Excited Coherent States Attached to Landau Levels

TL;DR

This paper introduces a new class of excited coherent states linked to Landau levels, demonstrating their controllable quantum fluctuations, nonclassical properties, and potential for cavity generation, expanding the understanding of quantum state engineering.

Contribution

The paper proposes a novel scheme for designing excited coherent states with adjustable quantum properties, including their relation to Landau levels and comparison with existing states.

Findings

Quantum fluctuations are highly controllable in these states.

States exhibit significant Poissonian statistics similar to Glauber states.

Flexibility in establishing nonclassical features like squeezing.

Abstract

A new scheme is proposed to design excited coherent states. where the states ${\beta}$,${\alpha}$ denote the Glauber two variable minimum uncertainty coherent states, which minimize minimum uncertainty conditions while carrier nonclassical properties too and n is an integer. They are converted into the Agarwal's type of the photon added coherent states, arbitrary Fock states and the Glauber two variable coherent states, respectively depending on which of the parameters $\b{eta}$,${\alpha}$ and $n$ equal to zero. It has been shown that the resolution of identity condition is realized with respect to an appropriate measure on the complex plane, too. We have compared our results with the similar quantum states of Agarwal's type and seen that in our case amount of quantum fluctuations are much controllable. Moreover, we have also more flexibility to establish and set-out of their features. Also, there is a discussion on the statistical properties, can unveil (non-)classical properties of these states. For instance their Poissonian statistics are significant similar to what we saw earlier in the Glauber two variable coherent states. Interestingly, depending on the particular choice of the parameters of the above scenarios, we are able to determine the status of compliance with squeezing properties in field quadratures. The last stage is devoted to some theoretical framework to generate them in cavities.