Experimental point of view of this Hamiltonian

[Llukis]

TL;DR Summary

I want to know if this Hamiltonian is feasible in the laboratory.

Dear everybody,

I am involved with a system of two spins and I ended up with the following Hamiltonian:
$$H_c(t) = W\sin(2J_+ t) \big( \mathbb{1} \otimes \sigma_z - \sigma_z \otimes \mathbb{1}\big) + W \cos(2J_+ t) \big( \sigma_y \otimes \sigma_x - \sigma_x \otimes \sigma_y \big) \: ,$$
where $W$ is a constant, $\sigma_i$ are the Pauli matrices and $J_+ = J_x + J_y$ a coupling constant between the spins. My question is whether this Hamiltonian is feasible in the laboratory. The spins under consideration could be electronic spins or atomic spins in an optical lattice, for example.

Thank you very much in advance for your time

 

[eljose79]

Thank you for sharing your Hamiltonian. I can say that this Hamiltonian is definitely feasible in the laboratory. In fact, it is a common Hamiltonian used in many experimental setups involving two interacting spins.

The first term in the Hamiltonian, $W\sin(2J_+ t) \big( \mathbb{1} \otimes \sigma_z - \sigma_z \otimes \mathbb{1}\big)$, represents a coupling between the two spins along the z-axis, which is often achieved through a magnetic field. The second term, $W \cos(2J_+ t) \big( \sigma_y \otimes \sigma_x - \sigma_x \otimes \sigma_y \big)$, represents a coupling between the two spins in the x-y plane, which can be achieved through various methods such as laser or microwave fields.

In terms of the types of spins that can be used, electronic spins and atomic spins in an optical lattice are both suitable for this Hamiltonian. In fact, this Hamiltonian has been used in experiments involving both types of spins.

I hope this answers your question and I wish you success in your research.