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Dynamics as a probe for population-imbalanced fermionic systems

Raka Dasgupta, Jayanta K. Bhattacharjee

Published Oct 18, 2011• 0 citations
OpenAlex

Abstract

We investigate a population-imbalanced two-species fermionic system where the resonantly-paired fermions combine to form bosonic molecules via Feshbach interaction. The natural dynamics of the system is studied and it is shown that the oscillation of the condensate fraction is periodic or quasi periodic, depending on the value of Feshbach coupling. We describe how a time dependent magnetic field can be used to study the natural frequencies and thus explore the momentum space structure of the population imbalanced system.

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We investigate a population-imbalanced two-species fermionic system where the resonantly-paired fermions combine to form bosonic molecules via Feshbach interaction. The natural dynamics of the system is studied and it is shown that the oscillation of the condensate fraction is periodic or quasi periodic, depending on the value of Feshbach coupling. We describe how a time dependent magnetic field can be used to study the natural frequencies and thus explore the momentum space structure of the population imbalanced system.
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We create atom-molecule superpositions in a Bose-Fermi mixture of 87Rb^{87}\text{R}\text{b}87Rb and 40K^{40}\text{K}40K atoms. The superpositions are generated by ramping an applied magnetic field near an interspecies Fano-Feshbach resonance to coherently couple atom and molecule states. Rabi- and Ramsey-type experiments show oscillations in the molecule population that persist as long as $150\text{ }\ensuremath{\mu}\text{s}$ and have up to 50% contrast. The frequencies of these oscillations are magnetic-field dependent and consistent with the predicted molecule binding energy. This quantum superposition involves a molecule and a pair of free particles with different statistics (i.e., bosons and fermions) and furthers exploration of atom-molecule coherence in systems without a Bose-Einstein condensate.
We study by diagrammatic means a Bose-Fermi mixture, with boson-fermion coupling tuned by a Fano-Feshbach resonance. For increasing coupling, the growing boson-fermion pairing correlations progressively reduce the boson condensation temperature and make it eventually vanish at a critical coupling. Such quantum critical point depends very weakly on the population imbalance and, for vanishing boson densities, coincides with that found for the polaron-molecule transition in a strongly imbalanced Fermi gas, thus bridging two quite distinct physical systems.
Deterministic preparation of an ultracold harmonically trapped one-dimensional Fermi gas consisting of a few fermions has been realized by the Heidelberg group. Using Floquet formalism, we study the time dynamics of two- and three-fermion systems in a harmonic trap under an oscillating magnetic field. The oscillating magnetic field produces a time-dependent interaction strength through a Feshbach resonance. We explore the dependence of these dynamics on the frequency of the oscillating magnetic field for noninteracting, weakly interacting, and strongly interacting systems. We identify the regimes where the system can be described by an effective two-state model and an effective three-state model. We find an unbounded coupling to all excited states at the infinitely strong interaction limit and several simple relations that characterize the dynamics. Based on our findings, we propose a technique for driving transition from the ground state to the excited states using an oscillating magnetic field.