SciPost Submission Page
Weakly interacting Bose gas with two-body losses
by Chang Liu, Zheyu Shi, Ce Wang
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Ce Wang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202305_00032v3 (pdf) |
| Date accepted: | 2024-04-08 |
| Date submitted: | 2024-03-22 12:10 |
| Submitted by: | Wang, Ce |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We study the many-body dynamics of weakly interacting Bose gases with two- particle losses. We show that both the two-body interactions and losses in atomic gases may be tuned by controlling the inelastic scattering process between atoms by an optical Feshbach resonance. Interestingly, the low-energy behavior of the scattering amplitude is governed by a single parameter, i.e. the complex s-wave scattering length a_c. The many-body dynamics are thus described by a Lindblad master equation with complex scattering length. We solve this equation by applying the Bogoliubov approximation in analogy to the closed systems. Various peculiar dynamical properties are discovered, some of them may be regarded as the dissipative counterparts of the celebrated results in closed Bose gases. For example, we show that the next-order correction to the mean-field particle decay rate is to the order of |n a_c^3|^1/2, which is an analogy of the Lee-Huang-Yang correction of Bose gases. It is also found that there exists a dynamical symmetry of symplectic group Sp(4,C) in the quadratic Bogoliubov master equation, which is an analogy of the SU(1,1) dynamical symmetry of the corresponding closed system. We further confirmed the validity of the Bogoliubov approximation by comparing its results with a full numerical calculation in a double-well toy model. Generalizations of other alternative approaches such as the dissipative version of the Gross-Pitaevskii equation and hydrodynamic theory are also discussed in the last.
Author comments upon resubmission
In the following, we address reviewer 3’s comments and suggestions.
(1)"Please, revise the manuscript for grammar issues"
We apologize for the grammatical issues in the article and appreciate the reviewer's suggestions.
We have carefully checked the grammar issues in the article and made corrections in the new version.
(2)"In the first sentence of section 2 the words “two-body losses” and “inelastic collisions” should be swapped"
We have made the correction in the revision as requested by the reviewer. We appreciate the reviewer's careful reading and rigorous logic.
(3) "Please, cite Refs [39-41] after Eq. (1)"
The reference has been added.
(4) "In figure 1 (and perhaps throughout the manuscript) Im(1/a_c) is shown as a positive quantity. The imaginary part of the complex scattering length is always negative."
As pointed by the referee, the imaginary part of the scattering length must be negative. Thus by our definition a_c = a_r + i*a_i with a_i < 0 , the imaginary part of 1/a_c = (a_r - i*a_i)/(a_r^2 + a_i^2) is positive.
(5) "Below Eq. (8), I’m unsure what the authors meant by “decaying to the environment”. Please, be more precise."
By decaying into the environment, we mean the atoms that go through inelastic collisions are no longer confined by the trapping potential.
We appreciate that the referee points out this unclear expression and we have added an explanation in the revised manuscript.
(6) "Near Eq. (20), please, define explicitly the relation a_c=a_r-i*a_i for the complex scattering length"
We define the relation as a_c=a_r + i*a_i with a_i a negative real number. We appreciate that the reviewer point out this confusion and we have added an explicit definition near Eq.(20).
List of changes
1. swap "inelastic collisions between particles" and "two-body losses" in section 2.
2. cite Refs [39-41] after Eq. (1)
3. Below Eq.(8), change
"This master equation describes Bose atoms $\hat{a}$ interacting with each other at a bare coupling constant $g_b$ while decaying to the environment at a bare coupling constant $\gamma_b$ though a two-particle losses process."
to
"This master equation describes the dynamics of Bose atoms, denoted by $\hat{a}$, as they interact with each other through a bare coupling constant $g_b$ while decaying to the environment (i.e. no longer confined by the trapping potential) via a two-body losses process characterized by a bare coupling constant $\gamma_b$."
4. Below Eq.(20), change "Here $\theta$ is defined as $\theta=-\arg(a_c)=-\arg(a_r+ia_i)\in[0,\pi]$."
to
"Here, $\theta$ is defined as $\theta=-\arg(a_c) =-\arg(a_r + ia_i) \in[0,\pi]$, where $a_c$ is expressed as two real parameters: $a_c=a_r+ia_i$."
5.A series of grammar issues have been corrected.
Published as SciPost Phys. 16, 116 (2024)