Abstract
We solve numerically exactly the many-body 1D model of bosons interacting via short-range and dipolar forces and moving in the box with periodic boundary conditions. We show that the lowest energy states with fixed total momentum can be smoothly transformed from the typical states of collective character to states resembling single particle excitations. In particular, we identify the celebrated roton state. The smooth transition is realized by simultaneous tuning short-range interactions and adjusting a trap geometry. With our methods we study the weakly interacting regime as well as the regime beyond the range of validity of the Bogoliubov approximation.
Highlights
In the 30s of the last century unusual properties of the Helium-II were discovered
We find with our numerically exact treatment that all the properties of the roton state discussed earlier can be understood by analysing contributions of different Fock states to its wave function
In both cases of interactions studied in this work, we find that the dominant contribution to the roton states comes from the so called W state |0−kmax, ...(N −1)0, 01, 12, ..., 0kmax, as one would expect for the Bogoliubov excitations [59]
Summary
In the 30s of the last century unusual properties of the Helium-II were discovered. The subsequent results of Allen and Misener [1], Kapitza [2] were simulating the development of theoretical models [3,4,5,6,7]. The qualitative theory of superfluidity is due to Landau [5,6,7] He deduced from the measurement of the specific heat [8] and the second sound velocity [9] that the excitations in the Helium-II must have a peculiar spectrum, with the local minimum [7]. In Helium the roton was observed experimentally [12], but rather unsatisfactory agreement between theory and measurement suggested that the exact nature of the rotonic excitation was still missing. It was understood many years later by means of subtle ansatzes for the roton’s wave function [13, 14]. There are still active studies of the roton state in this regime [15]
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