Trapping ultracold dysprosium: a highly magnetic gas for dipolar physics
Abstract
Ultracold dysprosium gases, with a magnetic moment ten times that of alkali atoms and equal only to terbium as the most magnetic atom, are expected to exhibit a multitude of fascinating collisional dynamics and quantum dipolar phases, including quantum liquid crystal physics. We report the first laser cooling and trapping of half a billion Dy atoms using a repumper-free magneto-optical trap (MOT) and continuously loaded magnetic confinement, and we characterize the trap recycling dynamics for bosonic and fermionic isotopes. The first inelastic collision measurements in the few partial wave, 100 K–1 mK, regime are made in a system possessing a submerged open electronic f-shell. In addition, we observe unusual stripes of intra-MOT 10 K sub-Doppler cooled atoms.
pacs:
37.10.De, 37.10.Gh, 37.10.Vz, 71.10.AyUltracold gases of extraordinarily magnetic atoms, such as dysprosium, offer opportunities to explore strongly correlated matter in the presence of the long-range, anisotropic dipole-dipole interaction (DDI). Such interactions in the presence (or absence) of polarizing fields can compete with short-range interactions to induce phases beyond those described by the nearest neighbor Hubbard model Bloch:2008 . Specifically, quantum liquid crystal (QLC) physics (see Ref. Fradkin:2009 and citations within) describes strongly correlated systems in which a Fermi surface can spontaneously distort (nematics) or cleave into stripes (smectics) Miyakawa:2008 ; *Fregoso:2009; *Quintanilla:2009. While material complexity can inhibit full exploration of QLC phases in condensed matter, QLC phases may be more extensively characterized in tunable ultracold gases. In contrast to ultracold ground state polar molecules Ye:2009 , ultracold Dy offers the ability to explore the spontaneously broken symmetries inherent in QLCs since the DDI is realized without a polarizing field. An exciting prospect lies in observing spontaneous magnetization in dipolar systems, e.g., the existence of a quantum ferro-nematic phase in ultracold fermionic Dy gases not subjected to a polarizing field Fregoso:2009b .
We report the first magneto-optical trap (MOT) and ultracold collisional rates of this highly complex atom. The stable atoms possessing the largest magnetic moments are the neighboring lanthanide rare-earths, Tb and Dy (both 10 Bohr magnetons () to within 0.6% Martin:1978 ; Tb ). Prior to the present work, the coldest Dy temperatures were achieved via buffer gas and adiabatic cooling to 50 mK with final densities of cm Newman:2008 , and Dy beams have been transversely pushed and unidirectionally cooled via photon scattering Leefer:2008 ; MetcalfBook99 .
Recent experiments using degenerate Cr, a bosonic S-state atom with 6 of magnetic moment, have begun to explore quantum ferrofluids Lahaye:2007 . With suitable scattering lengths, the larger magnetic moment—and larger DDImass ratio—of Dy should allow experimental access beyond the superfluid and Mott insulator regions of the extended Bose-Hubbard phase diagram to the density wave and supersolid regimes Yi:2007 . Co-trapping isotopes of Dy will allow exploration of dipolar Bose-Fermi mixtures of near equal mass. Studies of degenerate spinor gases Stamper-Kurn:2006 ; *Wu:2006 with large spins, and simulations of dense nuclear matter ^{1}^{1}1G. Baym and T. Hatsuda, private communication (2009). are further exciting avenues of research.
In addition, ultracold samples of Dy will aid precision measurements of parity nonconservation and variation of fundamental constants Leefer:2008 , single-ion implantation Mcclelland:2006 , and quantum information science Derevianko:2004 ; *Saffman:2008. The low-lying telecommunications band (1322 nm) and InAs quantum dot (QD) amenable (1001 nm) transitions (Fig. 1) will enable hybrid quantum circuits of atom-photonic or atom-QD systems. Novel collisional physics Doyle:2009 and complex molecular association phenomena are expected in clouds of these atoms possessing submerged open f-shells inside closed 5s and 6s electron shells.
Dy structure is similar to the recently magneto-optically trapped Er (7 ) Mcclelland:2006 . Despite the multitude of excited state population loss channels, the repumper-less Dy MOT forms in a similar fashion to Er’s: The large magnetic moment allows Dy to remain magnetically trapped in the MOT region while excited state population decays through the metastable states. No repumping lasers are necessary since a sufficient fraction of the atoms recycle to the MOT to overcome loss.
The Dy cooling and trapping apparatus consists of a high temperature oven, transverse cooling stage, Zeeman slower, and MOT trapping region. We elaborate on the design elsewhere SeoHo:2009 with brief details here. Nuggets of Dy are heated to 1250 C in a Ta crucible apertured to provide an atomic beam. Three ion pumps—located at the oven, transverse pumping stage, and MOT chamber—along with titanium sublimation, achieve a vacuum of Torr during MOT operation.
