How to calculate the on-site interaction in optical lattice

A
Thread starter laconic101
Start date Nov 10, 2018
Tags

Interaction Lattice Optical

In summary, to calculate the on-site interaction in an optical lattice, you need to consider the lattice potential, atomic scattering length, and lattice depth. This plays a crucial role in determining the behavior of ultracold atoms in these systems and can be calculated using the Hubbard model or Bose-Hubbard model. The on-site interaction affects the density profile of atoms by leading to the formation of Mott insulator states or affecting the density in superfluid states. It can be tuned by adjusting the lattice depth or atomic scattering length, and affects the stability of the system by causing heating, loss of atoms, and structural breakdown.

Nov 10, 2018

laconic101

We know the on-site interaction in optical lattice can be expressed as
U=4pi*ħ²a/m ∫d³x |w(x)|⁴

It's simply understood in a 3d system. But how to calculate this term in 1d and 2d system?

Physics news on Phys.org

Nov 10, 2018

BigJDubs

In 1D, the interaction can be expressed as U=4pi*ħ2 a/m ∫dx |w(x)|4.In 2D, the interaction can be expressed as U=4pi*ħ2 a/m ∫dxdy |w(x,y)|4.

1. How do I calculate the on-site interaction in an optical lattice?

To calculate the on-site interaction in an optical lattice, you will need to consider the lattice potential, the atomic scattering length, and the lattice depth. The interaction energy between two atoms in the lattice can be calculated using the Hubbard model or the Bose-Hubbard model.

2. What is the significance of on-site interaction in optical lattices?

The on-site interaction in optical lattices plays a crucial role in determining the behavior of ultracold atoms in these systems. It affects the dynamics and phase transitions of the atoms, and is essential for simulating condensed matter systems and studying quantum many-body physics.

3. How does the on-site interaction affect the density profile of atoms in an optical lattice?

The on-site interaction can lead to the formation of Mott insulator states, where the atoms are localized to a single lattice site due to strong repulsive interactions. It can also affect the density profile in superfluid states, where the atoms can move freely between lattice sites due to weaker interactions.

4. Can the on-site interaction in optical lattices be tuned?

Yes, the on-site interaction can be tuned by adjusting the lattice depth or the atomic scattering length. This can be achieved experimentally by changing the intensity of the laser beams used to create the lattice or by using Feshbach resonances to control the atomic interactions.

5. How does the on-site interaction affect the stability of an optical lattice system?

The on-site interaction can affect the stability of an optical lattice system by causing heating or loss of atoms due to inelastic collisions. It can also lead to the breakdown of the lattice structure and the formation of defects. Careful control and tuning of the on-site interaction is necessary to maintain the stability of the system.