A compact, laser cooling apparatus for simultaneous cooling of
lithium and rubidium
Keith Ladouceur, Bruce G. Klappauf, Janelle Van Dongen, Nina Rauhut, Bastian Schuster,
Arthur K. Mills, David J. Jones, and Kirk W. Madison
Department of Physics & Astronomy, University of British Columbia,
6224 Agricultural Road, Vancouver, BC, V6T 1Z1, Canada
We report on a dual species laser cooling apparatus capable of collecting over 108 87 Rb
or 85 Rb atoms from an atomic vapor or up to (8 ± 2) × 107 6 Li atoms directly into a
magneto-optic trap (MOT) from an effusive oven without the need for a Zeeman slower. The
use of a miniature atomic oven placed close to the trapping region yields a compact vacuum
system while still producing adequate lithium ensembles and a high quality vacuum in the
10−10 Torr range. The atomic sources, laser system, and vacuum system are described.
In addition, we use this system to study atom loss from the MOT due to interspecies
collisions between 6 Li and 85 Rb or 87 Rb. We report for the first time the heteronuclear loss
c 2008 Optical Society of America
coefficients for 6 Li–85 Rb mixtures. OCIS codes: (020.3320) Laser cooling. (020.7010) Laser trapping. (140.2020) Diodes lasers.
(140.3280) Laser amplifiers. (020.2070) Effects of collisions.
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1
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Introduction
The simultaneous laser cooling of multiple species in magneto-optic traps (MOTs) has become increasingly
common in recent years as the motivations for studying the physics of mixed species ultra-cold gases have
become more apparent. Trapping of different isotopes in the same apparatus has been useful for precise
measurements of isotopic differences of trapping performance (revealing the precise role of hyperfine changing
collisions in a MOT) and mixed-isotope light-assisted collisions in a MOT [1, 2]. In addition, multi-isotope
ensembles provide near equal mass mixtures of fermionic and bosonic components [3–5] and are well suited to
sympathetic cooling to lower temperatures because the collision partners have almost equal mass [6, 7]. Due
to Pauli exclusion, the evaporative cooling of magnetically trapped (i.e. spin polarized) fermionic species is
severely limited at low temperatures where only s-wave collisions occur. Sympathetic cooling of a fermionic
species by thermal contact with a cold bosonic atomic ensemble, even in the case of different masses, is a
viable scheme and further motivates the creation of dual species MOTs [4,8,9]. The simultaneous laser cooling
of different atomic species also offers the possibility to perform precise measurements of the heteronuclear
molecular potentials through photoassociation spectroscopy [10–13] and through the study of heteronuclear
Feshbach resonances [14–16]. Ultra-cold ensembles of heteronuclear molecules [17–20] have been proposed for
a wide variety of new applications in ultra-cold chemistry, quantum computation and quantum simulation
[21–23].
In this paper, we describe the features of a dual species trapping apparatus capable of collecting over 108
87
Rb or 85 Rb atoms from an atomic vapor or (8 ± 2) × 107 6 Li atoms directly from an miniature oven placed
close to the trapping region without the need for a Zeeman slower. The advantage of this configuration is
that it does not require additional slowing optics or solenoids and is therefore very compact in comparison to
a Zeeman slowed atomic source and yet yields a captured flux of more than 4 × 106 lithium atoms per second
with a high quality vacuum in the 10−10 Torr range. In the following sections, we present the important and
unique features of our experimental system, we describe the optimization and characterization of the dual
MOT, and we use this system to measure the MOT trap loss due to interspecies collisions between 6 Li and
85
Rb or 87 Rb. We report for the first time all of the heteronuclear loss coefficients for 6 Li–87 Rb and 6 Li–85 Rb
mixtures as well as the homonuclear loss coefficients for 6 Li, 85 Rb, and 87 Rb.
2.
Experimental setup
The MOT trapping region is centered within an optically polished Borosilicate cell (Pyrex box manufactured
by Starna Scientific Ltd, formerly Optiglass Ltd). This cell is bonded (by Technical Glass, Inc.) on both ends
to glass to metal transitions with the atomic sources introduced on one end and supported inside the cell
by a 2.75 inch conflat electrical feedthrough. The other end of the cell is connected through a stainless steel
bellows and 6 inch conflat cross to a 20 L s−1 Varian StarCell ion pump and a SAES CapaciTorr NEG pump.
