Design and fabrication of diffractive atom chips for laser cooling and trapping

2.9 MB·

by  J. P. Cotter

Noname manuscript No.
(will be inserted by the editor)
Design and fabrication of diffractive atom chips for laser cooling and
trapping
J. P. Cotter1,2, J. P. McGilligan3, P. F. Griffin3, I. M. Rabey1, K. Docherty4, E. Riis3, A. S. Arnold3,
and E. A. Hinds1
1 The Centre for Cold Matter, Blackett Laboratory, Imperial College London, SW7 2AZ, UK
2 University of Vienna, VCQ, Faculty of Physics, Boltzmanngasse 5, A-1090 Vienna, Austria
6 3 Department of Physics, SUPA, University of Strathclyde, Glasgow G4 0NG, UK
1 4 Kelvin Nanotechnology Ltd, Rankine Building, Oakfield Avenue, Glasgow G12 8LT, UK
0
2
Received: date / Revised version: date
n
a
J
Abstract It has recently been shown that optical re- polishing is required to achieve optical quality surfaces
1
flection gratings fabricated directly into an atom chip [4,18,19]. For these reasons the integrated pyramid is
2
provide a simple and effective way to trap and cool sub- unsuitable for applications requiring more than ∼ 104

] stantial clouds of atoms [1,2]. In this article we describe atoms. Fig. 1 illustrates a recent extension of this idea
s
c how the gratings are designed and micro-fabricated and wheretheMOTbeamsarenowformedusingmicrofabri-
i wecharacterisetheiropticalproperties,whichdetermine cateddiffractiongratings,whichreplacetheslopingwalls
t
p their effectiveness as a cold atom source. We use simple ofthepyramid[20,21].Thegratingsareeasilyfabricated
o
scalardiffractiontheorytounderstandhowthemorphol- on any standard substrate material, and can readily be
.
s ogyofthegratingsdeterminesthepowerinthediffracted made on the centimeter scale. This allows the MOT to
c
beams. capture up to 108 atoms above the surface of the chip,
i
s where they can be conveniently transferred to magnetic
y
h traps [6]. Because they only need a small depth of etch-
p ing,thegratingspreservethe2Dnatureofthestructure
[ and sit comfortably with other elements on the chip.
1 Introduction
Alternatively, for devices that only require the reliable
1
v
Atom chips are microfabricated devices which control
8
and manipulate ultracold atoms in a small, integrated
4
5 package.Becausetheyprovideaconvenientwaytotrap[3, Quadrupole
Magnetic Field
5 4,5], guide[6,7] and detect atoms[8], atom chips are be-
0 comingincreasinglyimportantforclocks[9],Bose-Einstein
.
1 condensates[10,11], matter wave interferometers[12,4,
0 13], and quantum metrology[14]. In recent years there
6 hasbeengreatprogresstowardsintegratingawiderange
1
ofoptical,electricandmagneticelementsintoatomchips, MOT
:
v but the magneto-optical trap (MOT)[15,16] - the ele- Region
i
X ment responsible for initial capture and cooling of the
r atoms - has remained external to the chip. θ
a Following[17],anearlyattempttointegratetheMOT
used deep pyramidal mirrors etched into a thick silicon Diffraction Chip
substrate.Thesemanipulateasingleincidentlaserbeam
Fig. 1 Principle of the grating chips. A normally-incident
into the overlapping beams required by a MOT. With
laser beam of intensity I is diffracted by metal reflection
beams of small size L, the number of atoms captured in
gratings,writtenintothesurfaceofachip,tomakefirstorder
scales as L6[5], a dependence that rolls over to L3.6 as
beamsofintensityI .Together,thesebeamsprovidethe
the size increases to some centimeters [15]. The large |m|=1
light required for trapping in the magnetic quadrupole field.
pyramids favoured by this scaling are not compatible
Theangularmomentumoftheinputbeam,indicatedbythe
with the normal 500µm thickness of a silicon wafer. Al- blue arrow, is opposite to the local magnetic field direction,
though thick wafers are available, days of etching are andthehelicityofthelightiswellpreservedafterdiffraction.
