NMR relaxation in the spin-1 Heisenberg chain

We consider the isotropic $S=1$ Heisenberg chain with a finite Haldane gap $\Delta$ and use state-of-the-art numerical techniques to investigate its dynamical properties at finite temperature, focusing on the nuclear spin-lattice relaxation rate $1/T_1$ measured in nuclear magnetic resonance (NMR) experiments for instance. In particular, we analyze the contributions from modes with momenta close to $q\approx 0$ and $q\approx \pi$ as a function of temperature. At high-temperature, we observe spin diffusion with a non-trivial exponent. At low-temperature, we argue that a simple activated behavior $1/T_1 \propto\exp(-\Delta/T)$ can only be observed at temperatures much smaller than the gap $\Delta$.Comment: published versio

Microwave-stimulated Raman adiabatic passage in a Bose-Einstein condensate on an atom chip

We report the achievement of stimulated Raman adiabatic passage (STIRAP) in the microwave frequency range between internal states of a Bose-Einstein condensate (BEC) magnetically trapped in the vicinity of an atom chip. The STIRAP protocol used in this experiment is robust to external perturbations as it is an adiabatic transfer, and power-efficient as it involves only resonant (or quasi-resonant) processes. Taking into account the effect of losses and collisions in a non-linear Bloch equations model, we show that the maximum transfer efficiency is obtained for non-zero values of the one- and two-photon detunings, which is confirmed quantitatively by our experimental measurements

Disorder-Induced Revival of the Bose-Einstein Condensation in Ni(Cl_{1-x}Br_{x})_{2}-4SC(NH_{2})_{2} at High Magnetic Fields.

Building on recent NMR experiments [A. Orlova et al., Phys. Rev. Lett. 118, 067203 (2017).PRLTAO0031-900710.1103/PhysRevLett.118.067203], we theoretically investigate the high magnetic field regime of the disordered quasi-one-dimensional S=1 antiferromagnetic material Ni(Cl_{1-x}Br_{x})_{2}-4SC(NH_{2})_{2}. The interplay between disorder, chemically controlled by Br-doping, interactions, and the external magnetic field, leads to a very rich phase diagram. Beyond the well-known antiferromagnetically ordered regime, an analog of a Bose condensate of magnons, which disappears when H≥12.3  T, we unveil a resurgence of phase coherence at a higher field H∼13.6  T, induced by the doping. Interchain couplings stabilize the finite temperature long-range order whose extension in the field-temperature space is governed by the concentration of impurities x. Such a "minicondensation" contrasts with previously reported Bose-glass physics in the same regime and should be accessible to experiments

Dynamical properties of the S=12S=\frac{1}{2} random Heisenberg chain

We use numerical techniques to study dynamical properties at finite temperature ($T$) of the Heisenberg spin chain with random exchange couplings, which realizes the random singlet (RS) fixed point in the low-energy limit. Specifically, we study the dynamic spin structure factor $S(q,\omega)$, which can be probed directly by inelastic neutron scattering experiments and, in the limit of small $\omega$, in nuclear magnetic resonance (NMR) experiments through the spin-lattice relaxation rate $1/T_1$. Our work combines three complementary methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Unlike the uniform system, whose low-energy excitations at low $T$ are restricted to $q$ close to $0$ and $\pi$, our study reveals a continuous narrow band of low-energy excitations in $S(q,\omega)$, extending throughout the Brillouin zone. Close to $q=\pi$, the scaling properties of these excitations are well captured by the RS theory, but we also see disagreements with some aspects of the predicted $q$-dependence further away from $q=\pi$. Furthermore we find spin diffusion effects close to $q=0$ that are not contained within the RS theory but give non-negligible contributions to the mean $1/T_1$. To compare with NMR experiments, we consider the distribution of the local $1/T_1$ values, which is broad, approximately described by a stretched exponential. The mean value first decreases with $T$, but starts to increase and diverge below a crossover temperature. Although a similar divergent behavior has been found for the static uniform susceptibility, this divergent behavior of $1/T_1$ has never been seen in experiments. Our results show that the divergence of the mean $1/T_1$ is due to rare events in the disordered chains and is concealed in experiments, where the typical $1/T_1$ value is accessed.Comment: 19 pages, 14 figure

Fast Pyrolysis of Biomass Under Gasification Conditions: Influence of Particle Size, Reactor Temperature and Gas Phase Reactions

N/

Experimental study of the role of trap symmetry in an atom-chip interferometer above the Bose-Einstein condensation threshold

We report the experimental study of an atom-chip interferometer using ultracold rubidium 87 atoms above the Bose-Einstein condensation threshold. The observed dependence of the contrast decay time with temperature and with the degree of symmetry of the traps during the interferometer sequence is in good agreement with theoretical predictions published in [Dupont-Nivet et al., NJP 18, 113012 (2016)]. These results pave the way for precision measurements with trapped thermal atoms.Comment: 11 pages, 4 figure

Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections

In Part II [3] of this paper, we have shown, using a classification of pencils of quadrics over the reals, how to determine quickly and efficiently the real type of the intersection of two given quadrics. For each real type of intersection, we design, in this third part, an algorithm for computing a near-optimal parameterization. We also give here examples covering all the possible situations, in terms of both the real type of intersection and the number and depth of square roots appearing in the coefficients

Near-Optimal Parameterization of the Intersection of Quadrics: Theory and Implementation

Colloque avec actes et comité de lecture. internationale.International audienceWe present an algorithm that computes an exact parametric form of the intersection of two real quadrics in projective three-space given by implicit equations with rational coefficients. This algorithm represents the first complete and robust solution to what is perhaps the most basic problem of solid modeling by implicit curved surfaces