- #1

deepalakshmi

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- TL;DR Summary
- How to evolve one photon using hamiltonian as beam splitter

During time evolution of one photon with vacuum state with hamiltonian as a^†b+b^†a, the answer is cos(t/ℏ)|0,1⟩+isin(t/ℏ)|1,0⟩. But i don't know how to do calculation to get this answer. Can someone please help me?

I tried to do this calculation:

|0⟩|1⟩(t)=e−iHtℏ|0⟩|1⟩

=(cos(tH/ℏ)−isin(tH/ℏ)) |0⟩|1⟩

=[cos(t/ℏ)−isin(t/ℏ)] H|0⟩|1⟩

=[cos(t/ℏ)−isin(t/ℏ)] [|0⟩|1⟩+i|1⟩|0⟩]

How to proceed?

I tried to do this calculation:

|0⟩|1⟩(t)=e−iHtℏ|0⟩|1⟩

=(cos(tH/ℏ)−isin(tH/ℏ)) |0⟩|1⟩

=[cos(t/ℏ)−isin(t/ℏ)] H|0⟩|1⟩

=[cos(t/ℏ)−isin(t/ℏ)] [|0⟩|1⟩+i|1⟩|0⟩]

How to proceed?

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