Ultrakalte bosonische Gase in optischen Resonatoren
Zusammenfassung der Projektergebnisse
Hybrid systems of ultracold atoms coupled to a photonic mode of an optical cavity show fascinating phenomena. One example is the well known Dicke phase transition, a self-organized phase transition in which photonic modes becomes spontaneously occupied. Depending on the coupling between the cavity mode and the atoms, the atoms can spontaneously order into a checkerboard density pattern due to the feedback mechanism between the atoms and the photonic mode. In this project we applied and developed different approaches in order to investigate such a self-organization transition and the dynamics. The full solution of the dynamics of the combined atomcavity system is very challenging: (i) the bosonic atoms in the optical lattice are strongly correlated, (ii) the coupling of the spatially extended cavity mode to the atoms and (iii) the dissipative nature of the cavity mode which originates from the leaking of the photons out of the imperfect cavity mirrors. We describe the combined and dissipative system by a Markovian master equation with a Lindblad dissipator. In order to determine the resulting dynamics we employed within this project mainly two different approaches. We identified self-organization transitions to complex many body states as chiral states, Meissner or vortex phases and Hofstadter like models using a mean-field description. The mean-field approach relies on a reduction of the model by adiabatically eliminating the cavity mode to an effective interacting bosonic model - with long-range processes - subjected to a self-consistency condition. We developed a self-consistent implementation of the matrix product state methods in order to solve this self-consistent effective model. In order to go beyond this mean-field description which lacks to treat the correlations between the atoms and the photonic field and neglects excited states of the atoms, we developed a novel numerically exact approach. This approach is an exact numerical treatment of the hybrid system by a matrix product state method which overcomes the challenges of the representation of the photonic mode, the dissipative coupling and the global coupling of the photonic mode to the atoms. It is best applicable in the case of an additional optical lattice present to confine the atoms. Using this matrix product state description of the model, one of our major findings within this project is that the nature of the dissipative phase transition totally changes its character going beyond the typically used mean-field approaches. Its nature becomes determined by fluctuations and typically excited states play an important role due to the presence of the dissipative coupling. This is in contrast to the zerotemperature phase transition often assumed using mean-field methods.
Projektbezogene Publikationen (Auswahl)
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Cavity-induced generation of nontrivial topological states in a two-dimensional Fermi gas. Physical Review A, 94(6).
Sheikhan, Ameneh; Brennecke, Ferdinand & Kollath, Corinna
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Dissipative time evolution of a chiral state after a quantum quench. Physical Review A, 94(4).
Wolff, Stefan; Sheikhan, Ameneh & Kollath, Corinna
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Cavity-induced artificial gauge field in a Bose-Hubbard ladder. Physical Review A, 96(6).
Halati, Catalin-Mihai; Sheikhan, Ameneh & Kollath, Corinna
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Cavity-induced spin-orbit coupling in an interacting bosonic wire. Physical Review A, 99(3).
Halati, Catalin-Mihai; Sheikhan, Ameneh & Kollath, Corinna
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Cavity-induced superconducting and 4kF charge-density-wave states. Physical Review A, 99(5).
Sheikhan, Ameneh & Kollath, Corinna
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Numerically Exact Treatment of Many-Body Self-Organization in a Cavity. Physical Review Letters, 125(9).
Halati, Catalin-Mihai; Sheikhan, Ameneh; Ritsch, Helmut & Kollath, Corinna
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Theoretical methods to treat a single dissipative bosonic mode coupled globally to an interacting many-body system. Physical Review Research, 2(4).
Halati, Catalin-Mihai; Sheikhan, Ameneh & Kollath, Corinna
