Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

Trends in Lattice Energy: Ion Size and Charge

Trends in Lattice Energy: Ion Size and Charge

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:

Lattice Centering and Coordination Number

Lattice Centering and Coordination Number

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
Imagine taking a large number of identical...

Atomic Orbitals

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.

Hybridization of Atomic Orbitals I

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Erratum: L-based numerical linked cluster expansion for square lattice models [Phys. Rev. E 108, 034126 (2023)].

Physical review. E·2025

Same author

Phantom energy in the nonlinear response of a quantum many-body scar state.

Science (New York, N.Y.)·2024

Same author

Numerical linked-cluster expansions for two-dimensional spin models with continuous disorder distributions.

Physical review. E·2024

Same author

L-based numerical linked cluster expansion for square lattice models.

Physical review. E·2023

Same author

Generalized Thermalization in Quantum-Chaotic Quadratic Hamiltonians.

Physical review letters·2023

Same author

Author Correction: Observation of hydrodynamization and local prethermalization in 1D Bose gases.

Nature·2023

Search research articles

Related Experiment Video

Updated: Jun 5, 2026

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Strongly interacting atom lasers in three-dimensional optical lattices.

Itay Hen¹, Marcos Rigol

¹Department of Physics, Georgetown University, Washington, D.C. 20057, USA.

Physical Review Letters

|January 15, 2011

Summary

Dynamical melting of Mott insulators creates atom lasers. Bosons condense at specific momenta, dependent on hopping amplitudes, enabling new quantum technologies.

Area of Science:

Quantum physics
Condensed matter physics
Atomic physics

Background:

Mott insulators are quantum states of matter with strong interactions.
Dynamical processes can drive phase transitions in quantum systems.
Atom lasers require controlled generation of coherent atomic matter waves.

Purpose of the Study:

To investigate the dynamical melting of a Mott insulator in a 3D lattice.
To explore the possibility of generating strongly interacting atom lasers.
To analytically determine the condensation momenta and their dependence on system parameters.

Main Methods:

Utilizing a Gutzwiller-type mean-field approach.
Performing analytical calculations for infinite on-site repulsion.

More Related Videos

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

Published on: February 4, 2017

Construction and Characterization of External Cavity Diode Lasers for Atomic Physics

Construction and Characterization of External Cavity Diode Lasers for Atomic Physics

Published on: April 24, 2014

Related Experiment Videos

Last Updated: Jun 5, 2026

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

Published on: February 4, 2017

Construction and Characterization of External Cavity Diode Lasers for Atomic Physics

Construction and Characterization of External Cavity Diode Lasers for Atomic Physics

Published on: April 24, 2014

Validating results with exact-diagonalization solutions for small systems.

Main Results:

Mott insulator melting leads to Bose-Einstein condensation at nonzero momenta.
Condensation momenta exhibit a simple dependence on hopping amplitudes.
Condensate occupation scales linearly with the initial number of atoms.

Conclusions:

Dynamical melting provides a novel route to generating atom lasers.
The findings offer precise control over atom laser properties through lattice parameters.
This work advances the understanding of quantum phase transitions and atom optics.