We report the realization of a novel degenerate Fermi mixture with an
SU(2)*SU(6) symmetry in a cold atomic gas. We successfully cool the mixture of
the two fermionic isotopes of ytterbium 171Yb with the nuclear spin I=1/2 and
173Yb with I=5/2 below the Fermi temperature T_ F as 0.46T_F for 171Yb and
0.54T_F for 173Yb. The same scattering lengths for different spin components
make this mixture featured with the novel SU(2)*SU(6) symmetry. The nuclear
spin components are separately imaged by exploiting an optical Stern-Gerlach
effect. In addition, the mixture is loaded into a 3D optical lattice to
implement the SU(2)*SU(6) Hubbard model. This mixture will open the door to the
study of novel quantum phases such as a spinor Bardeen-Cooper-Schrieffer-like
fermionic superfluid.Comment: 4 pages, 5 figures V2: revised reference

Murakami, Ryo

Sugawa, Seiji

Taie, Shintaro

Takahashi, Yoshiro

Takasu, Yosuke

Tsujimoto, Takuya

Yamazaki, Rekishu

English

arXiv

We report the realization of a novel degenerate Fermi mixture with an SU(2)×SU(6) symmetry in a cold atomic gas. We successfully cool the mixture of the two fermionic isotopes of ytterbium 171Yb with the nuclear spin I=1/2 and 173Yb with I=5/2 below the Fermi temperature T_{F} as 0.46TF for 171Yb and 0.54TF for 173Yb. The same scattering lengths for different spin components make this mixture featured with the novel SU(2)×SU(6) symmetry. The nuclear spin components are separately imaged by exploiting an optical Stern-Gerlach effect. In addition, the mixture is loaded into a 3D optical lattice to implement the SU(2)×SU(6) Hubbard model. This mixture will open the door to the study of novel quantum phases such as a spinor Bardeen-Cooper-Schrieffer-like fermionic superfluid

