ALLAN GRIFFIN Theoretical Condensed Matter and AMO Physics; BEC in Bose and Fermi superfluid gases.  Professor: B.Sc. and M.Sc., University of British Columbia (1961); Ph.D., Cornell University (1965). PDF at UCSD, La Jolla (1965-66). RESEARCH SABBATICALS: KFA Julich, Germany (1973); ILL, Grenoble, France (1980); Kyoto University, Japan (1987); University of Trento, Italy (1995); JILA, University of Colorado, Boulder, U.S.A. (1999). VISITING PROFESSOR: NIST, Gaithersburg, U.S.A. (2001); Collège de France, Paris (2001); University of Otago, N.Z. (2002). HONOURS: FRSC, Fellow of the American Physical Society, Bronze Medal of Collège de France. Fellow of CIFAR Quantum Materials Program Theory of ultracold quantum gases, especially the BCS-BEC crossover in superfluid Fermi gases.  Phone: (416)978-5199     Fax: (416)978-2537      e-mail: griffin@physics.utoronto.ca

NEW BOOK : BOSE-CONDENSED GASES AT FINITE TEMPERATURES.             This new book published by Cambridge gives a thorough summary of the dynamics of trapped Bose gases at finite temperatures, based on the research of A. Griffin, T. Nikuni and E. Zaremba. The coupled dynamics of the atoms in the Bose condensate and the thermal cloud is described by the simplified "ZNG model". This involves a generalized GP equation, with a source term allowing exchange of atoms with the thermal cloud. The non-condensate thermal cloud atoms are described by a kinetic equation, which includes the effects of collisions and mean fields involving the condensate atoms as well as usual collisions between the thermal atoms. These coupled equations are used to discuss collective modes in both the collisionless region (where collisions are a perturbation on the mean-field condensate dynamics) and the two-fluid region (where collisions play a crucial role in producing local equilibrium). Detailed derivations show how the Landau two-fluid hydrodynamics emerges in trapped Bose-condensed gases in the strong collision limit. This region can now be accessed in molecular Bose gases produced with Feshbach resonances in Fermi gases.

THE DISCOVERY OF SUPERFLUIDITY IN 1938

            An article of mine on the discovery of superfluidity in the period 1935-1938 has appeared in the August, 2008 issue of PhysicsWorld [Superfluidity: three people, two papers, one prize, by A. Griffin] . This is a shortened version of a longer article which gives a more detailed account of the discovery of superfluidity by Peter Kapitza, Jack Allen and Don Misener. My longer article can be downloaded here. The discovery of superfluidity: a chronology of events in 1935-1938. This material is copyrighted.

NEW LIGHT ON THE INTRIGUING HISTORY OF SUPERFLUIDITY IN LIQUID HELIUM

• Pdf of a public lecture given at LT25 in Amsterdam, Aug.6-13, 2008.


• For pdf of the paper, see A.Griffin, Journ. Physics: Condensed Matter, 21,164220 (2009)

BEC AND COOPER PAIRING IN TRAPPED QUANTUM GASES

               Eric Cornell, Wolfgang Ketterle and Carl Wieman received the 2001 Nobel Prize in Physics, for their discovery and fundamental studies of BEC in an atomic gas. By their pioneering work, they not only made an historic discovery but have opened a whole new research field involving ultracold atoms and coherent matter waves.

            In recent years, my research has been concerned with collective modes in superfluid ⁴He [1] and in high temperature superconductors.  I use many-body theory techniques based on thermal Green's functions.  I am now concentrating on similar problems in ultracold trapped atomic gases, including Bosons and Fermions.  This topic has become a major area of research since the successful discovery of BEC in an ultracold gas of ⁸⁷Rb atoms in Boulder in the summer of 1995.  Research continues to advance in this exciting area.

