Laser cooling to quantum degeneracy

4.6 MB·English

by  Simon Stellmer

Laser cooling to quantum degeneracy
Simon Stellmer,1 Benjamin Pasquiou,1 Rudolf Grimm,1,2 and Florian Schreck1
1Institut fu¨r Quantenoptik und Quanteninformation (IQOQI),
O¨sterreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
2Institut fu¨r Experimentalphysik und Zentrum fu¨r Quantenphysik, Universita¨t Innsbruck, 6020 Innsbruck, Austria
(Dated: January 22, 2013)
WereportonBose-Einsteincondensation(BEC)inagasofstrontiumatoms,usinglasercooling
as the only cooling mechanism. The condensate is formed within a sample that is continuously
Doppler cooled to below 1µK on a narrow-linewidth transition. The critical phase-space density
3 for BEC is reached in a central region of the sample, in which atoms are rendered transparent for
1 lasercoolingphotons. Thedensityinthisregionisenhancedbyanadditionaldipoletrappotential.
0 Thermal equilibrium between the gas in this central region and the surrounding laser cooled part
2 of the cloud is established by elastic collisions. Condensates of up to 105 atoms can be repeatedly
formed on a timescale of 100ms, with prospects for the generation of a continuous atom laser.
n
a
J PACSnumbers: 03.75.Jk,37.10.De

1
2
Lasercoolinghasrevolutionizedcontemporaryatomic assisted inelastic collisions, which lead to loss [17, 18].

and molecular physics in many respects, for example Another is the reabsorption of photons scattered dur-
]
s pushing the precision of clocks by orders of magnitude, ing laser cooling [19], which leads to an effective repul-
a
and enabling ion quantum computation [1]. Since the sion between the atoms and to heating of atoms in the
g
- earlydaysoflasercooling,thequestionhasbeenaskedif lowest energy states. Both effects increase with density
t the quantum degenerate regime could be reached using and make it impossible to reach quantum degeneracy.
n
a this efficient method as the only cooling process. De- For low phase-space density samples, this challenge has
u spite significant experimental and theoretical effort to been overcome by rendering the atoms transparent to
q overcome the limitations of laser cooling this goal has laser cooling photons [20–22] or by decreasing the pho-
.
t been elusive. So far, laser cooling had to be followed by ton scattering rate below the frequency of a confining
a
evaporative cooling to reach quantum degeneracy [2]. trap [5, 7, 23]. It has also been proposed to reduce re-
m
A gas of bosonic atoms with number density n and absorption by dimensional reduction of the sample [7].
-
d temperature T enters the quantum-degenerate regime Thesolutionstothethreechallengesimplementedsofar
n and forms a Bose-Einstein condensate if its phase-space are insufficient to reach quantum degeneracy. The high-
o density nλ3 exceeds a critical value of 2.612. Here, est phase-space densities ever attained are one order of
dB
c λ = h/(2πmk T)1/2 is the thermal de Broglie wave- magnitude too low [14, 24]. Surprisingly, this last order
[ dB B
of magnitude has been an insurmountable obstacle for a
length, where h and k are Planck’s and Boltzmann’s
B
1 constant, respectively, and m is the mass of an atom. decade.
v Since nλ3 ∝nT−3/2, low temperatures in combination InthisLetter,wepresentanexperimenthatovercomes
6 dB
with high densities have to be reached to obtain quan- all three challenges and creates a BEC of strontium by
7
tum degeneracy. Numerous studies, mainly carried out laser cooling. Our scheme is based on the combina-
7
4 in the 1980’s and 90’s, have paved the ground to the tion of three techniques, favored by the properties of
. present state of the art of laser cooling and have identi- this element, and does not rely on evaporation. Stron-
1
fied the limitations of this technique [3]. tiumpossessesatransitionwithsuchanarrowlinewidth
0
3 The longstanding goal of reaching the quantum de- (Γ/2π =7.4kHz) that simple Doppler cooling can reach
1 generate regime by laser cooling [4–8] can be discussed temperatures down to 350nK [14, 25, 26]. Using this
: in terms of three main experimental challenges. First, transition, we prepare a laser cooled sample of 107 84Sr
v
i temperatures in the low microkelvin regime have to be atoms in a large “reservoir” dipole trap. To avoid the
X reached. Only here, quantum degeneracy can be ob- detrimental effects of laser cooling photons, we render
r tained at a density that is low enough to avoid fast de- atoms transparent for these photons in a small spatial
a cayofthegasbymoleculeformation. Thischallengehas regionwithinthelasercooledcloud. Transparencyisin-
beenmetwithseverallasercoolingtechniques,asforex- ducedbyalightshiftontheopticallyexcitedstateofthe
ample Sisyphus cooling [9, 10], velocity selective coher- laser cooling transition. In the region of transparency,
entpopulationtrapping[11],Ramancooling[12],Raman we are able to increase the density of the gas, by accu-
sidebandcooling[13],orDopplercoolingonnarrowlines mulating atoms in an additional, small “dimple” dipole
[14]. The second challenge is the implementation of an trap [15, 16]. Atoms in the dimple thermalize with the
efficient trapping scheme that allows for accumulation reservoir of laser-cooled atoms by elastic collisions and
of atoms at high density in a particular region [15, 16]. form a BEC.
Thethird,andmostseverechallengeistoavoidthedetri- The details of our scheme are shown in Fig. 1. Based
mentaleffectsofthelasercoolingphotons,whichimpede on our previous work [27–29], we use several stages of
the required density increase. One such effect are light- laser cooling to prepare a sample of 84Sr atoms in the
2
(a) “tranbsepaamrency” (b) 3S1 s1h5iGftHonz tbhleue3Pd1etsutanteed,utsointghea“3tPr1an−sp3aSr1entcrya”nslaitsieornb[e3a0m].
