Superfluid behaviour of a two-dimensional Bose gas

Abstract

Owing to thermal fluctuations, two-dimensional (2D) systems cannot undergo a conventional phase transition associated with the breaking of a continuous symmetry 1 . Nevertheless they may exhibit a phase transition to a state with quasi-longrange order via the Berezinskii-Kosterlitz-Thouless (BKT) mechanism 2 . A paradigm example is the 2D Bose fluid, such as a liquid helium film 3 , which cannot condense at non-zero temperature although it becomes superfluid above a critical phase space density. The quasi-long-range coherence and the microscopic nature of the BKT transition were recently explored with ultracold atomic gases 4-6 . However, a direct observation of superfluidity in terms of frictionless flow is still missing for these systems. Here we probe the superfluidity of a 2D trapped Bose gas using a moving obstacle formed by a micrometre-sized laser beam. We find a dramatic variation of the response of the fluid, depending on its degree of degeneracy at the obstacle location.'Flow without friction' is a hallmark of superfluidity 7 . It corresponds to a metastable state in which the fluid has a non-zero relative velocity v with respect to an external body such as the wall of the container or an impurity. This metastable state is separated from the equilibrium state of the system (v = 0) by a large energy barrier, so that the flow can persist for a macroscopic time. The height of the barrier decreases as v increases, and eventually passes below a threshold (proportional to the thermal energy) for a critical velocity v c . The microscopic mechanism limiting the barrier height depends on the nature of the defect and is associated with the creation of phonons and/or vortices 7 . Whereas the quantitative comparison between experiments and theory is complicated for liquid 4 He, cold atomic gases in the weakly interacting regime are well suited for precise tests of many-body physics. In particular, superfluidity was observed in 3D atomic gases by stirring a laser beam or an optical lattice through bosonic [8][9][10][11][12] or fermionic 13 fluids and by observing the resulting heating or excitations. Here we transpose this search for dissipation-less motion to a disc-shaped, non-homogeneous 2D Bose gas. We use a small obstacle to locally perturb the system. The obstacle moves at constant velocity on a circle centred on the cloud, allowing us to probe the gas at a fixed density. We repeat the experiment for various atom numbers, temperatures and stirring radii and identify a critical point for superfluid behaviour.Our experiments are performed with 2D Bose gases of N = 35,000-95,000 87 Rb atoms confined in the vertical direction by the harmonic potential W (z) and in the horizontal plane by the radially symmetric harmonic potential V (r) (see ref. perturbed by a focussed laser beam, which moves at constant velocity on a circle centred on the cloud. The stirring beam has a frequency greater than the 87 Rb resonance frequency ('blue detuning' of ≈2 nm) and thus creates a repulsive potential which causes a dip in the d...

Room-temperature superfluidity in a polariton condensate

“…1b. In contrast to experiments on superfluidity in atomic condensates 6,7 , here the position of the defect is kept fixed in space, while the speed of the quasi-particle flow is controlled by using the excitation angle, which is directly related to the polariton group velocity v g =hk p /m LP , where k p is the polariton wavevector and m LP the effective mass. intensities for a polariton flow moving upwards across an obstacle with an exciting angle chosen such that the flow speed is 19 µm/ps.…”

Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

“…Suitable mixtures with a large mass ratio are 40 An alternative experimental route to accessing the nonequilibrium response of the Fermi gas to an impurity that is introduced suddenly is to create a local scattering potential by a narrow laser beam. This has been demonstrated in recent experiments [97,98]. While in such a setup one cannot perform the RF-absorption or Ramsey-interference experiments, an observation of the OC should be possible through energy-counting statistics; see Sec.…”

Microscopic theory of a phase transition in a critical region: Bose–Einstein condensation in an interacting gas

“…It is immediate to generalize them to any trapping potentials and boundary conditions. They open a way to solve the long-standing problem of the BEC and other phase transitions [1][2][3][4][5][6][7][8][9][10][11][12], including a restricted canonical ensemble problem [2], and describe numerous modern laboratory and numerical experiments on the critical phenomena in BEC of the mesoscopic systems [22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

“…It becomes possible due to the newly developed methods of (a) the nonpolynomial averages and contraction superoperators [15,16], (b) the partial difference (recurrence) equations [17][18][19] (a discrete analog of the partial differential equations) for superoperators, and (c) a characteristic function and cumulant analysis for a joint distribution of the noncommutative observables. They allow us to take into account (I) the constraints in a many-body Hilbert space, which are the integrals of motion prescribed by a broken symmetry in virtue of a Noether's theorem, and constraintcutoff mechanism, responsible for the very existence of a phase transition and its nonanalytical features, [4,20,21] (II) an insufficiency of a grand-canonical-ensemble approximation, which is incorrect in the critical region [2,8] because of averaging over the systems with different numbers of particles, both below and above the critical point, i.e., over the condensed and noncondensed systems at the same time, that implies an error on the order of 100% for any critical function, (III) a necessity to solve the problem for a finite system with a mesoscopic (i.e., large, but finite) number of particles N in order to calculate correctly an anomalously large contribution of the lowest energy levels to the critical fluctuations and to avoid the infrared divergences of the standard thermodynamic-limit approach [5][6][7][8][9][10][11] as well as to resolve a fine structure of the λ-point, (IV) a fact that in the critical region the Dyson-type closed equations do not exist for true Green's functions, but do exist for the partial 1-and 2-contraction superoperators, which reproduce themselves under a contraction.The problem of the critical region and mesoscopic effects is directly related to numerous modern experiments and numerical studies on the BEC of a trapped gas (including BEC on a chip), where N ∼ 10 2 − 10 7 , (see, for example, [22][23][24][25][26][27][28][29][30][31][32][33]) and superfluidit...…”

“…The problem of the critical region and mesoscopic effects is directly related to numerous modern experiments and numerical studies on the BEC of a trapped gas (including BEC on a chip), where N ∼ 10 2 − 10 7 , (see, for example, [22][23][24][25][26][27][28][29][30][31][32][33]) and superfluidity of 4 He in nanodroplets (N ∼ 10 8 − 10 11 ) [34] and porous glasses [35].…”