LETTERS

Rapid sympathetic cooling to Fermi
degeneracy on a chip
S. AUBIN*, S. MYRSKOG, M. H. T. EXTAVOUR, L. J. LEBLANC, D. MCKAY, A. STUMMER AND
J. H. THYWISSEN
Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada* e-mail: seth.aubin@utoronto.ca

Published online: 28 May 2006; doi:10.1038/nphys309

eutral fermions present new opportunities for testingmodels of many-body quantum systems, realizing
precision atom interferometry, producing ultra-cold
molecules, and investigating fundamental forces. However, since
they were ﬁrst observed1 , quantum degenerate Fermi gases(DFGs) have continued to be challenging to produce, and havebeen realized in only a handful of laboratories2–10 . In this letter,
we report the production of a DFG using a simple apparatus
based on a microfabricated magnetic trap. Similar approaches
applied to Bose–Einstein condensation of 87 Rb (refs 11,12)
have accelerated evaporative cooling and eliminated the needfor multiple vacuum chambers. We demonstrate sympathetic
cooling for the ﬁrst time in a microtrap, and cool 40 K to Fermi
degeneracy in just six seconds—faster than has been possible inconventional magnetic traps. To understand our sympathetic
cooling trajectory, we measure the temperature dependenceof the 40 K–87 Rb cross-section and observe its Ramsauer–
Townsend reduction.
Microfabricating the electromagnets used to trap ultra-cold
atoms leads to a series of experimental beneﬁts. Decreasing theradius R of a surface-mounted wire increases the maximum
magnetic ﬁeld gradient as R−1/2 (ref. 13). As the oscillation
frequency ω of the trapped atoms increases linearly with transverse
ﬁeld gradient, decreasing R from centimetres to micrometres canincrease the conﬁnement frequency by orders of magnitude. In
addition, one can imagine a ‘lab on a chip’, in which multiple
devices are integrated on a single device, expediting applications
for complex manipulation of fermionic atoms for simulationsof strongly correlated systems, quantum transport experiments,
collision-insensitive clocks, and precision interferometry14,15 . The
strong conﬁnement provided by a microfabricated electromagnet(μEM) trap also has a practical advantage: it facilitates fastercooling, which relaxes constraints on vacuum quality and leads toa tremendous simpliﬁcation over traditional DFG experiments that
require multiple ovens, Zeeman slowers, or two magneto-opticaltraps (MOTs).
In our system16 , the entire experimental cycle takes place ina single vapour cell (Fig. 1a). Counter-propagating laser beams
collect, cool, and trap 2 × 107 40 K and 109 87 Rb atoms in a MOT.
Atoms are transferred to a purely magnetic trap formed by externalN

quadrupole coils and transported to the chip 5 cm away. Figure 1b
shows several microscopic gold wires supported by the substrate.
In the presence of uniform magnetic ﬁelds, current ﬂowing throughthe central ‘Z’-shaped wire creates a magnetic ﬁeld minimum above
the chip. At the centre of this trap, the 40 K radial (longitudinal)
oscillation frequency is ω⊥ /2π = 826 ± 7 Hz (ωl /2π = 46.2 ±0√.7 Hz). The corresponding 87 Rb trap frequencies are a factor ofmRb /mK ≈ 1.47 smaller, where mRb and mK are the atomic massesof 87 Rb and 40 K, respectively.
After loading, the 1.1-mK-deep chip trap holds approximately
2 × 105 40 K and 2 × 107 87 Rb doubly spin-polarized atoms, at atemperature ∼300 μK. Lower temperatures are achieved by forced
evaporative cooling of 87 Rb. A transverse magnetic ﬁeld oscillating
at radiofrequency (RF) νRF (typically swept from 30 to 3.61 MHz)selectively removes the highest energy 87 Rb atoms by driving
spin-ﬂip transitions to untrapped states. The 40 K atoms, withsmaller Zeeman splittings, are not ejected but are sympatheticallycooled2,17,18 by thermalizing with the 87 Rb reservoir by means ofelastic 40 K–87 Rb collisions6,8,10,19 .
The evolution of temperature T and atom number N during
sympathetic cooling is measured by releasing atoms from the trap
and observing their expansion with absorptive imaging. Figure 2
shows the cooling of 40 K and 87 Rb to quantum degeneracy. In
the degenerate regime, bosons accumulate in the ground state(forming a Bose–Einstein condensate), whereas fermions ﬁll thelowest energy levels of the trap with near-unity occupation. Fermi
degeneracy can be quantiﬁed with the fugacity Z: the ground state
has occupation Z/(1 + Z), which approaches 1 in the high-Z
degenerate limit and Z in the non-degenerate limit. Owing to
the tight conﬁnement of the μEM trap, cooling increases the 40 K
fugacity by 1012 in only 6 s. The steep ascent of fermion fugacity
in Fig. 2 also demonstrates the eﬃciency of sympathetic cooling.
The inherent eﬃciency of sympathetic cooling is signiﬁcant, as 40 K
is a rare isotope, and is therefore more diﬃcult to collect fromvapour than 87 Rb. To our knowledge, this is the ﬁrst observation of
sympathetic cooling, of Fermi degeneracy, and of dual degeneracy
in a μEM trap.
Below T ≈ 1 μK, we observe two independent signatures of
Fermi degeneracy. First, we compare the r.m.s. cloud size of 40 K
and 87 Rb (or its non-condensed fraction) by ﬁtting the density

