# The Landau-Zener transition & spin-flipping in an external field

• omni-impotent
In summary, the conversation discusses processes that can cause "spin-flipping" for magnetic moments in a bias field along the z-axis. The application of an oscillating field in the xy-plane and the Landau-Zener transitions are mentioned. The LZ transition is described as a special case of the Rabi transition and the spin-flip probability is related to the energy gap and the perturbation in the x-axis. The possibility of spin-flips induced by a variation in the z-axis and the term "majorana spin-flipping" is also mentioned.

#### omni-impotent

Hello gentlemen,

I am trying to understand better processes that can cause "spin-flipping" to occur for magnetic moments in a bias field along the z-axis, Bz.

The application of a oscillating field in the xy-plane is well known to me. If the oscillating frequency is at the Larmor frequency, $$\omega_L = \gamma B$$ then the probability of a spin-flip will be given by $$sin(\omega_R t)$$, where $$\omega_R$$ is the Rabi frequency and t is the duration time the field is applied for.

I am trying to understand the Landau-Zener transitions. When I try to search google, I just get lots of hits for quantum qubit transitions. If I am interpreting correctly, the LZ transition is almost just a special case of the Rabi transition if the perturbation is just for a short time? The excitation is normally treated as a perturbing field in the x-axis B_x which varies linearly. The spin-flip probability is something like $$exp(-2 \pi \Gamma)$$, where $$\Gamma = \frac{B_x^2}{d\DeltaE/dt}$$. $$\DeltaE$$ is the size of the energy gap and for the magnetic moment example, it is $$2 \mu B$$. Am I right?

I am confused by this since why does the energy gap change if you're only applying a small perturbation in Bx?

Also, how can one treat a problem where the variations is in the z-axis? Something like a $$\delta_{B_Z}$$? Can this induce spin-flips? Can I use the Landau-Zener transition for this since $$\Delta_E$$ changes? What if this extra $$\delta_{B_Z}$$ causes the total BZ to go through zero?

ahhh... after some hours of searching, the phenomena I am referring to is called majorana spin-flipping. Anyone know anything about this?

## 1. What is the Landau-Zener transition?

The Landau-Zener transition, also known as the Landau-Zener-Stückelberg-Majorana transition, is a phenomenon in quantum mechanics where a two-level quantum system undergoes a sudden transition between its energy levels when an external field is varied at a certain rate.

## 2. What is spin-flipping in an external field?

Spin-flipping refers to the change in the spin state of a particle when it is subjected to an external magnetic or electric field. This can occur in various physical systems, such as atoms, nuclei, and electrons.

## 3. How does the Landau-Zener transition affect spin-flipping?

The Landau-Zener transition plays a crucial role in spin-flipping as it determines the probability of the particle undergoing a spin-flip. The rate at which the external field is varied and the strength of the field are the key factors that influence the probability of spin-flipping.

## 4. What applications does the Landau-Zener transition and spin-flipping have?

The Landau-Zener transition and spin-flipping have various applications in quantum technology, such as in spintronics, quantum computing, and quantum sensing. These phenomena are also studied in condensed matter physics to understand the behavior of electrons in materials.

## 5. Are there any real-world examples of the Landau-Zener transition and spin-flipping?

Yes, there are several real-world examples of the Landau-Zener transition and spin-flipping. One example is the study of nuclear magnetic resonance (NMR), where the spin states of nuclei are flipped using external magnetic fields. These phenomena are also observed in quantum dots, superconductors, and other quantum systems.