Freiburg 2024 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 9: Bosonic Quantum Gases II (joint session Q/A)

Q 9.7: Talk

Monday, March 11, 2024, 18:30–18:45, Aula

Quantum geometry of bosonic Bogoliubov quasiparticles — •Isaac Tesfaye and André Eckardt — Institut für Theoretische Physik, Technische Universität Berlin Hardenbergstraße 36, 10623 Berlin, Germany

Topological and geometrical features arising bosonic Bogoliubov-de Gennes (BdG) systems have mainly been studied by utilizing a symplectic (generalized) version of the Berry curvature and Chern number. These bosonic topological features may even solely arise due to the non-particle number conserving terms in the corresponding BdG Hamiltonian, making these systems inherently distinct from their non-interacting (fermionic) counterparts. Here, we propose the notion of the symplectic quantum geometric tensor (SQGT) whose imaginary part leads to the previously studied symplectic Berry curvature, while the real part gives rise to a symplectic quantum metric, providing a natural distance measure in the space of bosonic Bogoliubov modes. Moreover, previous proposals to verify the topology of bosonic BdG systems have relied solely on probing topologically protected chiral edge modes. Here, we propose how to measure all components of the SQGT by the use of periodic modulation of the systems’ parameters in a linear response regime and connect the symplectic Berry curvature to a generalized anomalous velocity term for Bogoliubov Bloch wave packets.
[1] R. Shindou et al., Phys. Rev. B 87, 174427 (2013).
[2] S. Furukawa and M. Ueda, New J. Phys. 17, 115014 (2015).
[3] T. Ozawa and N. Goldman, Phys. Rev. B 97, 201117 (2018).

Keywords: Bogoliubov; Geometry; Topology; BEC; Bosons