We report Bose-Einstein condensation of $^{88}$Sr, which has a small,
negative s-wave scattering length ($a_{88}=-2$\,$a_0$). We overcome the poor
evaporative cooling characteristics of this isotope by sympathetic cooling with
$^{87}$Sr atoms. $^{87}$Sr is effective in this role in spite of the fact that
it is a fermion because of the large ground state degeneracy arising from a
nuclear spin of $I=9/2$, which reduces the impact of Pauli blocking of
collisions. We observe a limited number of atoms in the condensate
($N_{max}\approx 10^4$) that is consistent with the value of $a_{88}$ and the
optical dipole trap parameters.Comment: 4 pages, 4 figure

de Escobar, Y. N. Martinez

DeSalvo, B. J.

Killian, T. C.

Mickelson, P. G.

Yan, M.

English

arXiv

We report Bose-Einstein condensation of Sr88, which has a small, negative s-wave scattering length (a88=−2a0). We overcome the poor evaporative cooling characteristics of this isotope by sympathetic cooling with Sr87 atoms. Sr87 is effective in this role despite the fact that it is a fermion because of the large ground-state degeneracy arising from a nuclear spin of I=9/2, which reduces the impact of Pauli blocking of collisions. We observe a limited number of atoms in the condensate (Nmax≈104) that is consistent with the value of a88 and the optical dipole trap parameters

Mickelson, P.G.

Martinez de Escobar, Y.N.

DeSalvo, B.J.

Killian, T.C.