This beam propagates downwards under a small angle
688 nm “transparency”
reservoir 4.4 MHz transition of 15◦ to vertical and has a beam waist of 26µm in the
3P plane of the reservoir trap (xy-plane). The beam has a
1 peak intensity of 0.7kW/cm2. It upshifts the 3P state
1
dimple 689 nm cooling by more than 10MHz and also influences the nearest
7.4 kHz transition molecularleveltiedtothe3P statesignificantly[30,31].
z gravity 1
cooling light 1S Related schemes of light-shift engineering were used to
0
y image the density distribution of atoms [32, 33], to im-
x
prove spectroscopy [34], or to enhance loading of dipole
(d)
traps [21, 22]. To demonstrate the effect of the trans-
parency laser beam, we take absorption images of the
(c)
cloud on the laser cooling transition. Figure 1(d) shows
light shift by 0.3 mm
a reference image without the transparency beam. In
“transparency” beam
presence of this laser beam, atoms in the central part of
(e)
the cloud are transparent for the probe beam, as can be
3P
y 1 seen in Fig. 1(e).
g
ner To increase the density of the cloud, a dimple trap
e
is added to the system. It consists of an infrared laser
1S0 (f) beam (wavelength 1065nm) propagating upwards under
reservoir a small angle of 22◦ to vertical and crossing the laser
dimple y cooled cloud in the region of transparency. In the plane
y z x of the reservoir trap, the dimple beam has a waist of
22µm. Thedimpleisrampedtoadepthofk ×2.6µK,
B
Figure1: Schemetoreachquantumdegeneracybylasercool- where it has trap oscillation frequencies of 250Hz in the
ing. (a)Acloudofatomsisconfinedinadeepreservoirdipole horizontal plane. Confinement in the vertical direction
trap and exposed to a single laser cooling beam (red arrow). is only provided by the reservoir trap and results in a
Atoms are rendered transparent by a “transparency” laser vertical trap oscillation frequency of 600Hz. Figure 1(f)
beam (green arrow) and accumulate in a dimple dipole trap shows a demonstration of the dimple trap in absence of
byelasticcollisions. (b)Levelschemeshowingthelasercool- thetransparencybeam. Thedensityintheregionofthe
ing transition and the transparency transition. (c) Potential
dimpleincreasessubstantially. However,withthedimple
experiencedby1S ground-stateatomsandatomsexcitedto
0 alonenoBECisformedbecauseofphotonreabsorption.
the 3P state. The transparency laser induces a light shift
1
on the 3P state, which tunes the atoms out of resonance The combination of the transparency laser beam and
1
with laser cooling photons. (d) to (f) Absorption images of the dimple trap leads to BEC. Starting from the laser
the atomic cloud recorded using the laser cooling transition. cooled cloud held in the reservoir trap, we switch on the
Theimagesshowthecloudfromaboveanddemonstratethe transparency laser beam and ramp the dimple trap to a
effectofthetransparencylaser(e)andthedimple(f). (d)is depth of k ×2.6µK. The potentials of the 1S and 3P
B 0 1
a reference image without these two laser beams.
statesinthissituationareshowninFig.1(c). Atomsac-
cumulateinthedimplewithoutbeingdisturbedbypho-
tonscattering. Elasticcollisionsthermalizeatomsinthe
reservoir trap [30]. The trap consists of an infrared dimple with the laser cooled reservoir. The phase-space
laser beam (wavelength 1065nm) propagating horizon- density in the dimple increases and a BEC emerges.
tally (x-direction). The beam profile is strongly elliptic, WedetecttheBECbytakingabsorptionimages24ms
with a beam waist of 300µm in the horizontal direc- after switching off all laser beams. Figure 2(a) shows
tion (y-direction) and 17µm along the field of gravity themomentumdistribution20msafterswitchingonthe
(z-direction). The depth of the reservoir trap is kept transparency beam, which is well described by a ther-
constant at kB × 9µK. After preparation of the sam- mal distribution. By contrast, we observe that 140ms
ple, another laser cooling stage is performed on the nar- later, an additional, central elliptical feature has devel-
row 1S0−3P1 intercombination line, using a single laser oped; see Fig. 2(b). This is the hallmark of the BEC.
beam propagating vertically upwards. The detuning of Although clearly present, the BEC is not very well visi-
thelasercoolingbeamfromresonanceis∼−2Γandthe bleinFig.2(b),becauseitisshroudedby8×106thermal
peakintensityis0.15µW/cm2,whichis0.05ofthetran- atoms originating from the reservoir. To show the BEC
sition’s saturation intensity. These parameters result in with higher contrast, we have developed a background
a photon scattering rate of ∼ 70s−1. At this point, the reduction technique. We remove the reservoir atoms by
ultracoldgascontains9×106 atomsatatemperatureof an intense flash of light on the 1S −3P transition ap-
0 1
900nK. plied for 10ms. Atoms in the region of transparency
To render the atoms transparent to cooling light in a remain unaffected by this flash. Only 5×105 thermal
centralregionofthelasercooledcloud,weinducealight atoms in the dimple remain and the BEC stands out
3
(a) (b) (c)
18 18 6
-2m)
120
1
y (
sit
n
e
ea d z t = 160 ms
ar y' t = 20 ms t = 160 ms reservoir removed
0 x' 0 0
15 15 2.5
-1m)
90 2.0
110 10
y ( 1.5
sit
n 1.0
de 5 5
ar 0.5
e
n
li 0 0 0.0
-1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0
x' (mm) x' (mm) x' (mm)
Figure 2: Creation of a BEC by laser cooling. Shown are time-of-flight absorption images and integrated density profiles of
theatomiccloudfordifferenttimestafterthetransparencylaserhasbeenswitchedon,recordedafter24msoffreeexpansion.