3
Fig. 1. Front view of rubidium dispensers and lithium oven.
The outer dimensions of the glass cell are 30 mm × 30 mm × 100 mm with a 5 mm wall thickness.
The rubidium vapour dispensers, as well as the effusive lithium oven, are located 10 cm from the trapping
region in order to maximize the capturable atom flux from the lithium oven. A small circular beam block
3 mm in diameter is situated between the oven and the trapping region in order to shield the MOT center
from the direct output of the effusive oven. This configuration is similar to that reported in [24], with the
exception that in this work the trapping light for lithium is single frequency and is not broadened in any
way to enhance the loading of the MOT. The lithium MOT loads directly from the effusive oven without any
additional slowing stages to compensate for the high average velocity of the lithium atoms from the oven,
such as a Zeeman slower [25]. The result is a compact vacuum system with a high quality vacuum and a Li
MOT with almost 108 atoms in steady state.
Key to achieving a good vacuum with an atomic oven less than 10 cm from the MOT was the careful
preparation of the enriched (95% 6 Li) sample and systematic degassing of the oven. Lithium is highly reactive
with both organic and inorganic reactants, including nitrogen and hydrogen. The initial sample of lithium
was cleaned with petroleum ether to remove residual oil from the surface in an argon filled glove-box. A clean
razor blade was used to remove the black exterior from all sides of the lithium sample. On a clean surface,
and with a new blade, the piece was reduced in size so that it fit easily within the oven reservoir.
The lithium oven, made of a non-magnetic alloy of nickel and chromium (80% nickel and 20% chromium),
consists of a cylindrical reservoir 7.6 mm long, 4 mm in diameter with an internal volume of 81 mm3 . The
resevoir is enclosed by a cap, connected by two spiral arms at the top which lock to the cap with a twisting
motion. As shown in Fig. 1, the cap is 5.2 mm long, 5 mm in diameter, and has a 0.8 mm hole through the
center. The two thin extensions of the cap serve as mechanical support and electrical contacts, and are the
major source of heating due to their small thickness (0.6 mm) and length (1.25 cm). At a current of 9 A,
the oven heats to approximately 250 ◦ C in 3 minutes. The atomic beam profile from the oven was measured
by fluorescence imaging and by observing the coating produced on a glass flat 10 cm away. The atomic flux
was primarily contained within an emission cone with an angular divergence of 15 degrees, corresponding to
4
the aspect ratio of the exit hole in the cap.
The lithium oven was degassed by heating it to increasing temperatures within an auxillary preparation
chamber such that the total pressure from outgassing never exceeded 10−5 Torr. This was also done so
that the melted lithium could incorporate into the nickel mesh that lined the reservoir while removing the
majority of the trapped nitrogen, oxygen, and hydrogen. The outgassed contaminants were identified and
monitored by a residual gas analyser (RGA). The oven was heated until the outgassed pressure at a current
of 10 A fell below the base pressure of the preparation chamber (5 × 10−8 Torr; 10 l s−1 pumping speed).
The mesh was critical for proper operation of the oven as it prevented the lithium from wicking out of the hot
oven. After degassing, the preparation chamber was flushed with argon (the use of dry nitrogen was avoided
since it was found to contaminate the lithium) and the oven was quickly moved to the experimental vacuum
chamber where a 6-day bakeout at 200 ◦ C was performed. We estimate that the usable lithium occupies 1/4
of the oven volume and therefore that a total of 11 mg is available. The performance of the lithium MOT
located 10 cm from the oven is shown in Fig. 3.
Rubidium is selectively released using a commercial SAES Getters dispenser. Passing a current through
the dispenser results in the emission of atomic 85 Rb and 87 Rb vapour at their natural abundances of 72.17%
and 27.83%.
