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.

Magnetotransport experiments on high mobility two-dimensional electron gases in GaAs͞AlGaAs heterostructures have revealed striking anomalies near half filling of several spin-resolved, yet highly excited, Landau levels. These anomalies include strong anisotropies and nonlinearities of the longitudinal resistivity r xx which commence only below about 150 mK. These phenomena are not seen in the ground state or first excited Landau level but begin abruptly in the third level. Although their origin remains unclear, we speculate that they reflect the spontaneous development of a generic anisotropic many-electron state. [S0031-9007(98) A magnetic field applied perpendicular to the plane of a two-dimensional electron gas (2DEG) resolves the energy spectrum into discrete Landau levels (LLs). As the field increases, the Fermi level drops down through the Landau ladder in a series of steps until, at high field, it resides in the lowest (N 0) level. In this situation the kinetic energy of the electrons is quenched and electron-electron interactions dominate the physics with the fractional quantized Hall effect (FQHE) as the most spectacular consequence [1]. After more than 15 years of study, much is known about electron correlations in this lowest LL case. The same cannot be said when the Fermi level is in a higher Landau level. In the second LL (N 1), the FQHE is virtually absent; only fragile and poorly understood states at Landau filling fractions n 7͞3, 5͞2, and 8͞3 are seen in the best samples. In the third and higher LLs (N $ 2) still less is known, although there have been interesting suggestions of charge density waves in the clean limit [2,3]. At very high N, and therefore very low magnetic field, the Landau level splitting becomes insignificant and the 2DEG assumes the character of a weakly disordered Fermi liquid.In this paper we report the observation of several dramatic anomalies in the low temperature magnetotransport of clean 2DEGs when the Fermi level lies near the middle of a spin-resolved highly excited Landau level. These effects, which commence only below about 150 mK, abruptly begin and are strongest in the third (N 2) LL, but persist up to about N 6. Including strong anisotropies and intriguing nonlinearities of the resistivity, these effects suggest a considerably more interesting tableau at high N than independent electrons moving in a disordered Landau band.The samples used in this study are GaAs͞AlGaAs heterojunctions grown by molecular beam epitaxy (MBE). Data from six samples (A through F) will be discussed. Samples A, B, and C were taken from one MBE wafer, D and E from a second, and F from a third. Each wafer was rotated during growth to ensure high homogeneity of the electron density n s . These densities (in units of 10 11 cm 22 ) are close to n s 2.67 for samples A, B, and C; n s 2.27 for samples D and E; and n s 1.52 for sample F. The low temperature mobility of each is m $ 9 3 10 6 cm 2 ͞V s. Each sample was cleaved (along ͗110͘ directions) into a 5 3 5 mm square from its parent ͗001͘ wa...

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 ...

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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

Quasi-particles with fractional charge and statistics, as well as modified Coulomb interactions, exist in a two-dimensional electron system in the fractional quantum Hall (FQH) regime. Theoretical models of the FQH state at filling fraction v = 5/2 make the further prediction that the wave function can encode the interchange of two quasi-particles, making this state relevant for topological quantum computing. We show that bias-dependent tunneling across a narrow constriction at v = 5/2 exhibits temperature scaling and, from fits to the theoretical scaling form, extract values for the effective charge and the interaction parameter of the quasi-particles. Ranges of values obtained are consistent with those predicted by certain models of the 5/2 state.

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...

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