# Projective phase measurements in one-dimensional Bose gases

### Submission summary

 As Contributors: Fabian Essler · Jörg Schmiedmayer · Yuri Daniel van Nieuwkerk Arxiv Link: https://arxiv.org/abs/1806.02626v2 Date accepted: 2018-10-15 Date submitted: 2018-09-05 Submitted by: van Nieuwkerk, Yuri Daniel Submitted to: SciPost Physics Discipline: Physics Subject area: Quantum Physics Approaches: Experimental, Theoretical

### 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.

### Ontology / Topics

See full Ontology or Topics database.

Published as SciPost Phys. 5, 046 (2018)

We thank the referees for their helpful comments. We have addressed the various points raised by the referees as follows:

Referee 1:

(1) We have changed the abstract and conclusion section in order to make clear what our original contributions are. Our main new results are (i) 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; and (ii) obtaining and presenting results for single-shot projective measurements.

(2) The question why interactions after release can be neglected is addressed in Imambekov et al. (2009), to which we have added a reference in the appropriate section.

(3) We have uniformized our notations for real parts.

Referee 2:

(1) We have added a statement that we use units in which $\hbar=1$.

(2) and (3) We have clarified our definitions of the speed of sound $v$, the Luttinger parameter $K$ and the tunnelling strength $\lambda$.

(4) We have clarified what we mean by “longitudinal expansion” and added a comment explaining why this remains a meaningful concept even though we use periodic boundary conditions for simplicity.

### List of changes

-We have rewritten the Abstract to more clearly reflect our original contributions. We have made similar changes to the Introduction and Conclusion.
-We have added a remark about the use of units in which $\hbar=1$. Also, we have clarified our definitions of the speed of sound $v$, the Luttinger parameter $K$ and the tunnelling strength $\lambda$. The notation for real parts of complex numbers has been uniformized.
-The question why interactions after release can be neglected is addressed in Imambekov et al. (2009), to which we have added a reference in the appropriate section.
-We have rewritten the first two paragraphs of Section 2 to clarify what we mean by “longitudinal expansion” and added a comment explaining why this remains a meaningful concept even though we use periodic boundary conditions for simplicity. A related comment has been added at the beginning of Section 3.
-We have added remarks to the Abstract and Conclusion about the possibility of extracting information about the symmetric sector from the interference pattern, as a perspective for further research.

### Submission & Refereeing History

Resubmission 1806.02626v2 on 5 September 2018
Submission 1806.02626v1 on 13 June 2018

## Reports on this Submission

### Report

I am satisfied with the author's responses and recommend the paper for publication.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Report

I am satisfied with the author's response to my criticism and I recommend the paper for publication.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -