Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-01T00:03:43.548Z Has data issue: false hasContentIssue false

16 - Second Sound in Ultracold Atomic Gases

from Part III - Condensates in Atomic Physics

Published online by Cambridge University Press:  18 May 2017

L. Pitaevskii
Affiliation:
Università di Trento
S. Stringari
Affiliation:
Università di Trento
Nick P. Proukakis
Affiliation:
Newcastle University
David W. Snoke
Affiliation:
University of Pittsburgh
Peter B. Littlewood
Affiliation:
University of Chicago
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Pitaevskii, L. P., and Stringari, S. 2016. Bose-Einstein Condensation and Superfluidity. Oxford University Press (New York).
[2] Matthews, M. R., Anderson, B. P., Haljan, P. C., Hall, D. S., Wieman, C. E., and Cornell, E. A. 1999. Vortices in a Bose-Einstein condensate. Phys. Rev. Lett., 83, 2498.Google Scholar
[3] Madison, K. W., Chevy, F., Wohlleben, W., and Dalibard, J. 2000. Vortex formation in a stirred Bose-Einstein condensate. Phys. Rev. Lett., 84, 806.Google Scholar
[4] Abo-Shaeer, J. R., Raman, C., Vogels, J. M., and Ketterle, W. 2001. Observation of vortex lattices in Bose-Einstein condensates. Science, 292, 476.Google Scholar
[5] Coddington, I., Engels, P., Schweikhard, V., and Cornell, E. A. 2003. Observation of Tkachenko oscillations in rapidly rotating Bose-Einstein condensates. Phys. Rev. Lett., 91, 100402.Google Scholar
[6] Zwierlein, M. W., Abo-Shaeer, J. R., Schirotzek, A., Schunck, C. H., and Ketterle, W. 2005. Vortices and superfluidity in a strongly interacting Fermi gas. Nature, 435, 1047.Google Scholar
[7] Guery-Odelin, D., and Stringari, S. 1999. Scissors mode and superfluidity of a trapped Bose-Einstein condensed gas. Phys. Rev. Lett., 83, 4452.Google Scholar
[8] Maragó, O. M., Hopkins, S. A., Arlt, J., Hodby, E., Hechenblaikner, G., and Foot, C. J. 2000. Observation of the scissors mode and evidence for superfluidity of a trapped Bose-Einstein condensed gas. Phys. Rev. Lett., 84, 2056.Google Scholar
[9] Riedl, S., Sanchez Guajardo, E. R., Kohstall, C., Hecker Denschlag, J., and Grimm, R. 2011. Superfluid quenching of the moment of inertia in a strongly interacting Fermi gas. New J. Phys., 13, 035003.Google Scholar
[10] Stringari, S. 1996. Collective excitations of a trapped Bose-condensed gas. Phys. Rev. Lett., 77, 2360.Google Scholar
[11] Onofrio, R., Raman, C., Vogels, J. M., Abo-Shaeer, J. R., Chikkatur, A. P., and Ketterle, W. 2000. Observation of superfluid flow in a Bose-Einstein condensed gas. Phys. Rev. Lett., 85, 2228.Google Scholar
[12] Miller, D. E., Chin, J. K., Stan, C. A., Liu, Y., Setiawan, W., Sanner, C., and Ketterle, W. 2007. Critical velocity for superfluid flow across the BEC-BCS crossover. Phys. Rev. Lett., 99, 070402.Google Scholar
[13] Albiez, M., Gati, R., Fölling, J., Hunsmann, S., Cristiani, M., and Oberthaler, M. K. 2005. Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. Phys. Rev. Lett., 95, 010402.Google Scholar
[14] Chin, C., Bartenstein, M., Altmeyer, A., Riedl, S., Jochim, S., Hecker Denschlag, J., and Grimm, R. 2004. Observation of the pairing gap in a strongly interacting Fermi gas. Science, 305, 1128.Google Scholar
[15] Ku, M. J. H., Sommer, A. T., Cheuk, L. W., and Zwierlein, M. W. 2012. Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas. Science, 335, 563.Google Scholar
[16] Donnelly, R. 2009. The two-fluid theory and second sound in liquid helium. Physics Today, 62, 34.Google Scholar
[17] Landau, L. D. 1941. The theory of superfuidity of helium II. J. Phys. USSR, 5, 71.Google Scholar
[18] Landau, L. D., and Lifshitz, E. M. 1987. Fluid Mechanics. Pergamon (Oxford).
[19] Tisza, L. 1940. Sur la théorie des liquides quantiques. Application a l'hélium liquid. J. Phys. Radium, 1, 164.Google Scholar
[20] Peshkov, V. P. 1946. J. Phys. USSR, 10, 389.
