Energy and structural properties of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator

Yan, Yangqian; Blume, D.

doi:10.1103/physreva.92.033626

Cited by 26 publications

(32 citation statements)

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“…[17]. Slightly larger clusters with similar interactions have also been considered previously [18][19][20][21]. Universal behavior was found for small clusters up to N ≤ 15.…”

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confidence: 70%

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Ground-State Properties of Unitary Bosons: From Clusters to Matter

et al. 2017

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The properties of cold Bose gases at unitarity have been extensively investigated in the last few years both theoretically and experimentally. In this Letter we use a family of interactions tuned to two-body unitarity and very weak three-body binding to demonstrate the universal properties of both clusters and matter. We determine the universal properties of finite clusters up to 60 particles and, for the first time, explicitly demonstrate the saturation of energy and density with particle number and compare with bulk properties. At saturation in the bulk we determine the energy, density, two-and three-body contacts, and the condensate fraction. We find that uniform matter is more bound than three-body clusters by nearly 2 orders of magnitude, the two-body contact is very large in absolute terms, and yet the condensate fraction is also very large, greater than 90%. Equilibrium properties of these systems may be experimentally accessible through rapid quenching of weakly interacting boson superfluids. DOI: 10.1103/PhysRevLett.119.223002 Introduction.-Strongly interacting fermionic cold atoms have been the subject of a great deal of study both theoretically and experimentally across the BEC to BCS transition, and especially at unitarity, where the two-body system has a nearly zero-energy bound state [1]. These systems are universal in that all properties, including ground-state energy, superfluid pairing gaps, superfluid transition temperatures, etc., are obtained as a set of universal dimensionless parameters multiplied by the Fermi energy or momentum of a free Fermi gas at the same density. Studies of bosonic superfluids, however, have concentrated on the weakly interacting regime described by the Gross-Pitaevski mean-field equation. These systems are comparatively simple to study as they were the first to be cooled to very low temperatures and their properties can be described in a mean-field picture.It has been known for some time that short-range twoand three-body interactions can be used to describe the lowenergy properties of small clusters of bosons. To obtain universal properties, the two-body interaction can similarly be taken to generate a zero-energy dimer, but a three-body interaction is required [2,3] to avoid the so-called "Thomas collapse" [4] of three or more particles. The resulting discrete scale invariance leads to geometric towers of states in systems with three [5] and more [6][7][8][9][10] bosons. Many atomic and nuclear few-body systems fall into this universality class [11].In this Letter we demonstrate that large clusters and bulk matter are stable with such interactions, and similarly to the fermionic case described by a fairly simple set of universal parameters. We provide the first estimates for the universal parameters describing the ground-state energy, the equilibrium density, two-and three-body contacts, and

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“…[17]. Slightly larger clusters with similar interactions have also been considered previously [18][19][20][21]. Universal behavior was found for small clusters up to N ≤ 15.…”

supporting

confidence: 70%

“…This can be seen in the results of Refs. [18,21] around N ¼ 15, and also in our results corresponding to the more bound trimers (open symbols with μ 2R3 ¼ 46 in Fig. 1 Studies of unitary bosons commonly employ a zerorange two-body interaction with three-body hard-core interaction of radius R 0 .…”

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Ground-State Properties of Unitary Bosons: From Clusters to Matter

et al. 2017

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“…The use of a repulsive three-body potential facilitates reaching the regime where the bound states of the threeand higher-body clusters are large compared to the length scales of the underlying interaction potentials [21][22][23]25]. Specifically, a non-zero d BBX can lead to a large BBX ground state trimer, which mimicks the behavior of large, universal excited Efimov trimer states.…”

Section: A System Hamiltonianmentioning

confidence: 99%

“…The properties of these resonance states, including their convergence to the universal limit, were studied using a momentum space based formalism [15,16]. The universal limit has also been reached-at least in an approximate fashionby increasing the size of the lowest Efimov trimer via a repulsive three-body potential [21][22][23]. This approach provides approximate values for the universal energy ratios but not, in general, about lifetimes.…”

Section: Introductionmentioning

confidence: 99%

Few-boson system with a single impurity: Universal bound states tied to Efimov trimers

Blume

2019

Phys. Rev. A

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Small weakly-bound droplets determine a number of properties of ultracold Bose and Fermi gases. For example, Efimov trimers near the atom-atom-atom and atom-dimer thresholds lead to enhanced losses from bosonic clouds. Generalizations to four-and higher-body systems have also been considered. Moreover, Efimov trimers have been predicted to play a role in the Bose polaron with large boson-impurity scattering length. Motivated by these considerations, the present work provides a detailed theoretical analysis of weakly-bound N -body clusters consisting of N − 1 identical bosons (denoted by "B") of mass m that interact with a single distinguishable impurity particle (denoted by "X") of mass M . The system properties are analyzed as a function of the mass ratio κ (values from κ = 1 to 50 are considered), where κ is equal to m/M , and the two-body s-wave scattering length aBX between the bosons and the impurity. To reach the universal Efimov regime in which the size of the BBX trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: resonance states are determined in the absence of BB and BBX interactions, bound states are determined in the presence of repulsive three-body boson-boson-impurity interactions, and bound states are determined in the presence of repulsive two-body boson-boson interactions. The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.PACS numbers:

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“…For example, the scaled pair and scaled triple distribution functions can share the same implementation since both are described by an operator of the form δ(r ref − r), where r ref is either the pair distance or the three-body hyperradius (see, e.g., Refs. [83,84] for the resulting distribution function). The (unscaled) pair distribution function, in contrast, is described by an operator of the form δ(r ref − r)/(4πr 2 ) and has to be implemented separately.…”

Section: Example: Structural Propertiesmentioning

confidence: 99%

Path integral Monte Carlo ground state approach: formalism, implementation, and applications

Yan

Blume

2017

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. Monte Carlo techniques have played an important role in understanding strongly-correlated systems across many areas of physics, covering a wide range of energy and length scales. Among the many Monte Carlo methods applicable to quantum mechanical systems, the path integral Monte Carlo approach with its variants has been employed widely. Since semi-classical or classical approaches will not be discussed in this review, path integral based approaches can for our purposes be divided into two categories: approaches applicable to quantum mechanical systems at zero temperature and approaches applicable to quantum mechanical systems at finite temperature. While these two approaches are related to each other, the underlying formulation and aspects of the algorithm differ. This paper reviews the path integral Monte Carlo ground state (PIGS) approach, which solves the time-independent Schrödinger equation. Specifically, the PIGS approach allows for the determination of expectation values with respect to eigen states of the few-or many-body Schrödinger equation provided the system Hamiltonian is known. The theoretical framework behind the PIGS algorithm, implementation details, and sample applications for fermionic systems are presented. : Formalism, implementation, and applications2 Path integral Monte Carlo ground state approach

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Energy and structural properties ofN-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator

Cited by 26 publications

References 53 publications

Ground-State Properties of Unitary Bosons: From Clusters to Matter

Ground-State Properties of Unitary Bosons: From Clusters to Matter

Few-boson system with a single impurity: Universal bound states tied to Efimov trimers

Path integral Monte Carlo ground state approach: formalism, implementation, and applications

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