85
2 2 S1/2
5 P3/2
F=3/2
267 MHz
F’=3
63 MHz
29 MHz
5 2 S1/2
F’=2
F’=1
F=3
3.036 GHz
F=1/2
ΓLi = 2π × 5.87 MHz
F’=3
5 2 P3/2
121 MHz
780 nm
228 MHz
Rb
F’=2
157 MHz
F’=1
72 MHz F’=0
780 nm
pump
pump
671 nm
2
F=2
5 2 S1/2
repump
2 P3/2
F’=1/2
1.7 MHz
F’=3/2
2.8 MHz
F’=5/2
F’=4
pump
2
87
Rb
repump
Li
repump
6
F=2
6.835 GHz
F=1
ΓRb = 2π × 6.07 MHz
Fig. 2. Atomic energy levels (not to scale) and transitions used for magneto-optic trapping
of lithium and rubidium atoms. A major difference between rubidium and lithium is that
the hyperfine level spacings in the excited state are very large compared to the natural
linewidth for rubidium (ΓRb = 2π × 6.07 MHz) while they are actually smaller than the
natural linewidth for lithium (ΓLi = 2π × 5.87 MHz).
The laser systems for lithium and rubidium are composed of grating-stabilized and injection-seeded diode
lasers (master and slave lasers). In total, five master lasers are required for the experiment. Each isotope
of Rb requires a separate master laser to generate the pump light, also referred to as the “cooling” light,
(F = 3 → F 0 = 4 for 85 Rb and F = 2 → F 0 = 3 for 87 Rb) and repump light (F = 2 → F 0 = 3 for
85
Rb and F = 1 → F 0 = 2 for 87 Rb) on the 52 S1/2 → 52 P3/2 transition for Rb trapping. The pump
(F = 3/2 → F 0 = 5/2) and repump (F = 1/2 → F 0 = 3/2) light tuned to the 22 S1/2 → 22 P3/2 transition for
lithium is generated from a single master laser. Fig. 2 shows a diagram of the atomic energy levels and the
pump and repump light tuned below their respective resonances by ∆νp and ∆νr . A major difference between
rubidium and lithium is that the hyperfine level spacings in the excited state are very large compared to
the natural linewidth for rubidium while they are actually smaller than the natural linewidth for lithium.
This has dramatic consequences on the operation of the MOTs. In the case of rubidium, the radiation
5
pressure exerted on the atoms in the MOT is primarily due to the pump or cooling light which is tuned
to an almost “closed transition” and only rarely excites off-resonantly a lower hyperfine level in the excited
state resulting in hyperfine pumping in the ground state. The atoms need only rarely scatter repump light
to counteract this optical pumping, and the repump beam therefore exerts an almost negligible force on the
atoms. Consequently, only a small intensity is required for the repump light and it can be introduced into
the MOT without concern for its polarization or direction. In stark contrast, the excited state spacing in
lithium is so small that the pump (cooling) light, which is typically tuned to the red of the transition by
several linewidths, excites with similar rates all three excited states, and the upper, F = 3/2, ground state
is rapidly depleted. In this case, the repump light has a similar scattering rate as the pump light of the same
intensity. It therefore contributes to cooling and exerts a force on atoms in the MOT comparable to that
exerted by the pump light. Consequently, both the pump and repump light must be introduced into the trap
along all three directions with similar intensities for the proper operation of the lithium MOT.
The master lasers are frequency stabilized using modulation-transfer saturated absorption spectroscopy in
a reference cell containing either rubidium or lithium atomic vapor. The stabilized linewidth of the master
lasers is estimated to be 1.5 MHz and was determined from a heterodyne beatnote measurement between
two master lasers locked to two different atomic transitions. The partial pressure of rubidium at room
temperature is 10−7 Torr providing an adequate optical depth in a 10 cm glass cell; however, the partial
pressure of lithium is exceedingly low (below 10−20 Torr) at room temperature and necessitates the use of a
heat pipe to perform absorption spectroscopy. Our heat pipe is a hollow nickel cylinder 10 cm long and with
a 1 cm inner diameter. The cylinder is enclosed by end caps with a 3 mm hole to allow the passage of light.
The heat pipe is filled with 1 g of lithium and lies inside a stainless steel tube 40 cm long and filled with
1 Torr of argon to limit the mean free path of the hot lithium so that the windows on the outer stainless
vacuum envelope are not coated. The heat pipe is heated to 410 ◦ C from the outside by thermal contact
with the stainless tube which is embedded in an insulated heating element. The vacuum windows reside far
from the insulated region and are at room temperature.
