Projective phase measurements in one-dimensional Bose gases
SciPost Physics Stichting SciPost 5:5 (2018) 046
Authors:
Yuri Daniel van Nieuwkerk, Jörg Schmiedmayer, Fabian Essler
Abstract:
We consider time-of-flight measurements in split one-dimensional Bose
gases. It is well known that the low-energy sector of such systems can
be described in terms of two compact phase fields
\hat{\phi}_{a,s}(x)ϕ̂a,s(x).
Building on existing results in the literature we discuss how a single
projective measurement of the particle density after trap release is in
a certain limit related to the eigenvalues of the vertex operator
e^{i\hat{\phi}_a(x)}eiϕ̂a(x).
We emphasize the theoretical assumptions underlying the analysis of
“single-shot” interference patterns and show that such measurements give
direct access to multi-point correlation functions of
e^{i\hat{\phi}_a(x)}eiϕ̂a(x)
in a substantial parameter regime. For experimentally relevant
situations, we derive an expression for the measured particle density
after trap release in terms of convolutions of the eigenvalues of vertex
operators involving both sectors of the two-component Luttinger liquid
that describes the low-energy regime of the split condensate. This opens
the door to accessing properties of the symmetric sector via an
appropriate analysis of existing experimental data.