(a) and (b) The appearance of an elliptic core at t = 160ms indicates the creation of a BEC. (c) Same as in (b), but to
increase the visibility of the BEC, atoms in the reservoir trap were removed before the image was taken. The fits (blue lines)
consistofGaussiandistributionstodescribethethermalbackgroundandanintegratedThomas-Fermidistributiondescribing
theBEC.Theredlinesshowthecomponentofthefitcorrespondingtothethermalbackground. Thex(cid:48)y(cid:48)-planeisrotatedby
45◦ around the z-axis with respect to the xy-plane and the field of view of the absorption images is 2mm × 1.4mm.
clearly; see Fig. 2(c). We use this background reduction k ×15µK for 2ms, which increases the temperature of
B
technique only for demonstration purposes, but not for the dimple gas by a factor two. We follow the evolu-
measuring atom numbers or temperatures. tion of the BEC atom number while the heating pulse is
Quantitative data on our experiment are obtained by applied every 200ms. A new BEC starts forming a few
two-dimensional fits to time-of-flight absorption images 10ms after each heating pulse for more than 30 pulses.
[30]. The atom number of the thermal cloud and of the WefindthattheobserveddecreaseintheBECsizefrom
BEC are extracted from fits to 24-ms expansion images, pulsetopulsestemsfromthereductionofthetotalatom
consisting of Gaussian distributions describing the ther- number in the system.
malbackgroundandanintegratedThomas-Fermidistri- Toclarifytherolelasercoolingplaysinourscheme,we
bution describing the BEC. Further absorption images perform a variation of the experiment. Here, we switch
taken after 4ms expansion time are used to determine off the laser cooling beam before ramping up the dim-
atomnumberandtemperatureofthegasinthereservoir ple and we do not use the transparency beam. Heat
and the dimple, respectively. released while ramping up the dimple or after a heating
We now analyze the dynamics of the system after the pulse is again distributed from the dimple to the whole
transparency laser beam has been switched on. As we system by elastic collisions, but this time not dissipated
increase the dimple strength to its final depth in 10ms, by laser cooling. Since the reservoir gas has a ten times
106 atoms accumulate in it and the temperature of the higher atom number than the dimple gas, the temper-
dimple gas increases; see Figs. 3(a) and (b). During the ature after thermalization is only increased by a small
next∼100msthedimplegasthermalizeswiththereser- amount. If the final temperature in the dimple is below
voir gas by elastic collisions [35, 36]. The temperature the critical temperature, a BEC is formed. This scheme
of the reservoir gas is hereby not increased, since the resembles the formation of a BEC by trap deformation,
energy transferred to it is dissipated by laser cooling. as demonstrated in [15] using a sample of atoms cooled
We carefully check that evaporation is negligible even by evaporation. We test the performance of this BEC
for the highest temperatures of the gas [30]. Already creation scheme again by repeated heating pulses. We
after 60ms a BEC is detected. Its atom number satu- can detect a BEC after at most five pulses. For more
rates at 1.1×105 after 150ms, as shown in Fig. 3(c). pulses,thetemperatureofthegasinthedimpleremains
Theatomnumberinthereservoirdecreasesslightly, ini- toohightoallowtheformationofaBEC.Thispoorbe-
tiallybecauseofmigrationintothedimpleandonlonger havior stands in stark contrast to the resilience of BEC
timescales because of light assisted loss processes in the formation to heating, if the system is continuously laser
laser cooled cloud. cooled.
Todemonstratethepowerofourlasercoolingscheme, The ability to reach the quantum degenerate regime
werepeatedlydestroytheBECandletitreform(Fig.4). by laser cooling has many exciting prospects. This
To destroy the BEC, we pulse the dimple trap depth to methodcanbeappliedtoanyelementpossessingalaser
4
1.2
(a)
1.0 30) 100
6mber (10) 00..68 x 1/10 number (1 6800
atom nu 00..24 dreimseprlveoir BEC atom 2400
0.0 0
(b) 0 200 400 600 3000 3200 3400
2.0 heating time (ms)
µK) pulse # 1 # 2 # 3 # 4 # 16 # 17 # 18
e ( 1.5
ur
at Figure4: RepeateddestructionandreformationoftheBEC.
per 1.0 ShownistheevolutionofBECatomnumberwhiletheBEC
m
e isdestroyedevery200ms(arrows)bysuddenlyincreasingthe
t 0.5
depth of the dimple trap. If the system is laser cooled, the
BEC atom number quickly increases again, which is shown
0.0
(c) here for up to 18 cycles (red circles). Without laser cooling,
30) 120 aBECisdetectableforatmostfiveheatingcycles, ofwhich
1
er ( 100 the first three are shown here (blue squares).
b
m 80
u
n
m 60
o
C at 40 We thank Matteo Zaccanti for careful reading of the
E
B 20 manuscript. We gratefully acknowledge support from
theAustrianMinistryofScienceandResearch(BMWF)
0
0 50 100 150 200 250 andtheAustrianScienceFund(FWF)throughaSTART
time (ms) grant under Project No. Y507-N20. As member of the
project iSense, we also acknowledge financial support of
Figure 3: Characterization of the BEC formation process the Future and Emerging Technologies (FET) program
after the transparency laser is switched on. Shown are the withintheSeventhFrameworkProgrammeforResearch
evolutionoftheatomnumberinthedimpleandthereservoir of the European Commission, under FET-Open grant
(a), the evolution of temperature in these regions (b) and No. 250072.
the BEC atom number (c). During the first 10ms of this
evolution,thedimpletrapisrampedon. After60msaBEC
is detected.
cooling transition with a linewidth in the kHz range
and suitable collision properties. Besides strontium this
encompasses several lanthanides [37, 38]. The technique
can also cool fermions to quantum degeneracy and it
can be extended to sympathetic cooling in mixtures
of isotopes or elements. Another tantalizing prospect
enabledbyvariationsofourtechniques,istherealization
of a continuous atom laser, which converts a thermal
beam into a laser-like beam of atoms. To realize such a
device, our scheme needs to be extended in two ways.
