26 research outputs found
Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
An open quantum system, whose time evolution is governed by a master
equation, can be driven into a given pure quantum state by an appropriate
design of the system-reservoir coupling. This points out a route towards
preparing many body states and non-equilibrium quantum phases by quantum
reservoir engineering. Here we discuss in detail the example of a \emph{driven
dissipative Bose Einstein Condensate} of bosons and of paired fermions, where
atoms in an optical lattice are coupled to a bath of Bogoliubov excitations via
the atomic current representing \emph{local dissipation}. In the absence of
interactions the lattice gas is driven into a pure state with long range order.
Weak interactions lead to a weakly mixed state, which in 3D can be understood
as a depletion of the condensate, and in 1D and 2D exhibits properties
reminiscent of a Luttinger liquid or a Kosterlitz-Thouless critical phase at
finite temperature, with the role of the ``finite temperature'' played by the
interactions.Comment: 9 pages, 2 figure
Bose-Einstein Condensation of Excitons in Bilayer Electron Systems
An ordered state of electrons in solids in which excitons condense was
proposed many years ago as a theoretical possibility but has, until recently,
never been observed. We review recent studies of semiconductor bilayer systems
that provide clear evidence for this phenomenon and explain why exciton
condensation in the quantum Hall regime, where these experiments were
performed, is as likely to occur in electron-electron bilayers as in
electron-hole bilayers. In current quantum Hall exciton condensates, disorder
induces mobile vortices that flow in response to a supercurrent and limit the
extremely large bilayer counterflow conductivity.Comment: 19 pages including 4 figure
Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2
Recent theories suggest that the excitations of certain quantum Hall states
may have exotic braiding statistics which could be used to build topological
quantum gates. This has prompted an experimental push to study such states
using confined geometries where the statistics can be tested. We study the
transport properties of quantum point contacts (QPCs) fabricated on a
GaAs/AlGaAs two dimensional electron gas that exhibits well-developed
fractional quantum Hall effect, including at bulk filling fraction 5/2. We find
that a plateau at effective QPC filling factor 5/2 is identifiable in point
contacts with lithographic widths of 1.2 microns and 0.8 microns, but not 0.5
microns. We study the temperature and dc-current-bias dependence of the 5/2
plateau in the QPC, as well as neighboring fractional and integer plateaus in
the QPC while keeping the bulk at filling factor 3. Transport near QPC filling
factor 5/2 is consistent with a picture of chiral Luttinger liquid edge-states
with inter-edge tunneling, suggesting that an incompressible state at 5/2 forms
in this confined geometry
Even-denominator fractional quantum Hall physics in ZnO
The fractional quantum Hall (FQH) effect emerges in high-quality two-dimensional electron systems exposed to a magnetic field when the Landau-level filling factor, ν_e, takes on a rational value. Although the overwhelming majority of FQH states have odd-denominator fillings, the physical properties of the rare and fragile even-denominator states are most tantalizing in view of their potential relevance for topological quantum computation. For decades, GaAs has been the preferred host for studying these even-denominator states, where they occur at ν_e = 5/2 and 7/2. Here we report an anomalous series of quantized even-denominator FQH states outside the realm of III–V semiconductors in the MgZnO/ZnO 2DES electron at ν_e = 3/2 and 7/2, with precursor features at 9/2; all while the 5/2 state is absent. The effect in this material occurs concomitantly with tunability of the orbital character of electrons at the chemical potential, thereby realizing a new experimental means for investigating these exotic ground states
Pseudopotentials for multiparticle interactions in the quantum Hall regime
In fractional quantum Hall physics, the Hilbert space is projected to a single Landau level and the entire Hamiltonian consists of just the projected interelectron interaction. Haldane's pseudopotential formalism has been an extremely useful tool both for understanding these interactions and for understanding the quantum Hall states that result. In the current paper, we consider the analog of this pseudopotential construction that results from general M -body interactions rather than the usual (Coulomb) two-body interaction. © 2007 The American Physical Society
Vortex lattices in rotating atomic Bose gases with non-local interactions
We study the groundstates of rotating atomic Bose gases with non-local interactions. We focus on the weak-interaction limit of a model involving s- and d-wave interactions. With increasing d-wave interaction, the mean-field groundstate undergoes a series of transitions between vortex lattices of different symmetries (triangular, square, "stripe" and "bubble" crystal phases). We discuss the stability of these phases to quantum fluctuations. Using exact diagonalization studies, we show that with increasing d-wave interaction, the incompressible Laughlin state at filling factor ν = 1 / 2 is replaced by compressible stripe and bubble states. © 2006 Elsevier Ltd. All rights reserved
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Quantum Phase Transitions and the v=5/2 Fractional Hall State in Wide Quantum Wells
We study the nature of the v = 5/2 quantum Hall state in wide quantum wells under the mixing of electronic subbands and Landau levels. A general method is introduced to analyze the Moore-Read Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, under periodic boundary conditions in a “quartered” Brillouin zone scheme containing both even and odd numbers of electrons. By examining the rotational quantum numbers on the torus, we show spontaneous breaking of the particle-hole symmetry can be observed in finite-size systems. In the presence of electronic-subband and Landaulevel mixing, the particle-hole symmetry is broken in such a way that the anti-Pfaffian state is unambiguously favored, and becomes more robust in the vicinity of a transition to the compressible phase, in agreement with recent experiments. DOI: 10.1103/PhysRevLett.109.26680
Graviton chirality and topological order in the half-filled Landau level
The fractional quantum Hall state at the Landau level filling factor 5/2 is extremely interesting because it is likely the first non-Abelian state, but its precise nature remains unclear after decades of study. We demonstrate this can be resolved by studying the chirality of its graviton excitations, using circularly polarized Raman scattering. We discuss the advantage of this bulk probe over the existing edge probes
Energetics of Pfaffian–anti-Pfaffian domains
In several recent works it has been proposed that, due to disorder, the experimentally observed ν = 5/2 quantum Hall state could be microscopically composed of domains of Pfaffian order along with domains of anti-Pfaffian order. We numerically examine the energetics required for forming such domains and conclude that for the parameters appropriate for recent experiments, such domains would not occur
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Berry Phase and Model Wave Function in the Half-Filled Landau Level
We construct model wavefunctions for the half-filled Landau level parameterized by “composite
fermion occupation-number configurations” in a two-dimensional momentum space which corre-
spond to a Fermi sea with particle-hole excitations. When these correspond to a weakly-excited
Fermi sea, they have large overlap with wavefunctions obtained by exact diagonalization of lowest-
Landau-level electrons interacting with a Coulomb interaction, allowing exact states to be identified
with quasiparticle configurations. We then formulate a many-body version of the single-particle
Berry phase for adiabatic transport of a single quasiparticle around a path in momentum space, and
evaluate it using a sequence of exact eigenstates in which a single quasiparticle moves incrementally.
In this formulation the standard free-particle construction in terms of the overlap between “periodic
parts of successive Bloch wavefunctions” is reinterpreted as the matrix element of a “momentum
boost” operator between the full Bloch states, which becomes the matrix elements of a Girvin-
MacDonald-Platzman density operator in the many-body context. This allows computation of the
Berry phase for transport of a single composite fermion around the Fermi surface. In addition to a
phase contributed by the density operator, we find a phase of exactly π for this process