            In the last few years, my research has concentrated on the dynamical behaviour of atomic Bose condensates at finite temperatures, where one has a condensate as well as the thermal cloud. My collaborators (Tetsuro Nikuni at the Tokyo University of Science and Eugene Zaremba at Queen's University) and I have written a series of papers [17,18, 19] on the derivation of a generalized "Gross-Pitaevskii" equation of motion for the condensate and a Boltzmann kinetic equation of the single-particle distribution function describing the non-condensate atoms. These ZNG equations are coupled through dynamic mean fields as well as collisions involving atoms from both components. This derivation has been given using methods analogous to those used in classical gases as well as the more powerful Kadanoff-Baym Green's function formalism. More recently, the discussion has been extended down to very low temperatures, where the thermal quasiparticles are collective in nature (i.e. given by a Bogoliubov spectrum, instead of a free-particle spectrum with a Hartree-Fock mean field).  This latter work is part of the Ph.D thesis of Milena Imamovic-Tomasovic [16,23,27].

            Recently Zaremba and coworkers have used the ZNG generalized GP equation and the kinetic equation for HF excitations to work out the temperature dependence of condensate growth as well as the frequency and damping of various kinds of collective modes in trapped gses. This latter work involved numerical solution of the kinetic equation by Monte Carlo simulation techniques [B. Jackson and E. Zaremba, PRL 87, 100404 (2001)]. The excellent agreement found with experimental data gives strong evidence that the ZNG formulation is an excellent starting point for the study of a wide variety of non-equilibrium properties of trapped Bose gases at finite temperatures.

            Starting from these ZNG equations of motion, one can then take moments over the kinetic equation to derive hydrodynamic equations for the thermal cloud degrees of freedom. The resulting coupled two-fluid hydrodynamic equations involve the collisions between the condensate and non-condensate atoms. These collisions lead to diffusive equilibrium between the two components, and give rise to a new characteristic relaxation rate for this process. The final step was achieved in a recent paper by Nikuni and Griffin [26] in which the deviations for local hydrodynamic eqilibrium were included using the Chapman-Enskog procedure. After considerable effort, we were able to write our coupled hydrodynamic equations in a form identical to the famous Landau-Khalatnikov two-fluid hydrodynamic equations, including damping from transport coefficients [24]. The latter equations are the basis of our understanding of superfluidity in liquid Helium 4.

            A by-product of the above derivation is that we determined exact expressions for the thermal conductivity, shear viscosity and the coefficients of second viscosity. Evaluating these expressions gives explicit results for the characteristic relaxation times in a trapped Bose gas. These determine the crossover between the collisionless and hydrodynamic region, as well as how fast local equilibrium is reached after the trapped gas is perturbed. The molecular Bose condensation which can now be produced in Fermi gases may allow us to study the two-fluid domain in the near future.

            Current work at Toronto is mainly in the physics of the BCS-BEC crossover in trapped Fermi superfluid gases.  In particular, we are studying the collective modes of the molecular Bose condensate and the relevance of two-fluid hydrodynamics near the Feshbach resonance (unitarity).

            For introductory accounts of my recent BEC work at finite temperature, I recommend my lectures given at various summer schools (Banff [22], Varenna [14] and Canberra [21]). For a brief review of the history of BEC studies before 1965, see my Varenna lecture [15]. For a general overview for the non-expert, a recent powerpoint colloquium of mine on ultracold atoms is given below under Recent Talks.

            At Toronto, there is an active experimental programme studying the physics of ultracold atoms. See the homepages of Aephraim Steinberg and Joseph Thywissen for a more detailed discussion of their research. I also keep contact with the theory group of Eugene Zaremba at Queen's University in Kingston.

