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Weakly interacting Bose gas with two-body losses
by Chang Liu, Zheyu Shi, Ce Wang
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Submission summary
| Authors (as registered SciPost users): | Ce Wang |
| Submission information | |
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| Preprint Link: | scipost_202305_00032v1 (pdf) |
| Date submitted: | 2023-05-19 10:30 |
| Submitted by: | Wang, Ce |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| 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.
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The authors have conducted a study on the dynamics of weakly interacting Bose gases with two-body losses. This research is highly relevant to cold atom experiments and addresses new theoretical frontiers, such as open systems and non-Hermitian systems. Specifically, the authors demonstrate that optical Feshbach resonance can effectively control inelastic scattering, resulting in a complex scattering length. They employed numerical solutions of the Lindblad equation and the Bogliubov approximation to analyze the system dynamics. Additionally, the authors investigated the dynamical symmetry of this system. Taking into account all of the above, I believe this paper is timely and provides a comprehensive understanding of the subject matter. The writing is clear and comprehensible. Therefore, I would like to recommend this publication for Scipost. Furthermore, I have a few suggestions for the authors:
(1) Providing a physical explanation of c_theta in Eq (20) would greatly assist readers in comprehending the physical implications of a complex scattering length, particularly when comparing it to a negative scattering length in closed system. This clarification would enhance the understanding of the phenomenon described.
(2) A clarification is required regarding the lack of change in gamma_b while the bare interaction g_b becomes g, as observed from Eq. (16) to (17). There must be some underlying considerations for this discrepancy. Hence, an explanation is necessary to address this inconsistency.
(3) By employing the dynamical symmetry, the system dynamics can be described by a set of first-order differential equations, as illustrated in Eq. (37). It would be valuable to investigate whether it is possible to analytically solve this set of equations. Exploring potential analytical solutions would further enhance the understanding of the system's behavior and contribute to the depth of the analysis.