needed to make pyramids of mm size and additional
2 J. P. Cotter et al.
θ
θ θ
(1- r) d
T
r d
S
d
Fig. 2 One-dimensional grating chips of three-fold radial Fig. 3 Ideallised diffraction grating profile, with period d,
symmetry, used to make 4-beam integrated MOTs. Red ar- dutyfactorr,anddepthT.S representstheeffectivelength
rows indicate the diffracted beams used for trapping. Chip of the bottom facet, which is shortened because some light
A is made by optical lithography, while chip B (shown mag- isshadowedbythestep.Normallyincidentlightisdiffracted
nified) is patterned by e-beam lithography. Insets: Scanning at an angle θ.
electron microscope images of the grating lines.
is somewhat higher because the polarisations of the up-
production of a MOT, the grating chip can be placed ward and downward beams are not the same.
outside the wall of a glass cell and used to trap atoms
To estimate the power diffracted from our gratings,
on the inside.
weapproximatethembytheidealprofileshowninFig.3.
Figure 2 shows two 1D-grating MOT chips which
Theelementaryperioddcontainsatopfaceofwidthrd
have already been demonstrated [1]. Chip A has three
and a bottom face of width (1−r)d that is lower by a
square grating areas arranged symmetrically to leave a
depth T. Light diffracted at an angle θ from the lower
planeareainthecentre.ChipBhasthesamegeometry,
face is shadowed by the step, so that the effective width
but the grating pattern covers the whole surface and,
ofthefaceisS =(1−r)d−T tanθ.Thephasedifference
in particular, extends all the way to the centre. In this
between rays coming from the centre of the top surface
article we describe the design and fabrication of each
and the centre of the effective bottom surface is
chip and compare the expected and measured optical
properties of each. The article is organised as follows. (cid:20) (cid:21)
1
In Sec. 2 we outline the simple scalar diffraction model φ=k (d−T tanθ)sinθ−T(1+cosθ) , (1)
2
that we used to design the chips. Section 3 describes
how the gratings were fabricated. In Sec. 4 we measure
thedimensionsofthefabricatedgratingsandtheoptical where k = 2π/λ and λ is the wavelength of the light.
properties of the diffracted beams, and we compare the WithanormallyincidentfieldEin,andassumingpower
performance achieved with the theoretical expectations. reflectivity ρ, the diffracted field at (large) distance R is
Finally in Sec. 5 we summarise our findings. approximated by the Fraunhofer integral.
2 Design of the chips E(θ) √ρ (cid:34)(cid:90) rd/2 (cid:90) S/2 (cid:35)
= √ dx eikxsinθ+eiφ dx eikxsinθ
TheatomstrappedbytheMOTareheldbyopticalscat- Ein Rλ −rd/2 −S/2
tering forces in the presence of a magnetic quadrupole (cid:32) N (cid:33)
(cid:88)
field. Ideally, these forces should sum to zero at the cen- × eikndsinθ . (2)
tre of the quadrupole, which can be achieved by appro- n=1
priate choices of intensity and polarisation of the light.
Thechipsdescribedherehavesymmetrythatautomati- Here, the first line describes the diffraction from one el-
cally balances the forces parallel to the surface, but bal- ementary unit of the grating, as illustrated in Fig. 3,
ance in the normal direction has to be designed. Let the while the last factor sums over the contribution from all
incident power P over an area A of the chip produce N grating periods.
in
power ηP in each diffracted beam. The corresponding Theintensitydistribution,obtainedbysquaringequa-
in
intensity is I = ηP /(Acosθ), where θ is the an- tion (2), has a comb of narrow peaks coming from the
diff in
gletothenormal,asshowninFig.1.WithN diffracted gratingfactor,withmaximaattheBragganglesgivenby
beamsparticipatingintheMOT,thetotalintensitycon- sinθ =mλ/d,wheremisaninteger.Becausemanylines
tributingtotheupwardforceisNI cosθ =NηP /A= ofthegratingareilluminated,thesingle-periodfactoris
diff in
NηI . The vertical balance of intensities therefore re- essentiallyconstantoverthesmallangularspreadacross
in
quires Nη = 1. For chips A and B in Fig. 2, which one of the Bragg peaks. This makes it straightforward
use three diffracted beams, this condition becomes η = to integrate across the mth Bragg peak to find the total
1/3 [21]. In practice, the optimum diffracted intensity diffracted power P in that order. The result is
m
Design and fabrication of diffractive atom chips for laser cooling and trapping 3
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Fig. 4 Power in a single diffraction order, normalised to the incident power and plotted as a function of duty factor r and
grating depth T divided by wavelength λ. Reflectivity is taken to be ρ = 1. (a) The zero-order case given by Eq. (5). This
is the region near minimum power, where r (cid:39) 1/2 and T (cid:39) λ/4. The minimum is wide enough to forgive minor fabrication
errors. (b) Fraction of power in the m=+1 order of chip A, calculated from Eq. (4) with d=1.19µm and λ=780nm. (c)
Fraction of power in the m=+1 order of chip B, calculated from Eq. (4) with d=1.48µm and λ=780nm.
