
Therefore the raw data show the antibunching effect as well as the Gaussian
spatial distribution of the cloud.
5. Proposed metrology experiment
As one of the possible applications of samples of ultracold 4He* and 3He*
atoms we envision to excite the “forbidden” 2 3S1 – 2 1S0 transition at 1.557
μm [15]. This transition is only magnetic-dipole (M1) allowed with an
Einstein A-coefficient of 6.1 × 10-8 s-1 [16]. The high-resolution potential is
very large as the natural linewidth of the transition is 8 Hz, fully determined
by the 20 ms lifetime of the 2 1S0 metastable state due to two-photon (2E1)
decay to the ground state. Measuring this transition will directly link the
orthohelium and parahelium system (see also Fig. 1). The absolute frequency
(for both isotopes) will provide sensitive tests of atomic theory for twoelectron systems, measuring QED contributions which are large for S-states.
Measuring the isotope shift, the main theoretical inaccuracy is in the
difference in mean nuclear charge radius of the 4He and 3He nucleus.
11
To measure the transition we theoretically investigated two setups: (1)
spectroscopy with a laser-cooled and collimated atomic beam as provided
from the Zeeman-slower and (2) spectroscopy in a one-dimensional optical
lattice, loaded from a magnetically trapped and evaporatively cooled cloud.
For both situations we solved the optical Bloch equations simplifying the
model neglecting the decay from 2 1S to 2 3S as well as the decay from 2 3S
to 1 1S (see Fig. 11). For the beam experiment we assume a 100 m/s Zeemanslowed atomic beam, transversely cooled to twice the Doppler limit. With an
atomic beam intensity of 1011 atoms per second, a 2 W 100 kHz laser beam
(1cm×1cm excitation region) will provide an on-resonance Rabi frequency
Ω= 61 s-1, which for an excitation time of 100 μs will lead to an excited state
population ρ22=4.6 × 10-7. A considerable flux of 5 × 103 atoms per second in
the 2 1S state then may be expected.
Figure 11: Relevant energy levels for 2 3S1 – 2 1S0 spectroscopy and decay rates.
The expected spectroscopic linewidth is 400 kHz in this case, limited by
Doppler broadening. Using 1083 nm light resonant with the 2 3S1 – 2 3P2
transition the nonexcited atoms can simply be deflected realizing a
(hopefully) zero-background signal on a metastable atoms detector. A
schematic view of the proposed setup, with three laser-atomic-beam
crossings depicted, is shown in Fig. 12.
Fig. 12: Schematic of the proposed setup to measure the 2 3S1 – 2 1S0 transition in a beam.
12
The one-dimensional lattice has more potential to achieve high accuracy. In
the experiments described in Section 4 an ultracold cloud at temperatures
around 1 μK of 3He*, 4He*, or a mixture was presented. Such a cloud may
be transferred to a far off-resonance dipole trap (FORT). When a single
retroreflected beam is used a one-dimensional lattice results which, when a
wavelength of 1.557 μm is used, can easily trap a cloud from our cloverleaf
trap at a temperature of a few μK. The experiment may be performed using
the same 2 W laser as discussed in the beam experiment as the trapping
potential is insensitive to the wavelength on a scale of an experiment on the
forbidden transition. A narrower linewidth laser, though, is useful here as the
width of the spectroscopy signal will now be limited by the laser linewidth as
Doppler broadening is suppressed by Lamb-Dicke narrowing. Detection is
now more challenging as the 2 1S atoms are anti-trapped and slow. Photo
ionization, or detection of ions due to Penning ionization with trapped 2 3S
atoms, are then options to consider.
The accuracy of the spectroscopy in the lattice will be limited by how
well the AC Stark shift due to the lattice potential can be controlled and
measured. Calculations predict a 2 MHz shift of the transition at the
maximum of the potential (the atoms are trapped in the light as the 1.557 μm
wavelength is red detuned from the 1083 nm transition). The best experiment
therefore will be to trap at a magic wavelength (where the AC Stark shifts of
the metastable states are equal), which will not be easy as the highest magic
wavelength available is 410 nm at which wavelength very high laser power
is required to trap He* atoms. A second magic wavelength occurs at 351 nm
and may be more suitable for spectroscopy on this forbidden transition.
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