Competing orders in the generalized Hund chain model at half-filling

By using a combination of several non-perturbative techniques -- a one-dimensional field theoretical approach together with numerical simulations using density matrix renormalization group -- we present an extensive study of the phase diagram of the generalized Hund model at half-filling. This model encloses the physics of various strongly correlated one-dimensional systems, such as two-leg electronic ladders, ultracold degenerate fermionic gases carrying a large hyperfine spin 3/2, other cold gases like Ytterbium 171 or alkaline-earth condensates. A particular emphasis is laid on the possibility to enumerate and exhaust the eight possible Mott insulating phases by means of a duality approach. We exhibit a one-to-one correspondence between these phases and those of the two-leg Hubbard ladder with interchain hopping. Our results obtained from a weak coupling analysis are in remarkable quantitative agreement with our numerical results carried out at moderate coupling.Comment: 26 pages, 14 figure

Effective algorithms for calculation of quasiprobability distributions of bright "banana'' states

Non-Gaussian quantum states, described by negative valued Wigner functions, are important both for fundamental tests of quantum physics and for emerging quantum information technologies. One of the promising ways of generation of the non-Gaussian states is the use of the cubic (Kerr) optical non-linearity, which produces the characteristic banana-like shape of the resulting quantum states. However, the Kerr effect in highly transparent optical materials is weak. Therefore, big number of the photons in the optical mode ($n\gtrsim10^6$) is necessary to generate an observable non-Gaussianity. In this case, the direct approach to calculation of the Wigner function becomes extremely computationally expensive. In this work, we develop quick algorithms for computing the Husimi and Wigner quasiprobability functions of these non-Gaussin states by means of the Kerr nonlinearity. This algorithm can be used for any realistic values of the photons number and the non-linearity.Comment: 24 pages, 10 figure

Exact low temperature results for transport properties of the interacting resonant level model

Using conformal field theory and integrability ideas, we give a full characterization of the low temperature regime of the anisotropic interacting resonant level (IRLM) model. We determine the low temperature corrections to the linear conductance exactly up to the 6th order. We show that the structure displays 'Coulomb deblocking' at resonance, i.e., a strong impurity-wire capacitive coupling enhances the conductance at low temperature.Comment: 4 pages, 2 figure

Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture

We investigate the nature of the Mott-insulating phases of half-filled 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of conformal field theory techniques and large-scale DMRG calculations, we show that the phase diagram strongly depends on the parity of $N$. First, we single out charged, spin-singlet, degrees of freedom, that carry a pseudo-spin ${\cal S}=N/2$ allowing to formulate a Haldane conjecture: for attractive interactions, we establish the emergence of Haldane insulating phases when $N$ is even, whereas a metallic behavior is found when $N$ is odd. We point out that the $N=1,2$ cases do \emph{not} have the generic properties of each family. The metallic phase for $N$ odd and larger than 1 has a quasi-long range singlet pairing ordering with an interesting edge-state structure. Moreover, the properties of the Haldane insulating phases with even $N$ further depend on the parity of N/2. In this respect, within the low-energy approach, we argue that the Haldane phases with N/2 even are not topologically protected but equivalent to a topologically trivial insulating phase and thus confirm the recent conjecture put forward by Pollmann {\it et al.} [Pollmann {\it et al.}, arXiv:0909.4059 (2009)].Comment: 25 pages, 20 figure

Fundamental limits of quantum-secure covert optical sensing

We present a square root law for active sensing of phase $\theta$ of a single pixel using optical probes that pass through a single-mode lossy thermal-noise bosonic channel. Specifically, we show that, when the sensor uses an $n$-mode covert optical probe, the mean squared error (MSE) of the resulting estimator $\hat{\theta}_n$ scales as $\langle (\theta-\hat{\theta}_n)^2\rangle=\mathcal{O}(1/\sqrt{n})$; improving the scaling necessarily leads to detection by the adversary with high probability. We fully characterize this limit and show that it is achievable using laser light illumination and a heterodyne receiver, even when the adversary captures every photon that does not return to the sensor and performs arbitrarily complex measurement as permitted by the laws of quantum mechanics.Comment: 13 pages, 1 figure, submitted to ISIT 201