TORONTO ULTRACOLD ATOM THEORY GROUP:

FORMER MEMBERS

• Edward Taylor, completed Ph.D. in Nov. 2007 ( Now a postdoctoral fellow, Department of Physics, Ohio State University, Columbus , Ohio).
• Satoru Konabe, visiting JSPS graduate student from Tokyo University of Science (Mar. 15 - Sept. 15, 2007).
• Dr. Duncan O'Dell, PDF (As of Jan. 1, 2007, Assistant Professor, Dept. of Physics, McMaster University).
• David Luxat, completed Ph.D. in February, 2005 (now a member of the research staff of AECL).
• Prof. Yoji Ohashi, Sabbatical visitor (Now, Associate Professor, Faculty of Science, Keio University, Yokohama, Japan).
• Shunji Tsuchiya, JSPS Graduate Fellow from Waseda University (Now a postdoc at Keio University, Japan).
• Dr. Tetsuro Nikuni, JSPS Fellow (Assistant Professor, Department of Physics, Tokyo University of Science, Shinjuku-ku, Tokyo).
• Dr. Jamie Williams, PDF (now at Wolfram Research, Champaign, Illinois).
• Milena Imamovic-Tomasovic, completed Ph.D., Sept., 2001 (Now in Financial Services).

Some Recent Talks

RECENT PUBLICATIONS ON BEC:

