Impurities in a one-dimensional Bose gas: the flow equation approach
A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuati...
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| Format: | Article |
| Language: | English |
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SciPost
2021-07-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.11.1.008 |
| _version_ | 1819071381789212672 |
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| author | Fabian Brauneis, Hans-Werner Hammer, Mikhail Lemeshko, Artem G. Volosniev |
| author_facet | Fabian Brauneis, Hans-Werner Hammer, Mikhail Lemeshko, Artem G. Volosniev |
| author_sort | Fabian Brauneis, Hans-Werner Hammer, Mikhail Lemeshko, Artem G. Volosniev |
| collection | DOAJ |
| description | A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak. |
| first_indexed | 2024-12-21T17:20:56Z |
| format | Article |
| id | doaj.art-fe59e5ecaab94980b92a3b4912edbc12 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-12-21T17:20:56Z |
| publishDate | 2021-07-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-fe59e5ecaab94980b92a3b4912edbc122022-12-21T18:56:10ZengSciPostSciPost Physics2542-46532021-07-0111100810.21468/SciPostPhys.11.1.008Impurities in a one-dimensional Bose gas: the flow equation approachFabian Brauneis, Hans-Werner Hammer, Mikhail Lemeshko, Artem G. VolosnievA few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.https://scipost.org/SciPostPhys.11.1.008 |
| spellingShingle | Fabian Brauneis, Hans-Werner Hammer, Mikhail Lemeshko, Artem G. Volosniev Impurities in a one-dimensional Bose gas: the flow equation approach SciPost Physics |
| title | Impurities in a one-dimensional Bose gas: the flow equation approach |
| title_full | Impurities in a one-dimensional Bose gas: the flow equation approach |
| title_fullStr | Impurities in a one-dimensional Bose gas: the flow equation approach |
| title_full_unstemmed | Impurities in a one-dimensional Bose gas: the flow equation approach |
| title_short | Impurities in a one-dimensional Bose gas: the flow equation approach |
| title_sort | impurities in a one dimensional bose gas the flow equation approach |
| url | https://scipost.org/SciPostPhys.11.1.008 |
| work_keys_str_mv | AT fabianbrauneishanswernerhammermikhaillemeshkoartemgvolosniev impuritiesinaonedimensionalbosegastheflowequationapproach |