- #1
KFC
- 488
- 4
Assume there is a two level system, two eigenstates are written as
[tex]|\psi_1\rangle = \cos\theta |1, g\rangle + \sin\theta |0, e\rangle[/tex]
and
[tex]|\psi_2\rangle = -\sin\theta |1, g\rangle + \cos\theta |0, e\rangle[/tex]
For the density operator of the system is written as
[tex]\rho = \frac{1}{2}|\psi_1\rangle\langle \psi_1| + \frac{1}{2}|\psi_2\rangle\langle \psi_2| = \frac{1}{2}|1, g\rangle\langle 1, g| + \frac{1}{2}|0, e\rangle\langle 0, e|[/tex]
where [tex]g[/tex] stands for ground state, [tex]e[/tex] stands for excited state, 0 and 1 stands for the number of photon.
If the inital state of the system is in [tex]|0, e\rangle[/tex], what's the probability of transition from [tex]|0, e\rangle \to |1, g\rangle[/tex] ? I am quite confuse how to use density operator to find the probability, shoud it be
[tex]\langle1, g|\rho|0, e\rangle[/tex]
or
[tex]\left|\langle1, g|\rho|0, e\rangle\right|^2[/tex] ?
[tex]|\psi_1\rangle = \cos\theta |1, g\rangle + \sin\theta |0, e\rangle[/tex]
and
[tex]|\psi_2\rangle = -\sin\theta |1, g\rangle + \cos\theta |0, e\rangle[/tex]
For the density operator of the system is written as
[tex]\rho = \frac{1}{2}|\psi_1\rangle\langle \psi_1| + \frac{1}{2}|\psi_2\rangle\langle \psi_2| = \frac{1}{2}|1, g\rangle\langle 1, g| + \frac{1}{2}|0, e\rangle\langle 0, e|[/tex]
where [tex]g[/tex] stands for ground state, [tex]e[/tex] stands for excited state, 0 and 1 stands for the number of photon.
If the inital state of the system is in [tex]|0, e\rangle[/tex], what's the probability of transition from [tex]|0, e\rangle \to |1, g\rangle[/tex] ? I am quite confuse how to use density operator to find the probability, shoud it be
[tex]\langle1, g|\rho|0, e\rangle[/tex]
or
[tex]\left|\langle1, g|\rho|0, e\rangle\right|^2[/tex] ?