Acousto-optic modulators in double pass configuration (to minimize beam steering) are used to fine tune
the frequency of the trapping light before the final stage of amplification. Our amplifiers are injection locked
single-mode diode lasers comprised of either the MLD780-100S5P from Intelite Inc. with 90 mW output at
780 nm or the HL6535M from Hitachi with 90 mW at 658 nm. We operate the MLD780-100S5P at 18 ◦ C and
125 mA which produces approximately 60 mW when injected. We use HL6535MG98 lasers from Opnext,
Inc. for the 671 nm amplifiers. These diodes are nominally 658 nm devices and were wavelength selected to
operate at or above 661 nm at a temperature of 25 ◦ C. By heating these lasers to 69 ◦ C, their free running
wavelength is between 667 and 668 nm. At this temperature, the output power is significantly reduced and
we observe an output of 30 mW at 164 mA. In contrast to the 780 nm amplifiers where the spectrum is very
pure (more than 99% of the output power of the diode is at the seed frequency), the output spectrum of
the 671 nm amplifiers, when injected with 1 mW of seed light, is observed to include a broad background
centered at the free running wavelength. Injection locking of laser diodes is a frequency pulling effect and
requires that one of the diode laser’s intrinsic cavity modes be in near resonance with the seed. The injection
behavior of laser diodes which do not have an anti-reflection coated front facet and which therefore have a
moderately high finesse is very sensitive to the diode current and temperature. At a fixed temperature, we
observe a discrete set of current ranges (a few mA wide) within which the amplifiers will lock and which are
separated by current ranges for which no amplification of the seed is observed. For the very highest current
ranges, we observe that as the current is varied across the range where amplification of the seed occurs,
the fraction of the output power contained at the seed frequency varies between 66 and 33%. Unfortunately
this performance could not be improved upon by varying the seed injection power. Other than reducing the
6
overall power of the injected seed, the broad background does not appear to have a deleterious effect on
the operation of the lithium MOT. However, this broad, non-resonant background is observed to limit the
apparent optical density of the MOT in absorption images.
Mechanical shutters and electro-optical modulators are used to control the overall power of the Rb and
Li MOT light after amplification. The light for trapping is combined into a single beam by way of several
polarization beam splitter cubes and a dichroic mirror. This combined beam is then expanded to a 1/e2
diameter of 8 mm, divided, and prepared with the correct polarization using dual wavelength optics and
introduced into the MOT cell along the three mutually orthogonal axes in a retro-reflection configuration.
This configuration was chosen over a 6 independent beam configuration in order to maximize the optical
power available for trapping. In addition, we observed that spatial filtering of the beams was unnecessary
and in fact detrimental since even a 20% loss in optical power resulted in more than a 30% reduction of the
lithium MOT number. The total optical power delivered to the dual species MOT is approximately 38 mW
and 4 mW at the Rb pump and repump frequencies and 11 mW and 6.5 mW at the Li pump and repump
frequencies respectively, assuming half the power of the lithium amplifiers is at the seed frequencies.
The atom numbers in the MOT are monitored by means of fluorescence detection. The fluorescence from
the Rb and Li MOTs are separated by a dichroic mirror and are detected independently on two Thorlabs
SMIPD2B photodiodes. Interference filters with a 10 nm transmission bandwidth centered at 671 nm and
780 nm are used to suppress cross-talk and spurious signals from room lights. The fluorescence measurements
from the photodiodes are used as the basis for calculating the atom number within the MOTs. In addition,
images of the dual MOT fluorescence are recorded by two charge-coupled device (CCD) cameras along
orthogonal directions. These images are used to characterize the spatial overlap of the clouds. We emphasize
here that the atom numbers reported in this manuscript represent lower bounds since it is difficult to
account for all imperfections and possible misalignments in the detection system (which necessarily occlude
fluorescence collection) and to account for the effect of non-uniform illumination due to the optical thickness
of the atomic clouds. Also, the scattering rate is computed assuming the atoms are located in the region of
highest intensity for all 6 MOT beams; however, slight misalignments of these trapping beams can reduce
the total illumination intensity and yet are observed to produce a stable MOT. All of these effects reduce
the total amount of fluorescence collected and therefore leads to a systematic underestimate of the number
of atoms present in the MOT.