[21] Taylor, E., Hu, H., Liu, X.-J., Pitaevskii, L. P., Griffin, A., and Stringari, S. 2009. First and second sound in a strongly interacting Fermi gas. Phys. Rev. A, 80, 053601.Google Scholar
[22] Pines, D., and Nozieres, P. 1990. Theory of Quantum Liquids. Addison-Wesley (Redwood City).
[23] Hu, H., Taylor, E., Liu, X.-J., Stringari, S., and Griffn, A. 2010. Second sound and the density response function in uniform superfluid atomic gases. New J. Phys., 12, 043040.Google Scholar
[24] Lifshitz, E. M. 1944. J. Phys. USSR, 8, 110.
[25] Dash, J. G., and Taylor, R. D. 1957. Hydrodynamics of oscillating disks in viscous fluids: density and viscosity of normal fluid in pure He4 from 1.2°K to the lambda point. Phys. Rev., 105, 7.Google Scholar
[26] Lee, T. D., and Yang, C. N. 1959. Low-temperature behavior of a dilute Bose system of hard spheres. II. Nonequilibrium properties. Phys. Rev., 113, 1406.Google Scholar
[27] Zaremba, E., Nikuni, T., and Griffin, A. 1999. Dynamics of trapped Bose gases at finite temperatures. J. Low Temp. Phys., 116, 277.Google Scholar
[28] Griffin, A., Nikuni, T., and Zaremba, E. 2009. Bose-Condensed Gases at Finite Temperatures. Cambridge University Press (New York).
[29] Verney, L., Pitaevskii, L., and Stringari, S. 2015. Hybridization of first and second sound in a weakly interacting Bose gas. EPL (Europhysics Letters), 111, 40005.Google Scholar
[30] Meppelink, R., Koller, S. B., and van der Straten, P. 2009. Sound propagation in a Bose-Einstein condensate at finite temperatures. Phys. Rev. A, 80, 043605.Google Scholar
[31] Zaremba, E. 1998. Sound propagation in a cylindrical Bose-condensed gas. Phys. Rev. A, 57, 518.Google Scholar
[32] Capogrosso-Sansone, B., Giorgini, S., Pilati, S., Pollet, L., Prokof'ev, N., Svistunov, B., and Troyer, M. 2010. The Beliaev technique for a weakly interacting Bose gas. New J. Physics, 12, 043010.Google Scholar
[33] Abrikosov, A. A., Gorkov, L. P., and Dzyaloshinskii, I. E. 1975. Methods of Quantum Field Theory in Statistical Physics. Dover (Mineola, NY).
[34] Baym, G., Blaizot, J.-P., Holzmann, M., Lalo, F., and Vautherin, D. 1999. The transition temperature of the dilute interacting Bose gas. Phys. Rev. Lett., 83, 1703.Google Scholar
[35] Arnold, P., and Moore, G. 2001. BEC transition temperature of a dilute homogeneous imperfect Bose gas. Phys. Rev. Lett., 87, 120401.Google Scholar
[36] Kashurnikov, V. A., Prokof'ev, N. V., and Svistunov, B. V. 2001. Critical temperature shift in weakly interacting Bose gas. Phys. Rev. Lett., 87, 120402.Google Scholar
[37] Ozawa, T., and Stringari, S. 2014. Discontinuities in the first and second sound velocities at the Berezinskii-Kosterlitz-Thouless transition. Phys. Rev. Lett., 112, 025302.Google Scholar
[38] Sidorenkov, L. A., Tey, M. K., Grimm, R., Hou, Y.-H., Pitaevskii, L., and Stringari, S. 2013. Second sound and the superfluid fraction in a Fermi gas with resonant interactions. Nature (London), 498, 78.
