Interspecies thermalization in an ultracold mixture of Cs and Yb in an optical trap
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- Durham Research Online Deposited in DRO: 17 July 2017 Version of attached le: Published Version Peer-review status of attached le: Peer-reviewed Citation for published item: Guttridge, A. and Hopkins, S.A. and Kemp, S.L. and Frye, M.D. and Hutson, J.M. and Cornish, S.L. (2017) 'Interspecies thermalization in an ultracold mixture of Cs and Yb in an optical trap.', Physical review A., 96 (1). 012704.
- Further information on publisher's website: https://doi.org/10.1103/PhysRevA.96.012704.
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- Interspecies thermalization in an ultracold mixture of Cs and Yb in an optical trap A. Guttridge,1,* S. A. Hopkins,1 S. L. Kemp,1 Matthew D. Frye,2,† Jeremy M. Hutson,2 and Simon L. Cornish1,‡ 1Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom 2Joint Quantum Centre (JQC) Durham-Newcastle, Department of Chemistry, Durham University, South Road, Durham, DH1 3LE, United Kingdom (Received 10 April 2017; published 14 July 2017).
- In addition, the long-range dipole-dipole interactions present between pairs of polar molecules make them useful in the study of dipolar quantum matter [35,36] and ultracold molecules confined in an optical lattice can simulate a variety of condensed-matter systems [37–39].
- A detailed description of their experimental apparatus can be found in Ref. , but the authors will summarize the main components here.
- During this stage 9 × 104 atoms are transferred into the ODT and the magnetic bias field is set to 22.3 G, corresponding to the Efimov minimum in the Cs three-body recombination rate .
- For each experimental run the number and temperature are determined by quickly turning off the ODT after a variable hold time and performing resonant absorption imaging of both species after a variable time of flight.
- The smaller initial number of Cs atoms is chosen to reduce the density of Cs such that the effects of three-body recombination play a relatively small role in the thermalization .
- Treatment of the number evolution of the Cs atoms requires careful attention due to the presence of Cs atoms both in the crossed-beam region of the trap and in the wings, where confinement is due to only a single ODT beam.
III. RATE EQUATIONS FOR THERMALIZATION
- To model the thermalization results, the authors formulate a set of coupled equations that describe the number and temperature kinetics.
- Kbg is the background loss rate, Ki,3 is the three-body loss coefficient, ni(r) is the density, and 〈. . .〉sp represents a spatial average.
- Ti,H is the recombination heating term, which accounts for the increase in temperature due to the release of the molecular binding energy during recombination .
- The authors choose to neglect the three-body loss coefficient for Yb, KYb,3, because they do not observe any evidence of three-body loss on the experimental timescale in single-species Yb experiments.
- The effective intraspecies collision rate per atom for thermalization is γii = 〈ni〉spσii v̄ii , where σii is an effective energy-independent scattering cross section.
IV. ANALYSIS OF RESULTS
- The coupled Eqs. (1) and (2) are solved numerically.
- The solid lines in Fig. 3 show the results of the fitted model, while the dashed lines show the results in the absence of interspecies collisions.
- The authors instead constrain the number of Cs atoms inside and outside this region using interpolating functions matched to the experimentally measured values.
- ṪCs,Heat = 4 ± 1 μK/s, it results from the sum of two heating mechanisms, recombination heating and heating from the optical potential.
- Due to the difference in the natural abundance (31.8% for 174Yb and 3.0% for 170Yb ) and the intraspecies scattering lengths (a174 = 105 a0 and a170 = 64 a0 ), the authors obtain a number of 170Yb atoms that is half that of 174Yb, leading to a greater final temperature for 170Yb.
OF SCATTERING LENGTHS
- Except near narrow Feshbach resonances, CsYb collisions can be treated as those of two structureless particles with an interaction potential V (R), which behaves at long range as 012704-4 −C6R−6.
- For CsYb, with ∼70 bound states , changes in the Yb isotope alter vD by less than 1, so that the scattering lengths for all possible isotopologs may be placed on a single curve.
- At the lowest temperatures, thermalization is governed by the elastic cross section σel = 4πa2.
- The authors vary the magnitude of its short-range part by a factor λ to vary the scattering length, while keeping the long-range part −C6R−6 fixed, with C6 taken from Ref. .
- The authors obtain optimal values of the potential scaling factor λ by least-squares fitting to the experimental cross sections.
VI. TOWARD A DOUBLY DEGENERATE MIXTURE
- In their current system, the authors can independently create BoseEinstein condensates of Cs and the two Yb isotopes with positive intraspecies scattering lengths and workable abundance, 174Yb and 170Yb.
- Note that the intraspecies scattering length for 172Yb is large and negative , precluding the creation of a large condensate.
- For 174Yb, the initial steps are the same as in preparing the 174Yb gas for the thermalization measurements (see Fig. 2), where the sample is loaded into the ODT at high power and evaporatively cooled.
- The authors then transfer 9 × 105 of these atoms into the ODT used previously for thermalization measurements (and for 174Yb BEC); this is also known as the dimple trap.
- Additionally, the two species require very different traps for efficient evaporative cooling.
- The authors have used a kinetic model to determine the cross sections for interspecies thermalization, taking account of additional heating effects that prevent complete thermalization of the two species.
- The authors have used the resulting interaction potential to calculate scattering lengths for all isotopologs of CsYb.
- The authors have cooled both 174Yb and Cs to degeneracy in the same apparatus, but cooling both species to degeneracy in the same optical trap will be challenging, as illustrated by the contrasting routines they use to produce independent BECs of the two species.
- The optimized CsYb potential will assist direct measurements of the CsYb binding energies using two-photon photoassociation spectroscopy [68,79].
- The data presented in this paper are available online .
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