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Journal articles on the topic 'Lattice tray'

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Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Sun, Zhihui, Jie Zhang, Hanxiao Wang, Guangshan Pan, Tianhua Wang, Lu Xie, and Qing Peng. "Defect, temperature, and strain effects on lattice heat conductivity of egg-tray graphene." Modelling and Simulation in Materials Science and Engineering 29, no. 4 (April 14, 2021): 045003. http://dx.doi.org/10.1088/1361-651x/abebcc.

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2

Wen, Yongshuang, Leian Zhang, Xuemei Huang, Ting Yuan, Junxiong Zhang, Yuzhi Tan, and Zhongbin Feng. "Design of and Experiment with Seedling Selection System for Automatic Transplanter for Vegetable Plug Seedlings." Agronomy 11, no. 10 (October 9, 2021): 2031. http://dx.doi.org/10.3390/agronomy11102031.

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In the process of vegetable plug seedling cultivation, packaging, and transportation, there may be missing, unhealthy or injured seedlings in the tray, which results in a missed planting or a low seedling survival rate after automatic transplanting. In this study, a seedling selection system with the function of seedlings identification, week seedlings elimination, and missing seedlings supplement was developed for an automatic transplanter. A plug seedling identification system based on a machine vision was used to detect vegetable plug seedlings based on the area characteristics of plug seedlings, stem leaves and plug bodies. The identification results were transmitted to a programmable logic controller (PLC), which controlled a nozzle to eliminate the unqualified seedlings from the conveyor belt lattice. When the empty conveyor belt lattice reaches the seedling throwing funnel, the rear conveyor belt lattice with the plug seedling is accelerated to ensure the continuity of seedlings supply. The adaptive fuzzy PID control algorithm was used to control the stepper motor of the conveyor belt to realize accurate seedling conveying and a seedling supplement. Using 30 days pepper plug seedlings as experimental seedlings, a comparative field experiment was carried out to evaluate the performance of the seedling selection system. The results showed that when the seedling selection system was turned on and the seedling extracting frequencies were 60, 80, and 100 plants/min, the success rates of plug seedling identification were 98.84%, 98.38%, and 96.99%, and the robust seedling rates were 98.05%, 97.78%, and 95.83%. The robust seedling rates were increased by 15.64%, 16.07%, and 13.89%, respectively, in contrast to turning off the seedling selection system.

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3

GAO, MENG, and LAN YIN. "VORTEX LATTICE STATE OF A SUPERFLUID FERMI GAS IN THE UNITARY REGION." International Journal of Modern Physics B 22, no. 23 (September 20, 2008): 3967–76. http://dx.doi.org/10.1142/s0217979208048814.

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In this paper, we study the structure of vortex lattices in a trapped superfluid Fermi gas in the unitary region near the superfluid transition temperature. A phenomenological approach based on the Ginzburg-Landau theory is used. Two types of stable triangular vortex lattices are found numerically at the same rotation frequency. In type (A), the trap center is occupied by a vortex; in type (B), there are three vortices closest to the trap center which is unoccupied. The lattice structures at different rotation frequencies and temperatures are analyzed. The vortex density increases linearly with the rotation frequency, very close to the analytical estimation. The superfluid and type-(B) vortex lattice do not disappear together. At high rotation frequencies, the vortex lattice disappears, but there exists a localized superfluid state near the trap center. The superfluid vanishes at a critical rotation frequency consistent with the theory for the upper critical magnetic field of type-II superconductors.

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4

LIU, M., L. H. WEN, L. SHE, A. X. CHEN, H. W. XIONG, and M. S. ZHAN. "SPLITTING AND TRAPPING OF BOSE-CONDENSED GASES IN MULTI-WELLS." Modern Physics Letters B 19, no. 06 (March 20, 2005): 303–12. http://dx.doi.org/10.1142/s0217984905008244.

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For the Bose-condensed gas in a one-dimensional optical lattice, several far-off resonant laser beams are used to split and trap the matter wavepacket after switching off both the magnetic trap and optical lattices. In the presence of two far-off resonant laser beams which are not symmetric about the centre of the matter wavepacket, we propose an experimental scheme to observe the collision between two side peaks after switching off the magnetic trap and optical lattice. We also discuss an experimental scheme to realize a coherent splitting and trapping of the matter wavepacket which has potential application in atom optics.

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5

Mighell, Alan D. "Ambiguities in powder pattern indexing: A ternary lattice metric singularity." Powder Diffraction 16, no. 3 (September 2001): 144–48. http://dx.doi.org/10.1154/1.1369789.