P /P of only one or two percent, making the design
0 in
robust against minor fabrication errors.
(cid:12) (cid:12)2
P ρ (cid:12)(cid:90) rd/2 (cid:90) S/2 (cid:12) We turn now to the first order beams, which (to-
m = (cid:12) dx ei2πmx/d+eiφ dx ei2πmx/d(cid:12) ,
P d2 (cid:12) (cid:12) gether with the incident beam) are responsible for mak-
in (cid:12) −rd/2 −S/2 (cid:12)
ing the MOT. The plots in Fig. 4(b) (for chip A) and
(3)
Fig. 4(c) (for chip B) show the power P in the m=+1
1
order(normalisedtoP )whenthegratingdepthT and
P being the power incident on the N illuminated lines in
in duty factor r are varied. We see that this power is close
of the grating. Evaluating these integrals,
to a maximum when the retro-reflected power is zero,
P ρ butcanbeincreasedalittlebyreducingr slightlybelow
m = [sin2(mπr)+sin2(mπS/d)
P m2π2 0.5. This has the effect of making rd and S more nearly
in
equal, which improves the contrast of the grating. A lit-
+2cos(φ)sin(mπr)sin(mπS/d)].
tle is also gained by reducing T/λ, so that the width S
(4)
of the lower surface is increased. As with the minimum
of P , this maximum of P is sufficiently forgiving that
Let us first consider diffraction into the m=0 order 0 1
we are not troubled by minor fabrication errors.
- i.e. retro-reflection of the incident beam. This needs
The MOT works because the scattering force in the
to be avoided as a strong upward beam of the wrong
presence of a magnetic field depends on the polarisa-
polarisation is detrimental to the MOT [1]. For chip A
tion of the light. For that reason, it would be ideal to
there is a plane surface in the central region, which can
go beyond this simple scalar model of the diffraction to
eitherbecutawaytoleaveanaperture,orcoatedwithan
considerpolarisation.However,thattheoryisquitechal-
absorbing layer. For chip B, where the grating structure
lengingandisbeyondthescopeofthisarticle.Insteadwe
runsallthewayintothemiddle,theretro-reflectioncan
have relied on experiment to determine the polarisation
besuppressedinsteadbyasuitablechoiceofthegrating
of the diffracted beam, as discussed further in section 4.
parameters. On using Eq. (1) to eliminate φ, Eq. (4)
gives
3 Fabrication
(cid:20) (cid:18) (cid:18) (cid:19)(cid:19)(cid:21)
P 4πT
0 =ρ 1+2r(r−1) 1−cos . (5) ChipsAandBareproducedbytwodifferentfabrication
P λ
in
methods, which we now describe.
(cid:16) (cid:17)
This goes to zero when r = 1 1+ i . Since r
2 tan(2πT/λ)
must be real we require tan(2πT/λ)=∞, which leaves 3.1 Chip A: Photo-lithography using silicon substrate
r = 1. It is desirable to minimise the depth T so that
2
S remains as large as possible for the first diffraction Chip A, shown in Fig. 2a, is a 32mm square of sili-
order. We therefore choose T = λ/4. Fig. 4(a) shows con in which three 8mm-square lamellar gratings are
how P /P varies when r and T deviate from this ideal etched by photolithography. This is then covered with
0 in
condition,astheyinevitablywillinpractice.Weseethat gold to achieve the desired high reflectivity at 780nm.
deviations of up to 10% in either T or r give rise to a We choose a grating period of 1.2µm, which is close to
4 J. P. Cotter et al.
lenged by the resolution we require. However, the large
size of the pattern over all does present a challenge.
