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Following the post in our neighboring chemistry community, I would like to understand the expected outcome when an ensemble of particles at their ground state is heated to gain additional energy halfway between the ground state and the first excited state.

(note that I assume we are applying heat to an ensemble of particles, as the chemistry post states that thermal energy cannot be transferred to a single particle).

I see two possible outcomes:

  1. all particles will be in a superposition of states (amplitude $1/\sqrt{2}$) between the ground state and the 1st excited state
  2. half the particles will jump to the 1st excited state and half will stay at the ground state

If we look at an ensemble of particles, is there even a difference between the two outcomes I listed?

Is there a physical way to change the state of a single particle by adding partial energy? I am not referring to an oscillation between the states that are common in superconducting qubits.

Edit: if the 2nd option is possible, why not have a more complex distribution of states, namely a small percentage of particles jump to high states (2nd, 3rd, 4th... excited states) such that the expectation of energy is conserved?

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