Kyoto University Research Information Repository

TitleRealization of a SU(2)×SU(6) system of fermions in a coldatomic gas.Author(s)Taie, Shintaro; Takasu, Yosuke; Sugawa, Seiji; Yamazaki,Rekishu; Tsujimoto, Takuya; Murakami, Ryo; Takahashi,YoshiroCitationPhysical review letters (2010), 105(19)Issue Date2010-11-01URL http://hdl.handle.net/2433/201983Right© 2010 The American Physical SocietyType Journal ArticleTextversionpublisherKyoto UniversityRealization of a SUð2Þ  SUð6Þ System of Fermions in a Cold Atomic GasShintaro Taie,1,* Yosuke Takasu,1 Seiji Sugawa,1 Rekishu Yamazaki,1,2 Takuya Tsujimoto,1Ryo Murakami,1 and Yoshiro Takahashi1,21Department of Physics, Graduate School of Science, Kyoto University, Japan 606-85022CREST, JST, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan(Received 19 May 2010; revised manuscript received 12 August 2010; published 1 November 2010)We report the realization of a novel degenerate Fermi mixture with an SUð2Þ  SUð6Þ symmetry in acold atomic gas. We successfully cool the mixture of the two fermionic isotopes of ytterbium 171Yb withthe nuclear spin I ¼ 1=2 and 173Yb with I ¼ 5=2 below the Fermi temperature TF as 0:46TF for 171Yb and0:54TF for173Yb. The same scattering lengths for different spin components make this mixture featuredwith the novel SUð2Þ  SUð6Þ symmetry. The nuclear spin components are separately imaged byexploiting an optical Stern-Gerlach effect. In addition, the mixture is loaded into a 3D optical lattice toimplement the SUð2Þ  SUð6Þ Hubbard model. This mixture will open the door to the study of novelquantum phases such as a spinor Bardeen-Cooper-Schrieffer-like fermionic superfluid.DOI: 10.1103/PhysRevLett.105.190401 PACS numbers: 05.30.Fk, 03.75.Ss, 37.10.Jk, 67.85.LmWhile SU(2) symmetry is ubiquitous in nature, realiza-tion of an SUðNÞ symmetry with N > 2 in condensedmatter physics is a rather special case. A system withhigher symmetry is expected to show novel behaviors inboth qualitative and quantitative ways. One remarkableexample is the Kondo effect in quantum dots, in whichthe SU(4) symmetry due to orbital degeneracy consider-ably increases the Kondo temperature, compared to theSU(2) case [1]. The SU(4) symmetry is also approximatelyrealized in graphene, and relevant quantum Hall magne-tism is discussed [2]. Ultracold atomic gases seem to begood candidates for exploring the physics of SUðNÞ be-cause of their variety of spin degrees of freedom and highcontrollability. However, it is difficult, though not impos-sible [3], to realize enlarged spin symmetries with alkaliatoms because of their complicated hyperfine structures.This difficulty can be overcome by using fermionic iso-topes of alkaline-earth-metal-like atoms in which the ab-sence of electronic spin in the ground states decouples theirnuclear spin from collision processes. In this case, thescattering lengths for any combination of spin componentsare the same, resulting in an SUð2Iþ 1Þ symmetry fornuclear spin I [4,5]. Recently, multicomponent fermionswith higher symmetry attract much attention and the pres-ence of rich quantum phases are predicted [3–6]. In par-ticular, a system of two-orbit SUðNÞ symmetry isintensively discussed in Refs. [5,7].In this Letter, we report the realization of a two-speciesFermi-Fermi degenerate gas mixture with a novel SUð2Þ SUð6Þ spin symmetry. This is attained by applying an all-optical evaporative cooling method to two ytterbium (Yb)fermionic isotopes of 171Yb with the nuclear spin I ¼ 1=2and 173Yb with I ¼ 5=2. While the spin-polarized two-species Fermi-Fermi mixture [8] is attractive to study manyunexplored quantum phenomena [9], it is natural to expectrich quantum phases with the Fermi-Fermi mixture withthe SUð2Þ  SUð6Þ spin symmetry [5,7]. As a first step, weload the mixture into a 3D optical lattice to implement theSUð2Þ  SUð6Þ Hubbard model where a variety of quan-tum phases has been recently discussed [5]. Another in-triguing example is the possibility of a spinor Bardeen-Cooper-Schrieffer (BCS) -like fermionic superfluidity dis-cussed in Ref. [10] where an interesting similarity betweenthe heteronuclear superfluids and spinor BEC at the mean-field level has been pointed out.The experimental procedure for preparing a mixture oftwo Yb isotopes is described in detail in Ref. [11] and webriefly summarize the method. Figure 1 shows the sche-matic view of our experimental setup. Yb atoms are loadedFIG. 