The atomic beam passes through a differential pumping tube before intersecting four 100 mW, 2 cm-long transverse cooling beams detuned -0.2 from the broad 421-nm transition ^{2}^{2}2Linewidth MHz; see Refs. SeoHo:2009 ; Martin:1978 . Transverse cooling enhances the optimized MOT population by a factor of 3–4. The atomic beam then passes through a spin-flip Zeeman slower MetcalfBook99 operating at -24 detuning from the 421-nm line. The power of the Zeeman slowing laser is 1 W at the slower entrance; we find a linear increase in MOT population until 1 W. Atoms in the slowed beam are captured by a 6-beam MOT with detuning from the 421-nm line and 12 mW in each 1.1-cm -waist beam (total intensity 36 mW/cm). We observe maximum MOT population for a 35 G/cm magnetic quadrupole gradient . The 421-nm lasers are derived from two doubled Ti:Sapphire lasers transfer-cavity locked to a Rb-stabilized diode laser.
As the 421-nm laser system is detuned to the red of isotopes 160 through 164, steady state MOT populations form in proportion to natural abundance, except for the fermions Dy and Dy. These isotopes’ MOT populations are and the expected, respectively, which is likely due to poor optical pumping to the state SeoHo:2009 , where , , and are the total electronic, nuclear, and total angular momenta.
Figure 2(a) describes our model of the Dy MOT recycling mechanism, which is a refinement of that proposed for the Er MOT Mcclelland:2006 . The blue cooling laser excites a fraction of the population to the 421-nm level, where it can decay with branching ratio to the metastable states. Upon decay, a fraction of the population is captured in the magnetic quadrupole trap (MT) of the MOT at rate . MOT recycling data, examples of which are shown in Figs. 2(b) and (c), support a dual decay path through the dark metastable states; with probability () the population decays through the slow (fast) branch at rate (). Population that reaches the ground state reloads the MOT at rate , which depends on MOT parameters.
There are two loss rates from the otherwise closed system (once loading from the Zeeman slower ceases). A portion of the MOT population can decay to non-magnetically trapped metastable states at rate . Additionally, metastable and ground state MT populations can be lost due to background and two-body inelastic collisions. Two-body loss is difficult to quantify in the metastable states, but we investigate ground state MT loss below: is faster than the ground state component of , and we neglect in the rate equations below.
Following the procedure outlined in Ref. Mcclelland:2006 , the rates in the MOT recycling model are determined by fitting the following equations to sets of MOT decay transients taken at various combinations of MOT beam intensity and detuning (see as an example the data in Fig. 3(b)):
(1) |
where , , , and are the populations of the MOT, fast (slow) metastable state decay channel, and MT, respectively. To obtain MOT recycling data with well defined initial conditions, the MOT is loaded with the Zeeman slowed atomic beam until reaching steady state, then the MOT, slower, and atomic beams are extinguished for s, during which most of the population in the metastable states decay to the ground state. The population equations are numerically fit to the data for nine combinations of MOT power and detuning for the fermion Dy and eight for the boson Dy. We verified that the hold time in the MT is sufficiently long that any residual population in does not affect fit results; all other variables are left free to vary. is extracted from the product by simultaneously fitting the ’s for each isotope to the function , where and mW/cm in the MOT.
Averaging the results, we find that for both isotopes
and . The rate is consistent with the corresponding bosonic Er () MOT quantity, and we suggest that the isotope-induced difference in Dy MOT decay rates arises from Dy’s hyperfine structure. Dy Zeeman slowing and MOT collection is possible because of the small ^{3}^{3}3 is consistent with Er’s and 4 smaller than that numerically estimated (private comm., V. Flambaum 2009). The and values indicate that 82% of the atoms are captured by the MT and 73% of those cascade through the slow channel. Dy level linewidths are mostly unknown, but we speculate that much of this population is captured by the low-lying and long-lived states near the 1322-nm telecom transition.
Using the measured rates as fixed constants, data of the maximum MOT recapture population (peaks of data such as in Fig. 2(b)) versus are fit to an exponential with only the initial and final MOT population as free variables. Good fits are obtained for s data, as shown in Fig. 2(c); we plot the fitted curve out to later times for comparison to data ^{4}^{4}4 at early times is due to the initial .. From these plots we can see that the population in the steady state MOT is only a fraction of the total number of trapped atoms. The “hidden” population in the continuously loaded MT is several times larger, filling the ground state MT at rate . With respect to the steady state MOT, we measure nearly () more Dy (Dy) atoms in the recaptured MOT. At optimal MOT parameters and after s of MT loading, we measure the total population of laser cooled and trapped atoms to be for Dy and for Dy. Populations are measured via fluorescence collection on a fast photodiode with atom number calibration to 10% from absorption imaging SeoHo:2009 .
