The Uhlmann Phase Winding in Bose-Einstein Condensates at Finite Temperature

Abstract

We investigate the Uhlmann phase, a generalization of the celebrated Berry phase, for Bose-Einstein condensates (BECs) at finite temperature. The Uhlmann phase characterizes topological properties of mixed states, in contrast to the Berry phase which is defined for pure states at zero temperature. Using the $SU(1,1)$ symmetry of the Bogoliubov Hamiltonian, we derive a general formula for the Uhlmann phase of BECs. Numerical calculations reveal that the Uhlmann phase can differ from the Berry phase in the zero-temperature limit, contrary to previous studies. As the temperature increases, the Uhlmann phase exhibits a winding behavior, and we relate the total winding degree to the Berry phase. This winding indicates that the Uhlmann phase takes values on a Riemann surface. Furthermore, we propose an experimental scheme to measure the Uhlmann phase of BECs by purifying the density matrix using an atomic interferometer.

13 pages, 8 figures

References in corpus (20)

• Atom Interferometers
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Topological indices for open and thermal systems via Uhlmann's phase
• Symmetry-protected Topological Phases at Finite Temperature
• SU(1,1) echoes for breathers in quantum gases
• Quantum dynamics of bosons in a two-ring ladder: dynamical algebra, vortex-like excitations and currents
• Two-species boson mixture on a ring: A group theoretic approach to the quantum dynamics of low-energy excitations
• Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications
• Topological Uhlmann phase transitions for a spin-j particle in a magnetic field
• Finite-temperature topological phase transitions of spin-$j$ systems in Uhlmann processes: General formalism and experimental protocols
• Control of anomalous diffusion of a Bose polaron
• Periodically and Quasi-periodically Driven Dynamics of Bose-Einstein Condensates
• Uhlmann phase of coherent states and the Uhlmann-Berry correspondence
• Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry
• Uhlmann holonomy against Lindblad dynamics of topological systems at finite temperatures
• Quantum Echo in Two-Component Bose-Einstein Condensates
• The Quantum Dynamics of Two-component Bose-Einstein Condensate: an $Sp(4,R)$ Symmetry Approach
• Proxy ensemble geometric phase and proxy index of time-reversal invariant topological insulators at finite temperatures
• Geometric phases of Topological Systems under Quench Process
• Thermal Uhlmann phase in a locally driven two-spin system

Cited by in corpus (1)

• Geometric phase and multipartite entanglement of Rydberg atom chains