Global-to-local incompatibility, monogamy of entanglement, and ground-state dimerization: Theory and observability of quantum frustration in systems with competing interactions

Frustration in quantum many body systems is quantified by the degree of incompatibility between the local and global orders associated, respectively, to the ground states of the local interaction terms and the global ground state of the total many-body Hamiltonian. This universal measure is bounded from below by the ground-state bipartite block entanglement. For many-body Hamiltonians that are sums of two-body interaction terms, a further inequality relates quantum frustration to the pairwise entanglement between the constituents of the local interaction terms. This additional bound is a consequence of the limits imposed by monogamy on entanglement shareability. We investigate the behavior of local pair frustration in quantum spin models with competing interactions on different length scales and show that valence bond solids associated to exact ground-state dimerization correspond to a transition from generic frustration, i.e. geometric, common to classical and quantum systems alike, to genuine quantum frustration, i.e. solely due to the non-commutativity of the different local interaction terms. We discuss how such frustration transitions separating genuinely quantum orders from classical-like ones are detected by observable quantities such as the static structure factor and the interferometric visibility.Comment: 11 pages, 7 figures. Matches published versio

Dependence of the BEC transition temperature on interaction strength: a perturbative analysis

We compute the critical temperature T_c of a weakly interacting uniform Bose gas in the canonical ensemble, extending the criterion of condensation provided by the counting statistics for the uniform ideal gas. Using ordinary perturbation theory, we find in first order $(T_c-T_c^0)/T_c^0 = -0.93 a\rho^{1/3}$, where T_c^0 is the transition temperature of the corresponding ideal Bose gas, a is the scattering length, and $\rho$ is the particle number density.Comment: 14 pages (RevTeX

Energy Spectrum of Anyons in a Magnetic Field

For the many-anyon system in external magnetic field, we derive the energy spectrum as an exact solution of the quantum eigenvalue problem with particular topological constraints. Our results agree with the numerical spectra recently obtained for the 3- and the 4-anyon systems.Comment: 11 pages in Plain LaTeX (plus 4 figures available on request), DFPD 92/TH/4

Decoherence of number states in phase-sensitive reservoirs

The non-unitary evolution of initial number states in general Gaussian environments is solved analytically. Decoherence in the channels is quantified by determining explicitly the purity of the state at any time. The influence of the squeezing of the bath on decoherence is discussed. The behavior of coherent superpositions of number states is addressed as well.Comment: 5 pages, 2 figures, minor changes, references adde

Exact Multiplicities in the Three-Anyon Spectrum

Using the symmetry properties of the three-anyon spectrum, we obtain exactly the multiplicities of states with given energy and angular momentum. The results are shown to be in agreement with the proper quantum mechanical and semiclassical considerations, and the unexplained points are indicated.Comment: 16 pages plus 3 postscript figures, Kiev Institute for Theoretical Physics preprint ITP-93-32

Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states

We address the estimation of the loss parameter of a bosonic channel probed by arbitrary signals. Unlike the optimal Gaussian probes, which can attain the ultimate bound on precision asymptotically either for very small or very large losses, we prove that Fock states at any fixed photon number saturate the bound unconditionally for any value of the loss. In the relevant regime of low-energy probes, we demonstrate that superpositions of the first low-lying Fock states yield an absolute improvement over any Gaussian probe. Such few-photon states can be recast quite generally as truncations of de-Gaussified photon-subtracted states.Comment: 4 pages, 3 figure

