## Projective phase measurements in one-dimensional Bose gases

Yuri D. van Nieuwkerk, Jörg Schmiedmayer, Fabian H. L. Essler

SciPost Phys. 5, 046 (2018) · published 8 November 2018

- doi: 10.21468/SciPostPhys.5.5.046
- Submissions/Reports

### 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 $\hat{\phi}_{a,s}(x)$. 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 $e^{i\hat{\phi}_a(x)}$. 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 $e^{i\hat{\phi}_a(x)}$ 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.

### Cited by 20

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Yuri Daniel van Nieuwkerk, -
^{2}Jörg Schmiedmayer, -
^{1}Fabian Essler

^{1}Rudolf Peierls Centre for Theoretical Physics, University of Oxford^{2}Technische Universität Wien / Vienna University of Technology [TUW]

- Engineering and Physical Sciences Research Council [EPSRC]
- European Research Council [ERC]
- Merton College, University of Oxford (through Organization: Merton College)
- VSB Fonds (through Organization: VSBfonds)