3.
3.A.
Results
Single Species Optimization
In a single species configuration, lithium and rubidium MOT numbers were first optimized independently
by carrying out an exhaustive search in the pump (∆νp ) and repump (∆νr ) detunings for a range of axial
magnetic field gradients between 10 to 50 G cm−1 . Although the lithium MOT showed improved performance
at high field gradients (above 30 G cm−1 ), the rubidium atom number was dramatically suppressed above
28 G cm−1 . A compromise of 23 G cm−1 was chosen as the operational magnetic field gradient. The optimum
MOT parameters at this magnetic field gradient are summarized in table 1.
The highest atom number we were able to trap for 6 Li was (8 ± 2) × 107 atoms using a detuning from
resonance of ∆νp = −5.8ΓLi and ∆νr = −4.4ΓLi for the pump and repump light, respectively. Note that
the saturation intensities given in table 1 are calculated for the case of an an isotropic pump field with
equal components in all three possible polarizations [26]. In addition, the lithium interaction was assumed
to include all of the allowed 22 P3/2 excited state levels due to our large detuning relative to the excited state
hyperfine splittings.
Fig. 3 shows the behavior of this oven loaded lithium MOT at a field gradient of 23 G cm−1 . The atomic
7
Table 1. Optimal parameter settings for each MOT in a single species configuration with
an axial field gradient of 23 G cm−1 : Wavelength and width of the D2 line, saturation
intensities (assuming isotropic light polarization), pump and repump intensities along all
three principle axes, relative detunings of the pump and repump light ( ∆νp and ∆νr ), and
the steady state atom number. The steady state Rb atom number depends on the amount
of Rb background vapor in the cell which in turn introduces additional loss in the lithium
MOT due to an increased background collision rate. This steady state Rb atom number was
taken at a Rb pressure which suppressed the Li MOT number by a factor of 20 from the
maximum (8 ± 2) × 107 .
6
λD2 ,vac (nm)
Γ/2π (MHz)
Isat (mW cm−2 )
Ip /Isat
Ir /Isat
∆νp (Γ)
∆νr (Γ)
N∞
Li
670.977
5.87
3.8
25
14
-5.8
-4.4
(8 ± 2) × 107
85
Rb/87 Rb
780.241
6.07
3.58 [26]
72
3.0
-1.8
-0.7
≥ (7 ± 2) × 107
loading rate (R), the inverse loss rate (Γ−1 ), and steady state atom number (NLi∞ ) of the 6 Li MOT are shown
as a function of the current supplied to the oven. These parameters were determined by fitting the loading
curve of the 6 Li MOT to the solution, N (t) = NLi∞ (1 − e−Γt ) of the differential equation Ṅ = R − ΓN . The
steady state number is then the product of the loading and inverse loss rates, NLi∞ = R
Γ . In this model we
neglect any loss due to homonuclear light assisted collisions and therefore the loss term due to collisions with
the residual background vapor, Γ, is overestimated. The corresponding inverse loss rate of the MOT (Γ−1 ) is
underestimated slightly but gives a good indication of the background pressure of the vacuum system limited
by outgassing from the oven. The longest inverse loss rates measured for lithium were on the order of 50 s
corresponding to a background vapor pressure of approximately 2 × 10−10 Torr [27]. As the temperature of
the oven increases so does the captured flux and the loss rate. At a current of Ioven = 9.5 A, the steady state
atom number is maximized. There exists a clear tradeoff between the inverse loss rate of the lithium MOT
and the steady state atom number, and by running the oven at 8 A instead of 9.5 A the inverse loss rate can
be increased by more than a factor of two with only a factor of two reduction in the trapped number.