1 (color online). Experimental setup. Laser beams for theOSG separation, optical pumping, and an optical lattice areshown. The OSG laser beam, whose wavelength is close tothat of the lattice, is slightly tilted with respect to others. Thisdoes not cause any serious errors in the observed spin popula-tion.PRL 105, 190401 (2010)Selected for a Viewpoint in PhysicsPHY S I CA L R EV I EW LE T T E R Sweek ending5 NOVEMBER 20100031-9007=10=105(19)=190401(4) 190401-1  2010 The American Physical Societyinto a magneto-optical trap (MOT) with the 1S0 $ 3P1transition ( ¼ 556 nm) after the deceleration by aZeeman-slower using the 1S0 $ 1P1 transition ( ¼399 nm). Next, the two isotopes are loaded into a crossedfar-off-resonant trap (FORT) with 532 nm light. The sym-pathetic evaporative cooling is performed by continuouslydecreasing the FORT trap depth. We note that both isotopesare cooled with full spin mixtures, as described later. Fromour previous photoassociation study [12], the small s-wavescattering length of0:15 nm is known for 171Yb, whereasthat for 173Yb is as large as 10.55 nm. We can employefficient evaporative cooling of 171Yb with 173Yb throughthe large interspecies scattering length of 30:6 nm.Theoretical estimate shows that the relative difference ofscattering lengths for nuclear spin states of alkaline earthatoms is on the order of 109 [5]. Experimentally, novisible splitting in the photoassociation resonance for173Yb was found in Ref. [12], which supports the SU(6)symmetry of 173Yb. The residual magnetic field is esti-mated to be smaller than 20 mG by measuring the Zeemansplitting of the ultranarrow 1S0 $ 3P2 transition. The cor-responding nuclear Zeeman energy in the ground state ison the order of 10 Hz for both isotopes.Before we describe the results for the two-species mix-ture, we show the results for single-species Fermi gas of173Ybwith an SU(6) symmetry to illustrate the nuclear spinselective imaging with an Optical Stern-Gerlach (OSG)effect. The spin selective imaging or detection is cruciallyimportant in many studies of Fermi gases with spin degreesof freedom. The separate imaging of each nuclear spincomponents is, however, very difficult with a usual Stern-Gerlach effect due to the small nuclear magnetic moments.Here in this work we successfully overcome this difficultyby exploiting the OSG effect produced by an off-resonantcircularly polarized laser beam [13]. It is noted that thespin-dependent light shift is the origin of the fictitiousmagnetic field considered here [14]. Figure 2(a) showsabsorption images of pure 173Yb degenerate gases with 6components without the OSG separation. Here, the 1S0 $1P1 transition is used for imaging. The fit to the Thomas-Fermi profile yields the temperature of 0:14TF and thenumber of atoms of 5:0 104. The Fermi temperature isgiven by TF ¼ ð6N=sÞ1=3@!=kB, where N is atom number,s ¼ 6 for 173Yb is the number of degenerate states, @ is thePlanck constant devided by 2, ! is mean trap frequency,and kB is the Boltzmann constant.While the achievement of quantum degeneracy of 173Ybhas already been reported [15], the spin population was notinvestigated. Figure 2(b) shows a schematic view of theOSG experiment. The OSG beam is focused just above theatom cloud with the waist of about 100 m to provide theatoms an dipole force due to the potential gradient. In thismeasurement, the pulse with the duration of 2.5 ms, thebeam power of 4 mW, and the detuning of about þ1 GHzwith respect to the 1S0ðFg ¼ 5=2Þ $ 3P1ðFe ¼ 7=2Þ tran-sition of 173Yb is used. Figure 2(c) shows the separatelyobserved images of spin components of 173Yb. Figure 2(d)shows the simulated distributions under the present experi-mental condition and assumption of no spin polarization.The overall feature of the observed distributions can bereproduced. The distortion of the initially isotropic mo-mentum distribution is caused by the nonuniform intensitygradient of the OSG beam. In order to image 173Yb atomswith mF ¼ 5=2 and mF ¼ 3=2 states separately, werepeat the measurement with an opposite sense of circularpolarization for the OSG beam. We find that the relativeimbalance of the spin population is smaller than 5%, whichshows almost no spin polarizations. The slight imbalancecan come from the initial preparation. The demonstratedtechnique is very useful for investigating the novel mag-netism induced for a system with high spin symmetry.Next we describe the experimental results for two-species Fermi-Fermi mixture. Figure 3 shows absorptionimages obtained after the final stage of the evaporativeFIG. 