1. Excitations in a Bose-Condensed Liquid, A. Griffin (Cambridge, N.Y., 1993), 310p. book reviewing the role of Bose broken symmetry on the nature of excitations in Bose fluids: Reprinted as a paperback, December, 2005.   NEW     See Erratum sheet.
2. Bose-Einstein Condensation, ed. by A. Griffin, D.W. Snoke and S. Stringari (Cambridge, N.Y., 1995), 610p. book with reviews on BEC before 1995. Also in paperback.
3. A. Griffin, Conserving and gapless approximations for an inhomogeneous Bose gas at finite temperature, Phys. Rev. B53, 9341 (1996).
4. A. Griffin, Rigorous density functional theory for inhomogeneous Bose-condensed fluids, Can. Journ. Phys. (Brockhouse issue) 73, 755 (1995).
5. A. Griffin and S. Stringari, Surface region of superfluid ⁴He as a dilute Bose-condensed gas, Phys. Rev. Lett. 76, 259 (1996).
6. W.C. Wu and A. Griffin, Quantized hydrodynamic model and the dynamic structure factor for a trapped Bose gas, Phys. Rev. A54, 4204 (1996).
7. A. Griffin, W.C. Wu and S. Stringari, Hydrodynamic modes in a trapped Bose gas above the Bose-Einstein transition, Phys. Rev. Lett., 78, 1838 (1997).
8. D.A.W. Hutchinson, E. Zaremba and A. Griffin, Finite temperature excitations of a trapped Bose gas, Phys. Rev. Lett. 78, 1842 (1997).
9. E. Zaremba, A. Griffin and N. Nikuni, Two-fluid hydrodynamics for a trapped weakly-interacting Bose gas, Phys. Rev. A57, 4695 (1998).
10. A. Griffin and E. Zaremba, First and second sound in a uniform Bose gas, Phys. Rev. A56, 4839 (1997).
11. T. Nikuni and A. Griffin, Hydrodynamic damping in trapped Bose gases, Journ. Low Temp. Physics, 111, 793 (1998).
12. Hua Shi and A. Griffin, Finite temperature excitations in a dilute Bose-condensed gas, Physics Reports, 304, 1 (1998). This is a long review-type article using Green's function techniques.
13. T. Nikuni and A. Griffin, Hydrodynamic modes and pulse propagation in cigar-shaped traps, Phys. Rev. A58, 4044 (1998).
14. Allan Griffin, Theory of excitations of the condensate and non-condensate at finite temperatures. Three lectures given at the BEC Varenna Summer School, July 7-17, 1998. Published in "Bose-Einstein Condensation in Atomic Gases", edited by M. Inguscio, S. Stringari and C. Wieman (IOS Press, Amsterdam, 1999), p. 591.
15. Allan Griffin, A Brief History of Our Understanding of BEC: From Bose to Beliaev. Lecture given at the BEC Varenna Summer School, July 7-17, 1998. Published in "Bose-Einstein Condensation in Atomic Gases", ed. by M. Inguscio, S. Stringari and C. Wieman (IOS Press, Amsterdam, 1999), p.1.
16. Milena Imamovic-Tomasovic and Allan Griffin, Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas, Phys. Rev. A60, 494 (1999).
17. T. Nikuni, E. Zaremba and A. Griffin, Two-Fluid Dynamics for a Bose-Einstein Condensate out of Local Equilibrium with the Noncondensate, Phys. Rev. Lett., 83, 10 (1999).
18. E. Zaremba, T. Nikuni and A. Griffin, Dynamics of trapped Bose gases at finite temperatures, Journ. Low Temp. Phys., 116, 277 (1999).
19. T. Nikuni, A. Griffin and E. Zaremba, Two-fluid hydrodynamics of a Bose gas including damping from normal fluid transport coefficients, Can. Journ. Phys. (Stoicheff Special Issue), 78, 415 (2000).
20. J.E. Williams and A. Griffin, Damping of condensate collective modes due to equilibration with the non-condensate, Phys. Rev. A63 , 023612 (2000).
21. A. Griffin, Condensate oscillations, kinetic equations and two-fluid hydrodynamics in a Bose gas, in "Bose-Einstein Condensation: From atomic physics to quantum liquids", ed. by C.M. Savage and M. Das (World Scientific, Singapore, 2000), p.65-115. Based on 4 lectures given at the 13^th Physics Summer School, Australian National University, Canberra, Jan. 17-28, 2000.
22. A. Griffin, BEC and the New World of Coherent Matter Waves, Three tutorial lectures given at the CRM Summer School in Banff, Alberta, June 27-July 10, 1999. See "Theoretical Physics at the End of the Twentieth Century", ed. by Y. Saint-Aubin and L. Vinet (Springer-Verlag, N.Y., 2002).
23. M. Imamovic-Tomasovic and A. Griffin, Generalized Boltzmann equation for a trapped Bose-condensed gas using the Kadanoff-Baym formalism, in "Recent Progress in Non-Equilibrium Green's functions", ed. by M. Bonitz (World Scientific, Singapore, 2000), p.404-417.
24. A. Griffin and T. Nikuni, Two-Fluid Hydrodynamics in Trapped Bose Gases and in Superfluid Helium, Invited paper, Proceedings of The International Symposium on Quantum Fluids and Solids, Minneapolis, June, 2000, published in Journ. Low Temp. Phys. 121 , 247 (2000).
25. J.E. Williams and A. Griffin, Damped Bogoliubov excitations of a condensate interacting with a static thermal cloud, Phys. Rev. A64 , 013606 (2001).
26. T. Nikuni and A. Griffin, Landau-Khalatnikov two-fluid hydrodynamics of a trapped Bose gas, Phys. Rev. A63, 033608 (2001).
27. M. Imamovic-Tomasovic and A. Griffin, Quasiparticle kinetic equation in a trapped Bose gas at low temperatures, Journ. of Low Temperature Physics, 122, 617 (2001).
28. T. Nikuni and A. Griffin, Temperature-dependent relaxation times in a trapped Bose-condensed gas, Phys. Rev. A65, 011601 (2001).
29. D. Luxat and A. Griffin, Coherent tunneling of atoms from Bose Condensed gases at finite temperatures, Phys. Rev. A65 , 043618 (2002).
30. J.E. Williams, E. Zaremba, B. Jackson, T. Nikuni and A. Griffin, Dynamical Instability of a Condensate Induced by a Rotating Thermal Gas, Phys. Rev. Lett. 88 , 070401 (2002).
31. Y. Ohashi and A. Griffin, The BCS-BEC Crossover in a gas of Fermi atoms with a Feshbach resonance, Phys. Rev. Lett. 89 , 130402 (2002).
32. Y. Ohashi and A. Griffin, Superfluid transition temperature in a trapped gas of Fermi atoms with a Feshbach resonance, Phys. Rev. A 67, 033603 (2003).
33. D. L. Luxat and A. Griffin, Dynamic correlation functions in one-dimensional quasi-condensates, Phys. Rev. A 67, 043603 (2003).
34. Y. Ohashi and A. Griffin, Superfluidity and collective modes in a uniform gas of Fermi atoms with a Feshbach resonance, Phys. Rev. A 67, 063612 (2003).
35. S. Tsuchiya and A. Griffin, Damping of Bogoliubov Excitations in Optical Lattices, Phys. Rev. A 70, 023611 (2004).
36. Y. Ohashi and A. Griffin, Fermi excitations in a trapped Fermi atomic Fermi gas with a molecular Bose condensate, submitted to PRL, Feb. 2, 2004.
37. A. Griffin, "The first BEC conference in Levico in 1993", in Journ. Phys. B: AMO Physics, April 14, 2004 issue. This is the Introduction to a special issue devoted to the proceedings of a Conference on the Theory of Quantum Gases and Quantum Coherence, held in Levico, Italy , June 12-14, 2003.
38. T. Nikuni and A. Griffin, Frequency and damping of hydrodynamic modes in a trapped Bose-condensed gas", Phys. Rev. A69, 023604 (2004) (16 pages).
39. Y. Ohashi and A. Griffin , "Single-particle excitations in a trapped gas of Fermi atoms in the BCS-BEC crossover region", Phys. Rev. A72, 013601 (2005) (25 pages).
40. Y. Ohashi and A. Griffin, "Collective modes and the effect of single-particle excitations in the BCS-BEC crossover region of a trapped Fermi superfluid", submitted to PRA on March 28, 2005.
    
