Binding of three identical bosons in two dimensions

Bruch, L. W.; Tjon, J.A.

doi:10.1103/physreva.19.425

Cited by 104 publications

(150 citation statements)

References 12 publications

Supporting

Mentioning

142

Contrasting

Order By: Relevance

“…Finally, we investigate the ratio between the total ground state energy of 2D systems with N + 1 and N particles. Our results are consistent with predictions based on zerorange treatments [9,16,17,18] but do not conclusively confirm them for N > 3. We comment on the relevance of the energy scale associated with the effective range.…”

supporting

confidence: 82%

“…i) 2D clusters with N particles [9,10,12] are predicted to become unbound when the mass m reaches a critical value m (N ) * [7]. This critical mass is predicted to be universal, i.e., m (N ) * = m * [10], and to be the same for the corresponding homogeneous system [8,19].…”

Section: Pacs Numbersmentioning

confidence: 99%

“…iii) The ratio between the ground state energies of a 2D system with N +1 atoms and those of a system with N atoms reaches, in the limit of zero-range interactions, a constant. This constant has been determined analytically for small 2D systems: E δ 3 /E δ 2 = 16.52 [9,16] and E δ 4 /E δ 3 = 11.94 [18]. For large systems, the ratio E δ N +1 /E δ N has been predicted to approach 8.57 [17].…”

mentioning

confidence: 99%

“…Effectively 2D atom traps have been realized recently [5,6]; extension to optical lattices with only a few atoms per lattice site is possible with today's technology. These systems are particularly interesting since Feshbach resonances allow the interaction strengths to be tuned through application of magnetic fields.Bosonic 2D systems interacting through short-range two-body potentials that support one zero angular momentum bound state are predicted to exhibit intriguing universal, that is, model-independent, behaviors [7,8,9,10,11,12,13,14,15,16,17,18]. i) 2D clusters with N particles [9,10,12] are predicted to become unbound when the mass m reaches a critical value m (N ) * [7].…”

mentioning

confidence: 99%

See 3 more Smart Citations

Threshold behavior of bosonic two-dimensional few-body systems

Blume

2005

Phys. Rev. B

View full text Add to dashboard Cite

Bosonic two-dimensional self-bound clusters consisting of N atoms interacting through additive van der Waals potentials become unbound at a critical mass m (N) * ; m (N) * has been predicted to be independent of the size of the system. Furthermore, it has been predicted that the ground state energy EN of the N -atom system varies exponentially as the atomic mass approaches m * . This paper reports accurate numerical many-body calculations that allow these predictions to be tested. We confirm the existence of a universal critical mass m * , and show that the near-threshold behavior can only be described properly if a previously neglected term is included. We comment on the universality of the energy ratio EN+1/EN near threshold. PACS numbers:Restricting the motion of particles to one or two dimensions can lead to properties that differ dramatically from those in three dimensions. The most prominent two-dimensional (2D) system is the surface of bulk matter. Another example are one-or two-atom layer thin films, e.g., atomic or molecular hydrogen films [1,2], grown on substrates. Neglecting the adatom-substrate interaction, many properties of such systems can be understood within a truly 2D framework. In addition to homogeneous 2D systems, it is interesting to consider 2D clusters (see, e.g., Refs. [3,4]). What happens when a finite number of atoms is restricted to 2D space? Inhomogeneous 2D systems can potentially be studied by placing a few atoms on the surface of a substrate or by confining atoms by external potentials. Effectively 2D atom traps have been realized recently [5,6]; extension to optical lattices with only a few atoms per lattice site is possible with today's technology. These systems are particularly interesting since Feshbach resonances allow the interaction strengths to be tuned through application of magnetic fields.Bosonic 2D systems interacting through short-range two-body potentials that support one zero angular momentum bound state are predicted to exhibit intriguing universal, that is, model-independent, behaviors [7,8,9,10,11,12,13,14,15,16,17,18]. i) 2D clusters with N particles [9,10,12] are predicted to become unbound when the mass m reaches a critical value m (N ) * [7]. This critical mass is predicted to be universal, i.e., m (N ) * = m * [10], and to be the same for the corresponding homogeneous system [8,19]. ii) For a given system size, the ground state energies E N near threshold are predicted to change exponentially as the atomic mass m decreases [7,11]. Similarly, for a given atomic mass, the ground state energies near threshold are predicted to change exponentially with varying system size [17]. iii) The ratio between the ground state energies of a 2D system with N +1 atoms and those of a system with N atoms reaches, in the limit of zero-range interactions, a constant. This constant has been determined analytically for small 2D systems: E δ 3 /E δ 2 = 16.52 [9,16] and E δ 4 /E δ 3 = 11.94 [18]. For large systems, the ratio E δ N +1 /E δ N has been predicted to approach 8.57 [17]...