A (cid:104)100(cid:105)-orientated 100mm-diameter silicon wafer is
coated with ZEP520A e-beam resist to a thickness of
(a) (b) 1μm
350nm, which is then patterned using a high speed e-
Fig. 5 (a) Scanning electron microscope images of chip A. beamwriter(VistecVB6with50MHzscanspeed).With
(a)Adeeptrenchcalibratestheetchingratepriortothemain 11chips,coveringatotalareaof44cm2,thistakes25hrs
fabrication and shows a profile close to that of our model, ofcontinuouswriting.Particularcareisneededtoensure
illustrated in Fig. 3. (b) The final chip after etching to a theelectronbeamdirectiondoesnotdriftoverthistime,
depth of T ∼195nm and coating with 200nm of gold. This
thereby introducing phase variations across individual
brings the duty factor r close to 1.
2 gratings. The wafer is then etched and cleaned in the
same way as chip A. The scanning electron microscope
imageinFig.6(a)showsthecentreoftheetchedgrating
theminimumthatcanbereliablymadebythismethod.
Although we aim for a duty factor of r = 1, the bottom and illustrates the high quality of the fabrication.
2 After evaporating 100nm of aluminium, the grat-
face is designed to be 700nm wide, anticipating that r
will move towards 1 after the gold is added. ing is imaged again, as shown in Fig. 6(b). From this
2 and similar scans we measure the final parameters T =
To begin, we make a reticle by direct ebeam writing
190(5)nm, d = 1.48(1)µm and r =0.46(5).
onchromium-coatedquartz.Thisisa5×magnifiedver-
sion of one square grating. A (cid:104)100(cid:105)-orientated 150mm-
diameter silicon wafer is then coated with SPR660 pho-
toresist to a thickness of 0.8µm and exposed to de- 4 Measurement of optical properties
magnified images of the reticle, using light of 365nm
wavelength. A stepper motor manoeuvres the reticle to The reflectivity of each chip was determined by mea-
each grating position in turn, to produce an image of 12 suring the power in a 780nm laser beam reflected from
chips - 32 gratings in total - on the wafer. The resist is a flat, un-etched area, and comparing this with the in-
thendeveloped,andtheexposedsiliconisremovedbyre- cident power. We found ρ = 0.972(6) for chip A and
activeionetchingusinganinductively-coupledSF /C F ρ=0.822(6) for chip B.
6 4 8
plasma.Withatypicaletchrateof∼5nm/s,thisforms InordertomeasurethediffractedpowerratioPm/Pin,
agratingofthedesireddepth-λ/4=195nm-inunder a few-milliwatt laser beam of 780nm wavelength was
1minute. The wafer is then stripped of the remaining spatially filtered using a single-mode fibre, then colli-
resist by plasma ashing, before cleaning with a piranha matedtoformabeamofapproximately1mmfull-width-
solutiontoremoveanyremainingorganiccontaminants. half-maximum.Thiswassentthroughapolarisingbeam
Figure5(a)showsascanningelectronmicroscopeimage splitter,thencircularlypolarisedbyaquarter-waveplate,
of a deep grating that was made to calibrate the etch as it would be to make a MOT. Roughly 1m from the
rate. One can see in this image the high quality of the wave plate, the light was retro-reflected from a flat area
profileandthefew-nmaccuracyofthewidthsproduced. of the chip and sent back through the wave plate and
In order to give the gratings a high reflectivity, we beam splitter. The circular polarisation of the incident
apply a 5nm-thick adhesion layer of chromium (by dc lightwasoptimisedbyadjustingtheangleofthequarter-
sputtering) followed by 200nm-thick layer of gold (by wave plate to extinguish the light returning through the
rf sputtering). The finished grating is shown in Fig. 5b. beam splitter. Next, a translation stage moved the chip
From this and similar scans we measure a final depth of so that the light was incident on a grating, and a power
T = 207(5)nm, a period of d = 1.19(1)µm and a duty meter then recorded the incident power Pin and the
factor of r = 0.51(5), the latter being due in part to power P1 diffracted into first order.
some systematic variation across the chip.
3.2 Chip B: Electron-beam lithography using silicon
substrate
Chip B is a 22mm square of silicon, coated with alu-
minium, in which a grating is etched by electron beam
lithography. The grating consists of nested triangles, as
shownmagnifiedinFig.2b,thatcontinueoutwardtofill
a 20mm square. The lamellar surface profile is designed Fig. 6 Scanning electron microscope images of chip B. (a)
tohaveadepthof195nm,aperiodof1.5µm,andaduty The centre of chip B, etched to a depth of 195nm, before
factor of 1 . Unlike the photolithography used for chip coating. The triangles are equilateral, but distorted by the
2
A, the e-beam fabrication used here is not at all chal- angle of view. (b) After coating with aluminium.
