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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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Lattice Centering and Coordination Number02:33

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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
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Hyperbolic and Inverse Hyperbolic Functions: Problem Solving01:30

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An arched gate can be effectively modeled using a hyperbolic cosine profile because this type of function is smooth and symmetric about the vertical axis. When the arch is centered at the origin, its maximum height occurs at the center point. This symmetry ensures that any height below the crown of the arch is reached at two horizontal positions that are equal in distance from the centerline but lie on opposite sides.To determine where the gate reaches a height of five meters, the height of the...
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Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Hyperbolic Functions01:25

Hyperbolic Functions

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A flexible cable suspended between two points at the same height naturally forms a curve known as a catenary. This shape results from the balance between the cable’s weight and the tension acting along its length, representing a state of mechanical equilibrium. Unlike simpler approximations, the true shape of a hanging cable is described using hyperbolic functions.Hyperbolic functions are closely related to exponential functions and are named for their connection to the geometry of the...
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Bewley Lattice Diagram01:12

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The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
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Updated: Jan 22, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Hyperbolic lattices in circuit quantum electrodynamics.

Alicia J Kollár1,2,3, Mattias Fitzpatrick4, Andrew A Houck4

  • 1Department of Electrical Engineering, Princeton University, Princeton, NJ, USA. akollar@umd.edu.

Nature
|July 5, 2019
PubMed
Summary

Superconducting circuits create novel hyperbolic lattices for quantum simulation. These artificial materials exhibit unique flat bands, paving the way for studying curved space physics on a chip.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Quantum information science

Background:

  • Cavity quantum electrodynamics with superconducting circuits is a leading platform for quantum computation and simulation.
  • Coplanar waveguide resonator lattices act as artificial materials for microwave photons.

Purpose of the Study:

  • To explore the potential of deformable lattice sites in superconducting circuits.
  • To create artificial materials exhibiting hyperbolic geometry for quantum simulation.

Main Methods:

  • Utilizing deformable lattice sites in coplanar waveguide resonator networks.
  • Numerical simulations of hyperbolic kagome lattice analogues.
  • Proof-of-principle experimental realization of a hyperbolic lattice.

Main Results:

  • Demonstration of superconducting circuits creating lattices in effective hyperbolic space.
  • Observation of unusual densities of states with spectrally isolated flat bands.
  • Experimental validation of the hyperbolic lattice concept.

Conclusions:

  • Superconducting circuits offer a unique platform for realizing hyperbolic lattices.
  • These hyperbolic lattices enable on-chip quantum simulation of materials and particles in curved space.
  • Opens new avenues for exploring fundamental physics in engineered quantum systems.