Temporal distribution of a single photon pulse in an interferometer experiment in vacuum via the Gaussian function ψ : ψ ( t ) = 1 ( 2 π σ 2 ) 1 / 4 e − t 2 4 σ 2 e i ω 0 t .It is normalised ∫ | ψ ( t ) | 2 d t = 1 ,and the fourier transform is the wave function in the frequency domain, ψ ~ ( ω ) = 1 2 π ∫ ψ ( t ) e − i ω t d t = ( 2 σ 2 π ) 1 4 e − σ 2 ( ω − ω 0 ) 2 ,such that | ψ ~ ( ω ) | 2 represents the frequency distribution of the photon.However, since a single photon pulse is still a electromagnetic pulse, is there any link between ψ ( t ) and the electric field E ( t ) of this pulse? Like that E ( t ) ∼ Re [ ψ ( t ) ] ∼ e − t 2 4 σ 2 cos ⁡ ( ω 0 t ) ?

Question

Temporal distribution of a single photon pulse in an interferometer experiment in vacuum via the Gaussian function    ψ :  ψ  (  t  )  =            1              (        2        π                  σ          2                          )                      1                          /                        4                                    e          −                        t          2                          4                      σ            2                                    e          i              ω        0            t          .It is normalised  ∫      |    ψ  (  t  )            |        2    d  t  =  1    ,and the fourier transform is the wave function in the frequency domain,            ψ      ~        (  ω  )  =      1          2      π        ∫  ψ  (  t  )      e          −      i      ω      t        d  t  =            (                          2                  σ          2                    π                          )                            1        4                  e          −              σ        2            (      ω      −              ω        0                    )        2                ,such that       |              ψ      ~        (  ω  )            |        2   represents the frequency distribution of the photon.However, since a single photon pulse is still a electromagnetic pulse, is there any link between   ψ  (  t  ) and the electric field   E  (  t  ) of this pulse? Like that  E  (  t  )  ∼  Re  [  ψ  (  t  )  ]  ∼      e          −                        t          2                          4                      σ            2                                cos  ⁡  (      ω    0    t  )    ?

Monica Dennis · Accepted Answer

Your single photon pulse wave function is an element of the first Fock layer (the zeroth is the vacuum layer) of the quantised Maxwell field Fock space. The electric field is still an operator but you can obtain its expectation value as   &amp;lt;  E  &amp;gt;=&amp;lt;      ψ        |    E      |        ψ    &amp;gt;.

Temporal distribution of a single photon pulse in an interferometer experiment in vacuum via the Gaussian function psi: psi(t)=1/((2 pi sigma^2))^1/4 e^(-t^2/4 sigma^2) e^(i omega_0 t)

Answered question

Answer & Explanation

New Questions in Electromagnetism