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IZ

B BIASIU

B IOFFE
z
x

y

νRF

103

103

100

100

10–3

10–3

10–6

10–6

10–9

104

105

106
Atom number

107

87Rb ground state occupation

40K fugacity

Figure 1 A simple apparatus for Fermi degeneracy. a, The dual-species MOT (red sphere) is formed at the intersection of six laser beams. The cloud is then magneticallytrapped using external quadrupole coils (blue), transported 5 cm vertically using an offset coil (purple), and compressed in the μEM trap. b, Schematic diagram of the central
region of the μEM chip. A magnetic trap is formed 180 μm above the surface at the location marked with a white ‘X’ by applying I Z = 2.0 A, I U = 30 mA, BBIAS = 21.4 G, andBIOFFE = 5.2 G. Wire widths from left to right are 20, 60, and 420 μm.

10–9Figure 2 Sympathetic cooling in a chip trap. Spin-polarized fermions without abosonic bath cannot be successfully evaporatively cooled (blue diamond). However,
if bosonic 87 Rb (red squares) is evaporatively cooled, then fermionic 40 K is
sympathetically cooled (blue dots) to quantum degeneracy (grey area). For bosonic87
Rb, the vertical axis is the occupation of the ground state; for fermionic 40 K, thevertical axis is the fugacity, as discussed in the text. These two quantities areequivalent in the non-degenerate limit. A typical run-to-run spread in atom number
is shown on the right-most point; all vertical error bars are smaller than themarker size.

proﬁles to a gaussian proﬁle. As described in the Methods section,
this is an appropriate method for ﬁnding the temperature of aclassical Boltzmann gas. Figure 3 shows that the apparent (thatis, gaussian-estimated) 40 K temperature approaches a ﬁnite value,
whereas the 87 Rb temperature approaches zero, even though thetwo gases are in good thermal contact. In fact, this deviation isevidence of the ‘Pauli pressure’ expected of a gas obeying Fermi
statistics2 : at zero temperature, fermions ﬁll all available states up
to the Fermi energy EF = h̄(6N ω2⊥ ωl )1/3 , where N is the numberof fermions, and h̄ is the reduced Planck’s constant. For ourtypical parameters, EF ≈ kB × 1.1 μK. We plot data with thermaland Bose-condensed 87 Rb separately, to show that the densitydependent attractive interaction between 40 K and 87 Rb does not

