Observation of the Efimovian expansion in scale-invariant Fermi gases
Steps to ultracold gas expansion
Cold atomic gases are often studied while confined in parabolic traps, with the largest atomic density at the center of the trap. When the trap is made shallower, the gas radially expands as the energy cost for atoms that are farther from the trap center decreases. Deng et al. observed an interesting effect when they reduced the characteristic frequency of the parabolic trap so that it was at any moment inversely proportional to the elapsed time. Instead of expanding continuously, a strongly interacting Fermi gas held in such a trap stalled at certain time points. These time points formed a geometric progression, a consequence of scale invariance in the strongly interacting limit.
Science, this issue p. 371
Abstract
Scale invariance plays an important role in unitary Fermi gases. Discrete scaling symmetry manifests itself in quantum few-body systems such as the Efimov effect. Here, we report on the theoretical prediction and experimental observation of a distinct type of expansion dynamics for scale-invariant quantum gases. When the frequency of the harmonic trap holding the gas decreases continuously as the inverse of time t, the expansion of the cloud size exhibits a sequence of plateaus. The locations of these plateaus obey a discrete geometric scaling law with a controllable scale factor, and the expansion dynamics is governed by a log-periodic function. This marked expansion shares the same scaling law and mathematical description as the Efimov effect.
Get full access to this article
View all available purchase options and get full access to this article.
Supplementary Material
Summary
Materials and Methods
Supplementary Text
Figs. S1 to S3
Table S1
Resources
File (deng-sm.pdf)
- Download
- 745.25 KB
References and Notes
1
Kinast J., Turlapov A., Thomas J. E., Chen Q., Stajic J., Levin K., Heat capacity of a strongly interacting Fermi gas. Science 307, 1296–1299 (2005).
2
Nascimbène S., Navon N., Jiang K. J., Chevy F., Salomon C., Exploring the thermodynamics of a universal Fermi gas. Nature 463, 1057–1060 (2010).
3
Horikoshi M., Nakajima S., Ueda M., Mukaiyama T., Measurement of universal thermodynamic functions for a unitary Fermi gas. Science 327, 442–445 (2010).
4
Navon N., Nascimbène S., Chevy F., Salomon C., The equation of state of a low-temperature Fermi gas with tunable interactions. Science 328, 729–732 (2010).
5
Ku M. J. H., Sommer A. T., Cheuk L. W., Zwierlein M. W., Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas. Science 335, 563–567 (2012).
6
Sidorenkov L. A., Tey M. K., Grimm R., Hou Y.-H., Pitaevskii L., Stringari S., Second sound and the superfluid fraction in a Fermi gas with resonant interactions. Nature 498, 78–81 (2013).
7
Cao C., Elliott E., Joseph J., Wu H., Petricka J., Schäfer T., Thomas J. E., Universal quantum viscosity in a unitary Fermi gas. Science 331, 58–61 (2011).
8
Sommer A., Ku M., Roati G., Zwierlein M. W., Universal spin transport in a strongly interacting Fermi gas. Nature 472, 201–204 (2011).
9
Stadler D., Krinner S., Meineke J., Brantut J.-P., Esslinger T., Observing the drop of resistance in the flow of a superfluid Fermi gas. Nature 491, 736–739 (2012).
10
Brantut J.-P., Grenier C., Meineke J., Stadler D., Krinner S., Kollath C., Esslinger T., Georges A., A thermoelectric heat engine with ultracold atoms. Science 342, 713–715 (2013).
11
Koschorreck M., Pertot D., Vogt E., Köhl M., Universal spin dynamics in two-dimensional Fermi gases. Nat. Phys. 9, 405–409 (2013).
12
Bardon A. B., Beattie S., Luciuk C., Cairncross W., Fine D., Cheng N. S., Edge G. J. A., Taylor E., Zhang S., Trotzky S., Thywissen J. H., Transverse demagnetization dynamics of a unitary Fermi gas. Science 344, 722–724 (2014).
13
Elliott E., Joseph J. A., Thomas J. E., Observation of conformal symmetry breaking and scale invariance in expanding Fermi gases. Phys. Rev. Lett. 112, 040405 (2014).
14
Efimov V., Energy levels arising from resonant two-body forces in a three-body system. Phys. Lett. B 33, 563–564 (1970).
