- #1
omni-impotent
- 12
- 0
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?
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?