Optimality of feedback control for qubit purification under inefficient measurement

A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However, the existing results suggest that such an enhancement is only possible when the measurement efficiency exceeds 0.5, which is difficult to achieve experimentally. We address the task of finding the global optimal feedback control for purifying a single qubit in the presence of measurement inefficiency. We use the Bloch vector length, a more physical and practical quantity than purity, to assess the quality of the state, and employ a backward-iteration algorithm to find the globally optimal strategy. Our results show that a speedup is available for quantum efficiencies well below 0.5, which opens the possibility of experimental implementation in existing systems

Symmetry-preserving Loop Regularization and Renormalization of QFTs

A new symmetry-preserving loop regularization method proposed in \cite{ylw} is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of irreducible loop integrals. The method simulates in many interesting features to the momentum cutoff, Pauli-Villars and dimensional regularization. The loop regularization method is also simple and general for the practical calculations to higher loop graphs and can be applied to both underlying and effective quantum field theories including gauge, chiral, supersymmetric and gravitational ones as the new method does not modify either the lagrangian formalism or the space-time dimension of original theory. The appearance of characteristic energy scale $M_c$ and sliding energy scale $\mu_s$ offers a systematic way for studying the renormalization-group evolution of gauge theories in the spirit of Wilson-Kadanoff and for exploring important effects of higher dimensional interaction terms in the infrared regime.Comment: 13 pages, Revtex, extended modified version, more references adde

Diffeomorphism Invariant Integrable Field Theories and Hypersurface Motions in Riemannian Manifolds

We discuss hypersurface motions in Riemannian manifolds whose normal velocity is a function of the induced hypersurface volume element and derive a second order partial differential equation for the corresponding time function $\tau(x)$ at which the hypersurface passes the point $x$. Equivalently, these motions may be described in a Hamiltonian formulation as the singlet sector of certain diffeomorphism invariant field theories. At least in some (infinite class of) cases, which could be viewed as a large-volume limit of Euclidean $M$-branesmoving in an arbitrary $M+1$-dimensional Riemannian manifold, the models are integrable: In the time-function formulation the equation becomes linear (with $\tau(x)$ a harmonic function on the embedding Riemannian manifold). We explicitly compute solutions to the large volume limit of Euclidean membrane dynamics in \Real^3 by methods used in electrostatics and point out an additional gradient flow structure in \Real^n. In the Hamiltonian formulation we discover infinitely many hierarchies of integrable, multidimensional, $N$-component theories possessing infinitely many diffeomorphism invariant, Poisson commuting, conserved charges.Comment: 15 pages, LATE

Transport through a molecular quantum dot in the polaron crossover regime

We consider resonant transport through a molecular quantum dot coupled to a local vibration mode. Applying the non-equilibrium Green function technique in the polaron representation, we develop a non-perturbative scheme to calculate the electron spectral function of the molecule in the regime of intermediate electron-phonon coupling. With increasing tunneling coupling to the leads, correlations between polaron clouds become more important at relatively high temperature leading to a strong sharpening of the peak structure in the spectral function. The detection of such features in the current-voltage characteristics is briefly discussed

Ground-state phase diagram of the Kondo lattice model on triangular-to-kagome lattices

We investigate the ground-state phase diagram of the Kondo lattice model with classical localized spins on triangular-to-kagome lattices by using a variational calculation. We identify the parameter regions where a four-sublattice noncoplanar order is stable with a finite spin scalar chirality while changing the lattice structure from triangular to kagome continuously. Although the noncoplanar spin states appear in a wide range of parameters, the spin configurations on the kagome network become coplanar as approaching the kagome lattice; eventually, the scalar chirality vanishes for the kagome lattice model.Comment: 7 pages, 3 figure

Full counting statistics for transport through a molecular quantum dot magnet

Full counting statistics (FCS) for the transport through a molecular quantum dot magnet is studied theoretically in the incoherent tunneling regime. We consider a model describing a single-level quantum dot, magnetically coupled to an additional local spin, the latter representing the total molecular spin s. We also assume that the system is in the strong Coulomb blockade regime, i.e., double occupancy on the dot is forbidden. The master equation approach to FCS introduced in Ref. [12] is applied to derive a generating function yielding the FCS of charge and current. In the master equation approach, Clebsch-Gordan coefficients appear in the transition probabilities, whereas the derivation of generating function reduces to solving the eigenvalue problem of a modified master equation with counting fields. To be more specific, one needs only the eigenstate which collapses smoothly to the zero-eigenvalue stationary state in the limit of vanishing counting fields. We discovered that in our problem with arbitrary spin s, some quartic relations among Clebsch-Gordan coefficients allow us to identify the desired eigenspace without solving the whole problem. Thus we find analytically the FCS generating function in the following two cases: i) both spin sectors lying in the bias window, ii) only one of such spin sectors lying in the bias window. Based on the obtained analytic expressions, we also developed a numerical analysis in order to perform a similar contour-plot of the joint charge-current distribution function, which have recently been introduced in Ref. [13], here in the case of molecular quantum dot magnet problem.Comment: 17 pages, 5 figure

GW quasi-particle spectra from occupied states only

We introduce a method that allows for the calculation of quasi-particle spectra in the GW approximation, yet avoiding any explicit reference to empty one-electron states. This is achieved by expressing the irreducible polarizability operator and the self-energy operator through a set of linear response equations, which are solved using a Lanczos-chain algorithm. We first validate our approach by calculating the vertical ionization energies of the benzene molecule and then show its potential by addressing the spectrum of a large molecule such as free-base tetraphenylporphyrin.Comment: 4 pages, 3 figure