Theory of superfluidity and drag force in the one-dimensional Bose gas
Theory of superfluidity and drag force in the one-dimensional Bose gas
Alexander Yu. Cherny1, Jean-Sébastien Caux2, Joachim Brand3()
1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Moscow region, Russia; 2. Institute for Theoretical Physics, Science Park 904, University of Amsterdam, 1090 GL Amsterdam, The Netherlands; 3. Centre for Theoretical Chemistry and Physics and New Zealand Institute for Advanced Study, Massey University, Private Bag 102904 North Shore, Auckland 0745, New Zealand
The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quantitative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Landau’s criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns. The dynamical breakdown of superfluidity in random potentials is discussed in relation to Anderson localization and the predicted superfluid–insulator transition in these systems.
. Theory of superfluidity and drag force in the one-dimensional Bose gas[J]. Frontiers of Physics, 2012, 7(1): 54-71.
Alexander Yu. Cherny, Jean-Sébastien Caux, Joachim Brand. Theory of superfluidity and drag force in the one-dimensional Bose gas. Front. Phys. , 2012, 7(1): 54-71.
A. G. Sykes, M. J. Davis, and D. C. Roberts, Phys. Rev. Lett. , 2009, 103(8): 085302 doi: 10.1103/PhysRevLett.103.085302
12
S. Gupta, K. W. Murch, K. L. Moore, T. P. Purdy, and D. M. Stamper-Kurn, Phys. Rev. Lett. , 2005, 95(14): 143201 doi: 10.1103/PhysRevLett.95.143201
13
C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. , 2007, 99(26): 260401 doi: 10.1103/PhysRevLett.99.260401
14
S. E. Olson, M. L. Terraciano, M. Bashkansky, and F. K. Fatemi, Phys. Rev. A , 2007, 76(6): 061404 doi: 10.1103/PhysRevA.76.061404
15
S. Palzer, C. Zipkes, C. Sias, and M. K?hl, Phys. Rev. Lett. , 2009, 103(15): 150601 doi: 10.1103/PhysRevLett.103.150601
16
J. Catani, G. Lamporesi, D. Naik, M. Gring, M. Inguscio, F. Minardi, A. Kantian, and T. Giamarchi, arXiv:1106.0828 , 2011
17
L. Fallani, L. De Sarlo, J. E. Lye, M. Modugno, R. Saers, C. Fort, and M. Inguscio, Phys. Rev. Lett. , 2004, 93(14): 140406 doi: 10.1103/PhysRevLett.93.140406
18
C. D. Fertig, K. M. O’Hara, J. H. Huckans, S. L. Rolston, W. D. Phillips, and J. V. Porto, Phys. Rev. Lett. , 2005, 94(12): 120403 doi: 10.1103/PhysRevLett.94.120403
19
J. Mun, P. Medley, G. K. Campbell, L. G. Marcassa, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. , 2007, 99(15): 150604 doi: 10.1103/PhysRevLett.99.150604
20
J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature , 2008, 453(7197): 891 doi: 10.1038/nature07000
21
G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature , 2008, 453(7197): 895 doi: 10.1038/nature07071
22
B. Deissler, M. Zaccanti, G. Roati, C. D’Errico, M. Fattori, M. Modugno, G. Modugno, and M. Inguscio, Nat. Phys. , 2010, 6(5): 354 doi: 10.1038/nphys1635
23
V. A. Kashurnikov, A. I. Podlivaev, N. V. Prokof’ev, and B. V. Svistunov, Phys. Rev. B , 1996, 53(19): 13091 doi: 10.1103/PhysRevB.53.13091
M. Girardeau, J. Math. Phys. , 1960, 1(6): 516 doi: 10.1063/1.1703687
27
M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. Rigol, arXiv:1101.5337 , 2011, to appear in Rev. Mod. Phys.
28
In this paper we use the linear momentum and coordinates and velocities. The angular momentum and angle and angular velocity can easily be written as Lz = pL/(2π), ? = 2πx/L, ωz = 2πv/L, respectively.