[39] Nozieres, P., and Schmitt-Rink, S. 1985. Bose condensation in an attractive fermion gas: from weak to strong coupling superconductivity. J. Low Temp. Phys., 59, 195.Google Scholar
[40] Hu, H., Liu, X.-J., and Drummond, P. D. 2006. Temperature of a trapped unitary Fermi gas at finite entropy. Phys. Rev. A, 73, 023617.Google Scholar
[41] Salasnich, L. 2010. Low-temperature thermodynamics of the unitary Fermi gas: superfluid fraction, first sound, and second sound. Phys. Rev. A, 82, 063619.Google Scholar
[42] Bertaina, G., Pitaevskii, L., and Stringari, S. 2010. First and second sound in cylindrically trapped gases. Phys. Rev. Lett., 105, 150402.Google Scholar
[43] Hou, Y.-H., Pitaevskii, L. P., and Stringari, S. 2013. First and second sound in a highly elongated Fermi gas at unitarity. Phys. Rev. A, 88, 043630.Google Scholar
[44] Ho, T.-L. 2004. Universal thermodynamics of degenerate quantum gases in the unitarity limit. Phys. Rev. Lett., 92, 090402.Google Scholar
[45] Burovski, E., Prokof'ev, N., Svistunov, B., and Troyer, M. 2006. Critical temperature and thermodynamics of attractive fermions at unitarity. Phys. Rev. Lett., 96, 160402.Google Scholar
[46] Goulko, O., and Wingate, M. 2010. Thermodynamics of balanced and slightly spinimbalanced Fermi gases at unitarity. Phys. Rev. A, 82, 053621.Google Scholar
[47] Haussmann, R., Rantner, W., Cerrito, S., and Zwerger, W. 2007. Thermodynamics of the BCS-BEC crossover. Phys. Rev. A, 75, 023610.Google Scholar
[48] Hohenberg, P. C. 1967. Existence of long-range order in one and two dimensions. Phys. Rev., 158, 383.Google Scholar
[49] Mermin, N. D., and Wagner, H. 1966. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys. Rev. Lett., 17, 1133.Google Scholar
[50] Berezinskii, V. L. 1972. Destruction of long-range order in one-dimensional and twodimensional systems possessing a continuous symmetry group. II. Quantum systems. Sov. Phys. JETP, 34, 610 [Zh. Eksp. Teor. Fiz. 61, 1144 (1971)].Google Scholar
[51] Kosterlitz, J. M., and Thouless, D. J. 1972. Long range order and metastability in two dimensional solids and superfluids (application of dislocation theory). J. Phys. C, 5, L124.Google Scholar
[52] Kosterlitz, J. M., and Thouless, D. J. 1973. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C., 6, 1181.Google Scholar
[53] Nelson, D. R., and Kosterlitz, J. M. 1977. Universal jump in the superfluid density of two-dimensional superfluids. Phys. Rev. Lett., 39, 1201.Google Scholar
[54] Desbuquois, R., Chomaz, L., Yefsah, T., Leonard, J., Beugnon, J., Weitenberg, C., and Dalibard, J. 2012. Superfluid behaviour of a two-dimensional Bose gas. Nature Phys., 8, 645.Google Scholar
[55] Prokof'ev, N., Ruebenacker, O., and Svistunov, B. 2001. Critical point of a weakly interacting two-dimensional Bose gas. Phys. Rev. Lett., 87, 270402.Google Scholar
[56] Prokof'ev, N., and Svistunov, B. 2002. Two-dimensional weakly interacting Bose gas in the fluctuation region. Phys. Rev. A, 66, 043608.Google Scholar
[57] Rancon, A., and Dupuis, N. 2012. Universal thermodynamics of a two-dimensional Bose gas. Phys. Rev. A, 85, 063607.Google Scholar
[58] Hung, C.-L., Zhang, X., Gemelke, N., and Chin, C. 2011. Observation of scale invariance and universality in two-dimensional Bose gases. Nature (London), 470, 236.
[59] Yefsah, T., Desbuquois, R., Chomaz, L., Günther, K. J., and Dalibard, J. 2011. Exploring the thermodynamics of a two-dimensional Bose gas. Phys. Rev. Lett., 107, 130401.Google Scholar
[60] Rudnick, I. 1978. Critical surface density of the superfluid component in He 4 films. Phys. Rev. Lett., 40, 1454.Google Scholar
[61] Bishop, D. J., and Reppy, J. D. 1978. Study of the superfluid transition in twodimensional He 4 films. Phys. Rev. Lett., 40, 1727.Google Scholar
[62] Petrov, D. S., Holzmann, M., and Shlyapnikov, G. V. 2000. Bose-Einstein condensation in quasi-2D trapped gases. Phys. Rev. Lett., 84, 2551.Google Scholar
[63] Tung, S., Lamporesi, G., Lobser, D., Xia, L., and Cornell, E. A. 2010. Observation of the presuperfluid regime in a two-dimensional Bose gas. Phys. Rev. Lett., 105, 230408.Google Scholar
[64] Ferrier-Barbut, I., Delehaye, M., Laurent, S., Grier, A. T., Pierce, M., Rem, B. S., Chevy, F., and Salomon, C. 2014. A mixture of Bose and Fermi superfluids. Science, 345, 1035.Google Scholar
[65] Zhu, Q., Zhang, C., and Wu, B. 2012. Exotic superfluidity in spin-orbit coupled Bose- Einstein condensates. Europhys. Lett., 100, 50003.Google Scholar
[66] Zheng, W., Yu, Z.-Q., Cui, X., and Zhai, H. 2013. Properties of Bose gases with the Raman-induced spin–orbit coupling. J. Phys. B, 46, 134007.Google Scholar
[67] Ozawa, T., Pitaevskii, L. P., and Stringari, S. 2013. Supercurrent and dynamical instability of spin-orbit-coupled ultracold Bose gases. Phys. Rev. A,, 87, 063610.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×