Non-equilibrium dynamics in tunnel-coupled Bose gases
<p>This thesis presents four theoretical studies on pairs of tunnel-coupled one-dimensional Bose gases. It first recapitulates how at low energies, the gases’ symmetric and antisymmetric combinations of density and phase are governed by two Tomonaga-Luttinger Liquids (TLL). Tunneling between t...
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| Format: | Thesis |
| Language: | English |
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2020
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| _version_ | 1797093667012345856 |
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| author | Van nieuwkerk, YD |
| author2 | Essler, F |
| author_facet | Essler, F Van nieuwkerk, YD |
| author_sort | Van nieuwkerk, YD |
| collection | OXFORD |
| description | <p>This thesis presents four theoretical studies on pairs of tunnel-coupled one-dimensional Bose gases. It first recapitulates how at low energies, the gases’ symmetric and antisymmetric combinations of density and phase are governed by two Tomonaga-Luttinger Liquids (TLL). Tunneling between the gases is believed to yield a quantum sine-Gordon model for the antisymmetric sector. The theoretical background and various applications of this model are summarized, before presenting the first new theoretical results. These show in detail how matter-wave interference measurements can access eigenvalues of the relative phase operator from the TLL, allowing to study the operator’s distribution functions and multi-point correlators. The derivation clarifies why this construction is limited to short expansion times and weak interactions and what modifications occur away from this limit. This leads to a new formula predicting longitudinal “density ripples”.</p>
<p>The second half of the thesis was stimulated by recent and unexplained experimental results in the tunnel-coupled case, where density-phase oscillations were seen to rapidly damp out. The work first studies whether this can be explained within a translationally invariant sine-Gordon model. Treating this model in a self-consistent harmonic approximation leads to a negative conclusion. Second, the next leading perturbation due to the tunnel-coupling is investigated in a box geometry. Although this yields a non-negligible coupling between the (anti)symmetric sectors, the effects are not strong enough to explain the damping. Finally, a new low-energy theory is developed, which does not rely on the TLL and which allows to study the roles of both higher excited levels of the transverse potential and of a realistic longitudinal potential. Strong damping is observed as a result of the longitudinal potential, with a dependence on the particle number that is compatible with experimental results. This indicates that performing the experiments in a hard-wall box potential might eliminate the damping effects.</p> |
| first_indexed | 2024-03-07T04:03:35Z |
| format | Thesis |
| id | oxford-uuid:c5689822-401d-4613-9c0d-d8471dd74cb9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:03:35Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | oxford-uuid:c5689822-401d-4613-9c0d-d8471dd74cb92022-03-27T06:30:40ZNon-equilibrium dynamics in tunnel-coupled Bose gasesThesishttp://purl.org/coar/resource_type/c_db06uuid:c5689822-401d-4613-9c0d-d8471dd74cb9One-dimensional quantum many-body physicsQuantum Field TheoryOut-of-equilibrium physicsEnglishHyrax Deposit2020Van nieuwkerk, YDEssler, F<p>This thesis presents four theoretical studies on pairs of tunnel-coupled one-dimensional Bose gases. It first recapitulates how at low energies, the gases’ symmetric and antisymmetric combinations of density and phase are governed by two Tomonaga-Luttinger Liquids (TLL). Tunneling between the gases is believed to yield a quantum sine-Gordon model for the antisymmetric sector. The theoretical background and various applications of this model are summarized, before presenting the first new theoretical results. These show in detail how matter-wave interference measurements can access eigenvalues of the relative phase operator from the TLL, allowing to study the operator’s distribution functions and multi-point correlators. The derivation clarifies why this construction is limited to short expansion times and weak interactions and what modifications occur away from this limit. This leads to a new formula predicting longitudinal “density ripples”.</p> <p>The second half of the thesis was stimulated by recent and unexplained experimental results in the tunnel-coupled case, where density-phase oscillations were seen to rapidly damp out. The work first studies whether this can be explained within a translationally invariant sine-Gordon model. Treating this model in a self-consistent harmonic approximation leads to a negative conclusion. Second, the next leading perturbation due to the tunnel-coupling is investigated in a box geometry. Although this yields a non-negligible coupling between the (anti)symmetric sectors, the effects are not strong enough to explain the damping. Finally, a new low-energy theory is developed, which does not rely on the TLL and which allows to study the roles of both higher excited levels of the transverse potential and of a realistic longitudinal potential. Strong damping is observed as a result of the longitudinal potential, with a dependence on the particle number that is compatible with experimental results. This indicates that performing the experiments in a hard-wall box potential might eliminate the damping effects.</p> |
| spellingShingle | One-dimensional quantum many-body physics Quantum Field Theory Out-of-equilibrium physics Van nieuwkerk, YD Non-equilibrium dynamics in tunnel-coupled Bose gases |
| title | Non-equilibrium dynamics in tunnel-coupled Bose gases |
| title_full | Non-equilibrium dynamics in tunnel-coupled Bose gases |
| title_fullStr | Non-equilibrium dynamics in tunnel-coupled Bose gases |
| title_full_unstemmed | Non-equilibrium dynamics in tunnel-coupled Bose gases |
| title_short | Non-equilibrium dynamics in tunnel-coupled Bose gases |
| title_sort | non equilibrium dynamics in tunnel coupled bose gases |
| topic | One-dimensional quantum many-body physics Quantum Field Theory Out-of-equilibrium physics |
| work_keys_str_mv | AT vannieuwkerkyd nonequilibriumdynamicsintunnelcoupledbosegases |