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Register a new userEfimov physics in heteronuclear four-body systems
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We study three- and four-body Efimov physics in a heteronuclear atomic system with three identical heavy bosonic atoms and one light atom. We show that exchange of the light atom between the heavy atoms leads to both three- and four-body features in the low-energy inelastic rate constants that trace to the Efimov effect. Further, the effective interaction generated by this exchange can provide an additional mechanism for control in ultracold experiments. Finally, we find that there is no true four-body Efimov effect - that is, no infinite number of four-body states in the absence of two- and three-body bound states - resolving a decades-long controversy.
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Efimov physics is drastically affected by the change of spatial dimensions. Efimov states occur in a tridimensional (3D) environment, but disappear in two (2D) and one (1D) dimensions. In this paper, dedicated to the memory of Prof. Faddeev, we will review some recent theoretical advances related to the effect of dimensionality in the Efimov phenomenon considering three-boson systems interacting by a zero-range potential. We will start with a very ideal case with no physical scales, passing to a system with finite energies in the Born-Oppenheimer (BO) approximation and finishing with a general system. The physical reason for the appearance of the Efimov effect is given essentially by two reasons which can be revealed by the BO approximation - the form of the effective potential is proportional to $1/R^2$ ($R$ is the relative distance between the heavy particles) and its strength is smaller than the critical value given by $-(D-2)^2/4$, where $D$ is the effective dimension.
The Efimov effect represents a cornerstone in few-body physics. Building on the recent experimental observation with ultracold atoms, we report the first experimental signature of Efimov physics in a heteronuclear system. A mixture of $^{41}$K and $^{87}$Rb atoms was cooled to few hundred nanoKelvins and stored in an optical dipole trap. Exploiting a broad interspecies Feshbach resonance, the losses due to three-body collisions were studied as a function of the interspecies scattering length. We observe an enhancement of the three-body collisions for three distinct values of the interspecies scattering lengths, both positive and negative. We attribute the two features at negative scattering length to the existence of two kind of Efimov trimers, namely KKRb and KRbRb.
The existence of the Efimov effect is drastically affected by the dimensionality of the space in which the system is embedded. The effective spatial dimension containing an atomic cloud can be continuously modified by compressing it in one or two directions. In the present article we determine for a general $AAB$ system formed by two identical bosons $A$ and a third particle $B$ in the two-body unitary limit, the dimensionsality $D$ for which the Efimov effect can exist for different values of the mass ratio $mathpzc{A}=m_B/m_A$. In addition, we provide a prediction for the Efimov discrete scaling factor, ${rm exp},(pi/s)$, as a function of a wide range of values of $mathpzc{A}$ and $D$, which can be tested in experiments that can be realized with currently available technology.
Universal behaviour has been found inside the window of Efimov physics for systems with $N=4,5,6$ particles. Efimov physics refers to the emergence of a number of three-body states in systems of identical bosons interacting {it via} a short-range interaction becoming infinite at the verge of binding two particles. These Efimov states display a discrete scale invariance symmetry, with the scaling factor independent of the microscopic interaction. Their energies in the limit of zero-range interaction can be parametrized, as a function of the scattering length, by a universal function. We have found, using a particular form of finite-range scaling, that the same universal function can be used to parametrize the energies of $Nle6$ systems inside the Efimov-physics window. Moreover, we show that the same finite-scale analysis reconciles experimental measurements of three-body binding energies with the universal theory.
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.
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