Controlling superfluid flows using dissipative impurities

Dear Editor, Thank you for considering our manuscript “Controlling superfluid flows using dissipative impurities”. Based on the reviewers comments, we have revised our manuscript and would like to resubmit it to SciPost Physics. Our responses to the reviewers comments can be found below. Your sincerely Martin Will, Jamir Marino, Herwig Ott, and Michael Fleischhauer

Reply to “Anonymous Report 1 on 2022-12-12 (Invited Report)”:

We like to thank the referee for the careful reading and for recommending our paper for publication in Scipost Physics.

Reply to “Anonymous on 2022-10-21 [id 2939]”:

We like to thank the referee for the careful reading and the helpful comments. In the following we will reply to them. We would like to emphasize that the SGPE Equation (1), is different from the one derived in [1] C. W. Gardiner and M. J. Davis, The Stochastic Gross–Pitaevskii Equation: II, Journal of Physics B: Atomic, Molecular and Optical Physics 36, 4731 (2003). The theory in [1] describes a Bose gas at finite temperature and the noise is caused by the interaction of the thermal reservoir with the condensed atoms. In contrast to this our work analyses the effect of a noisy potential onto a Bose gas, which is initially at zero temperature. The noise is induced externally, for example by a fluctuating laser field, see section 6 for more details. Answering the referees questions about the SGPE used in our work:

1. -5. To derive equation (1) (for v=0) we start with a Gross-Pitaevskii equation of a Bose Gas with a time dependent potential V(x,t), as derived in [2] C. J. Pethick and H. Smith, Bose-Einstein condensation in dilute gases, Cambridge University Press, and assume that the potential fluctuates globally, i.e. its spatio-temporal dependence factorizes in time and space V(x,t) = V(x) \eta(t). The term \eta(t) models the time-dependent fluctuations, which can be implemented in experiments by a noisy laser field. Since real fluctuations always have a finite correlation time, \eta(t) is a colored noise process. In the limit where the correlation time is short compared to all other timescales of the system it can be approximated by a delta correlated white noise process. As shown in section 6.5 of Ref. [3] C. Gardiner, Handbook of stochastic methods for physics, chemistry, and the natural sciences, Springer (1985), a white noise process which is a limit of a non-white noise process results in a Stratonovich stochastic differential equation, which is the reason it is used here rather than an Ito equation. However, the Stratonovich equation can be transformed into an Ito equation which then contains an effective damping term, see Equation (14) and (15).

2. Note that equation (2) contains no damping term, since also the term “-i v \delta_x” generates unitary dynamics. It remains an open question whether the system eventually reaches thermal equilibrium, however the present work mainly deals with the short to intermediate time evolution.

We clarified the mentioned points in the revision of the manuscript.

1. A paragraph after Eq. (1) has been changed to clarify why a Stratonovich stochastic differential equation is used, rather than an Ito one.
2. Added a paragraph at the end of section 2 to emphasize that the origin of the noise in the stochastic Gross-Pitaevskii equation Eqs. (1) and (2) is different from that in previous work.