41. Y. Ohashi and A. Griffin, "Single-particle excitations in a trapped gas of Fermi atoms in the BCS-BEC crossover region. II. Broad Feshbach resonance", Phys. Rev. A. 72, 063606 (2005) (8 pages).
42. A. Griffin, "John C. McLennan and his pioneering research on superfluid Helium", Physics in Canada 61, 31-38 (2005).
43. S. Tsuchiya and A. Griffin, "Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures", Phys. Rev. A 72, 053621 (2005) (7 pages).
44. E. Taylor and A. Griffin, "Two-fluid hydrodynamic modes in a trapped superfluid gas", Phys. Rev. A 72, 053630 (2005) (13 pages).
45. E. Taylor, A. Griffin, N. Fukushima and Y. Ohashi, "Pairing fluctuations and the superfluid density through the BCS-BEC crossover'', Phys. Rev. A 74, 063626 (2006) (14 pages).
46. N. Fukushima, Y. Ohashi, E. Taylor and A. Griffin, "Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures'', Phys. Rev. A 75, 033609 (2007) (10 pages).
47. E. Taylor, A. Griffin and Y. Ohashi, ''Spin-polarized Fermi superfluids as Bose-Fermi mixtures'', Phys. Rev. A 76, 023614 (2007) (12 pages).
48. E. Taylor, Hui Hu, Xia-Ji Liu and Allan Griffin, "Probing two-fluid hydrodynamics in a trapped Fermi superfluid at unitarity", submitted to PRL in Sept. 2007.
49. E. Taylor, Hui Hu, Xia-Ji Liu and Allan Griffin, "Variational theory of two-fluid hydrodynamic modes at unitarity", Phys. Rev. A 77, 033608 (2008) (15 pages).
50. A. Griffin, Superfluidity: three people, two papers, one prize, Physics World, August issue, 27-30 (2008).
51. A. Griffin, T.Nikuni and E.Zaremba, "Bose-condensed gases at finite temperatures", Cambridge University Press, February, 2009.
52. A. Griffin, "New light on the intriguing history of superfluidity in liquid ⁴He", Journ. Physics: Condensed Matter, 21,164220 (2009).
53. E. Taylor, H. Hu, X.-J. Liu, L. P. Pitaevskii, A. Griffin, S. Stringari, "First and second sound sound in a strongly interacting Fermi gas", Phys. Rev. A, 80 053601 (2009) (7 pages).
54. A. Griffin , "Laszlo Tisza (1907-2009): an appreciation", Journ. Low Temp. Phys. 157, 1573 (2009).
55. H. Hu, E. Taylor, X.-J. Liu , S. Stringari and A. Griffin, "Second sound and the density response function in uniform superfluid atomic gases", submitted to New Journ. Phys., Jan.6, 2010.

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