Multiparticle interference in electronic Mach-Zehnder interferometers

We study theoretically electronic Mach-Zehnder interferometers built from integer quantum Hall edge states, showing that the results of recent experiments can be understood in terms of multiparticle interference effects. These experiments probe the visibility of Aharonov-Bohm (AB) oscillations in differential conductance as an interferometer is driven out of equilibrium by an applied bias, finding a lobe pattern in visibility as a function of voltage. We calculate the dependence on voltage of the visibility and the phase of AB oscillations at zero temperature, taking into account long range interactions between electrons in the same edge for interferometers operating at a filling fraction $\nu=1$. We obtain an exact solution via bosonization for models in which electrons interact only when they are inside the interferometer. This solution is non-perturbative in the tunneling probabilities at quantum point contacts. The results match observations in considerable detail provided the transparency of the incoming contact is close to one-half: the variation in visibility with bias voltage consists of a series of lobes of decreasing amplitude, and the phase of the AB-fringes is practically constant inside the lobes but jumps by $\pi$ at the minima of the visibility. We discuss in addition the consequences of approximations made in other recent treatments of this problem. We also formulate perturbation theory in the interaction strength and use this to study the importance of interactions that are not internal to the interferometer.Comment: 20 pages, 15 figures, final version as publishe

Density matrix renormalization group for bosonic quantum Hall effect

We developed a density matrix renormalization-group technique to study quantum Hall fractions of fast rotating bosons. In this paper we present a discussion of the method together with the results which we obtain in three distinct cases of the narrow channel, cylinder and spherical geometries. In the narrow channel case, which is relevant to anisotropic confining traps in the limit of extremely fast rotation, we find a series of zero-temperature phase transitions in the strongly interacting regime as a function of the interaction strength between bosons. We compute energies and density profiles for different filling fractions on a cylinder and compare the convergence rates of the method in the cylinder and a sphere geometries.Comment: 8 pages, 7 figures, final version as publishe

Density wave and supersolid phases of correlated bosons in an optical lattice

Motivated by the recent experiment on the Bose-Einstein condensation of $^{52}$Cr atoms with long-range dipolar interactions (Werner J. et al., Phys. Rev. Lett., 94 (2005) 183201), we consider a system of bosons with repulsive nearest and next-nearest neighbor interactions in an optical lattice. The ground state phase diagram, calculated using the Gutzwiller ansatz, shows, apart from the superfluid (SF) and the Mott insulator (MI), two modulated phases, \textit{i.e.}, the charge density wave (CDW) and the supersolid (SS). Excitation spectra are also calculated which show a gap in the insulators, gapless, phonon mode in the superfluid and the supersolid, and a mode softening of superfluid excitations in the vicinity of the modulated phases. We discuss the possibility of observing these phases in cold dipolar atoms and propose experiments to detect them

Solution of a model for the two-channel electronic Mach-Zehnder interferometer

We develop the theory of electronic Mach-Zehnder interferometers built from quantum Hall edge states at Landau level filling factor \nu = 2, which have been investigated in a series of recent experiments and theoretical studies. We show that a detailed treatment of dephasing and non-equlibrium transport is made possible by using bosonization combined with refermionization to study a model in which interactions between electrons are short-range. In particular, this approach allows a non-perturbative treatment of electron tunneling at the quantum point contacts that act as beam-splitters. We find an exact analytic expression at arbitrary tunneling strength for the differential conductance of an interferometer with arms of equal length, and obtain numerically exact results for an interferometer with unequal arms. We compare these results with previous perturbative and approximate ones, and with observations.Comment: 13 pages, 9 figures, final version as publishe

Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes

Topological states of matter present a wide variety of striking new phenomena. Prominent among these is the fractionalisation of electrons into unusual particles: Majorana fermions [1], Laughlin quasiparticles [2] or magnetic monopoles [3]. Their detection, however, is fundamentally complicated by the lack of any local order, such as, for example, the magnetisation in a ferromagnet. While there are now several instances of candidate topological spin liquids [4], their identification remains challenging [5]. Here, we provide a complete and exact theoretical study of the dynamical structure factor of a two-dimensional quantum spin liquid in gapless and gapped phases. We show that there are direct signatures - qualitative and quantitative - of the Majorana fermions and gauge fluxes emerging in Kitaev's honeycomb model. These include counterintuitive manifestations of quantum number fractionalisation, such as a neutron scattering response with a gap even in the presence of gapless excitations, and a sharp component despite the fractionalisation of electron spin. Our analysis identifies new varieties of the venerable X-ray edge problem and explores connections to the physics of quantum quenches.Comment: 7 pages, 3 figure

Dynamics of Fractionalization in Quantum Spin Liquids

We present the theory of dynamical spin-response for the Kitaev honeycomb model, obtaining exact results for the structure factor (SF) in gapped and gapless, Abelian and non-Abelian quantum spin-liquid (QSL) phases. We also describe the advances in methodology necessary to compute these results. The structure factor shows signatures of spin-fractionalization into emergent quasiparticles -- Majorana fermions and fluxes of $Z_2$ gauge field. In addition to a broad continuum from spin-fractionalization, we find sharp ($\delta$-function) features in the response. These arise in two distinct ways: from excited states containing only (static) fluxes and no (mobile) fermions; and from excited states in which fermions are bound to fluxes. The SF is markedly different in Abelian and non-Abelian QSLs, and bound fermion-flux composites appear only in the non-Abelian phase.Comment: 21 pages, 14 figure

Equilibration of integer quantum Hall edge states

We study equilibration of quantum Hall edge states at integer filling factors, motivated by experiments involving point contacts at finite bias. Idealising the experimental situation and extending the notion of a quantum quench, we consider time evolution from an initial non-equilibrium state in a translationally invariant system. We show that electron interactions bring the system into a steady state at long times. Strikingly, this state is not a thermal one: its properties depend on the full functional form of the initial electron distribution, and not simply on the initial energy density. Further, we demonstrate that measurements of the tunneling density of states at long times can yield either an over-estimate or an under-estimate of the energy density, depending on details of the analysis, and discuss this finding in connection with an apparent energy loss observed experimentally. More specifically, we treat several separate cases: for filling factor \nu=1 we discuss relaxation due to finite-range or Coulomb interactions between electrons in the same channel, and for filling factor \nu=2 we examine relaxation due to contact interactions between electrons in different channels. In both instances we calculate analytically the long-time asymptotics of the single-particle correlation function. These results are supported by an exact solution at arbitrary time for the problem of relaxation at \nu=2 from an initial state in which the two channels have electron distributions that are both thermal but with unequal temperatures, for which we also examine the tunneling density of states.Comment: 12 pages, 5 figures, final version as publishe

Exact Results for Tunneling Problems of Bogoliubov Excitations in the Critical Supercurrent State

We show the exact solution of Bogoliubov equations at zero-energy in the critical supercurrent state for arbitrary shape of potential barrier. With use of this solution, we prove the absence of perfect transmission of excitations in the low-energy limit by giving the explicit expression of transmission coefficient. The origin of disappearance of perfect transmission is the emergence of zero-energy density fluctuation near the potential barrier.Comment: 6 pages, 3 figures; Proceedings of QFS200