Population loss at times s is likely due to background and inelastic collisions of ground state atoms in the MT. (Majorana spin flip losses are negligible at these ’s and trap densities.) We investigate these collision rates by absorption imaging the atoms confined in the MT at various delay times. After loading the MOT, we extinguish the MOT, Zeeman slower, and atomic beams while maintaining a constant . The MT is turned off at , and after 1 ms, an absorption image integrates on a 16-bit CCD camera for 200 s. Accounting for gravity , the images taken in the – plane containing the quadrupole axis (along ) are fit to the functional form Berglund:2007 :
where , is the mean magnetic moment of the atomic cloud, and (and similarly for ). We extract the mean cloud density , temperature , and versus , which we plot in Fig. 3 for several MT gradients.
The Dy density decay data in Fig. 3(a) are fit to the one plus two-body decay equation =, where is the loss rate due to background collisions and is a measure of inelastic two-body losses. For the three trap gradients, the extracted ’s and ’s are consistent with one another within 1; the weighted means are . Fitting the data to results in a worse . Temperature heating data—e.g., Fig. 3(b)—are fit to an exponential, resulting at early times to a heating rate of K/s, which is consistent with the heating rate in spin unpolarized Er and Cr MTs Berglund:2007 ; Hensler:2003 and is likely due to spin-relaxation collisions. The MT population is initially distributed among the weak-field seeking Zeeman states, and spin exchange collisions tend to polarize the sample toward . Indeed, increases with time, see Fig. 3(c), and reaches 8 within s in the high gradient G/cm trap.
The measured is likely due to an unresolved combination of inelastic spin exchange, magnetic dipole-dipole relaxation (MDDR), and anisotropic electrostatic-driven spin relaxation collisions. Compared to cm/s in 200 K spin-polarized Cr Hensler:2003 , is consistent with a MDDR scaling , though several times smaller than the full inelastic MDDR scaling presented in Ref. Hensler:2003 . In addition, is consistent with non-maximally spin-polarized Cr (1.110 cm/s) Hensler:2003 and with 500 mK inelastic Er–Er and Tm–Tm collision rates—3.0 and 1.1 cm/s, respectively Doyle:2009 ; the large magnitude of the latter rates are attributed to anisotropic electrostatic-driven spin relaxation collisions of these lanthanides. Further measurements will aim to elucidate these collisional processes in this complex atom SeoHo:2009 .
Temperature and density profiles contain unusual features common to both Dy and Dy MOTs. When care is taken to retroreflect and power balance all pairs of MOT beams, the MOTs are typically 30% fewer in population, though have larger mean density (10 versus 10 cm) than those with slight misadjustment. In ballistic expansion after extinguishing the MOT, a dual component gas is observed comprised of a dense symmetric core of 200 K atoms surrounded by a hot, 2–3 mK shell containing 70% of the atoms. Doppler cooling theory in 1D predicts a cloud temperature of 1.2 mK for the MOT parameters, but comparisons to the Er MOT Berglund:2007 suggest the entire intra-MOT population should be sub-Doppler cooled to 100 K as a consequence of the near equal Landé -factors in the ground and excited states ( 1.7%). Despite being slightly larger than in Er, numerical 1D sub-Doppler cooling simulations (based on Ref. Berglund:2007 and references within) indicate that the entire Dy MOT—accounting for typical size and —should be sub-Doppler cooled. The Er MOT, limited by Zeeman and MOT laser power, contained 500 fewer atoms; it is possible that the hot shell forms subsequent to the cold inner core, which will be investigated. At s, MT temperatures are 100–300 K depending on .
While ultracold cores are observed in other MOTs Jhe:2004 , a unique sub-Doppler cooled structure forms when the Dy MOT beams are slightly misbalanced or misaligned; an example of which is shown in Fig. 4. Depending on the particular misadjustment, either a dense vertical or horizontal stripe (or both) appear in the core of the cloud. The outer hot atoms remain at –3 mK temperatures, but the (vertical) stripe population acquires an anisotropic temperature distribution of and K. This latter temperature is consistent the 1D numerical sub-Doppler cooling calculation, but its precise measurement is hampered by the hot cloud presence. We offer no explanation other than to note no detection of stripe spin-polarization in Stern-Gerlach measurements (again hampered by the rapid hot cloud expansion), and that as decreases SeoHo:2009 . Under optimal operating conditions, the Dy MOT phase space density is as large as .
Future work includes narrow-line cooling to 1 K on the 1001-nm line Berglund:2008 and loading into a crossed optical dipole trap. Once optically confined, the large MT losses measured here might be avoided by trapping in the lowest energy Zeeman state. Elastic and inelastic collision rates in the single partial wave regime will be measured before attempting to evaporatively cool to degeneracy. The ultracold Dy produced with this method will open new avenues for research in quantum gases, precision measurement, and quantum information science.
Acknowledgements.
We thank A. Berglund, U. Ray, J. McClelland, B. DeMarco, E. Fradkin, and J. Ye for technical assistance and critical reading. We acknowledge support from the NSF, AFOSR, and ARO MURI on Quantum Circuits.References
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