The steady state Rb atom number depends on the amount of Rb background vapor in the cell which in
turn introduces additional loss in the lithium MOT due to an increased background collision rate. Therefore
the steady state rubidium and lithium atom numbers vary inversely as the Rb background vapor pressure is
increased. In the absence of homonuclear light assisted collision losses, the lithium MOT number in steady
Li
state is NLi∞ = R
γLi where the loss rate of lithium γLi = ΓLi,bg + ΓLi,Rb has contributions from collisions
with residual background gas (ΓLi,bg ) and with rubidium atoms (ΓLi,Rb ) introduced by the dispenser. Both
the rubidium load rate, RRb , and the loss term ΓLi,Rb are proportional to the rubidium vapor pressure
in the cell so they are proportional to each other, RRb ∝ ΓLi,Rb . Furthermore, if we neglect homonuclear
light assisted collisions in rubidium, the steady state rubidium MOT number is simply proportional to the
8
Fig. 3. A comparison of the loading rate (R), inverse loss rate (Γ−1 ), and steady state atom
number (NLi∞ ) for a single species Li MOT in the absence of background Rb vapour as a
function of the current supplied to the effusive oven with parameter values as defined in
table 1. The trend lines are only a guide to the eye.
∞
rubidium load rate and we have then ΓLi,Rb ∝ NRb
. We can therefore express the lithium MOT number in
∞
∞
∞
) where NLi∞ (0) is the lithium MOT
terms of the rubidium MOT number as NLi (NRb ) = NLi∞ (0)/(1 + NRb
atom number in the absence of any residual rubidium vapor and is a system dependent constant. For our
trapping parameters, is 2.5×10−7 . When the rubidium pressure is chosen to equalize the number of trapped
rubidium and lithium, 107 atoms of each species are present in the dual MOT. This atom number suppression
due to residual vapor is the primary limitation to the atom number in all multi-species MOTs where one or
more species is loaded from an atomic vapor. As was shown in the work of Taglieber et. al, the addition of a
Zeeman slower can produce a much larger lithium loading rate (by two orders of magnitude) allowing the Rb
vapor pressure to be run at a correspondingly higher pressure creating a larger Rb MOT while maintaining
the same size lithium MOT as that reported here [28]. Clearly the drawback of this approach to achieving
large vapor loaded MOTs is that the inverse loss rate due to background collisions in such a system is severely
limited.
3.B.
Dual Species Operation
In order to simultaneously trap Li and Rb, as discussed above, the axial field gradient was above the optimal
value for Rb and below that for Li. In addition, the Rb background pressure was chosen so that the Rb
MOT was comparable in number to the Li MOT. We observe, under these conditions, on the order of 107
atoms of each species are present in the dual MOT.
Because we use a retro-reflection configuration, the return beams are less intense and the radiation pressure
imbalance forces the MOT to reside a few mm away from the magnetic field zero. In addition, we observed
that, when optimized individually, the two MOT clouds do not overlap completely. In order to study trap
loss due to interspecies collisions between 6 Li and 85 Rb, 87 Rb, we carefully adjusted the alignment and power
balance of the rubidium and lithium trapping light as well as the external magnetic bias field so that the
9
Fig. 4. Experimental loading sequence of two spatially overlapping 6 Li and 87 Rb MOTs. 1)
Li is allowed to load in the absence of cold Rb in the MOT at an oven current of 9.5 A.
2) After 100 s the Rb repump light is turned on and the Rb MOT loads. The additional
atom loss induced by the Rb MOT suppresses the Li MOT and results in a new steady
state atom number. 3) Both MOTs are emptied by turning off the magnetic field gradient,
and after a short wait time the Rb MOT is allowed to load in absence of Li. 4) After 100 s
the Li repump light is turned on and the Li MOT loads. A drop in the Rb MOT number is
observed and the steady state numbers approach a new equilibrium. The reduction in the
87
Rb MOT number is 10%, a factor of 5 less than the 50% reduction observed in the 6 Li
MOT number. This illustrates the non-reciprocal nature of the heteronuclear loss terms.
clouds were well overlapped. We observed that this configuration was not optimal for the loading of either
species in single species operation; however, it was necessary to achieve the best possible spatial overlap of
the clouds to measure the interspecies collisions in the dual MOT. The atom number loading dynamics for
the atomic species A in the presence of the atomic species B is modelled by the following rate equation
Z
Z
dNA
2
= RA − ΓA NA − βA,A nA dV − βA,B nA nB dV
(1)
dt
where RA is the loading rate, ΓA the loss rate due to collisions between the trapped atoms of species A and
room-temperature residual gas, βA,A the loss rate due to homonuclear collisions between trapped atoms of
species A, βA,B the loss rate of atoms of species A due to heteronuclear collisions with trapped atoms of
species B, NA is the trapped atom number of species A, nA and nB are the density distributions of species
A and B, respectively.
