Command of Collective Dynamics by Topological Defects in Spherical Crystals

Yao, Zhenwei

doi:10.1103/physrevlett.122.228002

Cited by 19 publications

(11 citation statements)

References 40 publications

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“…Specifically, Susskind–Glogower, Pegg–Barnett, and Barnett–Pegg formalisms played a very important role in the studies of phase properties and the phase fluctuation . Thereafter, phase properties of various quantum states have been reported using these formalisms . Other approaches have also been used for the study of the phase properties.…”

Section: Introductionmentioning

confidence: 99%

Quantum Phase Properties of Photon Added and Subtracted Displaced Fock States

et al. 2019

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Quantum phase properties of photon added and subtracted displaced Fock states (and a set of quantum states which can be obtained as the limiting cases of these states) are investigated from a number of perspectives, and it is shown that the quantum phase properties are dependent on the quantum state engineering operations performed. Specifically, the analytic expressions for quantum phase distributions and angular Q distribution as well as measures of quantum phase fluctuation and phase dispersion are obtained. The uniform phase distribution of the initial Fock states is observed to be transformed by the unitary operation (i.e., displacement operator) into non-Gaussian shape, except for the initial vacuum state. It is observed that the phase distribution is symmetric with respect to the phase of the displacement parameter and becomes progressively narrower as its amplitude increases. The non-unitary (photon addition/subtraction) operations make it even narrower in contrast to the Fock parameter, which leads to broadness. The photon subtraction is observed to be a more powerful quantum state engineering tool in comparison to the photon addition. Further, one of the quantum phase fluctuation parameters is found to reveal the existence of antibunching in both the engineered quantum states under consideration. Finally, the relevance of the engineered quantum states in the quantum phase estimation is also discussed, and photon added displaced Fock state is shown to be preferable for the task.

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Section: Introductionmentioning

confidence: 99%

Quantum Phase Properties of Photon Added and Subtracted Displaced Fock States

et al. 2019

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“…Particles arranged on the surface of a sphere are known to exhibit a richness of defect structures in a variety of systems (e.g. [18][19][20][21][22][23][24][25][26][27][28]), which is a result of both the interparticle interaction and the spherical topology. Reference [29] finds the phase diagram and structures of purely repulsive soft colloidal particles constrained to a two-dimensional plane and to the surface of a spherical shell using numerical simulations.…”

Section: Resultsmentioning

confidence: 99%

The configurational entropy of colloidal particles in a confined space

Wan

2022

Preprint

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We calculate the configurational entropy of colloidal particles in a confined geometry interacting as hard disks using Monte Carlo integration method. In particular, we consider systems with three kinds of boundary conditions: hard, periodic and spherical. For small to moderate packing fraction φ values, we find the entropies per particle for systems with the periodic and spherical boundary conditions tend to reach a same value with the increase of the particle number N , while that for the system with the hard boundary conditions still has obvious differences compared to them within the studied N range. Surprisingly, despite the small system sizes, the estimated entropies per particle at infinite system size from extrapolations in the periodic and spherical systems are in reasonable agreement with that calculated using thermodynamic integration method. Besides, as N increases we find the pair correlation function begins to exhibit similar features as that of a large selfassembled system at the same packing fraction. Our findings may contribute to a better understanding of how the configurational entropy changes with the system size and the influence of boundary conditions, and provide insights relevant to engineering particles in confined spaces.

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“…Crystal-like order and defects have been studied in viruses 4,5 , metazoan epithelia 6 , and colloidal capsules [7][8][9] , where different ways of construction have been shown to lead to different degrees of order 10 . It is important to understand and determine the degree of (dis)order in spherical structures, as it can lead to different optic 11,12 , elastic 13,14 , and dynamic 15 properties. Order of the underlying spherical lattice can also significantly influence the orientations of anisotropically interacting particles positioned on it [16][17][18] .…”

Section: Introductionmentioning

confidence: 99%

Global order parameters for particle distributions on the sphere

2021

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Topology and geometry of a sphere create constraints for particles that lie on its surface which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately, requiring a careful treatment of systems with one or several characteristic length scales. All this can make it difficult to precisely determine whether a particular system is in a disordered, fluid-like, or crystal-like state. Here, we show how order transitions in systems of particles interacting on the surface of a sphere can be detected by changes in two hyperuniformity parameters, derived from spherical structure factor and cap number variance. We demonstrate their use on two different systems-solutions of the thermal Thomson problem and particles interacting via ultra-soft GEM-4 potential-each with a distinct parameter regulating their degree of ordering. The hyperuniformity parameters are not only able to detect the order transitions in both systems, but also point out the clear differences in the ordered distributions in each due to the nature of the interaction leading to them. Our study shows that hyperuniformity analysis of particle distributions on the sphere provides a powerful insight into fluid-and crystal-like order on the sphere.

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Command of Collective Dynamics by Topological Defects in Spherical Crystals

Cited by 19 publications

References 40 publications

Quantum Phase Properties of Photon Added and Subtracted Displaced Fock States

Quantum Phase Properties of Photon Added and Subtracted Displaced Fock States

The configurational entropy of colloidal particles in a confined space

Global order parameters for particle distributions on the sphere

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