signiﬁcantly aﬀect the release energy. A second signature of Fermi
statistics is evident in the shape of the cloud. Figure 3, bottom inset,
compares the residuals of a gaussian ﬁt (which assumes Boltzmann
statistics) with the residuals of a ﬁt which assumes Fermi–Diracstatistics. The Fermi distribution describes the data well, with aχ2 three times lower than the gaussian ﬁt. After all of the 87 Rb
atoms have been evaporated, we use Fermi–Dirac ﬁts to measuretemperature, and ﬁnd kB T /EF as low as 0.09 ± 0.05 with as many as
4 × 104 40 K atoms.
We empirically optimize the sympathetic cooling trajectory,
and ﬁnd that RF sweep times faster than 6 s are not successful,whereas 87 Rb alone can be cooled to degeneracy in 2 s. This
indicates that 40 K and 87 Rb rethermalize more slowly than 87 Rb withitself. Measuring the temperature ratio during sympathetic cooling(Fig. 4a) reveals that 40 K lags behind 87 Rb at high temperatures,
despite the fact that our optimal frequency ramp starts slowly(when the atoms are hottest), and accelerates at lower temperatures.
In the low-temperature limit, we do not expect the cross-species
thermalization to lag the 87 Rb–87 Rb thermalization, as the 40 K–87 Rb
cross-section σKRb = 1,480 ± 70 nm2 (ref. 20) exceeds the 87 Rb–87 Rb
cross-section, σRbRb = 689.6 ± 0.3 nm2 (ref. 21). However, several
conﬂicting values for σKRb have recently been presented10,19,20,22,23 .
We investigate σKRb further by measuring the cross-species
thermalization rate24 at several temperatures. Starting fromequilibrium, we abruptly cool 87 Rb by reducing νRF , wait for avariable hold time to allow cross-thermalization, and then measure
the 40 K temperature, as shown in the inset of Fig. 4b. We repeat thismeasurement at several temperatures, and ﬁt each to the model ofref. 25. We ﬁnd that the cross-section has a dramatic dependence on
temperature (see Fig. 4b), decreasing over an order of magnitude
between 10 and 200 μK.
The simplest model for atom–atom scattering uses a deltafunction contact potential. Figure 4b shows that the s-wave
scattering cross-section of this ‘naive’ model (further describedin the Methods section) would predict a higher σKRb thanσRbRb throughout the cooling cycle, in stark contrast to ourmeasurements. Better agreement is given by an eﬀective-range
model26 , which includes a reduction in scattering phase (andthus cross-section) below the naive expectation. Our highest
temperature data point lies below the eﬀective-range prediction,
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K:Rb temperature ratio

200 μm

EF
1.5

2.0

1.5

1.0
1

1.0
Fit residual

Apparent 40K temperature (kBTK40/E F)

2.0

0.5

10
Temperature (μK)

100

b

0

0

0.5

1.0

200
400
Radial distance (μm)
1.5

2.0

87Rb temperature (k T
B Rb87/EF)

Figure 3 Observation of Fermi statistics. Owing to Pauli pressure, Fermi
degenerate 40 K clouds seem to stop getting colder, even when the reservoir
temperature approaches zero. The apparent temperature of the fermions, asmeasured by gaussian ﬁts to images of 40 K clouds, is plotted versus temperature ofboth thermal (diamonds) and Bose-condensed (circles) 87 Rb. Data is compared with
its classical expectation (dashed line) and with a gaussian ﬁt of theoreticallygenerated ideal Fermi distribution (solid line). Both temperatures are scaled by the
Fermi energy EF of each 40 K cloud. Error bars are statistical (one standard deviation),with uncertainty smaller than the sizes of symbols for lower temperature data. Top
insets: Absorption images for kB T/EF = 0.35 (left) and 0.95 (right), including a
black circle indicating the Fermi energy EF . Bottom inset: At kB T/EF = 0.13+0.04−0.07
with the 87 Rb atoms completely evaporated, a closer look at the fermion cloud shape
reveals that it does not follow a Boltzmann distribution. The ﬁt residuals of a radiallyaveraged cloud proﬁle show a strong systematic deviation when assuming
Boltzmann (blue circles) instead of Fermi (red diamonds) statistics. A degenerate
Fermi cloud is ﬂatter at its centre than a Boltzmann distribution, and falls more
sharply to zero near its edge.

however a more-sophisticated analysis may be required to extract
a quantitative measurement for this point, due to severe trap
anharmonicity at high temperature. Overall, both data and theory
show that the 40 K–87 Rb cross-section is reduced well below
the 87 Rb–87 Rb cross-section for a large range of temperatures,
explaining the requirement for a slow initial RF frequency sweep
for sympathetic cooling. Below 20 μK, where no temperature lag isobserved, σKRb exceeds σRbRb .
We attribute the observed reduction in scattering cross-section
to the onset of the Ramsauer–Townsend eﬀect, in which thes-wave scattering phase and cross-section approach zero for aparticular value of relative energies between particles27 . At higher
temperatures, the scattering cross-section should increase again,
however free evaporation from our trap limits our measurements
to below 300 μK. Additional partial waves may also aﬀect
scattering above the p-wave threshold of 110 μK. Despite thehigh-temperature reduction in cross-section, 40 K and 87 Rb remain
relatively good sympathetic cooling partners. For instance, recent
measurements of 87 Rb–6 Li sympathetic cooling9 suggest a zerotemperature cross-section approximately 100 times smaller thanσKRb , that is, a maximum cross-section roughly equal to the lowest
value we measure here.
The high collision rates in mixtures trapped with a μEM allow
us to cool fermions sympathetically to quantum degeneracy in 6 s,
faster than previously possible. Our method is an alternative to100
Temperature (μK)