show abstract

supporting

confidence: 82%

Section: Pacs Numbersmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Threshold behavior of bosonic two-dimensional few-body systems

Blume

2005

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…Here, there is a universal hierarchy of trimer states for resonant short-range interactions, while clusters of four or more bosons can also form [10][11][12][13]. Even in the limit of a 2D geometry, where the Efimov effect is absent, both trimers [14] and tetramers [15] have been predicted. On the other hand, bound states of identical fermions are constrained to have odd angular momentum owing to Pauli exclusion and thus, even for attractive interactions, identical fermions are subject to a centrifugal barrier.…”

mentioning

confidence: 99%

Bound States in a Quasi-Two-Dimensional Fermi Gas

Levinsen

Parish

2013

Phys. Rev. Lett.

View full text Add to dashboard Cite

We consider the problem of N identical fermions of mass m " and one distinguishable particle of mass m # interacting via short-range interactions in a confined quasi-two-dimensional (quasi-2D) geometry. For N ¼ 2 and mass ratios m " =m # < 13:6, we find non-Efimov trimers that smoothly evolve from 2D to 3D. In the limit of strong 2D confinement, we show that the energy of the N þ 1 system can be approximated by an effective two-channel model. We use this approximation to solve the 3 þ 1 problem and we find that a bound tetramer can exist for mass ratios m " =m # as low as 5 for strong confinement, thus providing the first example of a universal, non-Efimov tetramer involving three identical fermions. DOI: 10.1103/PhysRevLett.110.055304 PACS numbers: 67.85.Àd, 05.30.Fk, 34.50.Às An understanding of the few-body problem can be important for gaining insight into the many-body system. In dimensions higher than one, few-body bound states can, for instance, impact the statistics of the many-body quasiparticle excitations. Indeed, for fermionic systems, the two-body bound state is fundamental to the understanding of the BCS-BEC crossover [1][2][3][4], while the existence of three-body bound states of fermions [5,6] with unequal masses can lead to dressed trimer quasiparticles in the highly polarized Fermi gas [7]. Even in one dimension (1D), few-body bound states can impact the many-body phase: It has already been shown that one can have a Luttinger liquid of trimers [8].In general, attractively interacting bosons readily form bound clusters, with the celebrated example being the Efimov effect in 3D [9]. Here, there is a universal hierarchy of trimer states for resonant short-range interactions, while clusters of four or more bosons can also form [10][11][12][13]. Even in the limit of a 2D geometry, where the Efimov effect is absent, both trimers [14] and tetramers [15] have been predicted. On the other hand, bound states of identical fermions are constrained to have odd angular momentum owing to Pauli exclusion and thus, even for attractive interactions, identical fermions are subject to a centrifugal barrier. For short-range s-wave [16] interactions in 3D, non-Efimov trimers consisting of two identical fermions with mass m " and one distinguishable particle with mass m # can only exist above the critical mass ratio m " =m # ' 8:2 [5], while Efimov trimers only appear once m " =m # * 13:6 [17]. However, the existence of larger (N þ 1)-body bound states involving N > 2 identical fermions remains largely unknown-it has only recently been shown that Efimov tetramers exist in 3D [18].In this Letter, we investigate the problem of N identical fermions interacting with one distinguishable particle in a confined quasi-2D geometry, where the centrifugal barrier is reduced and the binding of fermions should be favored. Such 2D geometries have recently been realised in ultracold atomic Fermi gases [19][20][21][22][23], where the fermions are confined to 2D with an effective harmonic potential. In addition to allowing one to ...

show abstract

Composed Particles, Trios and Quartets in Resonance Quantum Gases and Mixtures

Kagan

2013

Modern Trends in Superconductivity and Superfluidity

View full text Add to dashboard Cite

Binding of three identical bosons in two dimensions

Cited by 104 publications

References 12 publications

Threshold behavior of bosonic two-dimensional few-body systems

Threshold behavior of bosonic two-dimensional few-body systems

Bound States in a Quasi-Two-Dimensional Fermi Gas

Composed Particles, Trios and Quartets in Resonance Quantum Gases and Mixtures

Contact Info

Product

Resources

About