# Variational truncated Wigner approximation for weakly interacting Bose fields: Dynamics of coupled condensates

### Submission summary

 Authors (as Contributors): Christopher Mink
Submission information
Date accepted: 2021-12-08
Date submitted: 2021-11-29 12:55
Submitted by: Mink, Christopher
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Atomic, Molecular and Optical Physics - Theory
Approaches: Theoretical, Experimental, Computational

### Abstract

The truncated Wigner approximation is an established approach that describes the dynamics of weakly interacting Bose gases beyond the mean-field level. Although it allows a quantum field to be expressed by a stochastic c-number field, the simulation of the time evolution is still very demanding for most applications. Here, we develop a numerically inexpensive scheme by approximating the c-number field with a variational ansatz. The dynamics of the ansatz function is described by a tractable set of coupled ordinary stochastic differential equations for the respective variational parameters. We investigate the non-equilibrium dynamics of a three-dimensional Bose gas in a one-dimensional optical lattice with a transverse isotropic harmonic confinement. The accuracy and computational inexpensiveness of our method are demonstrated by comparing its predictions to experimental data.

Published as SciPost Phys. 12, 051 (2022)

We are grateful for the constructive reports from both referees and for the opportunity to carefully revise the manuscript accordingly. The text has been significantly improved based on the respective suggestions.

### List of changes

-The first mention of the residual (non-macroscopic) field has been moved to the introduction
-the caption of figure 1 now includes all relevant parameters.
-The change of variables in the functional Fokker-Planck equation and subsequent neglection of the residual field on p. 8-9 (most importantly eq. 22) have been overhauled to make the decoupling of the fields $\psi_0$ and $\psi_1$ more clear.
-a newly added paragraph at the end of section 5.1 motivates the experimental data and stresses that it is - in fact - newly obtained data.
-Section 5.2.2 has been reworked to explain why the overestimation of the number fluctuations is a generic artifact of few-mode approximations such as our variational ansatz.
-The new section 5.2.3 introduces local incoherent gains and losses to the optical lattice. We derive the positive-semidefinite diffusion matrix within the variational scheme and derive a set of stochastic differential equations. The incoherent contribution to the dynamics for a coupled and a single trap is shown in the new figure 6.

### Submission & Refereeing History

Resubmission 2106.05354v2 on 29 November 2021
Submission 2106.05354v1 on 29 June 2021

## Reports on this Submission

### Anonymous Report 2 on 2021-12-1 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2106.05354v2, delivered 2021-12-01, doi: 10.21468/SciPost.Report.3981

### Report

In the revised version of the paper and in their reply, the authors address most of the point that I raised in my previous report. In particular, a whole new section demonstrating the simulation of a dissipative system has been added, which nicely illustrates the generality of the described method. Overall, I am satisfied with the reply by the authors and the changes in revisions in the manuscript. Since the method seems to be very powerful and applicable for a broad range of problems, I recommend to publish the current version of the paper in SciPost Physics.

• validity: high
• significance: high
• originality: high
• clarity: high
• formatting: perfect
• grammar: perfect

### Report

I am satisfied with the corrections and answers to my questions, I recommend publishing.

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