Design and fabrication of diffractive atom chips for laser cooling and trapping 5
We measured each of the three gratings on chip A, 5 Summary and conclusions
with the results P /P = 0.326(2), 0.323(2)0.386(2).
1 in
Thesearetobecomparedwiththepowerratiogivenby Optical reflection gratings fabricated on an atom chip
Eq. (4) after inserting the measured grating dimensions offer a simple way to build a large, robust, integrated
and reflectivity. That gives 0.340+(21), in good agree- magneto-opticaltrap(MOT)foratoms[1].Inthispaper
−(36)
ment with the measurements. The small variation in we have discussed the main design considerations, and
both theory and experiment is due predominantly to have described how suitable chips can be fabricated us-
the variation of r. This translates into a variation of ingtwomethods:opticallithographyande-beamlithog-
thediffractedpowerbecausechipA,havingr =0.51(5), raphy.UsingscalarFraunhoferdiffractiontheoryandan
operates on the high-r side of the maximum plotted in idealisedmodelofthelamellarprofile,wehaveprovided
Fig. (4)(b), where the derivative with respect to r is not an account of the expected MOT beam intensities. This
zero. theory agrees well with experiment down to the level of
a few percent of the incident power, but not with the
Measurements on the three gratings of chip B gave higher-precisionmeasurementsmadeonthe aluminium-
P /P = 0.381(2), 0.381(2)0.380(2), showing a good coated chip B. We have shown that it is possible to sup-
1 in
levelofreproducibility.Thisisdueinparttobetteruni- presstheback-reflection,whileatthesametimediffract-
formity of the e-beam lithography, but also, chip B op- ing a large fraction of the power into the two first-order
erates with r =0.46(5), which is very close to the max- beams.Thepowerinthesebeamsdependsonthechoice
imum of the plot in Fig. (4)(c), where P is insensitive of period d, duty factor r and depth T of the grating.
1
to variation of r. The power ratio given by Eq. (4) for These parameters vary a little over the optically fabri-
chip B is 0.328+(2). While this is qualitatively similar to catedchipA,andratherlessoverthee-beamfabricated
−(9)
themeasuredfraction,itdoesnotagreewithinthemea- chip B. In either case, we show how to minimise the ef-
surement uncertainty and we cannot find any plausible fect of inhomogeneity on the diffracted beam intensity
adjustment of parameters that might bring them into by operating at the intensity maximum with respect to
agreement. We are forced to conclude that our diffrac- r and T. We also find that the circular polarisation of
tion theory is not able to predict the diffracted power the light is surprisingly well preserved after diffraction
with this high level of accuracy, and suspect that the into the first-order beams.
limitation is due to our use of the effective width S, de- The design principles and theoretical model devel-
finedbyrayopticsandthereforenotstrictlyjustified.In oped here make this new method accessible to anyone
thecaseofchipB,thezerothorderbeampassesthrough who may wish to incorporate such an integrated trap
theMOT,soitisimportantwiththischiptohavealow intoanatomchip.Weanticipatethatthisapproachwill
P . In order to measure this, we rotated the chip by facilitate future quantum technologies using cold and
0
approximately 5mrad to separate the m = 0 diffracted ultra-cold atoms[22].
beam from the incident beam. This measurement gave
P = 0.005(1), in good agreement with 0.007+(20) from
0 −(7) Acknowledgments
Eq. (4).
Becausemagneto-opticaltrappingiscompromisedby The authors acknowledge valuable conversations with
the wrong sense of circular polarisation, we looked for Alastair Sinclair of the National Physical Laboratory.
this in the first-order diffracted beams using a second ThisworkwassupportedbytheUKEPSRC,ESA(through
combination of quarter-wave plate and polarising beam ESTEC project TEC- MME/2009/66), the CEC FP7
splitter, adjusted to project the state of the beam onto (through project 247687; AQUTE). JPC was funded by
the basis of left- and right-handed polarisations. Pho- an EPSRC support fund and VCQ fellowship, P.G. by
todetectors at the two beam splitter outputs measured the Royal Society of Edinburgh and E.H. by the Royal
thepowersP andP ineachcircularpolarisation.The Society.
L R
fraction of power in the desired polarisation from the
threegratingsonChipAwas88%,90%and98%,andwe
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