First, the reservoir of laser cooled atoms needs to be
replenished, for example by sending a thermal beam
of atoms onto a part of the reservoir with sufficiently
high cooling laser intensity to allow capture of these
atoms. Second, a continuous beam of condensed atoms
needs to be outcoupled. Using magnetic species such
as dysprosium or erbium, outcoupling from the BEC
is possible by changing the internal state and thereby
the magnetic force on the atoms [39, 40]. Alternatively,
the reservoir can be connected to an outcoupling dipole
trap, creating a narrow channel where atoms can escape
without further interaction with the cooling light [41].
5
Supplemental Material sity I = πhcΓ /3λ3 = 40.7mW/cm2. The
sat,blue blue blue
detuning of the MOT light to resonance is −30MHz.
Metastable state reservoir — The blue MOT cy-
This Supplemental Material contains in-depth infor-
cle is not completely closed, as atoms in the excited 1P
1
mation about our approach to reach quantum degener-
state can decay into the metastable and magnetic 3P
2
acy by laser cooling. In Sec. I we give details on the ex-
state with a branching ratio of 1:150000. Atoms in this
perimentalsequence. InSec.IIwediscusstheparameter
state can be trapped in the quadrupole magnetic field
dependenceofBECcreationandpropertiesoftheBEC.
of the MOT. Since the lifetime of magnetically trapped
In Sec. III we show that evaporative cooling does not
3P -state atoms of ∼ 30s is about three orders of mag-
2
play a role in reaching quantum degeneracy. In Sec. IV
nitude longer than the leak time scale of the blue MOT,
we analyze the shifting of atomic and molecular transi-
metastablestateatomsaccumulateinthemagnetictrap.
tionsbythetransparencybeam. InSec.Vwemodelthe
We operate the MOT until about 108 atoms are accu-
density distributions of the BEC and the thermal cloud.
mulatedinthis“metastablestatereservoir”,whichtakes
∼10s. This accumulation of atoms allows us to use the
84Sr isotope, despite its low natural abundance.
I. EXPERIMENTAL SEQUENCE Red MOT — To increase the phase-space density
of the sample, we use a narrow-line “red” MOT op-
In the following, we discuss in detail the experimental erated on the 1S0 − 3P1 intercombination line, which
sequencewithwhichweobtainBECbylasercooling. We has a wavelength of λred = 689nm and a linewidth of
first describe the preparation of a sample of ultracold Γred/2π = 7.4kHz. Our red MOT laser has a linewidth
84Sr atoms in the reservoir dipole trap, which follows of about 2kHz and an absolute stability better than
closely the procedure used in our previous work [27–29]. 500Hz. The horizontal (upward, downward propagat-
Then we give details on the additional steps we take to ing) red MOT beams have a waist of 3.1mm (2.9mm,
produce a BEC. These details include information on 3.1mm). The Doppler temperature of the red MOT
the transparency beam, the dimple dipole trap and the TD,red = 180nK is comparable to the recoil tempera-
conditionsofthefinallasercoolingstage. Weendwitha ture Tr = (cid:126)2k2/(kBm) = 460nK, where k = 2π/λred is
discussion of our data acquisition and analysis method. thewavevectorofthecoolinglight, andmistheatom’s
mass. The temperature can approach T /2 when reduc-
r
ing the cooling light intensity to the saturation inten-
sity I =3µW/cm2 [25]. Not only the temperature
A. Sample preparation sat,red
but also the atom number decreases, when decreasing
the cooling light intensity, and a compromise between
Isotope choice — Of the three bosonic strontium
atom number and temperature has to be chosen. We
isotopes, 84Sr is best suited for our experiment, since its
typically reach temperatures of 800nK with samples of
scattering length of a84 = 124a0 (with a0 the Bohr ra- about 107atoms.
dius) allows efficient thermalization by elastic collisions.
The other bosonic isotopes are unsuitable for our task.
88Sr has a negligible scattering length of a = −1.4a J
88 0 3
and therefore does not thermalize. 86Sr suffers from 2
1
three-body inelastic loss because of a very large scat- 15 GHz 3DJ
teringlengtha =800a . Unfortunately84Srhasalow
86 0
naturalabundanceofonly0.56%. Toobtainalargesam- 3S
1
ple,weaccumulatemetastablestateatomsinamagnetic repump
497 nm
trap, as described below. transparency 2.3 MHz
688 nm
Atomic beam and blue MOT — A sample of 1P 4.4 MHz
strontium metal with natural isotopic composition is 1 1D2
heated in an oven under vacuum to about 600◦C in J
2
order to sublimate strontium atoms. The atoms form 1
an atomic beam after escaping the oven through a bun- b4l6u1e nMmOT 3PJ 0
dle of microtubes. 84Sr atoms in the atomic beam are 30.5 MHz
transversally cooled, Zeeman-slowed, and captured in
red MOT
a “blue” magneto-optical trap (MOT) with laser light 689 nm
red-detuned to the 1S −1P transition at 461nm; see 7.4 kHz
0 1
Fig. S1. This transition has a linewidth of Γ /2π =
blue
30.5MHz, corresponding to a Doppler temperature of 1S0
TD,blue = (cid:126)Γblue/(2kB) = 720µK. The MOT uses a singlet states triplet states
quadrupole magnetic field with vertically oriented axis
and a vertical field gradient of 55G/cm. The MOT FigureS1: Levelschemeofstrontiumwithallrelevantstates
beams have waists of 5mm and peak intensities of and transitions. The dotted arrows show the decay path of
10mW/cm2, which is a quarter of the saturation inten- atoms from the 1P1 state into the 3P2 state.
