# Thermal counting statistics in an atomic two-mode squeezed vacuum state

### Submission summary

 As Contributors: Marc Cheneau · Alexandre Dareau · Christoph Westbrook Arxiv Link: https://arxiv.org/abs/1904.04135v2 Date accepted: 2019-06-21 Date submitted: 2019-06-18 Submitted by: Westbrook, Christoph Submitted to: SciPost Physics Domain(s): Experimental Subject area: Atomic, Molecular and Optical Physics - Experiment

### Abstract

We measure the population distribution in one of the atomic twin beams generated by four-wave mixing in an optical lattice. Although the produced two-mode squeezed vacuum state is pure, each individual mode is described as a statistical mixture. We confirm the prediction that the particle number follows an exponential distribution when only one spatio-temporal mode is selected. We also show that this distribution accounts well for the contrast of an atomic Hong--Ou--Mandel experiment. These experiments constitute an important validation of our twin beam source in view of a future test of a Bell inequalities.

### Ontology / Topics

See full Ontology or Topics database.

### Author comments upon resubmission

Dear Editors
We thank the reviewers for their careful reading of the manuscript. In cases where we felt it was needed, we responded to the reviewers questions. Otherwise we have implemented the suggestions as listed below.

### List of changes

1. We have added two sentences to the introduction to emphasize the novelty of this work: "With this detector we are able to select a single atomic mode, and thus access the full counting statistics of that mode. We show that the population is thermal, decreasing exponentially with the atom number."

2. We have added the reference suggested by the reviewer, as well as another one on the same subject (Kheruntsyan et al. 2012). "In the case of twin-beam sources, auto- and cross-correlations have been measured and shown to be consistent with the presence of a two-mode squeezed vacuum [20,21], although in those experiments the counting statistics were not investigated."

3. Two sentences have been added to "Experiment" concerning the depletion: "The initial condensate contains about $10^5$ atoms and about 1% of these atoms are scattered into the four-wave mixing peaks. Thus the undepleted pump approximation used above should be valid."

4. We have amended table I to include the primary, known uncertainty, the quantum efficiency of the detector. We have also modified the discussion of this uncertainty to give a better indication of the sources.
"We show a comparison between the observed and predicted visibilities using this estimate. The uncertainty in the predicted visibility is determined by the 20\% uncertainty in the detection efficiency.Any error due to the detection efficiency is the same for the two realizations. This uncertainty is an underestimate because we cannot be sure that the number atoms in a given cell is the true number of atoms in the mode. As for the detection efficiency, this error would be the same in the two realizations. Other sources of uncertainty, statistical errors in the number of counts, beam splitter imperfections etc. contribute significantly less than the quantum efficiency to the uncertainty in the predicted visibility."

5. We have added a sentence in the abstract and two sentences in the introduction concerning the importance of characterizing the source for a Bell test. Abstract: " These tests constitute an important validation of our twin beam source in view of a future test of a Bell inequalities." Last paragraph of the introduction: "This type of source has also been proposed for a test of a Bell inequality using freely falling atoms. It is thus of great importance to have a good characterization of the particle source, and the experiments described below are an important part of this characterization."

6. We have added a reference to the thesis of P. Dussarrat in which an estimate of the mode size using the autocorrelation is given. (see response to reviewer 2)

7. We have amended the caption to Fig. 2 to indicate that the populations are expressed as probabilities.

8. We have deleted a sentence concerning confirmation of the linearity of the detector (see response to reviewer 2).

9. The phrase "singles count rate" has been changed simply to "count rate" (see response to reviewer 2).

10. Page 1, para 3 line 3 Replace “But” with “However”: done.

11. Page 3, para 2 line 14 replace “dispersion” with “variation”: done.

12. Figure 2, and anywhere else Replace “Count distribution” with “Counting statistics”: done.

13. Page 5, Second last line “Two uncorrelated thermal…” -> “In contrast, two uncorrelated…”: done.

14. Fig 4 replace “contrast” with “visibility”: done.

### Submission & Refereeing History

Resubmission 1904.04135v2 on 18 June 2019
Submission 1904.04135v1 on 9 April 2019

## Reports on this Submission

### Report

The authors have addressed my main criticisms, and I thank them for the additional data plots showing that the trend they observe is present independent of bin selection.

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### Report

I thank the authors for their response, in which they have satisfactorily addressed my concerns and questions.

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