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A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The existence of such singularities, therefore, has a practical impact on the indexing of powder patterns. Lattice metric singularities often involve lattices that are in a derivative relationship one to another. A variety of types of singularities are possible depending on the number of different lattices involved (i.e., binary, ternary, quaternary), on the nature of the derivative lattice relationship (i.e., subcell/supercell, composite), on the Bravais type of each of the lattices, and on the the volume ratio(s) of primitive cells defining the lattices. In the laboratory, an encounter with a singularity can lead one into a trap; viz., the investigator using an indexing program, or by other means, may determine only one of the lattices with a high figure of merit. When this happens, it is critical to recognize that there exists more than one indexing solution. In a previous work, a binary singularity was described involving a monoclinic and a rhombohedral lattice. In the present work, we describe a second type of singularity—a ternary singularity—in which the two of the three lattices are in a derivative composite relationship.

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6

Tran, Tien Duy, Yibo Wang, Alex Glaetzle, Shannon Whitlock, Andrei Sidorov, and Peter Hannaford. "Magnetic Lattices for Ultracold Atoms." Communications in Physics 29, no. 2 (May 14, 2019): 97. http://dx.doi.org/10.15625/0868-3166/29/2/13678.

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This article reviews the development in our laboratory of magnetic lattices comprising periodic arrays of magnetic microtraps created by patterned magnetic films to trap periodic arrays of ultracold atoms. Recent achievements include the realisation of multiple Bose-Einstein condensates in a 10 \(\mu\)m-period one-dimensional magnetic lattice; the fabrication of sub-micron-period square and triangular magnetic lattice structures suitable for quantum tunnelling experiments; the trapping of ultracold atoms in a sub-micron-period triangular magnetic lattice; and a proposal to use long-range interacting Rydberg atoms to achieve spin-spin interactions between sites in a large-spacing magnetic lattice.

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7

IYANIWURA, S., and M. J. WARD. "ASYMPTOTIC ANALYSIS FOR THE MEAN FIRST PASSAGE TIME IN FINITE OR SPATIALLY PERIODIC 2D DOMAINS WITH A CLUSTER OF SMALL TRAPS." ANZIAM Journal 63, no. 1 (January 2021): 1–22. http://dx.doi.org/10.1017/s1446181121000018.

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AbstractA hybrid asymptotic-numerical method is developed to approximate the mean first passage time (MFPT) and the splitting probability for a Brownian particle in a bounded two-dimensional (2D) domain that contains absorbing disks, referred to as “traps”, of asymptotically small radii. In contrast to previous studies that required traps to be spatially well separated, we show how to readily incorporate the effect of a cluster of closely spaced traps by adapting a recently formulated least-squares approach in order to numerically solve certain local problems for the Laplacian near the cluster. We also provide new asymptotic formulae for the MFPT in 2D spatially periodic domains where a trap cluster is centred at the lattice points of an oblique Bravais lattice. Over all such lattices with fixed area for the primitive cell, and for each specific trap set, the average MFPT is smallest for a hexagonal lattice of traps.

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8

Parker, Julia E., Stephen P. Thompson, Tom M. Cobb, Fajin Yuan, Jonathan Potter, Alistair R. Lennie, Sam Alexander, et al. "High-throughput powder diffraction on beamline I11 at Diamond." Journal of Applied Crystallography 44, no. 1 (November 27, 2010): 102–10. http://dx.doi.org/10.1107/s0021889810044948.

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A new capability designed for high-throughput (HT) structural analysis using the synchrotron powder diffraction beamline (I11) at Diamond Light Source is reported. With a high-brightness X-ray beam, multi-analyser detectors and fast data-acquisition procedures, high-quality diffraction data can be collected at a speed of ∼15–30 min per powder pattern for good crystalline materials. Fast sample changing at a rate of a few seconds per specimen is achieved with a robotic arm and pre-loaded capillary specimens on a multi-tray carousel (200-sample capacity). Additional equipment, such as an automatic powder-loading machine and a pre-alignment jig for the sample capillaries, is available to reduce preparation time. For demonstration purposes, the first results presented here are those from standard reference powders of Si, TiO2and TiO2/Si mixtures, obtained by analysing the data using Le Bail (instrumental calibration) and Rietveld refinements (quantitative agreement within 1%). The HT hardware was then used to study the structural phase evolution of a library of 31 La4Ni3−xFexO10heterometallic ceramic powders in less than 1 d. The powders were generated from a single heat treatment (at 1348 K in air for 12 h) of nanoceramic oxide co-precipitate precursors, made using a newly developed HT synthesis robot. Crystallographic details (symmetry and lattice parameters) were obtained as a function of Fe concentration. The results revealed that this approach was able to produce a pure Ruddlesden–Popper-type phase with an iron content of up tox= 0.5, significantly higher than has been achieved previously using more conventional synthesis routes and thus demonstrating the power of using the HT approach.

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9

Yu, Geng-Hua, Qi-Ming Xu, Chao Zhou, Liang Liang, Long Li, and Rui-Peng Chai. "Magic wavelengths of the optical clock transition at 877 nm of barium." Modern Physics Letters B 28, no. 23 (September 10, 2014): 1450183. http://dx.doi.org/10.1142/s0217984914501838.

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Magic wavelengths for laser trapping of barium atoms in the optical lattices are investigated while considering the optical clock transition at 877 nm between the 6s21S0 state and 6s5d 1D2 state. Theoretical calculation shows that there are several magic wavelengths with the linearly polarized trapping laser. The trap depths of the optical lattice and the slope of light shift difference with different magic wavelengths are also discussed and analyzed. Some of these magic wavelengths are selected and recommended for the optical lattice trapping laser.

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10

Ji, Xianming, Shuwu Xu, and Songbo Gu. "Generation of Atomic Optical Lattices by Dammann Gratings." Advances in Optical Technologies 2012 (April 17, 2012): 1–9. http://dx.doi.org/10.1155/2012/647657.

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We first calculated the diffraction intensity distributions of the Dammann gratings illuminated by Gaussian light wave. The empirical equations were deduced by numerical calculations to calculate the parameters, such as the spatial period, the maximum intensity, and the maximum intensity gradient, of the optical trap array composed by a set of Dammann gratings and a focus lens. Thus, a novel type of optical trap array for trapping cold atoms (or molecules) was proposed and its features were discussed. The results showed the optical trap array with very short period could be generated. High optical dipole potential could be presented so as to have strong attractive force to the atoms to form atomic optical lattices of high lattice density. Compared with the optical lattices formed by standing wave interferences of CO2 laser, there are many unique advantages of which are formed by Dammann gratings.

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11

Iyaniwura, Sarafa, and Michael Ward. "Asymptotic analysis for the mean first passage time in finite or spatially periodic 2D domains with a cluster of small traps." ANZIAM Journal 63 (July 30, 2021): 1–22. http://dx.doi.org/10.21914/anziamj.v63.15976.

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A hybrid asymptotic-numerical method is developed to approximate the mean first passage time (MFPT) and the splitting probability for a Brownian particle in a bounded two-dimensional (2D) domain that contains absorbing disks, referred to as "traps”, of asymptotically small radii. In contrast to previous studies that required traps to be spatially well separated, we show how to readily incorporate the effect of a cluster of closely spaced traps by adapting a recently formulated least-squares approach in order to numerically solve certain local problems for the Laplacian near the cluster. We also provide new asymptotic formulae for the MFPT in 2D spatially periodic domains where a trap cluster is centred at the lattice points of an oblique Bravais lattice. Over all such lattices with fixed area for the primitive cell, and for each specific trap set, the average MFPT is smallest for a hexagonal lattice of traps. doi:10.1017/S1446181121000018

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12

Pathak, Maitri R., and Ajay Nath. "Formation of Matter-Wave Droplet Lattices in Multi-Color Periodic Confinements." Symmetry 14, no. 5 (May 9, 2022): 963. http://dx.doi.org/10.3390/sym14050963.

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In the paper, we introduce a new model that addresses the generation of quantum droplets (QDs) in the binary Bose–Einstein condensate (BEC) mixture with mutually symmetric spinor components loaded in multi-color optical lattices (MOLs) of commensurate wavelengths and tunable intensities. The considered MOL confinement is the combination of the four-color optical lattice with an exponential periodic trap, which includes the complete set of the Fourier harmonics. Employing the one-dimensional (1D) extended Gross–Pitäevskii equation (eGPE), we calculate the exact analytical form of the wavefunction, MF/BMF nonlinearities, and MOL trap parameters. Utilizing the exact solutions, the formation of supersolid-like spatially periodic matter-wave droplet lattices and superlattices is illustrated under the space-periodic nonlinearity management. The precise positioning of the density maxima/minima of the droplet patterns at the center of the trap and tunable Anderson-like localization are observed by tuning the symmetry and amplitude of the considered MOL trap. The stability of the obtained solution is confirmed using the Vakhitov–Kolokolov (VK) criterion.

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13

Song, Daohong, Cibo Lou, Liqin Tang, Zhuoyi Ye, Jingjun Xu, and Zhigang Chen. "Experiments on Linear and Nonlinear Localization of Optical Vortices in Optically Induced Photonic Lattices." International Journal of Optics 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/273857.

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We provide a brief overview on our recent experimental work on linear and nonlinear localization of singly charged vortices (SCVs) and doubly charged vortices (DCVs) in two-dimensional optically induced photonic lattices. In the nonlinear case, vortex propagation at the lattice surface as well as inside the uniform square-shaped photonic lattices is considered. It is shown that, apart from the fundamental (semi-infinite gap) discrete vortex solitons demonstrated earlier, the SCVs can self-trap into stable gap vortex solitons under the normal four-site excitation with a self-defocusing nonlinearity, while the DCVs can be stable only under an eight-site excitation inside the photonic lattices. Moreover, the SCVs can also turn into stable surface vortex solitons under the four-site excitation at the surface of a semi-infinite photonics lattice with a self-focusing nonlinearity. In the linear case, bandgap guidance of both SCVs and DCVs in photonic lattices with a tunable negative defect is investigated. It is found that the SCVs can be guided at the negative defect as linear vortex defect modes, while the DCVs tend to turn into quadrupole-like defect modes provided that the defect strength is not too strong.

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14

Mighell, Alan D. "Lattice metric singularities and their impact on the indexing of powder patterns." Powder Diffraction 15, no. 2 (June 2000): 82–85. http://dx.doi.org/10.1017/s0885715600010873.

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A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The existence of such singularities, therefore, has a practical impact on the indexing of powder patterns. For example, when experimental data from ζ-LiBO2 were indexed, two solutions (a rhombohedral and a monoclinic lattice) with approximately the same figure of merit were found. These two lattices yield the same set of unique d-spacings even though they are characterized by different reduced cells with cell volumes in the ratio 2 to 1. From the indexing point of view, both answers are correct. A singularity of this type is common and not a mathematical rarity. In fact, any rhombohedral cell of this kind has a derivative monoclinic subcell, each of which gives the same set of unique calculated d-spacings. In actual cases like this, one can run into a trap. Due to experimental error and input parameters, an indexing program may determine only one of the cells with a high figure of merit. When this happens, it is critical to recognize that another solution exists, especially if one has determined the lower symmetry lattice.

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15

Sagaki, Daisuke, and Hiroki Shimakura. "Application of a $\mathbb {Z}_{3}$-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices." Transactions of the American Mathematical Society 368, no. 3 (July 1, 2015): 1621–46. http://dx.doi.org/10.1090/tran/6382.

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16

Jeong, Joo-Hyeok, Hyunjoon Park, Dongkyu Kim, and Dong-Hee Kim. "Magnetic Shell Structure of 2D-Trapped Fermi Gases in the Flat-Band Lieb Lattices." Applied Sciences 9, no. 3 (January 22, 2019): 365. http://dx.doi.org/10.3390/app9030365.

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We investigate the magnetic shell structure of repulsively interacting two-component Fermi gases trapped in a two-dimensional harmonic potential and loaded on the optical Lieb lattices. We employ the real-space dynamical mean-field theory (R-DMFT) to explicitly consider the trap potential in a self-consistent way. Computing the profiles of particle density and local magnetization across the lattice sites in the trap, we find that the incompressible core with ferrimagnetic ordering appears with the density plateau at the trap center, which is surrounded by the shell of the normal metallic phase. We examine the incompressibility of the core by adding more particles and creating the higher spin-population imbalance. While the core area expands from the outer shell with added particles and increased polarization, the excess particles are prohibited from going inside the core, and thus the density plateau is unchanged at the half-filling with the same magnetic ordering. In addition, we find that the feature of the phase separation differs with the sublattices, where the interstitial sites causing the flat band dispersion shows the signature of the abrupt transition in the density and magnetization at the boundary between the core and surrounding shells.

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17

GAO, XIANLONG, M. POLINI, M. P. TOSI, and B. TANATAR. "EFFECT OF DISORDER ON THE INTERACTING FERMI GASES IN A ONE-DIMENSIONAL OPTICAL LATTICE." International Journal of Modern Physics B 22, no. 25n26 (October 20, 2008): 4500–4510. http://dx.doi.org/10.1142/s0217979208050255.

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Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to a harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For sufficiently large disorder correlation length the enhancement in the inverse compressibility diminishes.

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18

Derzhko, Oleg, Johannes Richter, and Mykola Maksymenko. "Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons." International Journal of Modern Physics B 29, no. 12 (May 10, 2015): 1530007. http://dx.doi.org/10.1142/s0217979215300078.

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On a large class of lattices (such as the sawtooth chain, the kagome and the pyrochlore lattices), the quantum Heisenberg and the repulsive Hubbard models may host a completely dispersionless (flat) energy band in the single-particle spectrum. The flat-band states can be viewed as completely localized within a finite volume (trap) of the lattice and allow for construction of many-particle states, roughly speaking, by occupying the traps with particles. If the flat-band happens to be the lowest-energy one, the manifold of such many-body states will often determine the ground-state and low-temperature physics of the models at hand even in the presence of strong interactions. The localized nature of these many-body states makes possible the mapping of this subset of eigenstates onto a corresponding classical hard-core system. As a result, the ground-state and low-temperature properties of the strongly correlated flat-band systems can be analyzed in detail using concepts and tools of classical statistical mechanics (e.g., classical lattice-gas approach or percolation approach), in contrast to more challenging quantum many-body techniques usually necessary to examine strongly correlated quantum systems. In this review, we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. The main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems, we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat-band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki–Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems. Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.

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19

Bakalov, Bojko, and McKay Sullivan. "Twisted logarithmic modules of lattice vertex algebras." Transactions of the American Mathematical Society 371, no. 11 (November 2, 2018): 7995–8027. http://dx.doi.org/10.1090/tran/7703.

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20

Bostan, A., I. Kurkova, and K. Raschel. "A human proof of Gessel’s lattice path conjecture." Transactions of the American Mathematical Society 369, no. 2 (April 14, 2016): 1365–93. http://dx.doi.org/10.1090/tran/6804.

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21

Dermenjian, Aram, Christophe Hohlweg, and Vincent Pilaud. "The facial weak order and its lattice quotients." Transactions of the American Mathematical Society 370, no. 2 (October 24, 2017): 1469–507. http://dx.doi.org/10.1090/tran/7307.

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22

Wehrung, Friedrich. "Spectral spaces of countable Abelian lattice-ordered groups." Transactions of the American Mathematical Society 371, no. 3 (October 23, 2018): 2133–58. http://dx.doi.org/10.1090/tran/7596.

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23

Violante, Vittorio, Amalia Torre, and Giuseppe Dattoli. "Lattice Ion Trap: Classical and Quantum Description of a Possible Collision Mechanism for Deuterons in Metal Lattices." Fusion Technology 34, no. 2 (September 1998): 156–62. http://dx.doi.org/10.13182/fst98-a62.

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24

Basak, Tathagata. "The complex Lorentzian Leech lattice and the bimonster (II)." Transactions of the American Mathematical Society 368, no. 6 (October 5, 2015): 4171–95. http://dx.doi.org/10.1090/tran/6558.

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25

Reznikov, Andre, and Feng Su. "Lattice points counting and bounds on periods of Maass forms." Transactions of the American Mathematical Society 372, no. 3 (January 16, 2019): 2073–102. http://dx.doi.org/10.1090/tran/7684.

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26

Sheckelton, John P., James R. Neilson, and Tyrel M. McQueen. "Electronic tunability of the frustrated triangular-lattice cluster magnet LiZn2−xMo3O8." Materials Horizons 2, no. 1 (2015): 76–80. http://dx.doi.org/10.1039/c4mh00166d.

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Iglesias-Valiño, Óscar, and Francisco Santos. "Classification of empty lattice $4$-simplices of width larger than two." Transactions of the American Mathematical Society 371, no. 9 (January 24, 2019): 6605–25. http://dx.doi.org/10.1090/tran/7531.

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28

Colzani, Leonardo, Bianca Gariboldi, and Giacomo Gigante. "Mixed $L^{p}(L^{2})$ norms of the lattice point discrepancy." Transactions of the American Mathematical Society 371, no. 11 (March 7, 2019): 7669–706. http://dx.doi.org/10.1090/tran/7624.

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Heckenberger, Istvan, John Shareshian, and Volkmar Welker. "On the lattice of subracks of the rack of a finite group." Transactions of the American Mathematical Society 372, no. 2 (April 18, 2019): 1407–27. http://dx.doi.org/10.1090/tran/7644.

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Bilyk, Dmitriy, Xiaomin Ma, Jill Pipher, and Craig Spencer. "Diophantine approximations and directional discrepancy of rotated lattices." Transactions of the American Mathematical Society 368, no. 6 (September 9, 2015): 3871–97. http://dx.doi.org/10.1090/tran/6492.

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31

Risager, Morten S., and Anders Södergren. "Angles in hyperbolic lattices: The pair correlation density." Transactions of the American Mathematical Society 369, no. 4 (December 7, 2016): 2807–41. http://dx.doi.org/10.1090/tran/6770.

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32

Creutz, Darren, and Jesse Peterson. "Stabilizers of ergodic actions of lattices and commensurators." Transactions of the American Mathematical Society 369, no. 6 (November 8, 2016): 4119–66. http://dx.doi.org/10.1090/tran/6836.

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33

Dittmann, Moritz. "Reflective automorphic forms on lattices of squarefree level." Transactions of the American Mathematical Society 372, no. 2 (November 13, 2018): 1333–62. http://dx.doi.org/10.1090/tran/7620.

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34

LIU, SUJUAN, WEN WEN, and GUOXIANG HUANG. "EVOLUTION OF INTERFERENCE PATTERNS OF SUPERFLUID FERMI GASES RELEASED FROM A TWO-DIMENSIONAL OPTICAL LATTICE." International Journal of Modern Physics B 26, no. 03 (January 30, 2012): 1250017. http://dx.doi.org/10.1142/s0217979212500178.

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We study interference patterns and their time evolution of a superfluid fermionic gas released from a two-dimensional (2D) optical lattice below and above Feshbach resonance. We calculate initial distribution of many subcondensates formed in a combined potential of a parabolic trap and a 2D optical lattice in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC). By using Feynman propagator method combined with numerical simulations we investigate the interference patterns of the subcondensates for two different cases. One is when both the parabolic trap and optical lattice are switched off. In this case, interference pattern displays a main peak and many secondary peaks. The distance between these interference peaks grows as time increases. The other one is when only the 2D optical lattice is switched off. The interference pattern in this case is found to display decay and revival, and such behavior repeats periodically with increasing time. In different regimes of the BCS-BEC crossover, coherent arrays of interference patterns show different features, which can be used to characterize experimentally different properties in different superfluid regimes of the BCS–BEC crossover.

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35

Lu, Xiao-Jing, Andreas Ruschhaupt, Sofía Martínez-Garaot, and Juan Gonzalo Muga. "Noise Sensitivities for an Atom Shuttled by a Moving Optical Lattice via Shortcuts to Adiabaticity." Entropy 22, no. 3 (February 25, 2020): 262. http://dx.doi.org/10.3390/e22030262.

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We find the noise sensitivities (i.e., the quadratic terms of the energy with respect to the perturbation of the noise) of a particle shuttled by an optical lattice that moves according to a shortcut-to-adiabaticity transport protocol. Noises affecting different optical lattice parameters, trap depth, position, and lattice periodicity, are considered. We find generic expressions of the sensitivities for arbitrary noise spectra but focus on the white-noise limit as a basic reference, and on Ornstein–Uhlenbeck noise to account for the effect of non-zero correlation times.

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36

Enders, Florian, Arne Budweg, Peng Zeng, Jannika Lauth, Trevor A. Smith, Daniele Brida, and Klaus Boldt. "Switchable dissociation of excitons bound at strained CdTe/CdS interfaces." Nanoscale 10, no. 47 (2018): 22362–73. http://dx.doi.org/10.1039/c8nr07973k.

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RIGOL, MARCOS, and ALEJANDRO MURAMATSU. "FREE EXPANSION OF IMPENETRABLE BOSONS ON ONE-DIMENSIONAL OPTICAL LATTICES." Modern Physics Letters B 19, no. 18 (August 10, 2005): 861–81. http://dx.doi.org/10.1142/s0217984905008876.

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We review recent exact results for the free expansion of impenetrable bosons on one-dimensional lattices, after switching off a confining potential. When the system is initially in a superfluid state, far from the regime in which the Mott-insulator appears in the middle of the trap, the momentum distribution of the expanding bosons rapidly approaches the momentum distribution of non-interacting fermions. Remarkably, no loss in coherence is observed in the system as reflected by a large occupation of the lowest eigenstate of the one-particle density matrix. In the opposite limit, when the initial system is a pure Mott insulator with one particle per lattice site, the expansion leads to the emergence of quasicondensates at finite momentum. In this case, one-particle correlations like the ones shown to be universal in the equilibrium case develop in the system. We show that the out-of-equilibrium behavior of the Shannon information entropy in momentum space, and its contrast with one of non-interacting fermions, allows to differentiate the two different regimes of interest. It also helps in understanding the crossover between them.

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Perego, Elia, Lucia Duca, and Carlo Sias. "Electro-Optical Ion Trap for Experiments with Atom-Ion Quantum Hybrid Systems." Applied Sciences 10, no. 7 (March 25, 2020): 2222. http://dx.doi.org/10.3390/app10072222.

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In the development of atomic, molecular, and optical (AMO) physics, atom-ion hybrid systems are characterized by the presence of a new tool in the experimental AMO toolbox: atom-ion interactions. One of the main limitations in state-of-the-art atom-ion experiments is represented by the micromotion component of the ions’ dynamics in a Paul trap, as the presence of micromotion in atom-ion collisions results in a heating mechanism that prevents atom-ion mixtures from undergoing a coherent evolution. Here, we report the design and the simulation of a novel ion trapping setup especially conceived of for integration with an ultracold atoms experiment. The ion confinement is realized by using an electro-optical trap based on the combination of an optical and an electrostatic field, so that no micromotion component will be present in the ions’ dynamics. The confining optical field is generated by a deep optical lattice created at the crossing of a bow-tie cavity, while a static electric quadrupole ensures the ions’ confinement in the plane orthogonal to the optical lattice. The setup is also equipped with a Paul trap for cooling the ions produced by photoionization of a hot atomic beam, and the design of the two ion traps facilitates the swapping of the ions from the Paul trap to the electro-optical trap.

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Clark, Robert J., Tongyan Lin, Kenneth R. Brown, and Isaac L. Chuang. "A two-dimensional lattice ion trap for quantum simulation." Journal of Applied Physics 105, no. 1 (January 2009): 013114. http://dx.doi.org/10.1063/1.3056227.

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Puentes, Graciana. "Design and Construction of Magnetic Coils for Quantum Magnetism Experiments." Quantum Reports 2, no. 3 (July 17, 2020): 378–87. http://dx.doi.org/10.3390/quantum2030026.

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We report on the design and construction of a spin-flip Zeeman slower, a quadrupole magnetic trap and a Feshbach field for a new machine for ultra-cold Li-7. The small mass of the Li-7 atom, and the tight lattice spacing, will enable to achieve a 100-fold increase in tunneling rates over comparable Rb-87 optical lattice emulator experiments. These improvements should enable to access new regimes in quantum magnetic phase transitions and spin dynamics.

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Ceballos, Cesar, Arnau Padrol, and Camilo Sarmiento. "Geometry of $\nu $-Tamari lattices in types $A$ and $B$." Transactions of the American Mathematical Society 371, no. 4 (November 27, 2018): 2575–622. http://dx.doi.org/10.1090/tran/7405.

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Randol, Burton. "Hardy-type results on the average of the lattice point error term over long intervals." Transactions of the American Mathematical Society 370, no. 5 (October 31, 2017): 3113–27. http://dx.doi.org/10.1090/tran/7043.

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KIRSCH, ALEXANDER. "BIASED DIFFUSION: TRAP ANALYSIS IN TWO DIMENSIONS." International Journal of Modern Physics C 10, no. 04 (June 1999): 753–57. http://dx.doi.org/10.1142/s0129183199000577.

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A method for analyzing clusters which block the random walk of particles in two-dimensional biased diffusion on percolation lattices above the percolation threshold pc is presented, focusing on the arising problems and explaining the phase transition. The difficulties in a precise trap definition are illustrated. Different trap definitions result in different trap statistics, more or less capable of capturing the trend of the phase diagram.

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Wei, Jiao, Xianguo Geng, and Xin Zeng. "The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices." Transactions of the American Mathematical Society 371, no. 2 (September 10, 2018): 1483–507. http://dx.doi.org/10.1090/tran/7349.

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Lee, Gye-Seon, and Ludovic Marquis. "Anti-de Sitter strictly GHC-regular groups which are not lattices." Transactions of the American Mathematical Society 372, no. 1 (April 4, 2019): 153–86. http://dx.doi.org/10.1090/tran/7530.

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Forrester, Peter J., and Shi-Hao Li. "Classical discrete symplectic ensembles on the linear and exponential lattice: skew orthogonal polynomials and correlation functions." Transactions of the American Mathematical Society 373, no. 1 (September 23, 2019): 665–98. http://dx.doi.org/10.1090/tran/7957.