F. D. M. Haldane, Phys. Rev. Lett. , 1981, 47: 1840, note a misprint in Eq. (7) for the density-density correlator: the sign before the second therm should be minus.
31
C. Raman, M. K?hl, R. Onofrio, D. S. Durfee, C. E. Kuklewicz, Z. Hadzibabic, and W. Ketterle, Phys. Rev. Lett. , 1999, 83(13): 2502 doi: 10.1103/PhysRevLett.83.2502
32
A. Y. Cherny, J. S. Caux, and J. Brand, Phys. Rev. A , 2009, 80(4): 043604 doi: 10.1103/PhysRevA.80.043604
V. N. Popov, Functional Integrals in Quantum Field Theory and Statistical Physics, Dordrecht: Reidel, 1983 doi: 10.1007/978-94-009-6978-0
53
V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge: Cambridge University Press, 1993, see Section XVIII.2
Note that the field theory predictions of [67] actually include a singularity also for ω>ω+(k), with a universal shoulder ratio. We neglect this here since it gives only a small correction to the results.
69
We slightly change the notations: our ω±and±μ±correspond to ω1,2 and μ1,2 in Ref. [67], respectively. We also denote the density of particles n and the Fermi wavevector for quasiparticles q0 instead of D and q used in Refs. [53, 67], respectively .
70
V. N. Golovach, A. Minguzzi, and L. I. Glazman, Phys. Rev. A , 2009, 80(4): 043611 doi: 10.1103/PhysRevA.80.043611
71
Y. Kagan, N. V. Prokof’ev, and B. V. Svistunov, Phys. Rev. A , 2000, 61(4): 045601 doi: 10.1103/PhysRevA.61.045601
72
J. M. Ziman, Principles of the Theory of Solids, Cambridge: Cambridge University Press, 1972
L. Sanchez-Palencia, D. Clément, P. Lugan, P. Bouyer, G. V. Shlyapnikov, and A. Aspect, Phys. Rev. Lett. , 2007, 98(21): 210401 doi: 10.1103/PhysRevLett.98.210401
84
P. Lugan, D. Clément, P. Bouyer, A. Aspect, M. Lewenstein, and L. Sanchez-Palencia, Phys. Rev. Lett. , 2007, 98(17): 170403 doi: 10.1103/PhysRevLett.98.170403
85
P. Lugan, D. Clément, P. Bouyer, A. Aspect, and L. Sanchez-Palencia, Phys. Rev. Lett. , 2007, 99(18): 180402 doi: 10.1103/PhysRevLett.99.180402
86
T. Paul, P. Schlagheck, P. Leboeuf, and N. Pavloff, Phys. Rev. Lett. , 2007, 98(21): 210602 doi: 10.1103/PhysRevLett.98.210602
G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, Phys. Rev. Lett. , 2008, 100(8): 084103 doi: 10.1103/PhysRevLett.100.084103
89
G. M. Falco, T. Nattermann, and V. L. Pokrovsky, Phys. Rev. B , 2009, 80(10): 104515 doi: 10.1103/PhysRevB.80.104515
90
I. L. Aleiner, B. L. Altshuler, and G. V. Shlyapnikov, Nat. Phys. , 2010, 6(11): 900 doi: 10.1038/nphys1758
91
J. Radi?, V. Ba?i?, D. Juki?, M. Segev, and H. Buljan, Phys. Rev. A , 2010, 81(6): 063639 doi: 10.1103/PhysRevA.81.063639
92
J. W. Goodman, Statistical Properties of Laser Speckle Patterns, in: Laser Speckle and Related Phenomena, edited by J.-C. Dainty , Berlin: Springer-Verlag, 1975, pp 9–75 doi: 10.1007/BFb0111436
93
D. Clément, A. F. Varón, J. A. Retter, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, New J. Phys. , 2006, 8(8): 165 doi: 10.1088/1367-2630/8/8/165
94
D. Pines and P. Nozières, The Theory of Quantum Liquids: Normal Fermi Liquids, New York: W. A. Benjamin, 1966, see Eq. (2.69)