Wavefunctional approach to the bilayer \nu =1 system and a possibility for a double non-chiral pseudospin liquid

We systematically discuss candidate wave functions for the ground state of the bilayer \nu = 1 as the distance between the layers is varied. Those that describe increased intralayer correlations at finite distance show a departure from the superflid description for smaller distances. They may support finite energy meron excitations and a dissipative collective mode in the place of the Goldstone mode of the ordered phase i.e. describe a vortex metal phase, or imply even an incompressible, pseudospin liquid, behavior. Therefore they describe possible outcomes of quantum disordering at finite distance between the layers. The vortex metal phase may show up in experiments in the presence of disorder at lower temperatures and explain the observed "imperfect superfluidity", and the pseudospin liquid phase may be the cause of the thermally activated (gapped) behavior of the longitudinal and Hall resistances at higher temperatures in counterflow experiments.Comment: 10 pages, 4 figure

Ground state, quasi-hole, a pair of quasihole wavefunctions and instability in bilayer quantum Hall systems

Bilayer quantum Hall system (BLQH) differ from its single layer counterparts (SLQH) by its symmetry breaking ground state and associated neutral gapless mode in the pseudo-spin sector. Due to the gapless mode, qualitatively good groundstate and low energy excited state wavefunctions at any finite distance is still unknown. We investigate this important open problem by the Composite Boson (CB) theory developed by one of the authors to study BLQH systematically. We derive the ground state, quasi-hole and a pair of quasihole wavefunctions from the CB theory and its dual action. We find that the ground state wavefunction differs from the well known $(111)$ wavefunction at any finite $d$. In addition to commonly known multiplicative factors, the quasi-hole and a pair of quasi-holes wavefunctions also contain non-trivial normalization factors multiplying the correct ground state wavefunction. All the distance dependencies in all the wavefunctions are encoded in the spin part of the ground state wavefunction. The instability encoded in the spin part of the groundstate wavefunction leads to the pseudo-spin density wave formation proposed by one of the authors previously. Some subtleties related to the Lowest Landau Level (LLL) projection of the wavefunctions are briefly discussed.Comment: 9 pages, 1 figure, REVTEX, Final version to appear in Phys. Rev.

Fermions in the Lowest Landau Level: Bosonization, W∞W_{\infty} Algebra, Droplets, Chiral Boson

We present field theoretical descriptions of massless (2+1) dimensional nonrelativistic fermions in an external magnetic field, in terms of a fermionic and bosonic second quantized language. An infinite dimensional algebra, $W_{\infty}$, appears as the algebra of unitary transformations which preserve the lowest Landau level condition and the particle number. In the droplet approximation it reduces to the algebra of area-preserving diffeomorphisms, which is responsible for the existence of a universal chiral boson Lagrangian independent of the electrostatic potential. We argue that the bosonic droplet approximation is the strong magnetic field limit of the fermionic theory. The relation to the $c=1$ string model is discussed.Comment: 16 page

Broken symmetry, excitons, gapless modes and topological excitations in Trilayer Quantum Hall systems

We study the interlayer coherent incompressible phase in Trilayer Quantum Hall systems (TLQH) at total filling factor $\nu_{T}=1$ from three approaches: Mutual Composite Fermion (MCF), Composite Boson (CB) and wavefunction approach. Just like in Bilayer Quantum Hall system, CB approach is superior than MCF approach in studying TLQH with broken symmetry. The Hall and Hall drag resistivities are found to be quantized at $h/e^{2}$. Two neutral gapless modes with linear dispersion relations are identified and the ratio of the two velocities is close to $\sqrt{3}$. The novel excitation spectra are classified into two classes: Charge neutral bosonic 2-body bound states and Charge $\pm 1$ fermionic 3-body bound states. In general, there are two 2-body Kosterlize-Thouless (KT) transition temperatures and one 3-body KT transition. The Charge $\pm 1$ 3-body fermionic bound states may be the main dissipation source of transport measurements. The broken symmetry in terms of $SU(3)$ algebra is studied. The structure of excitons and their flowing patterns are given. The coupling between the two Goldstone modes may lead to the broadening in the zero-bias peak in the interlayer correlated tunnelings of the TLQH. Several interesting features unique to TLQH are outlined. Limitations of the CB approach are also pointed out.Comment: 10 pages, 3 figures, Final version to be published in Phys. Rev.

Liouvillian Approach to the Integer Quantum Hall Effect Transition

We present a novel approach to the localization-delocalization transition in the integer quantum Hall effect. The Hamiltonian projected onto the lowest Landau level can be written in terms of the projected density operators alone. This and the closed set of commutation relations between the projected densities leads to simple equations for the time evolution of the density operators. These equations can be used to map the problem of calculating the disorder averaged and energetically unconstrained density-density correlation function to the problem of calculating the one-particle density of states of a dynamical system with a novel action. At the self-consistent mean-field level, this approach yields normal diffusion and a finite longitudinal conductivity. While we have not been able to go beyond the saddle point approximation analytically, we show numerically that the critical localization exponent can be extracted from the energetically integrated correlation function yielding $\nu=2.33 \pm 0.05$ in excellent agreement with previous finite-size scaling studies.Comment: 9 pages, submitted to PR

Uncertainty Principle and Off-Diagonal Long Range Order in the Fractional Quantum Hall Effect

A natural generalization of the Heisenberg uncertainty principle inequality holding for non hermitian operators is presented and applied to the fractional quantum Hall effect (FQHE). This inequality was used in a previous paper to prove the absence of long range order in the ground state of several 1D systems with continuous group symmetries. In this letter we use it to rule out the occurrence of Bose-Einstein condensation in the bosonic representation of the FQHE wave function proposed by Girvin and MacDonald. We show that the absence of off-diagonal long range order in this 2D problem is directly connected with the $q^2$ behavior of the static structure function $S(q)$ at small momenta.Comment: 10 pages, plain TeX, UTF-09-9

Tunneling, dissipation, and superfluid transition in quantum Hall bilayers

We study bilayer quantum Hall systems at total Landau level filling factor $\nu=1$ in the presence of interlayer tunneling and coupling to a dissipative normal fluid. Describing the dynamics of the interlayer phase by an effective quantum dissipative XY model, we show that there exists a critical dissipation $\sigma_c$ set by the conductance of the normal fluid. For $\sigma > \sigma_c$, interlayer tunnel splitting drives the system to a $\nu=1$ quantum Hall state. For $\sigma <\sigma_c$, interlayer tunneling is irrelevant at low temperatures, the system exhibits a superfluid transition to a collective quantum Hall state supported by spontaneous interlayer phase coherence. The resulting phase structure and the behavior of the in-plane and tunneling currents are studied in connection to experiments.Comment: 4 RevTex pages, revised version, to appear in Phys. Rev. Let

Theory of Microwave Parametric Down Conversion and Squeezing Using Circuit QED

We study theoretically the parametric down conversion and squeezing of microwaves using cavity quantum electrodynamics of a superconducting Cooper pair box (CPB) qubit located inside a transmission line resonator. The non-linear susceptibility \chi_2 describing three-wave mixing can be tuned by dc gate voltage applied to the CPB and vanishes by symmetry at the charge degeneracy point. We show that the coherent coupling of different cavity modes through the qubit can generate a squeezed state. Based on parameters realized in recent successful circuit QED experiments, squeezing of 95% ~ 13dB below the vacuum noise level should be readily achievable.Comment: 4 pages, accepted for publication in Phys. Rev. Let

Meron excitations in the nu =1 quantum Hall bilayer and the plasma analogy

We study meron quasiparticle excitations in the \nu = 1 quantum Hall bilayer. Considering the well known single meron state, we introduce its effective form, valid in the longdistance limit. That enables us to propose two (and more) meron states in the same limit. Further, establishing a plasma analogy of the (111) ground state, we find the impurities that play the role of merons and derive meron charge distributions. Using the introduced meron constructions in generalized (mixed) ground states and corresponding plasmas for arbitrary distance between the layers, we calculate the interaction between the construction implied impurities. We also find a correspondence between the impurity interactions and meron interactions. This suggests a possible explanation of the deconfinement of the merons recently observed in the experiments.Comment: 5 pages, 3 figure