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SciPost Physics

SciPost Physics Vol. 2 issue 2 (March - April 2017)

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Decoherence and pointer states in small antiferromagnets: A benchmark test

Hylke C. Donker, Hans De Raedt, Mikhail I. Katsnelson

SciPost Phys. 2, 010 (2017) · published 23 March 2017 | · pdf

We study the decoherence process of a four spin-1/2 antiferromagnet that is coupled to an environment of spin-1/2 particles. The preferred basis of the antiferromagnet is discussed in two limiting cases and we identify two $\it{exact}$ pointer states. Decoherence near the two limits is examined whereby entropy is used to quantify the $\it{robustness}$ of states against environmental coupling. We find that close to the quantum measurement limit, the self-Hamiltonian of the system of interest can become dynamically relevant on macroscopic timescales. We illustrate this point by explicitly constructing a state that is more robust than (generic) states diagonal in the system-environment interaction Hamiltonian.
Quantum Monte Carlo detection of SU(2) symmetry breaking in the participation entropies of line subsystems

David J. Luitz, Nicolas Laflorencie

SciPost Phys. 2, 011 (2017) · published 24 March 2017 | · pdf

Using quantum Monte Carlo simulations, we compute the participation (Shannon-R\'enyi) entropies for groundstate wave functions of Heisenberg antiferromagnets for one-dimensional (line) subsystems of length $L$ embedded in two-dimensional ($L\times L$) square lattices. We also study the line entropy at finite temperature, i.e. of the diagonal elements of the density matrix, for three-dimensional ($L\times L\times L$) cubic lattices. The breaking of SU(2) symmetry is clearly captured by a universal logarithmic scaling term $l_q\ln L$ in the R\'enyi entropies, in good agreement with the recent field-theory results of Misguish, Pasquier and Oshikawa [arXiv:1607.02465]. We also study the dependence of the log prefactor $l_q$ on the R\'enyi index $q$ for which a transition is detected at $q_c\simeq 1$.
One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance

Yannis Brun, Jérôme Dubail

SciPost Phys. 2, 012 (2017) · published 4 April 2017 | · pdf

The one-particle density matrix of the one-dimensional Tonks-Girardeau gas with inhomogeneous density profile is calculated, thanks to a recent observation that relates this system to a two-dimensional conformal field theory in curved space. The result is asymptotically exact in the limit of large particle density and small density variation, and holds for arbitrary trapping potentials. In the particular case of a harmonic trap, we recover a formula obtained by Forrester et al. [Phys. Rev. A 67, 043607 (2003)] from a different method.
Assessment of Quantum Annealing for the Construction of Satisfiability Filters

Marlon Azinović, Daniel Herr, Bettina Heim, Ethan Brown, Matthias Troyer

SciPost Phys. 2, 013 (2017) · published 7 April 2017 | · pdf

Satisfiability filters, introduced by S. A. Weaver et al. in 2014, are a new and promising type of filters to address set membership testing. In order to construct satisfiability filters, it is necessary to find disparate solutions to hard random $k$-SAT problems. This paper compares simulated annealing, simulated quantum annealing and walkSAT, an open-source SAT solver, in terms of their ability to find such solutions. The results indicate that solutions found by simulated quantum annealing are generally less disparate than solutions found by the other solvers and therefore less useful for the construction of satisfiability filters.
A note on generalized hydrodynamics: inhomogeneous fields and other concepts

Benjamin Doyon, Takato Yoshimura

SciPost Phys. 2, 014 (2017) · published 22 April 2017 | · pdf

Generalized hydrodynamics (GHD) was proposed recently as a formulation of hydrodynamics for integrable systems, taking into account infinitely-many conservation laws. In this note we further develop the theory in various directions. By extending GHD to all commuting flows of the integrable model, we provide a full description of how to take into account weakly varying force fields, temperature fields and other inhomogeneous external fields within GHD. We expect this can be used, for instance, to characterize the non-equilibrium dynamics of one-dimensional Bose gases in trap potentials. We further show how the equations of state at the core of GHD follow from the continuity relation for entropy, and we show how to recover Euler-like equations and discuss possible viscosity terms.
Electromagnetically induced transparency with Rydberg atoms across the Breit-Rabi regime

J. B. Naber, A. Tauschinsky, H. B. van Linden van den Heuvell, R. J. C. Spreeuw

SciPost Phys. 2, 015 (2017) · published 25 April 2017 | · pdf

We present experimental results on the influence of magnetic fields and laser polarization on electromagnetically induced transparency (EIT) using Rydberg levels of $^{87}$Rb atoms. The measurements are performed in a room temperature vapor cell with two counter-propagating laser beams at 480nm and 780nm in a ladder-type energy level scheme. We measure the EIT spectrum of a range of $ns_{1/2}$ Rydberg states for $n=19-27$, where the hyperfine structure can still be resolved. Our measurements span the range of magnetic fields from the low field linear Zeeman regime to the high field Paschen-Back regimes. The observed spectra are very sensitive to small changes in magnetic fields and the polarization of the laser beams. We model our observations using optical Bloch equations that take into account the full multi-level structure of the atomic states involved and the decoupling of the electronic $J$ and nuclear $I$ angular momenta in the Breit-Rabi regime. The numerical model yields excellent agreement with the observations. In addition to EIT related experiments, our results are relevant for experiments involving coherent excitation to Rydberg levels in the presence of magnetic fields.