0

Cross section (nm2)

1,000

10

1

30
25

0

0.5
Hold time (s)1.010Temperature (μK)

100

Figure 4 Cross-species thermalization. a, The ratio of the temperature of 40 K to
the temperature of 87 Rb approaches unity as the 40 K temperature is lowered during
sympathetic cooling. b, Measurements of σ KRb (diamonds) are compared with the‘naive’ model (dashed) and an effective-range model (solid), both described in the
text. Inset: We measure cross-thermalization by abruptly reducing the temperatureof 87 Rb and watching the temperature of 40 K relax versus time. The data shown has
an asymptotic 40 K temperature of 27 μK. The highest temperature point in b (open
diamond) did not completely thermalize, and is discussed further in the text. For
reference, the s-wave σ RbRb is also shown (dotted). The error bars shown in all partsof the ﬁgure are statistical (one standard deviation), with the exception of thehorizontal temperature error bars in b, which show the spread between initial andﬁnal 40 K temperature.

all-optical trapping and cooling, which has been used with 6 Li toachieve Fermi degeneracy in 3.5 s (ref. 28). However, magnetic traps
allow cooling of fermions without direct evaporative loss, which is
critical in the case of 40 K because of its low isotopic abundance. In
conclusion, we have achieved simultaneous quantum degeneracy ofbosonic and fermionic atoms in a μEM trap and demonstrated an
approach that can simplify future research with cold fermions. One
prospect is the observation of Pauli blocking in light scattering oﬀ
degenerate fermions29,30 . The high μEM trap frequencies boost theratio of Fermi energy EF to the recoil energy h̄2 k2 /2mK to ∼2.5,
within the range necessary to explore such quantum optical eﬀects.

METHODSLOADING

Our experimental cycle is similar to that described in ref. 16, with several key
modiﬁcations emphasized here and in the main text. Approximately 600 mW ofincoherent 405-nm light desorbs 87 Rb and 40 K atoms from the Pyrex vacuum
cell walls, boosting the MOT atom number 100-fold compared with loadingfrom the background vapour. Potassium alone is ﬁrst loaded into the MOT for
25 s, after which 87 Rb is loaded for an additional 3–5 s, while maintaining the386

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40
K population. Both MOTs operate with a detuning of −26 MHz, until the last
10 ms, when 40 K is compressed with a −5 MHz detuning. After MOT loading,
3 ms of optical molasses cooling is applied to the 87 Rb atoms, and the 40 K
atoms are optically pumped into the |F = 9/2, mF = 9/2 hyperﬁneground state.

MICROELECTROMAGNET TRAP

7-μm-thick gold wires are patterned lithographically and electroplated on asilicon substrate. Two defects are present near the centre of the principal
Z-wire, which result in the formation of three ‘dimples’ in the trapping
potential. We use the magnetic gradient generated by 30 mA of current throughthe U-wire to centre the magnetic trap on one of these dimples.
FITTING ABSORPTION IMAGE DATA