2 (color online). Optical Stern-Gerlach separation of nuclear spins. (a) Time-of-flight image of a degenerate Fermi gas of 173Ybwithout the OSG separation. The image is taken after 12 ms ballistic expansion. The azimuthally averaged distribution is also shownon the right hand side. The temperature of 0:14TF is determined from the Thomas-Fermi fit (red line). The observed distribution clearlydeviates from the classical Gaussian shape, indicated by the gray line. (b) Schematic view of an OSG effect. The atoms in the mF ¼þ5=2 state is pushed downward in the figure, whereas the mF ¼ 5=2 upward. (c) Optical Stern-Gerlach separation of spincomponents in the Fermi gas of 173Yb. The expansion time is 8 ms. Integration of the images along the horizontal axis are also shownon the right hand side. (d) The simulated distribution under the current experimental condition is shown.PRL 105, 190401 (2010) P HY S I CA L R EV I EW LE T T E R Sweek ending5 NOVEMBER 2010190401-2cooling. Starting from the 2 105 171Yb and 8 105173Yb atoms in the FORT, about 12 s evaporation resultsin the coldest temperatures of less than 100 nK. It is notedthat the image of each isotope is taken using the twoindependent probe beam with a sequential measurementfor the same sample. We fit the measured momentumdistribution with a Gaussian distribution and obtain theatom numbers of 171Yb and 173Yb are 8:0 103 and 1:1104, respectively. The temperatures are 95 nK for 171Yband 87 nK for 173Yb, and we estimate T=TF to be 0.46 for171Yb, and 0.54 for 173Yb, respectively [16]. In this tem-perature regime, the fits with the Fermi-Dirac distributiongive almost the same value for T=TF as the Gaussiandistributions. We also note that this is the first realizationof a quantum degenerate gas of 171Yb.The OSG separation is also applied to the mixture gas of171Yb and 173Yb. The same detuning of OSG laser light asused for pure 173Yb sample is also applicable for simulta-neously separate the nuclear spin components of bothisotopes. Again, we confirm that the atoms are almostequally distributed over all nuclear spin states for both171Yb and 173Yb [see Figs. 4(a) and 4(b)].It is worth noting that by applying optical pumping to173Yb via the 1S0ðFg ¼ 5=2Þ $ 3P1ðFe ¼ 3=2Þ transition,we can prepare an almost equal mixture of mF ¼ þ3=2andmF ¼ þ5=2 states. By numerically simulating the rateequations, we find that the relative imbalance is on theorder of 104, assuming perfect light polarization andbalanced initial spin population. In this case, conservationof the atom numbers with each spin leads to an reducedSUð2Þ  SUð2Þ symmetry [5]. In addition, optical pumpingalso enables to create a spin-polarized mixture of 171Yband 173Yb. Here, the 1S0 $ 1P1 (Fe ¼ Fg) transition isused for optical pumping. The polarized mixture is cooleddown via interspecies collisions only, and the suppressionof three-body losses allows us to cool the sample down tolower temperature, 0:33TF for171Yb and 0:30TF for173Yb.The spin distribution after optical pumping is examined bythe OSG separation and shown in Figs. 4(c) and 4(d).Finally, the mixture is successfully loaded into a 3Doptical lattice to implement the SUð2Þ  SUð6Þ Hubbardmodel. A variety of quantum phases in such a system isdiscussed [5]. The 3D lattice is formed with three orthogo-nal standing waves with a lattice constant d of 266 nm. Thequasimomentum distribution spreads over the entire firstBrillouin zone as the characteristic density  ¼Nd3ðm!2=2JÞ3=2 [17] increases. Here, m is the atomicmass and J is the hopping matrix element. Figure 5 showsthe quasimomentum distribution (a) for 171Yb and (b) forFIG. 3 (color online). Time-of-flight images of the quantumdegenerate Fermi-Fermi mixture with spin degrees of freedom,(a) for two-spin mixture of 171Yb and (b) for 6-spin mixture of173Yb. The expansion time is 9 ms for 171Yb and 8 ms for 173Yb.The density distributions integrated over the vertical direction yare also shown on the right hand side. From the Gaussian fits wecan estimate the temperatures T ¼ 95 nK and T ¼ 87 nK for171Yb and 173Yb, respectively. The dotted lines correspond to theFermi velocities vF ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2kBTF=mpfor each isotope. The imagesare averaged over 5 independent measurements.FIG. 4 (color online). Left: Optical Stern-Gerlach separationof spin components in the 171Yb 173Yb quantum degeneratemixture (a) for 171Yb and (b) for 173Yb. The expansion time is6 ms and the images are averaged over 8 independent measure-ments. Integrations of the images along the horizontal axis arealso shown on the right hand side. Right: Spin manipulation byoptical pumping, applied to single-species samples. (c) The OSGseparation is applied after optical pumping to the mF ¼ þ1=2state of 171Yb. (d) For 173Yb, optical pumping allows us toprepare either a single-component gas in the mF ¼ þ5=2 state(left) or a two-component mixture of the mF ¼ þ3=2 state andthe mF ¼ þ5=2 state (right).PRL 105, 190401 (2010) P HY S I CA L R EV I EW LE T T E R Sweek ending5 NOVEMBER 2010190401-3173Yb for the lattice height of 10Er measured by a band-mapping technique. Here Er is the recoil energy and isabout 200 nK in this experiment. The measured distribu-tion indicates an insulating state, which is consistent withthe values of  calculated as 800 for 171Yb and 3000 for173Yb [18]. The strong interaction effect is revealed by ourrecent observation of Bloch oscillations in a 3D opticallattice, which is beyond the scope of this Letter and will bediscussed elsewhere.In conclusion, we demonstrate