Dynamics of the BCS-BEC crossover from a few-body perspective

Javier von Stecher, Chris H. Greene

The spectrum of two spin-up and two spin-down fermions in a trap is calculated using a correlated Gaussian basis throughout the range of the BCS-BEC crossover. These accurate calculations provide a few-body solution to the crossover problem. This solution is used to study the time evolution of the system as the scattering length is changed, mimicking experiments with Fermi gases near Fano-Feshbach resonances. The structure of avoiding crossings in the spectrum allow us to understand the dynamics of the system as a sequence of Landau-Zener transitions. Finally, we propose a ramping scheme to study atom-molecule coherence.

Wu-Ming Liu, Emmanuel Kengne

Guo-Jian Qiao, Miao-Miao Yi, Xin Yue +1 more

We revisit the quantization of the order parameter, which we refer to as third quantization, from the perspective of the commutation relation between the phase operator of the order parameter and the particle-number operator. We show that this macroscopic commutation relation does not constitute an independent fundamental postulate added to quantum mechanics, but instead emerges naturally from second quantization in the thermodynamic limit for both bosonic and fermionic many-body systems. In this sense, both Bose-Einstein condensates (BECs) and Bardeen-Cooper-Schrieffer (BCS) states can be understood as macroscopic quantum states described by bosonic coherent states: in BEC, bosons condense into a single coherent mode with a well-defined phase, while in BCS systems, collective excitations of Cooper pairs can also acquire an effectively bosonic coherent description. On this basis, we propose a new macroscopic interpretation of the BCS-BEC crossover. To characterize this crossover, we model a conventional superconductor as an assembly of macroscopically separated superconducting segments. As the intra-segment coupling increases, the system evolves from a BCS-like regime toward a BEC-like regime, in which the segments collectively behave as macroscopic coherent states. Inter-segment tunneling then locks their phases, establishes global phase coherence, and gives rise to a bulk Bose-Einstein condensate. The phase diagram of the BCS-BEC crossover can thus be understood as a manifestation of a macroscopic quantum process governed by the coherent-state dynamics of the order parameter. Our results provide a unified perspective on BEC, BCS superconductivity, and the BCS-BEC crossover within the framework of third quantization.

Yoji Ohashi

Jonas Siegl, Wolf Weimer, Kai Morgener +3 more

J. von Stecher

In this dissertation, we analyze both many- and few-body systems under external confinement with tunable interactions. First, we develop a density-renormalization ap-proach for describing two-component fermionic systems with short-range interactions. This renormalized zero-range interaction eliminates the instabilities produced by a bare Fermi pseudopotential and provides a simple description of the interactions from the weakly interacting BCS region up to unitarity. In the second part of the thesis, we focus on few-body systems in the BCS-BEC crossover. To obtain the solutions, we implement two different numerical techniques: a correlated-Gaussian-basis-set expansion and a fixed-node diffusion Monte Carlo tech-nique. We also develop an innovative numerical technique for obtaining solutions to the four-body problem in the hyperspherical representation. Our solutions provide an accurate description of few-body trapped systems. The analysis of two-, three-, and four-body systems, for instance, provides a few-body per-spective on the BCS-BEC crossover problem. The analysis of the spectrum of such systems allows us to visualize important pathways for molecule formation. We then use