Density and Spin Linear Response of Atomic Fermi Superfluids with Population Imbalance in BCS-BEC Crossover

We present a theoretical study of the density and spin (representing the two components) linear response of Fermi superfluids with tunable attractive interactions and population imbalance. In both linear response theories, we find that the fluctuations of the order parameter must be treated on equal footing with the gauge transformations associated with the symmetries of the Hamiltonian so that important constraints including various sum rules can be satisfied. Both theories can be applied to the whole BCS-Bose-Einstein condensation crossover. The spin linear responses are qualitatively different with and without population imbalance because collective-mode effects from the fluctuations of the order parameter survive in the presence of population imbalance, even though the associated symmetry is not broken by the order parameter. Since a polarized superfluid becomes unstable at low temperatures in the weak and intermediate coupling regimes, we found that the density and spin susceptibilities diverge as the system approaches the unstable regime, but the emergence of phase separation preempts the divergence.Comment: 15 pages, 5 figure

BCS thermal vacuum of fermionic superfluids and its perturbation theory

The thermal field theory is applied to fermionic superfluids by doubling the degrees of freedom of the BCS theory. We construct the two-mode states and the corresponding Bogoliubov transformation to obtain the BCS thermal vacuum. The expectation values with respect to the BCS thermal vacuum produce the statistical average of the thermodynamic quantities. The BCS thermal vacuum allows a quantum-mechanical perturbation theory with the BCS theory serving as the unperturbed state. We evaluate the leading-order corrections to the order parameter and other physical quantities from the perturbation theory. A direct evaluation of the pairing correlation as a function of temperature shows the pseudogap phenomenon results from the perturbation theory. The BCS thermal vacuum is shown to be a generalized coherent and squeezed state. The correspondence between the thermal vacuum and purification of the density matrix allows a unitary transformation, and we found the geometric phase in the parameter space associated with the transformation.Comment: 14 pages, 2 figure

Beyond the Innovation: An Exploratory Study of Designing Web-based Self-services

AbstractCustomized web-based self-services play an important role in today's product/service innovation. Compared to traditional tangible services, helpful web-based self-services and off-line services may better facilitate creativity, accelerate value co-creation, and reduce the costs and risks of development and commercialization. Therefore, in order to offer a conceptual framework for a web-based self-service system that enhances the fuzzy-front end (FFE) of new product/service development, this study analyzed the needs and challenges found during the transition of the Dechnology (Design Thinking plus Technology Innovation) project at the Industrial Technology Research Institute (ITRI), the largest R&D organization in Taiwan. Through literature review, in-depth interviews, and participatory action research, we formalized five core system modules, including: 1) user behavior and lifestyle, 2) thematic trend analysis, 3) technology screening and translation, 4) idea visualization, and 5) O2O service connection, with corresponding design principles for supporting user creativity in a web-based self-services environment. Finally, this study proposes a conceptual framework integrated with service design to serve as an important reference for enterprises that undergo similar innovation projects in the future

Local geometry and quantum geometric tensor of mixed states

The quantum geometric tensor (QGT) is a fundamental concept for characterizing the local geometry of quantum states. After casting the geometry of pure quantum states and extracting the QGT, we generalize the geometry to mixed quantum states via the density matrix and its purification. The gauge-invariant QGT of mixed states is derived, whose real and imaginary parts are the Bures metric and the Uhlmann form, respectively. In contrast to the imaginary part of the pure-state QGT that is proportional to the Berry curvature, the Uhlmann form vanishes identically for ordinary physical processes. Moreover, there exists a Pythagorean-like equation that links different local distances and reflect the underlying fibration. The Bures metric reduces to the Fubini-Study metric as temperature approaches zero if the eigenvalues of the density matrix do not change during the process, establishing a correspondence between pure and mixed states. We also present two examples with contrasting local geometries and discuss experimental implications.Comment: 22 pages, 3 figure

Geometric phases of mixed quantum states: A comparative study of interferometric and Uhlmann phases

Two geometric phases of mixed quantum states, known as the interferometric phase and Uhlmann phase, are generalizations of the Berry phase of pure states. After reviewing the two geometric phases and examining their parallel-transport conditions, we specify a class of cyclic processes that are compatible with both conditions and therefore accumulate both phases through their definitions, respectively. Those processes then facilitate a fair comparison between the two phases. We present exact solutions of two-level and three-level systems to contrast the two phases. While the interferometric phase exhibits finite-temperature transitions only in the three-level system but not the two-level system, the Uhlmann phase shows finite-temperature transitions in both cases. Thus, using the two geometric phases as finite-temperature topological indicators demonstrates the rich physics of topology of mixed states.Comment: 12 pages, 2 figures, submitte