It is important to note that the order of the subindices in the heteronuclear loss term βA,B is crucial,
as βA,B and βB,A are not reciprocal quantities due to the different MOT recapture probabilities for species
A and B [29]. The recapture probabilities differ because of differences in the MOT capture velocities and
the mass differences of the atoms which results in different final velocities after an inelastic heteronuclear
10
collision. The trap loss parameters βA,A and βA,B are determined by fitting the loading dynamics and steady
state MOT numbers to the above model in the case of single and double species loading.
Fig. 4 shows the time evolution of the atom numbers during a typical experimental loading sequence.
The decrease of the steady state atom number in the dual MOT configuration as compared to the single
MOT configuration is attributable to losses incurred from collisions between trapped lithium and rubidium
atoms. The loading dynamics of the single species MOT is used to determine the parameters RA , ΓA , the
homonuclear βA,A term, and the steady state atom number. Once the steady state is achieved, each MOT
is imaged (in single species operation) using two independent and orthogonally positioned CCD cameras.
These images allow for the determination of the overlap of the atomic density distributions.
We compute the overlap integrals using the 2D images of the atomic clouds. These images are taken in
single species operation along two orthogonal imaging axes and it is assumed that the shape and position of
the clouds (i.e. the shape of the normalized density distribution) is constant throughout the measurement
sequence and in the presence of the other species. This assumption of constant geometry is justified since the
density in our MOTs never exceeds 2.5 × 1010 cm−3 . Previous work has shown that MOTs grow in number
with constant volume up to densities larger than 3 × 1010 cm−3 where the outward pressure on the cloud
from multiple scattering becomes significant [30].
We define the normalized density distribution as ρA ≡ NnA∞ , where NA∞ is the steady state atom number
A
of species A in the presence of species B. In this case, the heteronuclear term can be computed by solving
Eq. 1 in steady state to give
R
RA − ΓA NA∞ − βA,A (NA∞ )2 ρ2A dV
R
βA,B =
.
(2)
NA∞ NB∞ ρA ρB dV
We compute the overlap and self-overlap integrals for the normalized distributions from the cloud images
and assume these geometric factors do not change during the loading of the MOTs. Our evaluation of the
integrals from 2D images relies on the assumption that the density distribution can be written as a product
of three independent functions along the x, y, and z axes (i.e. that ρA (x, y, z) = f (x)g(y)h(z)). This latter
assumption will always overestimate the overlap and therefore provide a lower bound on βLi,Rb as it excludes
pathological distributions which would conspire to reside in the same volume of space but with no overlap.
We observe that the overlap integrals for the normalized distributions vary by less than 20% for the two
images taken along orthogonal axes and we estimate the overlap from the average of the two.
Table 2 shows the results of our measurements for both the homonuclear and heteronuclear collision loss
coefficients compared with previously published results where available. The primary uncertainty arises from
our uncertainty in the absolute atom numbers in the MOT.
In agreement with previous studies on Rb MOTs, we observe that β85 Rb,85 Rb is significantly larger than
β87 Rb,87 Rb ; however, our absolute values are more than a factor of 10 larger than those of Ref. [31]. In that
work of Gensemer et al., the β85 Rb,85 Rb and β87 Rb,87 Rb values were observed to vary with intensity and the
values quoted in table 2 were obtained at a total trap intensity 6 times lower and a magnetic field gradient
5 times lower than in this experiment. No previously published data exists for β6 Li,6 Li , and our value is
significantly larger than β7 Li,7 Li for similar MOT parameters. We also report for the first time heteronuclear
loss coefficients for 6 Li–85 Rb mixtures and find similar results to that for 6 Li–87 Rb mixtures. We note here
that although β6 Li,6 Li enters into the determination of β6 Li,85 Rb and β6 Li,87 Rb , because it is so small in
comparison its influence on the heteronuclear term is almost negligible. In particular, the heteronuclear term
changes by less than 10% if we artificially set β6 Li,6 Li = 0.
