We have created polaritons in a harmonic potential trap analogous to atoms in optical traps. The trap can be loaded by creating polaritons 50 micrometers from its center that are allowed to drift into the trap. When the density of polaritons exceeds a critical threshold, we observe a number of signatures of Bose-Einstein condensation: spectral and spatial narrowing, a peak at zero momentum in the momentum distribution, first-order coherence, and spontaneous linear polarization of the light emission. The polaritons, which are eigenstates of the light-matter system in a microcavity, remain in the strong coupling regime while going through this dynamical phase transition.

The tunneling conductance between two parallel 2D electron systems has been measured in a regime of strong interlayer Coulomb correlations. At total Landau level filling n T 1 the tunnel spectrum changes qualitatively when the boundary separating the compressible phase from the ferromagnetic quantized Hall state is crossed. A huge resonant enhancement replaces the strongly suppressed equilibrium tunneling characteristic of weakly coupled layers. The possible relationship of this enhancement to the Goldstone mode of the broken symmetry ground state is discussed. PACS numbers: 71.10.Pm, 73.40.Hm, 73.40.Gk When two parallel two-dimensional electron systems (2DES) are sufficiently close together, interlayer Coulomb interactions can produce collective states which have no counterpart in the individual 2D systems [1][2][3]. One of the simplest, yet most interesting, examples occurs when the total electron density, N T , equals the degeneracy, eB͞h, of a single spin-resolved Landau level produced by a magnetic field B. In the balanced case (i.e., with layer densities N 1 N 2 N T ͞2), the Landau level filling factor of each layer viewed separately is n hN T ͞2eB 1͞2. If the separation d between the layers is large, they behave independently and are well described as gapless composite fermion liquids. No quantized Hall effect (QHE) is seen. On the other hand, as d is reduced, the system undergoes a quantum phase transition [4-6] to an incompressible state best described by the total filling factor n T 1͞2 1 1͞2 1. A quantized Hall plateau now appears at r xy h͞e 2 . Both Coulomb interactions and interlayer tunneling contribute to the strength of this QHE but there is strong evidence from experiment [3,7] and theory [1,8] that the incompressibility survives in the limit of zero tunneling. This remarkable collective state exhibits a broken symmetry [9][10][11][12], spontaneous interlayer phase coherence, and may be viewed as a kind of easy-plane ferromagnet. The magnetization of this ferromagnet exists in a pseudospin space; electrons in one layer are pseudospin up, while those in the other layer are pseudospin down. Numerous interesting properties are anticipated, including linearly dispersing Goldstone collective modes (i.e., pseudospin waves), a finite temperature Kosterlitz-Thouless transition, dissipationless transport for currents directed oppositely in the two layers, and bizarre topological defects in the pseudospin field [9][10][11][12][13]. To date, most experimental results on this system have derived from electrical transport measurements [3,4,7,14,15] although recently an optical study has been reported [16].In this paper we report on a new study of the double layer n T 1 ferromagnetic quantum Hall state, and its transition at large layer separation to a compressible phase, using the method of tunneling spectroscopy. Earlier experiments have shown that there is a strong suppression of the equilibrium tunneling between two widely separated parallel 2DESs at high magnetic field [17,18]. This suppression is a ...

Low-temperature, electronic transport in Landau levels N > 1 of a twodimensional electron system is strongly anisotropic. At half-filling of either spin level of each such Landau level the magnetoresistance either collapses to form a deep minimum or is peaked in a sharp maximum, depending on the in-plane current direction. Such anisotropies are absent in the N = 0 and N = 1 Landau level, which are dominated by the states of the fractional quantum Hall effect. The transport anisotropies may be indicative of a new many particle state, which forms exclusively in higher Landau levels.Typeset using REVT E X 1

We have measured the transport properties of high-quality quantum wires fabricated in GaAs-AlGaAs by using cleaved edge overgrowth. The low temperature conductance is quantized as the electron density in the wire is varied. While the values of the conductance plateaus are reproducible, they deviate from multiples of the universal value of 2e 2 ͞h by as much as 25%. As the temperature or dc bias increases the conductance steps approach the universal value. Several aspects of the data can be explained qualitatively using Luttinger liquid theory although there remain major inconsistencies with such an interpretation. [S0031-9007(96) One-dimensional (1D) electronic systems, so-called Luttinger liquids, are expected to show unique transport behavior as a consequence of the Coulomb interaction between carriers [1][2][3][4]. Even for Coulomb energies smaller than the electron kinetic energy correlated electron behavior is expected. Because of the large quantum mechanical zero point motion of the electrons, these correlations are short ranged and their spatial extent is expected to increase in a power law manner as the system's temperature is lowered [4]. The longer correlation length causes the system to be more susceptible to pinning by local impurities. Therefore the conductance of a 1D system is expected to be suppressed at low temperature even for a wire with just a few impurities [4][5][6]. This remarkable results as well as many other non-Fermi liquid properties of the Luttinger model remain largely untested by experiments due to the lack of a suitable 1D wire [7].One of the fingerprints of a noninteracting 1D conductor is its quantized conductance in multiples of the universal value G O 2e 2 ͞h [8]. This quantization results from an exact compensation of the increasing electron velocity and the decreasing density of states as the number of carriers increases. Therefore, as subsequent 1D electronic subband are filled with electrons, the conductance appears as a series of plateaus or steps with values equal to G Q multiplied by the number of partly occupied wire modes ͑N͒.In an earlier publication, mainly focusing on our novel wire fabrication process, we determined the transport mean free path as well as the energy and mode spectrum in the wire using magneto-transport spectroscopy [9]. The exceptionally long transport mean free path in excess of 10 mm and the exceedingly large subband spacing of 20 meV make these wires ideal for studying effects of electron-electron ͑e-e͒ interactions in 1D. Here we present results of such an investigation as temperature and bias voltage are varied.Transport through the wires at low temperatures (0.3 K) presents a significant mystery. Although the wire's conductance is quantized in equal steps showing plateaus that are flat to within 5%, the quantized conductance is reproducibly lower than NG Q . This reduction is of fixed amount for a particular wire width and can be as large as 25%. At higher temperatures and dc biases the conductance approaches NG Q . We discuss three differen...

We report on measurements of quantum many-body modes in ballistic wires and their dependence on Coulomb interactions, obtained by tunneling between two parallel wires in an GaAs/AlGaAs heterostructure while varying electron density. We observed two spin modes and one charge mode of the coupled wires and mapped the dispersion velocities of the modes down to a critical density, at which spontaneous localization was observed. Theoretical calculations of the charge velocity agree well with the data, although they also predict an additional charge mode that was not observed. The measured spin velocity was smaller than theoretically predicted.