Abstract
We study the two-dimensional three-body problem in the general case of three distinguishable particles interacting through zero-range potentials. The Faddeev decomposition is used to write the momentum-space wave function. We show that the large-momentum asymptotic spectator function has the same functional form as derived previously for three identical particles. We derive the analytic relations between the three different Faddeev components for the three distinguishable particles. We investigate the one-body momentum distributions both analytically and numerically and analyze the tail of the distributions to obtain two- and three-body contact parameters. We specialize from the general cases to the examples of two identical, interacting or non-interacting, particles. We find that the two-body contact parameter is not a universal constant in the general case and show that the universality is recovered when a subsystem is composed of two identical non-interacting particles. We also show that the three-body contact parameter is negligible in the case of one non-interacting subsystem compared to the situation where all the subsystems are bound. As an example, we present the results for mixtures of lithium with two cesium or two potassium atoms, which are systems of current experimental interest.
Highlights
The surprising and unexpected predictions from quantum mechanics have been challenging our classical intuition for a century
An interesting example of an unexpected quantum mechanical prediction that was experimentally confirmed in cold atomic gases is the so-called Efimov effect, which predicts that three identical bosons interacting through short range potentials present infinitely many bound states, where the energies between states are geometrically spaced
The two- and three- body contact parameters were studied for a 3D system of three identical bosons in [17, 16, 23] and for mixed-species systems in [24]. These results show that the influence of non-equal masses in three-body systems goes beyond changing the contact parameters values
Summary
The surprising and unexpected predictions from quantum mechanics have been challenging our classical intuition for a century. The theoretical difference arising from changing system dimension could most likely be verified in cold atomic gases experiments in the near future since experimentalists are already able to change dimensionality of such systems and build experiments in effectively one (1D) or two (2D) spatial dimensions Another important theoretical prediction, that was recently reported in [9], is the emergence of a parameter in the study of two-component Fermi gases, the two-body contact parameter, C2, which connects universal relations between two-body correlations and many-body properties [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19].
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