Rice University Research Repository

RAPID COMMUNICATIONSPHYSICAL REVIEW A 81, 051601(R) (2010)Bose-Einstein condensation of 88Sr through sympathetic cooling with 87SrP. G. Mickelson, Y. N. Martinez de Escobar, M. Yan, B. J. DeSalvo, and T. C. KillianRice University, Department of Physics and Astronomy, Houston, Texas 77251, USA(Received 18 March 2010; published 5 May 2010)We report Bose-Einstein condensation of 88Sr, which has a small, negative s-wave scattering length(a88 = −2a0). We overcome the poor evaporative cooling characteristics of this isotope by sympathetic coolingwith 87Sr atoms. 87Sr is effective in this role despite the fact that it is a fermion because of the large ground-statedegeneracy arising from a nuclear spin of I = 9/2, which reduces the impact of Pauli blocking of collisions. Weobserve a limited number of atoms in the condensate (Nmax ≈ 104) that is consistent with the value of a88 and theoptical dipole trap parameters.DOI: 10.1103/PhysRevA.81.051601 PACS number(s): 03.75.Hh, 67.85.HjBose-Einstein condensation of 88Sr has been pursued forover a decade because of the promise of efficient laser coolingto high phase space density using the (5s2) 1S0–(5s5p) 3P1narrow intercombination line [1] and loading of optical dipoletraps that operate at the magic wavelength for this transition[2]. Recent interest in 88Sr has focused on long-coherencetime interferometers [3], optical frequency standards [4,5],and the existence of low-loss optical Feshbach resonances[6,7]. There has also been great interest generally in quantumdegenerate gases of alkaline-earth metal atoms and atoms withsimilar electronic structures because of potential applicationsin quantum computing in optical lattices [8–10] and creationof novel quantum fluids [11].Early attempts to evaporatively cool 88Sr to quantumdegeneracy in an optical dipole trap [2,12] were not successfuldespite initial phase space densities as high as 10−1, presum-ably because of a small elastic scattering cross section. Thiswas confirmed by measurements of the scattering lengths of allstrontium isotopes using photoassociative [13,14] and Fourier-transform [15] spectroscopy of Sr2 molecular potentials,which found that a88 = −2a0, where a0 = 5.29 × 10−11 mis the Bohr radius. Magnetic Feshbach resonances, whichare typically used to overcome poor evaporation properties,do not exist in 88Sr because of its closed-shell ground stateand lack of nuclear spin. Here, we report Bose-Einsteincondensation (BEC) of 88Sr through sympathetic coolingwith 87Sr.Divalent atoms such as strontium and ytterbium [16,17]often possess a large number of stable isotopes, which enablesmass tuning of the s-wave scattering length. For strontium,the stable isotopes and abundances are 88Sr (82.6%),87Sr(7.0%),86Sr (9.9%), and 84Sr (0.6%). In such systems, thelikelihood of finding an isotope with a scattering length thatenables efficient evaporative cooling is very high, as wasrecently demonstrated through the condensation of 84Sr (a84 =123a0) [18,19]. For an isotope that has a poor scattering lengthfor evaporative cooling, there are also numerous opportunitiesto find another isotope that can be used effectively forsympathetic cooling. For 88Sr, the fermionic isotope 87Sris well suited for this role. It has a large and positives-wave scattering length of a87 = 96a0 [14,15] which leads toefficient thermalization and evaporation as long as the systemis not highly polarized. The inter-isotope scattering lengthis reasonable, a88−87 = 55a0 [14,15], so that, in a mixture,collisions with 87Sr will efficiently cool (and evaporate) 88Sr.Dipolar and spin-flip collisional losses are absent because ofthe closed-shell ground state.Bosons are normally used to sympathetically cool fermions[20] rather than the other way around, because identicalfermions suffer from collisional Pauli blocking, which reducesevaporation efficiency in the quantum degenerate regime[21]. For sympathetic cooling with the bosonic isotopes ofstrontium, resonant collisions (a86 = 823a0, a88−84 = 1790a0)[14,15] should lead to large losses due to three-body collisions[12], which make attaining high densities difficult. We do notobserve significant limitations due to Pauli blocking in theexperiments reported here, and we suspect this is because87Sr has a large nuclear spin (I = 9/2) and ground-statedegeneracy. This suppresses the Fermi temperature and allows88Sr to be cooled to high phase space density before Pauliblocking of 87Sr collisions becomes important.Details about our apparatus can be found inRefs. [14,19,25]. Formation of ultracold mixtures of strontiumisotopes benefits from the ability to magnetically trap atomsin the metastable (5s5p) 3P2 state [12,26–28], which has a10-min lifetime [29]. One isotope is trapped from a Zeemanslowed beam in a magneto-optical trap (MOT) operating onthe (5s2) 1S0–(5s5p) 1P1 transition at 461 nm (Fig. 1). Thistransition is not closed and approximately 1 in 105 excitationsresults in an atom decaying through the (5s4d) 1D2 state to the(5s5p) 3P2 state, where it can be trapped in the quadrupolemagnetic field of the MOT. After accumulating a desirednumber of atoms, limited by the loading rate and observed3P2 lifetime of about 25 s, the cooling laser frequency isthen changed to cool and accumulate another isotope. In ourexperiment, we load 88Sr for 3 s and then 87Sr [22] for 30 s.The laser parameters for trapping 88Sr are given in Ref. [26].For trapping 87Sr [27], the laser is approximately 70 MHzred-detuned from the 1S0(F = 9/2)–1P1(F = 11/2) transition(slightly more than 2, where  = 30.5 MHz is the naturallinewidth of the transition [30]).3P2 atoms are returned to the ground state using 60 ms of3 W/cm2 of excitation on the (5s5p) 3P2–(5s4d) 3D2 transi-tion at 3 µm [25]. The isotope shift (f87 − f88 = 110 MHz)[25] is small compared to the ∼500 MHz width of therepumping efficiency curve [31] for 88Sr and the ∼3 GHzwidth of the hyperfine structure in 87Sr [25]. We tune the3 µm laser 1.6 GHz blue-detuned from the 88Sr resonance,1050-2947/2010/81(5)/051601(4) 051601-1 ©2010 The American Physical SocietyRAPID COMMUNICATIONSP. G. MICKELSON et al. PHYSICAL REVIEW A 81, 051601(R) (2010)FIG. 1. (Color online) Partial level diagram for 88Sr (- -) and 87Sr(—) showing hyperfine structure and isotope shifts [22–24]. Totalquantum number F is indicated for 87Sr levels.which optimizes the 87Sr repumping while reducing the 88Srnumber by 80%. This is a reasonable compromise giventhat the number of 87Sr atoms is the limiting factor in theexperiment. The 461 nm MOT is left on at the optimal 87Srdetuning to maximize the number of captured 87Sr atoms,but this is only ∼5 natural linewidths red-detuned of the88Sr 1S0–1P1 transition [22,23], so it also serves to aidrecapture of this isotope. We typically recapture approximately1.1 × 107 88Sr and 3 × 107 87Sr at temperatures of a fewmillikelvin.The 461 nm light is then extinguished and 689 nmlight is applied to drive the (5s2) 1S0–(5s5p) 3P1 transitions(Fig. 1) and create intercombination-line MOTs for eachisotope. The resonance frequencies in each isotope are well-resolved compared to the 7.4 kHz transition linewidth, sothe simultaneous MOTs are compatible with each other. Theparameters of the 1S0–3P1 lasers for 88Sr and 87Sr [31] aresimilar to the conditions in Ref. [1] and Ref. [32], respectively.As many as 70% of the atoms are initially captured inthe intercombination-line MOT. (For experiments with oneisotope, the intercombination-line lasers for the other isotopeare omitted.)After 400 ms of 1S0-3P1 laser cooling, an optical dipoletrap (ODT) consisting of two crossed beams is overlappedfor 100 ms with the intercombination-line MOT with modestpower (3.9 W) per beam. The ODT is formed by a singlebeam derived from a 20 W multimode, 1.06 µm fiber laserthat is recycled through the chamber to produce a trap withequipotentials that are nearly oblate spheroids, with the tightaxis close to vertical. Each beam has a waist of approximatelyw = 90 µm in the trapping region.Immediately after extinction of the 689 nm light, the ODTpower is ramped in 30 ms to 7.5 W to obtain a trap depthof 25 µK. Typically the atom number, temperature, and peakdensity at this point for both 88Sr and 87Sr are 3 × 106, 7 µK,and 2.5 × 1013 cm−3. The peak phase space density (PSD) for88Sr is 10−2.For diagnostics, we record 1S0–1P1 resonant absorptionimages of samples after a time of flight varying from 10to 40 ms. Because of broadening of the resonance due tohyperfine structure, the 87Sr atoms present would contributesignificantly to the absorption when imaging at the 88Sr reso-nance frequency. To remove 87Sr atoms and obtain clean 88SrFIG. 2. (Color online) (A) Temperature evolution in an ODTwith a trap depth of U/kB = 23 µK for samples of 88Sr and87Sr alone and for each in a mixture. The number of eachisotope present initially is approximately 106. (B) Number and(C) temperature for a mixture along a typical forced evaporationtrajectory.images, light resonant with the 1S0(F = 9/2)–3P1(F = 11/2)transition in 87Sr is applied during the first 2 ms of the timeof flight. 87Sr atoms are imaged with linearly polarized lightresonant with the 1S0(F = 9/2)–1P1(F = 11/2) transition,and the contamination due to 88Sr is small and easily accountedfor [31].To investigate the collisional properties of the differentisotopes and the mixture, the evolution of number andtemperature was recorded in a fixed potential [Fig. 2(A)].For 88Sr alone, evaporation is inefficient and a typical ratioof the trap depth to the sample temperature is η ≈ 4, asobserved previously [12]. 87Sr, however, approaches η ≈ 9.Modeling [33] of the free-evaporation trajectory for 87Sr alonesuggests a moderate degree of polarization [31] that will beinvestigated in future studies. The temperatures of 87Sr and88Sr atoms in a mixture with peak densities of 8 × 1012 cm−3track each other closely and approach η ≈ 8, indicating that87Sr provides efficient sympathetic cooling of 88Sr.Figure 2 shows the number (B) and temperature (C) fora typical forced evaporation trajectory with a mixture. Wedecrease the laser power according to P = P0/(1 + t/τ )β +Poffset, with time denoted by t , β = 1.4, and τ = 1.5 s. Thistrajectory without Poffset was designed [34] to yield efficientevaporation when gravity can be neglected. Gravity is asignificant effect in this trap for Sr, and to avoid decreasingthe potential depth too quickly at the end of the evaporation,we set Poffset = 0.7 W, which corresponds to the power atwhich gravity causes the trap depth to be close to zero. Thelifetime of atoms in the ODT is 30 s. This allows efficientevaporation and an increase of PSD by a factor of 100 for aloss of one order of