(a) Let ψ_0(q) be the wavefunction corresponding to the vacuum state |0⟩ is the representation of the position operator
Posted: Mon May 09, 2022 2:16 pm
(a) Let ψ_0(q) be the wavefunction corresponding to the vacuum state |0⟩ is the representation of the position operator ˆq. Use the annihilation operator expression in quadrature terms ˆq, ˆp to obtain a differential equation for ψ_0(q) and solve it (thereby showing that the zero-photon vacuum state does indeed exist and it is a well-behaved state). Plot |ψ_0(q)|^2 and deduce that, even in the state vacuum, the quadratures show fluctuations (dispersion). Explain why it was
quadratures are expected to fluctuate.
(b) Construct a coherent state with an expected value of the number of photons equal to 5.
Find the probability that the state has 10 photons, the probability that it has
5 photons and the probability that it has 0 photons. Graph the probability of the number
of photons in the interval [0, 20] photons.
PLEASE WRITE THE STEP BY STEP WITH ALL THE ALGEBRA AND ANSWER ALL THE PARAGRAPHS OR I'M GOING TO DOWNVOTE. INCLUDE THE GRAPH PLEASE AND ALL.THE PARAMETERS YOU USE.
quadratures are expected to fluctuate.
(b) Construct a coherent state with an expected value of the number of photons equal to 5.
Find the probability that the state has 10 photons, the probability that it has
5 photons and the probability that it has 0 photons. Graph the probability of the number
of photons in the interval [0, 20] photons.
PLEASE WRITE THE STEP BY STEP WITH ALL THE ALGEBRA AND ANSWER ALL THE PARAGRAPHS OR I'M GOING TO DOWNVOTE. INCLUDE THE GRAPH PLEASE AND ALL.THE PARAMETERS YOU USE.