6
To load the red MOT, metastable state atoms are arepulledtowardsthelowerpartofanellipsoidofequal
transferred into the 1S ground state by optical pump- magneticfieldmagnitudelocatedaroundthequadrupole
0
ingviathe5s5d3D state. Thetemperatureofthesam- magnetic field center. On this ellipsoid, the atoms are
2
ple recovered from the metastable state reservoir is on in resonance with the cooling light and levitated by it,
the order of the Doppler temperature of the blue MOT, giving the MOT a pancake shape, roughly matched by
T = 720µK, which is three orders of magnitude the shape of the reservoir dipole trap. The dipole trap
D,blue
higher than the final temperature reached with the red is located 600(100)µm below the center of quadrupole
MOT. We initially use red MOT parameters that allow field, where the B-field has a magnitude of 75(10)mG
to capture such a high temperature sample and then and is oriented nearly vertically. To overlap the MOT
ramp these parameters to conditions in which a high with the dipole trap, we carefully adjust the MOT laser
phase space density is reached. The intensity and fre- detuning. Figures S2(c) and (d) show the temperature
quency of the MOT light during the capture phase and and atom number evolution of the atomic cloud, while
the subsequent ramps are given in Figs. S2(a) and (b). it is loaded into the reservoir dipole trap. At the end-
Duringthecapturephase, theredMOTlaserbeamsare point of the ramp, the intensities of the horizontal (up-
frequency-modulated to increase the capture velocity of ward, downward propagating) MOT beams are 0.6I
sat
the MOT. In addition, the quadrupole magnetic field (0.5I ,0I ). Thedetuningfromtheσ+-coolingtran-
sat sat
gradient is suddenly lowered to 1.15(5)G/cm in the ver- sitionisabout−20kHz. Withthegivennon-zeroB-field
tical direction, which increases the capture volume, and atthepositionoftheatoms,thiscorrespondstoadetun-
then maintained at this value for the remainder of the ingofabout150kHzfromtheunperturbedπ-transition.
experimental sequence. The detuning of the MOT light Laser cooling of the atoms in the dipole trap is influ-
is reduced to compress the atomic cloud, and the inten- enced by Zeeman and light shifts. The vertical gradient
sity is reduced to lower the temperature. This provides of 1.15G/cm translates to a negligible shift of 600µG
optimal conditions for loading the reservoir dipole trap. acrossthesample,assuminganestimatedverticalsizeof
Reservoir dipole trap — The reservoir dipole trap 5µm. Thehorizontalgradientis0.63G/cm,andthehor-
is a large-volume dipole trap consisting of a horizon- izontalradiusofthecloudisratherlarge: about200µm,
tally propagating beam. This beam is derived from a giving a shift of 12mG between the center and the out-
5-W fiber laser operating at a wavelength of 1065nm sides, which corresponds to a significant frequency shift
with a linewidth of 0.5nm (IPG ytterbium fiber laser, of 25kHz. The dipole trap induces a non-negligible dif-
model YLD-5-1064-LP). The beam contains up to 2W ferential AC Stark shift on the 1S0 and 3P1 states. We
of power and is linearly polarized in the vertical direc- canreducethisshiftbychoosingtheoptimizedpolariza-
tion. Cylindrical lenses are used to create a horizon- tions for the horizontal and vertical dipole trap beams
tally elongated beam profile. The beam has a vertical mentioned above, such that the magnitude of the shift
(horizontal) waist of 17.3(2)µm (298(3)µm), yielding is about 10kHz [26]. Assuming that the atoms explore
an aspect ratio of about 1:17. The trap frequencies are one tenth of the trap depth, we obtain a shift across the
600(6)Hz (35.3(4)Hz, 5.78(6)Hz) in the vertical (trans- sample of about 1kHz, which is negligible.
verse horizontal, axial horizontal) direction at a power About 9 × 106 atoms are captured in the reservoir
of 1760(35)mW as used in the experiment. Including dipole trap at a temperature of 830nK. The achievable
gravitationalsagging, thepotentialdepthinthevertical temperature is density-dependent. A reduction of the
directionis∼k ×9µK.Theerrorsgivenherearedomi- atom number by a factor two leads to a temperature re-
B
natedbytheuncertaintyinthemeasurementofthelaser duction of ∼ 100nK. Over the course of one hour, the
beam powers, which we assume to be 2%. The uncer- variationofatomnumberbetweenexperimentalcyclesis
taintyinthetraposcillationfrequenciesismuchsmaller, about1%,andthetemperaturevariationisbelow10nK.
andothereffects,suchastransmissionlossesoftheglass After loading of the dipole trap, the intensity of the up-
cell and gravitational sagging in the dipole trap, are ac- ward cooling beam is reduced by a factor of 10, and
counted for. the horizontal beams are turned off. Such a sample is
the starting point for the subsequent laser cooling into
We increase the axial frequency slightly by a sec-
quantum degeneracy.
ond, near-vertical beam with 297(3)µm waist and cir-
cular polarization, using a second fiberlaser of the same
modelasmentionedabove. Atthepowerof740(15)mW
used in the experiment, it has a trap depth of only B. Transparency beam
k ×0.29(1)µK and increases the trap frequency in the
B
x-direction to 8.14(8)Hz. This increased axial trap fre-
Immediately after completion of the dipole trap load-
quency slightly increases the density of the sample and
ing, the transparency beam is turned on. This beam is
reduces the timescale of BEC formation. It has no fur-
derivedfromafree-runningmasterdiodelaserwithafre-
ther effects, and otherwise identical results are obtained
quencystabilityoforder100MHz/day. Thefrequencyis
without this additional beam. blue detuned by 15GHz from the 3P −3S transition,
1 1
Loading of the reservoir dipole trap — When and constantly monitored by a wavemeter. The beam is
the intensity of the MOT beams is low, gravity plays circularly polarized and focused onto the center of the
an important role in the MOT dynamics. The atoms atomic cloud with a waist of 26.2(3)µm, again calcu-
7
(a) (b)
7
0
MOT I MOT II MOT III MOT IV MOT V
6 horizontal -1
upward 0
5 downward -2 kHz) -20
3 intensity (10I)sat 234 intensity (I)sat1024680 detuning (MHz) ---543 detuning ( -1---0864-0000150 -100time (-m50s) 0
-150 -100 -50 0 -6
1 time (ms)
-7
0
-8
-600 -500 -400 -300 -200 -100 0 -600 -500 -400 -300 -200 -100 0
time (ms) time (ms)
(c) (d)
18 1600
16
1400
14
1200
6er (10) 12 e (nK) 1000
m numb 108 mperatur 800
ato 6 te 600
400
4
2 200
0 0
-250 -200 -150 -100 -50 0 -250 -200 -150 -100 -50 0
time (ms) time (ms)
Figure S2: Narrow-line MOT and dipole trap loading. The narrow-line cooling consists of five consecutive stages, labeled
MOT I through V: a 50-ms capture MOT, during which the repumping of atoms from the 3P to the 1S state takes place,
2 0
a compression MOT of 100ms, two cooling MOT stages of 100ms and 250ms, and a 100-ms hold time at final parameters.