It is interesting to compare the heteronuclear terms β6 Li,85 Rb and β6 Li,87 Rb with β85 Rb,6 Li and β87 Rb,6 Li .
Cold collisions in the presence of light produce atom loss from the MOT by two generic mechanisms: inelastic
collisions and ground state molecule formation. In the former case, a pair of atoms collide in an excited
11
Table 2. Homonuclear and heteronuclear collision loss coefficients for rubidium and lithium
mixtures. The ellipsis indicate values for which no data is available.
Term
β85 Rb,85 Rb
β87 Rb,87 Rb
β6 Li,6 Li
β7 Li,7 Li
This work [cm3 s−1 ]
(1.0 ± 0.7) × 10−10
(2.0 ± 1.0) × 10−11
(5.0 ± 3.0) × 10−11
...
Published Value [cm3 s−1 ]
> 7 × 10−12 [31]
> 2 × 10−12 [31]
...
3 × 10−12 [32]
β6 Li,85 Rb
β6 Li,87 Rb
(4.0 ± 2.0) × 10−10
(2.5 ± 1.0) × 10−10
...
(1.5 ± 0.5) × 10
[33], 8 × 10−12 [28]
β85 Rb,6 Li
β87 Rb,6 Li
(5.0 ± 2.5) × 10−11
(1.7 ± 0.7) × 10−11
...
...
−10
electronic state and relax to a lower state during the collision converting the difference of internal energies
into relative kinetic energy. If the resulting velocities are large enough, the atoms will escape from the MOT
despite the dissipative radiation pressure forces. In the latter case, the colliding pair undergoes a spontaneous
Raman scattering event to form a ground state dimer which is essentially transparent to the trapping light
and both atoms are lost from the MOT. If all of the Li-Rb light assisted collisions formed ground state dimers,
one would expect the heteronuclear terms to be reciprocal, β6 Li,85 Rb = β85 Rb,6 Li and β6 Li,87 Rb = β87 Rb,6 Li .
On the other hand, conservation of energy and momentum implies that the kinetic energy evolved in an
inelastic collision is not distributed equally among partners with unequal mass and therefore, because of
recapture in the MOT, the heteronuclear loss coefficients are not expected to be reciprocal. For an inelastic
collision between atoms initially at rest, the velocity away from the center of mass will be different by the
mass ratio, which is a factor of more than 14 for lithium and rubidium. Certain collisions can therefore
produce free lithium atoms with velocities well above and free rubidium atoms with velocities well below
the MOT capture velocity. Consider, for example, an inelastic collision between a ground state 87 Rb and
an excited state 6 Li atom which induces fine structure relaxation in the lithium atom. This would evolve
an energy of h × 10 GHz (the 6 Li fine structure splitting) accelerating the 87 Rb to 2.5 m/s and the 6 Li to
35.3 m/s. Given a typical MOT capture velocity of 20 m/s, this could produce lithium loss with little or no
rubidium atom loss. Ground state hyperfine relaxation of rubidium (evolving 6.8 and 3.0 GHz for 87 Rb and
85
Rb, respectively) would produce similar results and also contributes to the heteronuclear loss terms. In
this work, we find the β6 Li,85 Rb and β6 Li,87 Rb terms are a factor of 10 larger than the β85 Rb,6 Li and β87 Rb,6 Li
terms implying most of the collisions result in unbound atoms and not ground state molecules.
In summary, we have presented an apparatus for simultaneously trapping either 85 Rb or 87 Rb and 6 Li from
an effusive lithium oven without the use of a Zeeman slower. This dual MOT is capable of collecting over
(7±2)×107 87 Rb or 85 Rb atoms and (8±2)×107 6 Li atoms. The use of a miniature atomic oven placed close
to the trapping region yields a compact vacuum system while still producing adequate lithium ensembles
for this and other work. We have presented the features of our apparatus, described the optimization and
characterization of the dual MOT, and presented measurements of interspecies collisions in Li-Rb mixtures.
B.G.K. acknowledges support from the Canadian Institute for Advanced Research. This research was
supported by the Canadian Foundation for Innovation, and the Natural Sciences and Engineering Research
12
Council of Canada.
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