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VELARDE, MANUEL G., ALEXANDER P. CHETVERIKOV, WERNER EBELING, DIRK HENNIG, and JOHN J. KOZAK. "ON THE MATHEMATICAL MODELING OF SOLITON-MEDIATED LONG-RANGE ELECTRON TRANSFER." International Journal of Bifurcation and Chaos 20, no. 01 (January 2010): 185–94. http://dx.doi.org/10.1142/s0218127410025508.

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We discuss here possible models for long-range electron transfer (ET) between a donor (D) and an acceptor (A) along an anharmonic (Morse–Toda) one-dimensional (1d)-lattice. First, it is shown that the electron may form bound states (solectrons) with externally, mechanically excited solitons in the lattice thus leading to one form of soliton-mediated transport. These solectrons generally move with supersonic velocity. Then, in a thermally excited lattice, it is shown that solitons can also trap electrons, forming similar solectron bound states; here, we find that ET based on hopping can be modeled as a diffusion-like process involving not just one but several solitons. It is shown that either of these two soliton-assisted modes of transport can facilitate ET over quite long distances.

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Hatsuda, Rei, and Emiko Arahata. "Monopole dynamics of Bose–Fermi mixtures in a three-dimensional optical lattice on a harmonic trap." International Journal of Modern Physics B 34, no. 09 (April 10, 2020): 2050073. http://dx.doi.org/10.1142/s0217979220500733.

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Motivated by recent developments in experimental studies of Bose–Fermi mixtures, we investigate monopole oscillation dynamics of Bose–Fermi mixtures in a three-dimensional (3D) optical lattice and an external isotropic harmonic trap potential. We use dynamical Gutzwiller approximation and calculate time dependence of the average spatial extent of particles in a coexisting phase where superfluid bosons and metal fermions coexist. With the trap potential, the bosons concentrate at and around the center of the potential and the fermions surround the bosons. They begin to demonstrate monopole oscillations when the trap potentials are suddenly changed to the ones with smaller curvature. In particular, the correlation between the oscillations of the bosons and fermions is different depending on the condition of the initial confinement. We also show the case where only one of the two trap potentials is changed.

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Fukuyama, Yoshimitsu, Nobuhiro Yasuda, Kunihisa Sugimoto, and Shigeru Kimura. "X-ray diffraction measurement of a single nanometre-sized particle levitated in air by an optical-trap sample holder." Journal of Synchrotron Radiation 27, no. 1 (January 1, 2020): 67–74. http://dx.doi.org/10.1107/s1600577519013651.

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A single-beam optical-trap sample holder for X-ray diffraction measurements with synchrotron radiation has been developed. The sample holder was used to obtain an X-ray diffraction image of a single ZnO particle levitated in air, without mechanical contact, by the optical gradient force exerted by a focused laser beam. The diffraction image showed a Debye ring pattern, which was similar to a powder diffraction pattern of an assemblage of ZnO particles. While the ZnO particle is held by the optical trap in air, it rotates irregularly. Therefore, the Debye ring pattern of the ZnO particle can be clearly obtained even if the ZnO particle is a single grain. Lattice parameters and crystallite size of the single ZnO particle were determined simultaneously. The lattice parameters were determined to be a = 3.2505 ± 0.0005 Å and c = 5.207 ± 0.006 Å, which are consistent with those of the assemblage of ZnO particles. The crystallite size determined by the Scherrer method was 193.4 ± 26.2 nm.

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Zhu, Liuhao, Miaomiao Tang, Hehe Li, Yuping Tai, and Xinzhong Li. "Optical vortex lattice: an exploitation of orbital angular momentum." Nanophotonics 10, no. 9 (June 9, 2021): 2487–96. http://dx.doi.org/10.1515/nanoph-2021-0139.

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Abstract Generally, an optical vortex lattice (OVL) is generated via the superposition of two specific vortex beams. Thus far, OVL has been successfully employed to trap atoms via the dark cores. The topological charge (TC) on each optical vortex (OV) in the lattice is only ±1. Consequently, the orbital angular momentum (OAM) on the lattice is ignored. To expand the potential applications, it is necessary to rediscover and exploit OAM. Here we propose a novel high-order OVL (HO-OVL) that combines the phase multiplication and the arbitrary mode-controllable techniques. TC on each OV in the lattice is up to 51, which generates sufficient OAM to manipulate microparticles. Thereafter, the entire lattice can be modulated to desirable arbitrary modes. Finally, yeast cells are trapped and rotated by the proposed HO-OVL. To the best of our knowledge, this is the first realization of the complex motion of microparticles via OVL. Thus, this work successfully exploits OAM on OVL, thereby revealing potential applications in particle manipulation and optical tweezers.

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