Degenerate Fermi clouds are ﬁtted using a semiclassical expression for theAf2 (Z)
optical density: Af2 (Z exp [−2 /2r 2 ]), where  is the radial coordinate,νis the peak optical density, Z the fugacity, and f ν (q) = − ∞=1 (−q) / is the−22
Fermi–Dirac function. The temperature is given by kB T = r mK /(ω⊥ + t 2 ),where r is the ﬁt width and t is the time of ﬂight. The atom number is extractedusing N = 2πr 2 f3 (Z)A/σl , where σl is the resonant absorption cross-section.
T /TF can be extracted directly from the fugacity using (T /TF )−3 = 6f3 (Z).
Non-degenerate clouds are ﬁtted to a gaussian distribution A exp [−2 /2r 2 ],with the same interpretation of r . Probes along both x̂ and ŷ (see Fig. 1) wereused for imaging. Comparison of temperature measurements along axes of
expansion suggest a 20-nK kick (possibly magnetic) is given to clouds along ẑ ,and that other temperatures agree systematically at the 5% level. Data forresiduals shown in Fig. 3, bottom inset, are radially averaged about an ellipse
deﬁned by the two trap frequencies of the image plane. This one-dimensionalradial data set is binned into 2-pixel bins, and ﬁtted as described.
SCATTERING THEORIESThe ‘naive’ interaction model discussed in the text gives
σKRb = 4πa2 /(1 + a2 k2 ), where a is the s-wave scattering length and k is therelative wave vector in the centre of mass frame. Figure 4b shows the thermallyaveraged theory curves. Including the next-order correction in the s-wave
scattering amplitude f (k) = −[1/a + ik + k2 re /2 + ···]−1 requires an eﬀective
range, which we calculate using ref. 26 to be re = 20.2 ± 0.3 nm, for
aKRb = −10.8 ± 0.3 nm (ref. 20).
ANALYSIS OF THERMALIZATION DATA

When the 87 Rb atom number NRb is much larger than the 40 K atom number,the relaxation of the 40 K temperature T to TRb is described byu̇ = −uτ −1 (1 + mRb u/(mRb + mK ))1/2 (1 + u/2)−(3/2) , whereu ≡ (T /TRb ) − 1, and thermalization time τ given by√√mK m2Rb ω2⊥ ωl
1
2 σKRbNRb ,= 2
τ 3π kB TRb (mK + mRb )3/2
in which trap frequencies are for 87 Rb (ref. 25). Fitting for τ allows us to extract
σKRb . Note that all thermalization data is taken with NK below 4% of NRb .
The data in Fig. 4b is analysed assuming a temperature-independent
cross-section within the range of initial to ﬁnal temperature. To check thisassumption, we re-analyse the data using a self-consistent method that assumes
an eﬀective-range temperature dependence, and ﬁnd a small upward shift ofthe best-ﬁt cross-section values. Using this shift as an estimate of themethodology-dependent systematic error, we ﬁt our four lowest temperature
measurements with the eﬀective-range model, and ﬁnd
aKRb = −9.9 ± 1.4 ± 2.2 nm, in agreement with ref. 20. The second uncertainty
reported is systematic, and also includes uncertainty in the 87 Rb
number calibration.

