Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions

Abstract

The occupation of more than one single-particle state and hence the emergence of fragmentation is a many-body phenomenon universal to systems of spatially confined interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one-and two-dimensional systems. We solve the full many-body Schrödinger equation of the system using the recursive implementation of the multiconfigurational time-dependent Hartree for bosons method, R-MCTDHB. The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density and interaction strength is assessed. It is found that for contact interactions, the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long-ranged the interactions become. The degree of fragmentation is increasing, keeping the particle number N fixed, when the density is decreasing as expected in one spatial dimension. We demonstrate that this remains, nontrivially, true also for long-range interactions in two spatial dimensions. We, finally, find that within our fully self-consistent approach, the fragmentation degree, to a good approximation, decreases universally as N −1/2 when only N is varied.

Management of the correlations of UltracoldBosons in triple wells

“…To quantify the fragmentation, coherence, and correlation properties of the many-boson system we discuss the behavior of the natural occupations, We have verified that the above findings for the natural occupations and the fragmentation of the state also hold for the case of long-range interactions of the form W r r x x [58][59][60]61]. The natural occupations follow the same pattern as their contact-interaction counterparts, but the restoration of coherence seems to happen at even larger values α as compared to the case of contact interactions.…”

Causality and quantum criticality in long-range lattice models

“…We are interested in the consequences of adding longrange terms to a fermionic model in Eq. (30). For example, one can add both long-range hopping and long-range pairing terms, Hopping :…”

“…Furthermore, it is shown in detail that the response to a local perturbation obtains a general scaling form, which is determined by the value of these two exponents. Note that approximate numerical approaches to many-body models with long-range interactions [29][30][31][32] also exist (in the context of ultracold systems or elsewhere). In contrast, our field-theory treatment is well suited to extracting universal aspects of the long-distance and long-time behavior of the many-body system, and specifically the critical exponents (beyond their meanfield values) in the thermodynamic limit, which are usually difficult to access via numerical methods.…”

Many-body quantum metrology with scalar bosons in a single potential well

“…As observed above, these η and ξ have signs opposite to those of a double well and |ξ| = 1. Because we later on use the fact that the ground state of the system is fragmented, we restrict our analysis to a small number of particles (N = 50), because the two-mode fragmentation degree approximately decreases as N −1/2 , all other parameters fixed [59].…”