Universal short-range correlations in bosonic helium clusters

Bazak, Betzalel; Valiente, Manuel; Barnea, Nir

doi:10.1103/physreva.101.010501

Cited by 13 publications

(14 citation statements)

References 43 publications

(65 reference statements)

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“…Two Efimov trimers were measured [39,40], which are the remains of the otherwise infinite geometric tower of Efimov states that emerges as a → ∞. Larger clusters are predicted [41][42][43][44] by modern He-He pair potentials [45,46], but have not yet been observed.…”

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confidence: 99%

Four-Body Scale in Universal Few-Boson Systems

et al. 2019

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The role of an intrinsic four-body scale in universal few-boson systems is the subject of active debate. We study these systems within the framework of effective field theory. For systems of up to six bosons we establish that no four-body scale appears at leading order (LO). However, we find that at next-to-leading (NLO) order a four-body force is needed to obtain renormalized results for binding energies. With the associated parameter fixed to the binding energy of the four-boson system, this force is shown to renormalize the five-and six-body systems as well. We present an original ansatz for the short-distance limit of the bosonic A-body wave function from which we conjecture that new A-body scales appear at N A−3 LO. As a specific example, calculations are presented for clusters of helium atoms. Our results apply more generally to other few-body systems governed by a large scattering length, such as light nuclei and halo states, the low-energy properties of which are independent of the detailed internal structure of the constituents.

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confidence: 99%

Four-Body Scale in Universal Few-Boson Systems

et al. 2019

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“…N [34]. The premise is that the short-distance pair correlations of the N -body cluster, if scaled by an overall factor, collapse approximately.…”

Section: Structural Observablesmentioning

confidence: 99%

“…(11) differs by an overall factor from the operator employed in Ref. [34]. Correspondingly, we convert the results from Ref.…”

Section: Structural Observablesmentioning

confidence: 99%

“…For the physical point, this is demonstrated, to the best of our knowledge, for the first time in this work. The collapse of the pair, triple, and higher-order distribution functions for interatomic distances around r ≈ r vdW was noted in the literature, motivating the adaption of the nbody Tan contact (n = 2, 3, • • • ) [55][56][57][58][59][60] to quantum clusters that exhibit weak universality (two-body potentials with van der Waals tail and strongly repulsive hard-wall like short-distance repulsion) [34]. This work compares the two-body contact with results from the literature and additionally introduces a (2 + 1) contact.…”

Section: Introductionmentioning

confidence: 95%

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Structural properties of bosonic He clusters with N=2-10 for different potential models at the physical point and at unitarity

Yates,

Blume

2022

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Since the 4 He dimer supports only one weakly bound state with an average interatomic distance much larger than the van der Waals length and no deeply bound states, 4 HeN clusters with N > 2 are a paradigmatic model system with which to explore foundational concepts such as large swave scattering length universality, van der Waals universality, Efimov physics, and effective field theories. This work presents structural properties such as the pair and triple distribution functions, the hyperradial density, the probability to find the N th particle at a given distance from the center of mass of the other N − 1 atoms, and selected contacts. The kinetic energy release, which can be measured via Coulomb explosion in dedicated size-selected molecular beam experiments-at least for small N -, is also presented. The structural properties are determined for three different realistic 4 He-4 He interaction potentials and contrasted with those for an effective low-energy potential model from the literature that reproduces the energies of 4 HeN clusters in the ground state for N = 2 to N = ∞ at the 95 % level with just four input parameters. The study is extended to unitarity (infinite s-wave scattering length) by artificially weakening the interaction potentials. In addition to contributing to the characterization of small bosonic helium quantum droplets, our study provides insights into the effective low-energy theory's predictability of various structural properties.

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“…The nuclear neutron-proton contact was introduced in nuclear physics [44], and the general nuclear contact matrices were defined [45] in the context of generalized contacts for realistic interactions [46][47][48][49][50]. There are also other works using Coulomb [51] and realistic atom-atom interactions [52] with the generalized contact formalism.…”

Section: Introductionmentioning

confidence: 99%

Large-momentum tail of one-dimensional Fermi gases with spin-orbit coupling

2020

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We study the contacts, large-momentum tail, radio-frequency spectroscopy, and some other universal relations for an ultracold one-dimensional (1D) two-component Fermi gas with spin-orbit coupling (SOC). Different from previous studies, we find that the q −8 tail in the spin-mixing (off-diagonal) terms of the momentum distribution matrix is dependent on the two SOC parameters in the laboratory frame for 1D systems, where q is the relative momentum. This tail can be observed through time-of-flight measurement as a direct manifestation of the SOC effects on the many-body level. Besides the traditional 1D even-wave scattering length, we find that two new physical quantities must be introduced due to the SOC. Consequently, two new adiabatic energy relations with respect to the two SOC parameters are obtained. Furthermore, we derive the pressure relation and virial theorem at short distances for this system. To find how the SOC modifies the large-momentum behavior, we take the SOC parameters as perturbations since the strength of the SOC should be much smaller than the corresponding strength scale of the interatomic interactions. In addition, by using the operator product expansion method, we derive the asymptotic behavior of the large-momentum distribution matrix up to the q −8 order and find that the diagonal terms of the distribution matrix include the contact of traditional 1D even-wave scattering length as the leading term and the SOC modified terms beyond the leading term, the off-diagonal term is beyond the subleading term and is corrected by the SOC parameters. We also find that the momentum distribution matrix shows spin-dependent and anisotropic features. Furthermore, we calculate the momentum distribution matrix in the laboratory frame for the experimental implication. In addition, we calculate the high-frequency tail of the radio-frequency spectroscopy and find that the presence of the contact related to the center-of-mass momentum in the radio-frequency spectral is due to the SOC effects. This paper paves the way for exploring the profound properties of many-body quantum systems with SOC in one dimension.

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Universal short-range correlations in bosonic helium clusters

Cited by 13 publications

References 43 publications

Four-Body Scale in Universal Few-Boson Systems

Four-Body Scale in Universal Few-Boson Systems

Structural properties of bosonic He clusters with N=2-10 for different potential models at the physical point and at unitarity

Large-momentum tail of one-dimensional Fermi gases with spin-orbit coupling

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