TheendoftheMOTphaseischosenastheoriginofthetimeaxis. (a)IntensityoftheMOTbeamsinunitsofthesaturation
intensity I = 3µW/cm2. The intensity of the horizontal, upward, and downward MOT beams can be set independently.
sat
The downward MOT beam has little effect and is turned off before the other ones (see inset). (b) Frequency of the MOT
beams, given as detuning from the Zeeman-shifted σ+ transition. The light is frequency-modulated in the first two MOT
stages. For clarity, only every tenth line of the resulting frequency comb is shown here. Atom number (c) and temperature
(d)dropsignificantlyduringtheendofMOTstageIV.ThedropinatomnumberhappensastherestoringforceoftheMOT
becomes too weak to support atoms against gravity, and all atoms outside the dipole trap are lost. The last 100ms of hold
time do not reduce the temperature further, but this stage is crucial to increase the density of atoms in the dipole trap.
lated from trap frequency measurements. The power at the center of the transparency beam. In this way,
used is 7.5(2)mW, translating to a peak intensity of atoms illuminated by the transparency beam are trans-
7×105mW/cm2 = 7MW/m2. The beam propagates parent to laser cooling photons. Note that this scheme
downwards,atanangleof15◦ toverticalduetogeomet- is drastically different to a scenario in which the cool-
rical restrictions. ing beam would contain a small dark spot imaged onto
the dimple region: in this case, atoms in the dimple re-
The transparency beam has a strong influence on the
gion could still absorb cooling light scattered by atoms
3P state. ThedifferentialACStarkshiftofthe1S −3P
1 0 1 in the reservoir. Our method differs also from the dark
cooling transition is on the order of +10MHz, such that
spot MOT technique, since we do not change the inter-
thecoolinglightisred-detunedby>1000Γ foratoms
red
8
TableSI:ParametersofthedipoletrapbeamsusedfortheexperimentsdescribedintheLetter. Gravitationalsaggingistaken
into account in the calculation of the horizontal dipole trap depth.
beam waist x waist y waist z P U/k f f f
B x y z
(µm) (µm) (µm) (mW) (µK) (Hz) (Hz) (Hz)
horizontal 298(3) 17.3(2) 1760(35) 9.2(2) 5.78(6) 35.3(4) 600(6)
vertical 297(3) 297(3) 740(15) 0.29(1) 5.73(6) 5.73(6) ∼0
dimple 22.4(2) 22.4(2) 38.3(8) 2.6(1) 228(2) 228(2) ∼0
nal state of the atom in the region of transparency. A 0.15µK at the beginning of the experimental sequence
careful analysis of the magnitude of the AC Stark shift and ramped in 10ms to a depth of k × 2.6µK after
B
of the 3P state is given in Sec. IV. the transparency beam is switched on. The ramp speed
1
The transparency beam also creates an attractive is not adiabatic with respect to the horizontal trap fre-
trapping potential for the 1S state with a depth of quenciesofthereservoirtrap, andatomsfromthereser-
0
k × 0.5µK. Because of similar beam orientation and voircontinuetoaccumulateinthedimplefor10msafter
B
waists, the potential created by the transparency beam the ramp. At this point, the temperature of the gas in
resemblesthepotentialcreatedbythedimplebeam,but the dimple is twice the temperature of the reservoir gas.
has only about 20% of its depth. Thermal contact with the laser-cooled reservoir lowers
the temperature on a timescale of ∼100ms. In thermal
equilibrium, the dimple leads to a peak density increase
C. Cooling light byafactorof30comparedtothereservoir. Thisdensity
increase is the origin of the gain in phase-space density.
The BEC phase transition is observed 50ms after
The cooling light consists of an upward propagating,
ramping the dimple to high power. The BEC grows
circularly polarized beam, red detuned by about 15kHz
fromtheσ+1S −3P transition. Ithasapowerof20nW to slightly more than 105atoms after another 100ms.
0 1
and a peak intensity of 0.15µW/cm2, corresponding to ThelocalharmonicpotentialconfiningtheBECisdom-
inated horizontally by the dimple trap and vertically
0.05I . Thelighthasthesamesourceasthelightused
sat
by the horizontal dipole trap, leading to trap frequen-
forthenarrow-lineMOT.Anydesiredcoolingrateofup
cies of 228(2)Hz in the horizontal plane and 600(6)Hz
tomany100nK/mscanbeachievedbyasuitablecombi-
in the vertical direction. The BEC is pancake-shaped
nationofdetuningandintensity,wherealargerdetuning
withahorizontal(vertical)Thomas-Fermiradiusof5µm
can be compensated by an increased intensity. We find
(2µm).
a fixed relation between cooling rate and induced decay
rate, whichisindependentonthecombinationofdetun-
ing and intensity. There is a lower temperature limit
of about 450nK, below which cooling is accompanied E. Absorption imaging and data analysis
by rapidly increasing loss rates. For the experiments
described in the Letter, we use only one upward prop-
We use time-of-flight absorption images to deduce all
agating cooling beam, and we find that the addition of
relevant information from our atomic samples. We are
furthercoolingbeamsfromotherdirectionsdoesnotim-
interested in the following quantities: atom number in
prove the performance.
thedimpleandinthereservoir, temperatureofthedim-
ple and of the reservoir, and number of atoms in the
condensate.
