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Register a new userFew-boson system with a single impurity: Universal bound states tied to Efimov trimers
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Authors
D. Blume
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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 $kappa$ (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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The dimensionality of a system can fundamentally impact the behaviour of interacting quantum particles. Classic examples range from the fractional quantum Hall effect to high temperature superconductivity. As a general rule, one expects confinement to favour the binding of particles. However, attractively interacting bosons apparently defy this expectation: while three identical bosons in three dimensions can support an infinite tower of Efimov trimers, only two universal trimers exist in the two dimensional case. We reveal how these two limits are connected by investigating the problem of three identical bosons confined by a harmonic potential along one direction. We show that the confinement breaks the discrete Efimov scaling symmetry and destroys the weakest bound trimers. However, the deepest bound Efimov trimer persists under strong confinement and hybridizes with the quasi-two-dimensional trimers, yielding a superposition of trimer configurations that effectively involves tunnelling through a short-range repulsive barrier. Our results suggest a way to use strong confinement to engineer more stable Efimov-like trimers, which have so far proved elusive.
We report on the measurement of four-body recombination rate coefficients in an atomic gas. Our results obtained with an ultracold sample of cesium atoms at negative scattering lengths show a resonant enhancement of losses and provide strong evidence for the existence of a pair of four-body states, which is strictly connected to Efimov trimers via universal relations. Our findings confirm recent theoretical predictions and demonstrate the enrichment of the Efimov scenario when a fourth particle is added to the generic three-body problem.
A powerful experimental technique to study Efimov physics at positive scattering lengths is demonstrated. We use the Feshbach dimers as a local reference for Efimov trimers by creating a coherent superposition of both states. Measurement of its coherent evolution provides information on the binding energy of the trimers with unprecedented precision and yields access to previously inaccessible parameters of the system such as the Efimov trimers lifetime and the elastic processes between atoms and the constituents of the superposition state. We develop a comprehensive data analysis suitable for noisy experimental data that confirms the trustworthiness of our demonstration.
Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is much larger than the range of the interaction. The binding energies of these states are described as a function of the scattering length and one three-body parameter by a transcendental equation involving a universal function of one angular variable. We provide an accurate and convenient parametrization of this function. Moreover, we discuss the effective treatment of range corrections in the universal equation and compare with a strictly perturbative scheme.
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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