m (Created page with "= Mixtures of coherent and thermal fields = When {{I}} started my PhD, there arose the need to describe mixtures of coherent and thermal states, specifically the diagonal ele...") |
m |
||
| Line 3: | Line 3: | ||
When {{I}} started my PhD, there arose the need to describe mixtures of coherent and thermal states, specifically the diagonal elements $p(n)$ of the density matrix (or probability to have $n$ particles) and the postdoc there came up with something that looked hideous to me: $p_{\mathrm{coh}}(n)+p_{\mathrm{th}}(n)$ (normalized). | When {{I}} started my PhD, there arose the need to describe mixtures of coherent and thermal states, specifically the diagonal elements $p(n)$ of the density matrix (or probability to have $n$ particles) and the postdoc there came up with something that looked hideous to me: $p_{\mathrm{coh}}(n)+p_{\mathrm{th}}(n)$ (normalized). | ||
| − | {{cite|laussy06a}} | + | I was stuyding [[Glauber]]'s $P$ function formalism then, where it was stated how to admix various fields from their $P$ function. Strangely enough, the statistics $p(n)$ for a mixture of coherent and thermal fields were not worked out, so I did it myself and we used this version instead for the paper.{{cite|laussy06a}} |
| + | |||
| + | Of course, such a basic result had been derived before. Apparently the first time by [[G. Lachs]]{{cite|lachs65a}}. One can also find the result in Teich and Saleh's excellent book [[Fundamentals of Photonics]]. | ||
| + | |||
| + | Possibly also related B. Picinbono and M. Rousseau, Phys. Rev. A '''1''':635 | ||
| + | (1970). | ||
== References == | == References == | ||
<references /> | <references /> | ||
Latest revision as of 20:27, 27 January 2024
Mixtures of coherent and thermal fields
When I started my PhD, there arose the need to describe mixtures of coherent and thermal states, specifically the diagonal elements $p(n)$ of the density matrix (or probability to have $n$ particles) and the postdoc there came up with something that looked hideous to me: $p_{\mathrm{coh}}(n)+p_{\mathrm{th}}(n)$ (normalized).
I was stuyding Glauber's $P$ function formalism then, where it was stated how to admix various fields from their $P$ function. Strangely enough, the statistics $p(n)$ for a mixture of coherent and thermal fields were not worked out, so I did it myself and we used this version instead for the paper.[1]
Of course, such a basic result had been derived before. Apparently the first time by G. Lachs[2]. One can also find the result in Teich and Saleh's excellent book Fundamentals of Photonics.
Possibly also related B. Picinbono and M. Rousseau, Phys. Rev. A 1:635 (1970).
