Experimental point of view of this Hamiltonian

In summary, the conversation discusses a Hamiltonian involving two spins, which is commonly used in experimental setups. The Hamiltonian includes two terms representing couplings along the z-axis and in the x-y plane, which can be achieved through various methods such as magnetic fields or laser/microwave fields. Both electronic spins and atomic spins in an optical lattice are suitable for this Hamiltonian.
  • #1
Llukis
19
8
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 :smile:
 
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  • #2

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.
 

Related to Experimental point of view of this Hamiltonian

1. What is the experimental point of view of this Hamiltonian?

The experimental point of view of a Hamiltonian refers to the physical interpretation and application of the mathematical equations that describe a system's energy and dynamics. It involves conducting experiments and collecting data to test and validate the predictions made by the Hamiltonian.

2. How is the Hamiltonian derived from experimental data?

The Hamiltonian is derived from experimental data by analyzing the behavior and interactions of a system and using mathematical techniques to formulate equations that accurately describe the system's energy and dynamics. These equations are then refined and validated through further experiments and data analysis.

3. What role does the Hamiltonian play in experimental physics?

The Hamiltonian is a fundamental tool in experimental physics as it allows scientists to make predictions about the behavior of a system and design experiments to test those predictions. It also helps in understanding the underlying principles and mechanisms governing the system's dynamics.

4. How does the Hamiltonian approach differ from other experimental methods?

The Hamiltonian approach differs from other experimental methods in that it is based on mathematical equations and principles, rather than purely empirical observations. It also allows for a more systematic and quantitative analysis of a system's energy and dynamics, leading to more accurate predictions and a deeper understanding of the system.

5. Can the Hamiltonian be used to model any system?

While the Hamiltonian is a powerful tool in experimental physics, it may not be suitable for modeling every system. It is most commonly used in systems with well-defined and predictable dynamics, such as classical mechanics and quantum mechanics. However, it can also be adapted and applied to more complex systems with some modifications.

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