Cornwall-Jackiw-Tomboulis effective field theory to nonuniversal equation of state of an ultracold Bose gas
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912084359380992 |
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| author | Zhang, Yi Liang, Zhaoxin |
| author_facet | Zhang, Yi Liang, Zhaoxin |
| contents | The equation of state (EOS) serves as a cornerstone in elucidating the properties of quantum many-body systems. A recent highlight along this research line consists of the derivation of the nonuniversal Lee-Huang-Yang (LHY) EOS for an ultracold quantum bosonic gas with finite-range interatomic interactions using one-loop effective path-integral field theory. The purpose of this work is to extend Salasnich's pioneering work to uncover beyond-LHY corrections to the EOS by employing the Cornwall-Jackiw-Tomboulis (CJT) effective field theory, leveraging its two-loop approximation. In this end, we expand Salasnich's remarkable findings of EOS to the next leading order characterized by $\left(ρa_{\text{s}}^{3}\right)^{2}$, with $ρ$ and $a_{\text{s}}$ being the density and the $s$-wave scattering length. Notably, we derive analytical expressions for quantum depletion and chemical potential, representing the next-to-LHY corrections to nonuniversal EOS induced by finite-range effects. Moreover, we propose an experimental protocol of observing the nonuniversal next-to-LHY corrections to the EOS by calculating fractional frequency shifts in the breathing modes. The nonuniversal beyond-LHY EOS in this work paves the way of using LHY effects in quantum simulation experiments and for investigations beyond the LHY regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cornwall-Jackiw-Tomboulis effective field theory to nonuniversal equation of state of an ultracold Bose gas Zhang, Yi Liang, Zhaoxin Quantum Gases The equation of state (EOS) serves as a cornerstone in elucidating the properties of quantum many-body systems. A recent highlight along this research line consists of the derivation of the nonuniversal Lee-Huang-Yang (LHY) EOS for an ultracold quantum bosonic gas with finite-range interatomic interactions using one-loop effective path-integral field theory. The purpose of this work is to extend Salasnich's pioneering work to uncover beyond-LHY corrections to the EOS by employing the Cornwall-Jackiw-Tomboulis (CJT) effective field theory, leveraging its two-loop approximation. In this end, we expand Salasnich's remarkable findings of EOS to the next leading order characterized by $\left(ρa_{\text{s}}^{3}\right)^{2}$, with $ρ$ and $a_{\text{s}}$ being the density and the $s$-wave scattering length. Notably, we derive analytical expressions for quantum depletion and chemical potential, representing the next-to-LHY corrections to nonuniversal EOS induced by finite-range effects. Moreover, we propose an experimental protocol of observing the nonuniversal next-to-LHY corrections to the EOS by calculating fractional frequency shifts in the breathing modes. The nonuniversal beyond-LHY EOS in this work paves the way of using LHY effects in quantum simulation experiments and for investigations beyond the LHY regime. |
| title | Cornwall-Jackiw-Tomboulis effective field theory to nonuniversal equation of state of an ultracold Bose gas |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2408.09668 |