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21 pages, 3682 KiB

Open AccessArticle

Classical and Quantum Gases on a Semiregular Mesh

by Davide De Gregorio and Santi Prestipino

Appl. Sci. 2021, 11(21), 10053; https://doi.org/10.3390/app112110053 - 27 Oct 2021

Cited by 3 | Viewed by 1918

The main objective of a statistical mechanical calculation is drawing the phase diagram of a many-body system. In this respect, discrete systems offer the clear advantage over continuum systems of an easier enumeration of microstates, though at the cost of added abstraction. With this in mind, we examine a system of particles living on the vertices of the (biscribed) pentakis dodecahedron, using different couplings for first and second neighbor particles to induce a competition between icosahedral and dodecahedral orders. After working out the phases of the model at zero temperature, we carry out Metropolis Monte Carlo simulations at finite temperature, highlighting the existence of smooth transitions between distinct “phases”. The sharpest of these crossovers are characterized by hysteretic behavior near zero temperature, which reveals a bottleneck issue for Metropolis dynamics in state space. Next, we introduce the quantum (Bose-Hubbard) counterpart of the previous model and calculate its phase diagram at zero and finite temperatures using the decoupling approximation. We thus uncover, in addition to Mott insulating “solids”, also the existence of supersolid “phases” which progressively shrink as the system is heated up. We argue that a quantum system of the kind described here can be realized with programmable holographic optical tweezers. Full article

(This article belongs to the Special Issue Computer Simulation of Quantum and Classical Systems)

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37 pages, 4365 KiB

Open AccessEditor’s ChoiceArticle

Self-Organization in Cold Atoms Mediated by Diffractive Coupling

by Thorsten Ackemann, Guillaume Labeyrie, Giuseppe Baio, Ivor Krešić, Josh G. M. Walker, Adrian Costa Boquete, Paul Griffin, William J. Firth, Robin Kaiser, Gian-Luca Oppo and Gordon R. M. Robb

Atoms 2021, 9(3), 35; https://doi.org/10.3390/atoms9030035 - 23 Jun 2021

Cited by 12 | Viewed by 4813

Abstract

This article discusses self-organization in cold atoms via light-mediated interactions induced by feedback from a single retro-reflecting mirror. Diffractive dephasing between the pump beam and the spontaneous sidebands selects the lattice period. Spontaneous breaking of the rotational and translational symmetry occur in the 2D plane transverse to the pump. We elucidate how diffractive ripples couple sites on the self-induced atomic lattice. The nonlinear phase shift of the atomic cloud imprinted onto the optical beam is the parameter determining coupling strength. The interaction can be tailored to operate either on external degrees of freedom leading to atomic crystallization for thermal atoms and supersolids for a quantum degenerate gas, or on internal degrees of freedom like populations of the excited state or Zeeman sublevels. Using the light polarization degrees of freedom on the Poincaré sphere (helicity and polarization direction), specific irreducible tensor components of the atomic Zeeman states can be coupled leading to spontaneous magnetic ordering of states of dipolar and quadrupolar nature. The requirements for critical interaction strength are compared for the different situations. Connections and extensions to longitudinally pumped cavities, counterpropagating beam schemes and the CARL instability are discussed. Full article

(This article belongs to the Special Issue Collective Atomic and Free-Electron Lasing)

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19 pages, 2557 KiB

Open AccessArticle

Ultracold Bosons on a Regular Spherical Mesh

by Santi Prestipino

Entropy 2020, 22(11), 1289; https://doi.org/10.3390/e22111289 - 13 Nov 2020

Cited by 4 | Viewed by 2026

Abstract

Here, the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh (“Platonic mesh”) and interacting through an extended Bose-Hubbard Hamiltonian has been studied. Only the hard-core version of the model for two instances of Platonic mesh is considered here. Using the mean-field decoupling approximation, it is shown that the system may exist in various ground states, which can be regarded as analogs of gas, solid, supersolid, and superfluid. For one mesh, by comparing the theoretical results with the outcome of numerical diagonalization, I manage to uncover the signatures of diagonal and off-diagonal spatial orders in a finite quantum system. Full article

(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals)

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12 pages, 788 KiB

Open AccessArticle

Spectral Function of a Boson Ladder in an Artificial Gauge Field

by Roberta Citro, Stefania De Palo, Nicolas Victorin, Anna Minguzzi and Edmond Orignac

Condens. Matter 2020, 5(1), 15; https://doi.org/10.3390/condmat5010015 - 10 Mar 2020

Cited by 4 | Viewed by 3553

Abstract

We calculate the spectral function of a boson ladder in an artificial magnetic field by means of analytic approaches based on bosonization and Bogoliubov theory. We discuss the evolution of the spectral function at increasing effective magnetic flux, from the Meissner to the Vortex phase, focussing on the effects of incommensurations in momentum space. At low flux, in the Meissner phase, the spectral function displays both a gapless branch and a gapped one, while at higher flux, in the Vortex phase, the spectral function displays two gapless branches and the spectral weight is shifted at a wavevector associated to the underlying vortex spatial structure, which can indicate a supersolid-like behavior. While the Bogoliubov theory, valid at weak interactions, predicts sharp delta-like features in the spectral function, at stronger interactions we find power-law broadening of the spectral functions due to quantum fluctuations as well as additional spectral weight at higher momenta due to backscattering and incommensuration effects. These features could be accessed in ultracold atom experiments using radio-frequency spectroscopy techniques. Full article

(This article belongs to the Special Issue Fluctuations and Highly Non-linear Phenomena in Superfluids and Superconductors II)

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17 pages, 1903 KiB

Open AccessArticle

On the Phase Diagrams of ⁴He Adsorbed on Graphene and Graphite from Quantum Simulation Methods

by Thomas L. Badman and Jeffrey M. McMahon

Crystals 2018, 8(5), 202; https://doi.org/10.3390/cryst8050202 - 4 May 2018

Cited by 8 | Viewed by 4452

Abstract

The ground-state phase diagrams of

^{4}

The ground-state phase diagrams of

^{4}

He adsorbed on graphene and graphite are calculated using quantum simulation methods. In this work, a systematic investigation of the approximations used in such simulations is carried out. Particular focus is placed on the helium–helium (He–He) and helium–carbon (He–C) interactions, as well as their modern approximations. On careful consideration of other approximations and convergence, the simulations are otherwise (numerically) exact. The He–He interaction as approximated by a sum of pairwise potentials is quantitatively assessed. A similar analysis is made for the He–C interaction, but more thoroughly and with a focus on surface corrugation. The importance of many-body effects is discussed. Altogether, the results provide “reference data” for the considered systems. Using comparisons with experiments and first-principle calculations, conclusions are drawn regarding the quantitative accuracy of these modern approximations to these interactions. Full article

(This article belongs to the Special Issue Quantum Crystals)

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