D. Dimple The temperature and atom number of the dimple
and reservoir regions are measured in absorption images
The local increase in density is facilitated by the dim- taken after 4ms of free expansion; see Fig. S3(a). After
ple beam. This beam is aligned almost vertically, with this short time, the clouds from the two regions can still
an angle of 22◦ (37◦) towards vertical (the transparency be clearly distinguished in the horizontal direction (x(cid:48)-
beam)duetogeometricalrestrictions. Itisderivedfrom direction), but have expanded well beyond their initial
thesamelasersourceastheverticaldipoletrap,hascir- size in the vertical direction (z-direction) to allow ther-
cular polarization and a waist of 22.4(2)µm. The dim- mometry. Since the atomic clouds are very dense and
ple beam is centered in the plane of the reservoir trap nearly opaque to resonant imaging light, we image at a
withthetransparencybeamtowithin5µm. Atapower detuning of 48MHz ≈ 1.5Γ, which reduces the absorp-
of 38.3(8)mW, the dimple provides horizontal trap fre- tion cross section by a factor of about 12. We employ a
quenciesof228(2)Hzandhasnegligibletrapfrequencies 2D double-Gaussian fit to the data. The temperature is
in the vertical direction. In presence of the dimple, we derived from the vertical expansion only.
referonlytotheregionoutsideofthedimpleasthereser- The overall atom number and the BEC atom number
voir. aredeterminedfromabsorptionimagestakenafterafree
The dimple trap is set to a small depth of k × expansion time of 24ms; see Fig. S3(b). We fit the data
B
9
(a) (b) dependence of the total atom number N, at these low-
300 18
-2m) est achievable temperatures. We find that NBEC ∝ N.
120 This behavior can be explained by the model described
1
ensity ( inTSreca.pV.depth — We independently vary the trap
ea d z depth of horizontal beam and dimple around the val-
ar 0 y' x' tex = 4 ms 0 tex = 24 ms ues presented in the Letter. A variation in trap depth
15 of the horizontal beam by a factor of 1.7 changes the
-1m) 30 BEC atom number by at most 15%, and a variation of
9nsity (10 212055 10 dbiemrpblye aptowmeorsbty30a%fa.ctAorborofa2d.5, gchloabnaglems tahxeimautommonfutmhe-
de 10 5 BEC atom number exists, which is where we perform
near 5 our experiments.
li 0 0 An important constraint on the trap depth is the de-
-1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0
x' (mm) x' (mm) sire to avoid evaporation. This constraint is fulfilled by
the conditions chosen; see Sec. III for details.
FigureS3: Typicalabsorptionimagesusedtodeterminetem-
Dimple — We find that the BEC atom number de-
peratures and atom numbers. (a) Absorption image after a
pendsonlyweaklyonthedimplesize. Wevarythewaist
short expansion time t =4ms. A two-dimensional double-
ex
of the dimple beam between 20 and 50µm, but find no
Gaussian fit is used to extract atom number and tempera-
ture individually for dimple and reservoir. (b) Absorption appreciablechangeinBECatomnumber. TheBECfor-
image after a long expansion time t = 24ms. A tri-modal mation time, however, is increased for larger waists. We
ex
two-dimensional fit, consisting of two Gaussians and an in- alsovarytheramp-uptimeofthedimplebetween0and
tegrated Thomas-Fermi distribution, are used to extract the 100ms, but find no influence on temperature or BEC
atom number of the thermal component and the BEC. The atom number after a 250-ms equilibration time.
panels below the absorption images show the density distri-
bution integrated along the z-direction (black) and the fits
(blue). Theredcurvesshowthecontributionsofthereservoir
B. Transparency beam
(a) and of the thermal component (b).
Thetransparencybeamisthekeynoveltyofourwork.
with a 2D distribution consisting of two Gaussians for A detailed study of the non-trivial shifting of the laser
thethermalatomsandanintegratedThomas-Fermidis- cooling transition can be found in Sec. IV.
tributions for the BEC. Two Gaussians are used to take Frequency — The transparency beam is employed
into account the two different sources of thermal atoms, to locally shift the energy of the 3P state by about
1
the reservoir and the dimple. If only one Gaussian is +10MHz. This wouldinprinciplebepossiblewithlight
employed to describe all thermal atoms, the BEC atom blue-detuned to any transition originating from the 3P
1
number deduced from the Thomas-Fermi part of the fit state. We chose to work in the vicinity of the 3P −3S
1 1
increases by about 50%. transition at 688nm for two reasons: The availability
All measurements are performed three times, and the of diode lasers, and the negligible influence on the 1S0
averagevaluesandstatisticalerrorbarsofatomnumber state.
andtemperaturearegiveninFigs.3and4oftheLetter. In our experiment, the transparency beam is blue-
detunedbyabout15GHzfromthe3P −3S transition.
1 1
In a series of measurements, we set the detuning to dif-
ferent values and vary the intensity of the transparency
II. CHARACTERIZATION OF LASER-COOLED
beam while searching for the appearance of a BEC. We
BECS
never observe BEC formation for frequencies around or
red-detuned to the 3P − 3S transition. We observe
The BEC formation depends on various parameters. 1 1
BEC formation only in a frequency range between 6
In this section, we will explore the influence of these
and 30GHz blue detuning, where the upper bound of
parameters on the system and show that our method
30GHz is probably limited by the available laser power
of laser cooling to quantum degeneracy works in a very
of 10mW.
broad range of parameters.