15
Braaten E., Hammer H.-W., Universality in few-body systems with large scattering length. Phys. Rep. 428, 259–390 (2006).
16
Kraemer T., Mark M., Waldburger P., Danzl J. G., Chin C., Engeser B., Lange A. D., Pilch K., Jaakkola A., Nägerl H.-C., Grimm R., Evidence for Efimov quantum states in an ultracold gas of caesium atoms. Nature 440, 315–318 (2006).
17
Knoop S., Ferlaino F., Mark M., Berninger M., Schobel H., Nagerl H., Grimm R., Observation of an Efimov-like trimer resonance in ultracold atom–dimer scattering. Nat. Phys. 5, 227–230 (2009).
18
Williams J. R., Hazlett E. L., Huckans J. H., Stites R. W., Zhang Y., O’Hara K. M., Evidence for an excited-state Efimov trimer in a three-component Fermi gas. Phys. Rev. Lett. 103, 130404 (2009).
19
Pollack S. E., Dries D., Hulet R. G., Universality in three- and four-body bound states of ultracold atoms. Science 326, 1683–1685 (2009).
20
Berninger M., Zenesini A., Huang B., Harm W., Nägerl H. C., Ferlaino F., Grimm R., Julienne P. S., Hutson J. M., Universality of the three-body parameter for Efimov states in ultracold cesium. Phys. Rev. Lett. 107, 120401 (2011).
21
Roy S., Landini M., Trenkwalder A., Semeghini G., Spagnolli G., Simoni A., Fattori M., Inguscio M., Modugno G., Test of the universality of the three-body Efimov parameter at narrow Feshbach resonances. Phys. Rev. Lett. 111, 053202 (2013).
22
Bloom R. S., Hu M.-G., Cumby T. D., Jin D. S., Tests of universal three-body physics in an ultracold Bose-Fermi mixture. Phys. Rev. Lett. 111, 105301 (2013).
23
Kunitski M., Zeller S., Voigtsberger J., Kalinin A., Schmidt L. P., Schöffler M., Czasch A., Schöllkopf W., Grisenti R. E., Jahnke T., Blume D., Dörner R., Observation of the Efimov state of the helium trimer. Science 348, 551–555 (2015).
24
Zaccanti M., Deissler B., D’Errico C., Fattori M., Jona-Lasinio M., Müller S., Roati G., Inguscio M., Modugno G., Observation of an Efimov spectrum in an atomic system. Nat. Phys. 5, 586–591 (2009).
25
Huang B., Sidorenkov L. A., Grimm R., Hutson J. M., Observation of the second triatomic resonance in Efimov’s scenario. Phys. Rev. Lett. 112, 190401 (2014).
26
Tung S. K., Jiménez-García K., Johansen J., Parker C. V., Chin C., Geometric scaling of Efimov states in a ⁶Li-¹³³Cs mixture. Phys. Rev. Lett. 113, 240402 (2014).
27
Pires R., Ulmanis J., Häfner S., Repp M., Arias A., Kuhnle E. D., Weidemüller M., Observation of Efimov resonances in a mixture with extreme mass imbalance. Phys. Rev. Lett. 112, 250404 (2014).
28
Anderson M. H., Ensher J. R., Matthews M. R., Wieman C. E., Cornell E. A., Observation of Bose-Einstein condensation in a dilute atomic vapor. Science 269, 198–201 (1995).
29
Davis K. B., Mewes M.-O., Andrews M. R., van Druten N. J., Durfee D. S., Kurn D. M., Ketterle W., Bose-Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995).
30
O’Hara K. M., Hemmer S. L., Gehm M. E., Granade S. R., Thomas J. E., Observation of a strongly interacting degenerate Fermi gas of atoms. Science 298, 2179–2182 (2002).
31
Fort C., Fallani L., Guarrera V., Lye J. E., Modugno M., Wiersma D. S., Inguscio M., Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide. Phys. Rev. Lett. 95, 170410 (2005).
32
Sanchez-Palencia L., Clément D., Lugan P., Bouyer P., Shlyapnikov G. V., Aspect A., Anderson localization of expanding Bose-Einstein condensates in random potentials. Phys. Rev. Lett. 98, 210401 (2007).
33
Greiner M., Mandel O., Esslinger T., Hänsch T. W., Bloch I., Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).
34
Castin Y., Exact scaling transform for a unitary quantum gas in a time dependent harmonic potential. C. R. Phys. 5, 407–410 (2004).
