Coherent Decay of Bose-Einstein Condensates

Abstract

As the coldest form of matter known to exist, atomic Bose-Einstein condensates are unique forms of matter where the constituent atoms lose their individual identities, becoming absorbed into the cloud as a whole. Effectively, these gases become a single macroscopic object that inherits its properties directly from the quantum world. In this work, I describe the quantum properties of a zero temperature condensate where the atoms have a propensity to pair, thereby leading to a molecular character that coexists with the atoms. Remarkably, the addition of this molecular component is found to induce a quantum instability that manifests itself as a collective decay of the assembly as a whole. As a signature of this phenomenon, there arises a complex chemical potential in which the imaginary part quantifies a coherent decay into collective phonon excitations of a collapsing ground state. The unique decay rate dependencies on both the scattering length and the density can be experimentally tested by tuning near a Feshbach resonance. Being a purely quantum mechanical effect, there exists no mechanical picture corresponding to this coherent many-body process. The results presented can serve as a model for other systems with similar underlying physics.

Nonexponential decay of Feshbach molecules

“…To determine the decay rate, one performs the analytic continuation of the self energy from the upper to the lower complex half-plane, through the branch cut. The continuation results in the following expression for the self-energy on the second Riemann sheet: the propagator (38) in the lower half-plane of the second Riemann sheet, which satisfies…”

“…The analytic properties of the propagator (38), discussed in the previous section, provide the basis to characterize the stability properties of the molecular state with varying binding energy E B . If the binding energy is significantly smaller than zero, we expect the molecular state to be stable and very well approximated by |ψ M,0 , while hybridization with the atomic sector would increase as the magnetic field approaches the resonance.…”

“…Feshbach resonances give rise to a variety of physical phenomena, including the crossover, at thermal equilibrium, between a BCS state of atomic (fermionic) Cooper pairs and a Bose-Einstein condensation of weakly bound bosonic molecules [26][27][28][29], and represents a powerful instrument to investigate the atomic structure and interaction potentials [30,31]. The possibility to obtain a stable molecular state by adiabatically varying the mag-netic field in presence of a resonance [33][34][35][36], as well as the effects of atom-molecule coherence in the evolution of the system [37,38], have been extensively investigated.…”