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Register a new userUniversal behavior of few-boson systems using potential models
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The universal behavior of a three-boson system close to the unitary limit is encoded in a simple dependence of many observables in terms of few parameters. For example the product of the three-body parameter $kappa_*$ and the two-body scattering length $a$, $kappa_* a$ depends on the angle $xi$ defined by $E_3/E_2=tan^2xi$. A similar dependence is observed in the ratio $a_{AD}/a$ with $a_{AD}$ the boson-dimer scattering length. We use a two-parameter potential to determine this simple behavior and, as an application, to compute $a_{AD}$ for the case of three $^4$He atoms.
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Two-, three-, and four-boson systems are studied close to the unitary limit using potential models constructed to reproduce the minimal information given by the two-body scattering length $a$ and the two-body binding energy or virtual state energy $E_2$. The particular path used to reach the unitary limit is given by varying the potential strength. In this way the energy spectrum in the three- and four-boson systems is computed. The lowest energy states show finite-range effects absorbed in the construction of level functions that can be used to study real systems. Higher energy levels are free from finite-range effects, therefore the corresponding level functions tend to the zero-range universal function. Using this property a zero-range equation for the four-boson system is proposed and the four-boson universal function is computed.
We apply a functional renormalisation group to systems of four bosonic atoms close to the unitary limit. We work with a local effective action that includes a dynamical trimer field and we use this field to eliminate structures that do not correspond to the Faddeev-Yakubovsky equations. In the physical limit, we find three four-body bound states below the shallowest three-body state. The values of the scattering lengths at which two of these states become bound are in good agreement with exact solutions of the four-body equations and experimental observations. The third state is extremely shallow. During the evolution we find an infinite number of four-body states based on each three-body state which follow a double-exponential pattern in the running scale. None of the four-body states shows any evidence of dependence on a four-body parameter.
Universal behaviour in few-bosons systems close to the unitary limit, where two bosons become unbound, has been intensively investigated in recent years both experimentally and theoretically. In this particular region, called the unitary window, details of the inter-particle interactions are not important and observables, such as binding energies, can be characterized by a few parameters. With an increasing number of particles the short-range repulsion, present in all atomic, molecular or nuclear interactions, gradually induces deviations from the universal behaviour. In the present letter we discuss for the first time a simple way of incorporating non-universal behaviour through one specific parameter which controls the smooth transition of the system from universal to non-universal regime. Using a system of $N$ helium atoms as an example we calculate their ground state energies as trajectories within the unitary window and also show that the control parameters can be used to determine the energy per particle in homogeneous systems when $N rightarrow infty$.
A recent rejuvenation of experimental and theoretical interest in the physics of few- body systems has provided deep, fundamental insights into a broad range of problems. Few-body physics is a cross-cutting discipline not restricted to conventional subject ar- eas such as nuclear physics or atomic or molecular physics. To a large degree, the recent explosion of interest in this subject has been sparked by dramatic enhancements of experimental capabilities in ultracold atomic systems over the past decade, which now permit atoms and molecules to be explored deep in the quantum mechanical limit with controllable two-body interactions. This control, typically enabled by magnetic or electromagnetically-dressed Fano-Feshbach resonances, allows in particular access to the range of universal few-body physics, where two-body scattering lengths far exceed all other length scales in the problem. The Efimov effect, where 3 particles experienc- ing short-range interactions can counterintuitively exhibit an infinite number of bound or quasi-bound energy levels, is the most famous example of universality. Tremendous progress in the field of universal Efimov physics has taken off, driven particularly by a combination of experimental and theoretical studies in the past decade, and prior to the first observation in 2006, by an extensive set of theoretical studies dating back to 1970. Because experimental observations of Efimov physics have usually relied on resonances or interference phenomena in three-body recombination, this connects naturally with the processes of molecule formation in a low temperature gas of atoms or nucleons, and more generally with N-body recombination processes. Some other topics not closely related to the Efimov effect are also reviewed in this article, including ...
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 $kappa$ (values from $kappa=1$ to $50$ are considered), where $kappa$ is equal to $m/M$, and the two-body $s$-wave scattering length $a_{text{BX}}$ 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.
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