35
Pitaevskii L. P., Rosch A., Breathing modes and hidden symmetry of trapped atoms in two dimensions. Phys. Rev. A 55, R853–R856 (1997).
36
Vogt E., Feld M., Fröhlich B., Pertot D., Koschorreck M., Köhl M., Scale invariance and viscosity of a two-dimensional Fermi gas. Phys. Rev. Lett. 108, 070404 (2012).
37
Hofmann J., Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas. Phys. Rev. Lett. 108, 185303 (2012).
38
Taylor E., Randeria M., Apparent low-energy scale invariance in two-dimensional Fermi gases. Phys. Rev. Lett. 109, 135301 (2012).
39
Gao C., Yu Z., Breathing mode of two-dimensional atomic Fermi gases in harmonic traps. Phys. Rev. A 86, 043609 (2012).
40
Nishida Y., Moroz S., Son D. T., Super Efimov effect of resonantly interacting fermions in two dimensions. Phys. Rev. Lett. 110, 235301 (2013).
41
Volosniev A. G., Fedorov D. V., Jensen A. S., Zinner N. T., Borromean ground state of fermions in two dimensions. J. Phys. At. Mol. Opt. Phys. 47, 185302 (2014).
42
Gao C., Wang J., Yu Z., Revealing the origin of super Efimov states in the hyperspherical formalism. Phys. Rev. A 92, 020504 (2015).
43
Hou Y., Pitaevskii L., Stringari S., Scaling solutions of the two-fluid hydrodynamic equations in a harmonically trapped gas at unitarity. Phys. Rev. A 87, 033620 (2013).
44
Deng S., Diao P., Yu Q., Wu H., All-optical production of quantum degeneracy and molecular Bose-Einstein condensation of 6Li. Chin. Phys. Lett. 32, 053401 (2015).
(0)eLetters
eLetters is a forum for ongoing peer review. eLetters are not edited, proofread, or indexed, but they are screened. eLetters should provide substantive and scholarly commentary on the article. Embedded figures cannot be submitted, and we discourage the use of figures within eLetters in general. If a figure is essential, please include a link to the figure within the text of the eLetter. Please read our Terms of Service before submitting an eLetter.
Log In to Submit a ResponseNo eLetters have been published for this article yet.
Information & Authors
Information
Published In
Science
Volume 353 | Issue 6297
22 July 2016
22 July 2016
Copyright
Copyright © 2016, American Association for the Advancement of Science.
Submission history
Received: 13 December 2015
Accepted: 21 June 2016
Published in print: 22 July 2016
Acknowledgments
We thank P. Zhang for helpful discussions. This research is supported by the National Natural Science Foundation of China (NSFC) (grant nos. 11374101 and 91536112) and the Shu Guang project (14SG22) of Shanghai Municipal Education Commission and Shanghai Education Development Foundation. Z.S. and H.Z. are supported by MOST (grant no. 2016YFA0301604), Tsinghua University Initiative Scientific Research Program and NSFC grant no. 11325418. R.Q. is supported by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China under grant no. 15XNLF18 and no. 16XNLQ03.
Authors
Metrics & Citations
Metrics
Article Usage
Altmetrics
Citations
Cite as
- Shujin Deng et al.
Export citation
Select the format you want to export the citation of this publication.
Cited by
- Observation of a superradiant quantum phase transition in an intracavity degenerate Fermi gas, Science, 373, 6561, (1359-1362), (2021)./doi/10.1126/science.abd4385
- Discovery of log-periodic oscillations in ultraquantum topological materials, Science Advances, 4, 11, (2018)./doi/10.1126/sciadv.aau5096
- Superadiabatic quantum friction suppression in finite-time thermodynamics, Science Advances, 4, 4, (2018)./doi/10.1126/sciadv.aar5909
Loading...
View Options
Check Access
Log in to view the full text
AAAS login provides access to Science for AAAS Members, and access to other journals in the Science family to users who have purchased individual subscriptions.
- Become a AAAS Member
- Activate your AAAS ID
- Purchase Access to Other Journals in the Science Family
- Account Help
Log in via OpenAthens.
Log in via Shibboleth.
More options
Register for free to read this article
As a service to the community, this article is available for free. Login or register for free to read this article.
Buy a single issue of Science for just $15 USD.