This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: E x ( z ) is ˆ E x ( z ) = E sin( kz ) ± a + a † ² where E is a normalization constant, and a is the photon annihilation operator. We also deﬁne the photon number operator ˆ n by ˆ n = a † a. (a) Let the state of cavity ﬁeld at time t = 0 be | Ψ(0) i = | m i , where m is an integer. Determine | Ψ( t ) i . Then compute the average values of ˆ E x and ˆ n at time t , along with their variances σ E x ( t ) and σ n ( t ) as deﬁned in Section 3.5.1. (b) As above, but for | Ψ(0) i = ( | m i + e iϕ | m + 1 i ) / √ 2, where m is a positive integer, and ϕ is a phase. 1 (c) Use (3.62) to establish an uncertainty relation between the electric ﬁeld and the photon number. Verify that your answers above are consistent with this uncer-tainty relation. 2...
View Full Document