Intensity — We observe the formation of a BEC
only above a certain critical intensity I of the trans-
c
parency beam, which depends on its frequency. The
A. BEC atom number BEC atom number quickly grows for larger intensities,
and saturates at about 2I . The experiment is per-
c
Total atom number and temperature — The formedataround10I ,correspondingtoapeakintensity
c
lowestachievabletemperaturedependsonthetotalatom of 0.7kW/cm2.
number in the system as a consequence of red MOT dy- Spectral filtering — The 3P − 3S transition is
1 1
namics. We measure the BEC atom number N in 1.428nm (or 902GHz or 30cm−1) away from the 1S −
BEC 0
10
3P intercombinationtransition,andoff-resonantexcita- find that the timescale required to accumulate atoms in
1
tionoftheintercombinationtransitionisnegligible. The thedimpleismuchshorterthanthetimescalerequiredto
light originating from the laser diode, however, contains thermalize the dimple gas with the reservoir; see Fig. 3.
incoherentfluorescencelight,alsoknownasresidualam- Thus,theBECformationtimeislimitedbythethermal-
plified spontaneous emission (ASE). This light covers a izationtimescale. Thistimescaleislinkedtotheelastic
broadspectrumwithawidthofabout20THz,whichin- collision rate, which depends on the density of the sam-
cludes the 1S −3P transition. A spectrometer is used ple. To test this relation, we vary the density by two
0 1
to estimate the spectral power of the incoherent back- means, changing the reservoir atom number and chang-
ground P to be on the order of 10−12P in a 1kHz ing the reservoir trap frequency. We observe an increase
ASE 0
wideband1THzawayfromthelaserline,whereP isthe informationtimeaswedecreasetheatomnumber,down
0
power in the laser line. The scattering of these incoher- to a minimum atom number of about 1×106atoms, be-
ent photonslimits the lifetime ofa BECto 800ms when low which no BEC forms in our trap geometry. Using
illuminated by unfiltered transparency light. Spectral the trap parameters of the experiment described in the
filtering of the light allows us to reduce the amount of Letter, the fastest formation time is about 50ms for the
resonantlightbyafactorof500, leadingtoanincreased maximum achievable atom number of 10×106. An in-
lifetime of 10s. The lifetime measurement is performed crease of the axial frequency from 8Hz to 40Hz reduces
withapureBECobtainedbystandardevaporation,and the formation time to about 20ms. The timescale of
its lifetime is limited to 10s by inelastic collisions. BEC formation (following abrupt changes of the ther-
Waist — The transparency beam needs to be well- mal distribution) was studied in previous experiments
aligned with the dimple beam, and it needs to cover the [35, 36] and found to depend on the scattering rate, in
BEC entirely. We vary the waist of the transparency agreement with our measurements.
beambetween10and55µm. Forcomparison,thedimple Reservoir lifetime — A sample of 9×106 atoms at
waistis22µmandtheThomas-FermiradiusoftheBEC 800nK confined in the horizontal dipole trap has a life-
in the xy-plane is 5µm. Given an appropriate adjust- time of ∼30s. When adding the dimple beam to obtain
ment of the intensity, we can create laser-cooled BECs settings identical to the ones used in the experiment de-
within the entire range of transparency beam waists ex- scribed in the Letter, the lifetime is reduced to 3.4(1)s.
amined. The purification method described in Fig. 2(c), Webelievethatthislifetimeismainlylimitedby3-body
duringwhichreservoiratomsareselectivelyremoved,be- collisionsinthedimpleregion,asthereservoirconstantly
comes increasingly inefficient for larger beam sizes, as replenishes the dimple population. The cooling light in-
also parts of the reservoir are shielded. A larger beam duces an additional decay, which is strongly dependent
sizemakesthesysteminsensitivetomisalignmentsofthe on intensity and detuning. For the values used in the
beams, which we verify experimentally. experiment, the lifetime of the reservoir is reduced to
Localdensityincrease—Onemightspeculatethat about 2.5s.
thetransparencybeamleadstoanincreaseinatomden-
BEC lifetime —Weobservethatthelifetimeofour
sity purely by elimination of photon emission and re-
BEC is linked to the lifetime of the reservoir gas. The
absorption cycles, which act as an effective repulsion.
reasonisthatanyatomlossfromtheBECisquicklyand
This is not the case. We do observe a small density in-
continuously replaced by atoms from the reservoir. A
crease induced by the transparency beam, but it can be
BEC exists as long as the total atom number in the sys-
explained entirely by its trapping potential for atoms in tem is above ∼106 atoms. In order to measure the bare
the 1S state.
0 lifetime of the BEC without constant replenishment, we
create a BEC, remove the atoms in the reservoir, and
turn off the cooling light and the transparency light.
C. Timescales The lifetime of this BEC is 1.0(1)s, probably limited
by heating and loss resulting from inelastic 3-body colli-
sions. The same result is obtained for an identical BEC
Collision rate and thermalization — The peak
created by conventional evaporation and re-compressed
scattering rate of thermal atoms in the dimple region is
3100s−1, foundattheedgeoftheBEC(seeSec.V).The into the dimple. By contrast, the lifetime of a BEC in
presenceofthereservoir,thetransparencylight,andthe
scatteringratedecreaseswithdistancefromthecenterof
the dimple, down to 50s−1 outside of the dimple region. coolinglightcorrespondstothereservoirlifetimeof2.5s.
We observe that thermalization happens on a timescale Performance of the transparency beam — The
ofabout100ms,whichcorrespondstoabout5collisions; transparencybeamisabsolutelynecessarytoprotectthe
compare Fig. 3(b). This number matches well with the BEC from destruction by the cooling light. With the
expectationofabout3collisionsrequiredforthermaliza- transparency beam turned off and the BEC subjected
tion. to cooling light, we measure a decay rate of about 1ms,
BECformationtime—Westudythetimerequired and the BEC is completely destroyed in less than 3ms.
for the BEC to form after the dimple has been ramped To demonstrate the ability of the transparency light
up. For a BEC to be created, the atom number in the to protect the BEC from resonant photons, we measure
dimplehastobehighenoughandthetemperaturebelow the lifetime of a BEC after removal of the reservoir and
a critical temperature for the given atom number. We inpresenceorabsenceofboth,thetransparencyandthe