the successful realizationof two-species Fermi-Fermi degenerate gas mixture of thefermionic isotopes of 171Yb with I ¼ 1=2 and 173Yb withI ¼ 5=2 with spin degrees of freedom. The nuclear spincomponents for each fermion are separately imaged byexploiting an optical Stern-Gerlach effect. The mixture issuccessfully loaded into a 3D optical lattice to implementthe SUð2Þ  SUð6Þ Hubbard model. Exploring spinorBCS-like superfluid or Kondo physics [19] would be thenext step. The required temperature seems to be accessiblewith slight improvement of the current conditions. Weexpect an efficient optical Feshbach resonance effect toachieve fermionic superfluid due to the large negativeinterspecies scattering length of 30:6 nm [20,21].We acknowledge M. A. Cazalilla for first pointing outthe SU(6) symmetry for 173Yb and importance of separatespin detection, and S. Uetake and T. Fukuhara for theirexperimental help. This work was supported by the Grant-in-Aid for Scientific Research of JSPS (No. 18204035,21102005C01 (Quantum Cybernetics), 21104513A03(DYCE), 22684022), GCOE Program ‘‘The NextGeneration of Physics, Spun from Universality andEmergence’’ from MEXT of Japan, FIRST, and MatsuoFoundation. S. T. and S. S. acknowledge supports fromJSPS.*taie@scphys.kyoto-u.ac.jp[1] S. Sasaki et al., Phys. Rev. Lett. 93, 017205 (2004).[2] K. Nomura and A.H. MacDonald, Phys. Rev. Lett. 96,256602 (2006).[3] C. Honerkamp and W. Hofstetter, Phys. Rev. Lett. 92,170403 (2004).[4] M.A. Cazalilla, A. F. Ho, and M. Ueda, New J. Phys. 11,103033 (2009).[5] A. V. Gorshkov et al., Nature Phys. 6, 289 (2010).[6] C. Wu, J. P. Hu, and S. C. Zhang, Phys. Rev. Lett. 91,186402 (2003); C. Wu, Mod. Phys. Lett. B 20, 1707(2006); M. Hermele, V. Gurarie, and A.M. Rey, Phys.Rev. Lett. 103, 135301 (2009).[7] C. Xu, Phys. Rev. B 81, 144431 (2010).[8] M. Taglieber et al., Phys. Rev. Lett. 100, 010401 (2008).[9] W.V. Liu and F. Wilczek, Phys. Rev. Lett. 90, 047002(2003); T. Mizushima, K. Machida, and M. Ichioka, Phys.Rev. Lett. 94, 060404 (2005); D. E. Sheehy and L.Radzihovsky, Phys. Rev. Lett. 96, 060401 (2006); M.Iskin and C.A. R. Sa´ de Melo, Phys. Rev. Lett. 99,080403 (2007).[10] D. B.M. Dickerscheid, Y. Kawaguchi, and M. Ueda, Phys.Rev. A 77, 053605 (2008).[11] T. Fukuhara et al., Phys. Rev. A 79, 021601(R) (2009).[12] M. Kitagawa et al., Phys. Rev. A 77, 012719 (2008).[13] T. Sleator et al., Phys. Rev. Lett. 68, 1996 (1992).[14] C. Cohen-Tannoudji and J Dupont-Roc, Phys. Rev. A 5,968 (1972).[15] T. Fukuhara et al., Phys. Rev. Lett. 98, 030401 (2007).[16] The strong attractive interaction between 171Yb and 173Ybcan affect the width of the measured momentum distribu-tion. We estimate the increase in the trap frequency due tothe mean-field potential to be 20%–30%, resulting in thereduction of the actual T=TF. On the contrary, the con-version of the negative interaction energy into the kineticenergy during the expansion time causes the underestima-tion of the temperature by 10%. Therefore we canexpect that the actual T=TF of the sample is 15% lowerthan that reported in the text.[17] M. Rigol and A. Muramatsu, Phys. Rev. A 69, 053612(2004).[18] M. Ko¨hl et al., Phys. Rev. Lett. 94, 080403 (2005).[19] M. Foss-Feig, M. Hermele, and A.M. Rey, Phys. Rev. A81, 051603(R) (2010).[20] K. Enomoto et al., Phys. Rev. Lett. 101, 203201 (2008).[21] R. Ciuryło, E. Tiesinga, and P. S. Julienne, Phys. Rev. A71, 030701(R) (2005).FIG. 5 (color online). Quasimomentum distribution of(a) 171Yb and (b) 173Yb in the SUð2Þ  SUð6Þ two-speciesmixture in an optical lattice. The density distributions integratedalong the vertical direction are also shown below. The atomnumbers are 0:4 104 for 171Yb and 1:5 104 for 173Yb,respectively. The images are taken after linear ramping downof the lattice in 0.5 ms, followed by a ballistic expansion of (a)12 and (b) 13 ms. The dotted lines indicate the domain of the 1stBrillouin zone, which equals twice the recoil momentum @k. Thetails in the measured distribution may be due to the breakdownof adiabaticity during the band-mapping sequence.PRL 105, 190401 (2010) P HY S I CA L R EV I EW LE T T E R Sweek ending5 NOVEMBER 2010190401-4

Physical Review Letters

Realization of a SU(2)×SU(6) system of fermions in a cold atomic gas.

Shintaro Taie

Yosuke Takasu

Seiji Sugawa

Rekishu Yamazaki

Takuya Tsujimoto

Ryo Murakami

Yoshiro Takahashi

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Realization of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>SU</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>×</mml:mo><mml:mi>SU</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>6</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>System of Fermions in a Cold Atomic Gas

Realization of SU(2)*SU(6) Fermi System

Realization of SU(2)*SU(6) Fermi System

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