Discriminating quantum gravity models by gravitational decoherence

Several phenomenological approaches to quantum gravity assume the existence of a minimal measurable length and/or a maximum measurable momentum near the Planck scale. When embedded into the framework of quantum mechanics, such constraints induce a modification of the canonical commutation relations and thus a generalization of the Heisenberg uncertainty relations, commonly referred to as generalized uncertainty principle (GUP). Different models of quantum gravity imply different forms of the GUP. For instance, in the framework of string theory the GUP is quadratic in the momentum operator, while in the context of doubly special relativity it includes an additional linear dependence. Among the possible physical consequences, it was recently shown that the quadratic GUP induces a universal decoherence mechanism, provided one assumes a foamy structure of quantum spacetime close to the Planck length. Along this line, in the present work we investigate the gravitational decoherence associated to the linear-quadratic GUP and we compare it with the one associated to the quadratic GUP. We find that, despite their similarities, the two generalizations of the Heisenberg uncertainty principle yield decoherence times that are completely uncorrelated and significantly distinct. Motivated by this result, we introduce a theoretical and experimental scheme based on cavity optomechanics to measure the different time evolution of nonlocal quantum correlations corresponding to the two aforementioned decoherence mechanisms. We find that the deviation between the two predictions occurs on time scales that are macroscopic and thus potentially amenable to experimental verification. This scenario provides a possible setting to discriminate between different forms of the GUP and therefore different models of quantum gravity.Comment: v1: 11 pages, 2 figures; v2: 11 pages, 2 figures, title, abstract and references slightly edited and updated for better clarity; no change in the physics; v3: 14 pages, 3 figures, title changed, new section and clarifications adde

Hierarchies of Geometric Entanglement

We introduce a class of generalized geometric measures of entanglement. For pure quantum states of $N$ elementary subsystems, they are defined as the distances from the sets of $K$-separable states ($K=2,...,N$). The entire set of generalized geometric measures provides a quantification and hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows to discriminate among the different contributions. The extended measures are applied to the study of entanglement in different classes of $N$-qubit pure states. These classes include $W$ and $GHZ$ states, and their symmetric superpositions; symmetric multi-magnon states; cluster states; and, finally, asymmetric generalized $W$-like superposition states. We discuss in detail a general method for the explicit evaluation of the multipartite components of geometric entanglement, and we show that the entire set of geometric measures establishes an ordering among the different types of bipartite and multipartite entanglement. In particular, it determines a consistent hierarchy between $GHZ$ and $W$ states, clarifying the original result of Wei and Goldbart that $W$ states possess a larger global entanglement than $GHZ$ states. Furthermore, we show that all multipartite components of geometric entanglement in symmetric states obey a property of self-similarity and scale invariance with the total number of qubits and the number of qubits per party.Comment: 16 pages, 7 figures. Final version, to appear in Phys. Rev.

Broadband detection of squeezed vacuum: A spectrum of quantum states

We demonstrate the simultaneous quantum state reconstruction of the spectral modes of the light field emitted by a continuous wave degenerate optical parametric amplifier. The scheme is based on broadband measurement of the quantum fluctuations of the electric field quadratures and subsequent Fourier decomposition into spectral intervals. Applying the standard reconstruction algorithms to each bandwidth-limited quantum trajectory, a "spectrum" of density matrices and Wigner functions is obtained. The recorded states show a smooth transition from the squeezed vacuum to a vacuum state. In the time domain we evaluated the first order correlation function of the squeezed output field, showing good agreement with the theory.Comment: 11 pages, 5 figure

A multidisciplinary approach to study the reproductive biology of wild prawns

This work aims to provide deeper knowledge on reproductive biology of P. kerathurus in a multidisciplinary way. Upon 789 examined females, 285 were found inseminated. The logistic equation enabled to estimate the size at first maturity at 30.7 mm CL for female. The Gono-Somatic Index (GSI) showed a pronounced seasonality, ranged from 0.80 ± 0.34 to 11.24 ± 5.72. Histological analysis highlighted five stages of ovarian development. Gonadal fatty acids analysis performed with gas chromatograph evidenced a pronounced seasonal variation; total lipids varied from 1.7% dry weight (dw) in Winter, to 7.2% dw in Summer. For the first time, a chemometric approach (Principal Component Analysis) was applied to relate GSI with total lipid content and fatty acid composition of gonads. The first two components (PC1 and PC2) showed that seasonality explained about 84% of the variability of all data set. In particular, in the period February-May, lipids were characterized by high PUFAs content, that were probably utilized during embryogenesis as energy source and as constituent of the cell membranes. During the summer season, gonads accumulated saturated FAs, that will be used during embryogenesis and early larval stages, while in the cold season total lipids decreased drastically and the gonad reached a quiescent state