Received 20 December 2005; accepted 24 April 2006; published 28 May 2006.
References
1. DeMarco, B. & Jin, D. S. Onset of Fermi degeneracy in a trapped atomic gas. Science 285,
1703–1706 (1999).
2. Truscott, A. G., Strecker, K. E., McAlexander, W. I., Partridge, G. B. & Hulet, R. G. Observation of
Fermi pressure in a gas of trapped atoms. Science 291, 2570–2572 (2001).
3. Schreck, F. et al. Quasipure Bose-Einstein condensate immersed in a Fermi sea. Phys. Rev. Lett. 87,
080403 (2001).
4. Granade, S. R., Gehm, M. E., O’Hara, K. M. & Thomas, J. E. All-optical production of a degenerate
Fermi gas. Phys. Rev. Lett. 88, 120405 (2002).
5. Hadzibabic, Z. et al. Two-species mixture of quantum degenerate Bose and Fermi gases. Phys. Rev.
Lett. 88, 160401 (2002).
6. Roati, G., Riboli, F., Modugno, G. & Inguscio, M. Fermi–Bose quantum degenerate 40 K-87 Rb mixture
with attractive interaction. Phys. Rev. Lett. 89, 150403 (2002).
7. Bartenstein, M. et al. Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi
gas. Phys. Rev. Lett. 92, 120401 (2004).
8. Köhl, M., Moritz, H., Stöferle, T., Günter, K. & Esslinger, T. Fermionic atoms in a three dimensional
optical lattice: observing Fermi surfaces, dynamics, and interactions. Phys. Rev. Lett. 94,
080403 (2005).
9. Silber, C. et al. Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases. Phys.
Rev. Lett. 95, 170408 (2005).
10. Ospelkaus, C., Ospelkaus, S., Sengstock, K. & Bongs, K. Interaction-driven dynamics of 40 K/87 Rb
Fermi–Bose gas mixtures in the large particle number limit. Phys. Rev. Lett. 96, 020401 (2006).
11. Hänsel, W., Hommelhoﬀ, P., Hänsch, T. W. & Reichel, J. Bose-Einstein condensation on a
microelectronic chip. Nature 413, 498–501 (2001).
12. Ott, H., Fortagh, J., Schlotterbeck, G., Grossmann, A. & Zimmermann, C. Bose-Einsteincondensation in a surface microtrap. Phys. Rev. Lett. 87, 230401 (2001).
13. Groth, S. et al. Atom chips: Fabrication and thermal properties. Appl. Phys. Lett. 85,
2980–2982 (2004).
14. Thywissen, J. H., Westervelt, R. M. & Prentiss, M. Quantum point contacts for neutral atoms. Phys.
Rev. Lett. 83, 3762–3765 (1999).
15. Wang, Y.-J. et al. Atom Michelson interferometer on a chip using a Bose-Einstein condensate. Phys.
Rev. Lett. 94, 090405 (2005).
16. Aubin, S. et al. Trapping fermionic 40 K and bosonic 87 Rb in a chip trap. J. Low Temp. Phys. 140,
377–396 (2005).
17. Myatt, C. J., Burt, E. A., Ghrist, R. W., Cornell, E. A. & Wieman, C. E. Production of two overlapping
Bose-Einstein condensates by sympathetic cooling. Phys. Rev. Lett. 78, 586–589 (1997).
18. Schreck, F. et al. Sympathetic cooling of bosonic and fermionic lithium gases towards quantum
degeneracy. Phys. Rev. A 64, 011402 (2001).
19. Goldwin, J. et al. Measurement of the interaction strength in a Bose-Fermi mixture with 87 Rb and 40 K.
Phys. Rev. A 70, 021601 (2004).
20. Ferlaino, F. et al. Feschbach spectroscopy of K-Rb atomic mixture. Phys. Rev. A 73, 040702 (2006).
21. van Kempen, E. G. M., Kokkelmans, S. J. J. M. F., Heinzen, J. J. & Verhaar, B. J. Interisotope
determination of ultracold rubidium interactions from three high-precision experiments. Phys. Rev.
Lett. 88, 93201 (2002).
22. Modugno, G. et al. Collapse of a degenerate Fermi gas. Science 297, 2240–2243 (2002).
23. Inouye, S. et al. Observation of heteronuclear Feshbach resonances in a mixture of bosons andfermions. Phys. Rev. Lett. 93, 183201 (2004).
24. Anderlini, M. et al. Sympathetic cooling and collisional properties of a Rb-Cs mixture. Phys. Rev. A
71, 061401 (2005).
25. Mosk, A. et al. Mixture of ultracold lithium and cesium atoms in an optical dipole trap. Appl. Phys. B
73, 791–799 (2001).
26. Flambaum, V. V., Gribakin, G. F. & Harabati, C. Analytical calculation of cold-atom scattering. Phys.
Rev. A 59, 1998–2005 (1999).
27. Townsend, J. S. A Modern Approach to Quantum Mechanics 393 (McGraw-Hill, New York, 1992).
28. O’Hara, K. M. et al. Observation of a strongly interacting degenerate Fermi gas of atoms. Science 298,
2179–2182 (2002).
29. Busch, Th., Anglin, J. R., Cirac, J. I. & Zoller, P. Inhibition of spontaneous emission in Fermi gases.
Europhys. Lett. 44, 1–6 (1998).
30. DeMarco, B. & Jin, D. S. Exploring a quantum degenerate gas of fermionic atoms. Phys. Rev. A 58,
R4267–R4270 (1998).

Acknowledgements
We would like to thank D. Jin, J. Dalibard, J. Bohm, and D. Guery-Odelin for helpful conversations
about scattering theory, and A. Simoni for sending us unpublished 40 K–87 Rb cross-section calculations.
We also thank N. Bigelow, A. Aspect, T. Schumm, and H. Moritz for stimulating conversations,P. Bouyer and R. Nyman for providing a tapered ampliﬁer used in this work, and J. Estève forfabricating the chip used in this work. This work is supported by the NSERC, CFI, OIT, PRO, CRC,
and Research Corporation. S.A., L.J.L. and D.M. acknowledge support from NSERC. M.H.T.E.
acknowledges support from OGS.
Correspondence and requests for materials should be addressed to S.A.

Competing ﬁnancial interests
The authors declare that they have no competing ﬁnancial interests.
Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/

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