magnitude in the number of atoms. The87Sr and 88Sr remain in equilibrium with each other during051601-2RAPID COMMUNICATIONSBOSE-EINSTEIN CONDENSATION OF 88Sr THROUGH . . . PHYSICAL REVIEW A 81, 051601(R) (2010)FIG. 3. (Color online) Appearance of Bose-Einstein condensa-tion in absorption images (left) and areal density profiles (right). Datacorrespond to 16 ms (bottom) or 22 ms (top three) of free expansionafter indicated evaporation times (t). Images on the left have the sametime stamp as on the right. The areal density profiles are from avertical cut through the center of the atom cloud, and temperaturesare extracted from two-dimensional Bose-Einstein distribution fits tothe thermal pedestal. At 7.5 s, a bimodal distribution is evident,indicative of Bose-Einstein condensation. A pure condensate isshown at 9 s of evaporation. The Maxwell-Boltzmann distributiondoes not accurately describe low-velocity atoms near degeneracy,and the Bose-Einstein distribution does not describe the condensatecontribution. So in these respective regimes, a central region slightlylarger than the condensate radius is excluded from fitting. For bimodaldata, fugacity is constrained to 1.the evaporation. 87Sr atoms are lost at a slightly faster rate, asexpected because essentially every collision involves an 87Sratom.Figure 3 shows false color two-dimensional renderings of(left) and one-dimensional slices through (right) the time-of-flight absorption images recorded after 16 or 22 ms ofexpansion for various points along the evaporation trajectory.At 5 s of evaporation, the distribution is fit well by aMaxwell-Boltzmann distribution, but at 6 s, a Boltzmanndistribution fit to the high-velocity wings clearly underes-timates the number of atoms at low velocity. A fit usingthe Bose-Einstein distribution [35], however, matches thedistribution well. The fugacity obtained from this fit is1.0, indicating this is close to the critical temperature forcondensation. With further evaporation (7.5 s), a narrow peakemerges at low velocity. This bimodal distribution is a clearsignature of the presence of a Bose-Einstein condensate. Apure condensate is observed near the end of the evaporationtrajectory (9 s).At the transition temperature, 2 × 105 87Sr atoms remainat a temperature of 0.2 µK. This corresponds to T/TF =0.9 for an unpolarized sample, which is nondegenerate andabove the point at which Pauli blocking significantly impedesevaporation efficiency [21].1.2 1.3 1.4 1.502000400060008000100001200014000ODT Power [W]Number of Atoms in BEC Data ModelFIG. 4. (Color online) Comparison of observed condensate num-ber and maximum condensate number predicted by a model of thetrapping potential along the evaporation trajectory.88Sr has a negative scattering length, so one expects acollapse of the condensate when the system approaches acritical number of condensed atoms given by [36]Ncr = 0.575 aho|a88| . (1)Here aho = [h̄/(mω)]1/2 is the harmonic oscillator length,where m is the atom mass, h̄ is the reduced Planck constant,and ω = (ωxωyωz)1/3 is the geometric average of the oscillatorfrequencies. One should also see large fluctuations in thenumber of condensed atoms during the evaporation due torepeated collapses and refilling of the condensate. To inves-tigate this, we recorded the condensate number for variouspoints in the evaporation trajectory over many experimentalruns. For absorption images with a condensate and thermalpedestal, we fit the wings of the thermal cloud, which arebeyond the condensate radii of about 23 µm, to a Bosedistribution with fugacity set to 1. The residuals of the fitrepresent the condensate atoms which are fit with the standardThomas-Fermi functional form [19,37] to determine theirnumber.Figure 4 shows the observed condensate number along theevaporation trajectory from 7 to 10 s, as well as the maximumvalues of Ncr predicted by Eq. (1) for a waist of w = 100 µmand a88 = −1.6a0, which are within the uncertainty rangesfor these parameters. Uncertainties in knowledge of the trapbecome larger at low ODT power because of the increasinglyimportant role of gravity, which weakens the trap. Significantvariation in condensate number is seen. A model of the atom ki-netics would be required to make a quantitative statement aboutthe agreement between the observed and the expected numberdistributions.We have described Bose-Einstein condensation of 88Srthrough sympathetic cooling with 87Sr. The observed max-imum number of condensed atoms is consistent with thesmall, negative value of a88. Because of the weak interactions,it should be possible to change the sign of the scatteringlength with an optical Feshbach resonance [6,7] while keepinginduced inelastic losses low. This suggests many possible051601-3RAPID COMMUNICATIONSP. G. MICKELSON et al. 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Bose-Einstein condensation of 88Sr through sympathetic cooling with 87Sr

Bose-Einstein Condensation of $^{88}$Sr Through Sympathetic Cooling with
  $^{87}$Sr

Bose-Einstein Condensation of $^{88}$ Sr Through Sympathetic Cooling with $^{87}$ Sr

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Bose-Einstein Condensation of 88^{88}88Sr Through Sympathetic Cooling with 87^{87}87Sr

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Bose-Einstein Condensation of $^{88}$ Sr Through Sympathetic Cooling with $^{87}$ Sr