Adiabatic Crossing of Many-body Resonances

Kajsa-My Tempest, S. Jonsell

Here we present a four-channel model that incorporates a magnetically tunable Feshbach resonance in a system of three atoms that interact via pairwise van der Waals interactions. Our method is designed to model recent experiments where the tunability of the scattering length has been used to study three-body Efimov states, which appear in the limit of a diverging two-body scattering length. Using this model, we calculate three-body adiabatic and effective potential curves and study how the strength (or width) of the Feshbach resonance affects the three-body potential that is connected to the Efimov effect. We find that the position of the repulsive barrier, which has been used to explain the so-called van der Waals universality in broad resonances, is slightly shifted as the narrow resonance limit is approached and that this shift is correlated to the appearance of two avoided crossings in the adiabatic energy landscape. More importantly, the attractive well is markedly shifted upward in energy and is extremely shallow for the narrowest resonance. We argue that this behavior is connected to the breakdown of van der Waals universality for weak (narrow) resonances.

Marco Merkli

Adolfo del Campo

Joona Marjamäki, Robert van Leeuwen, Riku Tuovinen

Avoided crossings in the correlated many-body spectrum play a central role in determining the conditions for adiabatic state preparation in interacting quantum systems. We investigate this connection in finite spin-boson systems by combining exact diagonalization of the many-body spectrum with time-dependent simulations of adiabatic switching protocols. By comparing the adiabatically prepared state with the exact ground state, we determine the switching times required for reliable preparation as a function of the spin-boson coupling strength and bosonic mode structure. We show that regions of small many-body level spacings, associated with avoided crossings, impose the strongest constraints on adiabatic preparation and explain the observed dependence of the required switching times on the interaction strength. Furthermore, while the ground-state energy follows the overall spectral trends, local observables such as Pauli matrix expectation values exhibit additional non-monotonic behavior arising from coherent oscillations in finite systems. These findings can provide concrete benchmarks for both the theoretical treatment of open quantum systems and practical implementations in quantum simulation and qubit control.

A. P. Itin, Päivi Törmä

We consider dynamics of a slowly time-dependent Dicke model, which represents a many-body generalization of the Landau-Zener model. In particular, the model describes narrow Feshbach resonance passage in an ultracold gas of Fermi atoms. Adiabaticity is destroyed when a parameter crosses a critical value, even at very slow sweeping rates of a parameter. The dynamics crucially depends on direction of the sweep. We apply our recent analysis (A. P. Itin and P. T\"orm\"a, e-print arXiv:0901.4778) to the ``inverse'' sweep through the resonance, corresponding (in a context of Feshbach resonance passage) to dissociation of molecules. On a level of the mean-field approximation, the dynamics is equivalent to a molecular condensate formation from Bose atoms within a two-mode model. Mapping the system to a Painlev\'e equation allows us to calculate deviation from adiabaticity at very slow sweeps analytically.

Antoine Browaeys