Recording of our website. See it live at https://gohsu.com/rabi-oscillations.

What we built

The two plots above shows how the probabilities of a particle being in the spin-up state and in the spin-down state vary with time given other parameters such as mass or magnetic field.

The left plot graphs probability vs time: the curve at the top is the probability of being in the spin-up state and the curve at the bottom is the probability of being in the spin down state. You will see that the probabilities add up to 1 -- the particle will be in one of the states with 100 % chance.

The plot to the right is a visualization of the spin at any given time. The two arrows represent the probability of the particle being in the two states, with a longer arrow meaning greater probability. Hence, if you see one long arrow pointing up and no arrow pointing down, the particle is with 100 % certainty in the spin-up state.

Why we built this

Solutions to physical problems with time-dependent potentials are quite rare. In most cases, we resort to time-dependent perturbation theory to obtain an approximate answer, valid only at early times and for small potentials. One of the few exactly solvable problems is the two-level system with the Hamiltonian, which can be seen as coupling the magnetic moment of a particle to an oscillating magnetic field. This can be solved to obtain the the probability distribution of a particle initially in the spin-up/spin-down state! (More info on the website.)

The simplicity of this physical problem's solution makes it a perfect one to visualize. This website will ideally act as an aid in understanding how different parameters in the two-level system with the Hamiltonian affect electron spin.