We study the semisuper-Efimov effect, which is found for four identical bosons with a resonant three-body interaction in 2D, in various systems. Based on solutions of bound-state and renormalization-group equations, we first demonstrate an emergence of the semisuper-Efimov effect in mass-imbalanced bosons in 2D. Compared with the Efimov and the super-Efimov effects, the mass ratio-dependent scaling parameter is unexpectedly found to take on a finite value even for extremely mass-imbalanced situations, where the mass ratio is 0 or $\infty$. By a renormalization-group analysis, we also show that a weak two-body interaction sustains the semisuper-Efimov effect. Finally, we liberate the universality of the semisuper-Efimov effect from 2D by showing that bosons with linear-dispersion relation support the semisuper-Efimov effect in 1D.
Wave-particle duality in quantum mechanics allows for a halo bound state whose spatial extension far exceeds a range of the interaction potential. What is even more striking is that such quantum halos can be arbitrarily large on special occasions. The two examples known so far are the Efimov effect and the super Efimov effect, which predict that spatial extensions of higher excited states grow exponentially and double exponentially, respectively. Here, we establish yet another new class of arbitrarily large quantum halos formed by spinless bosons with short-range interactions in two dimensions…
We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible…
In recent years extensive theoretical and experimental studies of universal few-body physics have led to advances in our understanding of universal Efimov physics [1]. The Efimov effect, once considered a mysterious and esoteric effect, is today a reality that many experiments in ultracold quantum gases have successfully observed and continued to explore [2-14]. Whereas theory was the driving force behind our understanding of Efimov physics for decades, recent experiments have contributed an unexpected discovery. Specifically, measurements have found that the so-called three-body parameter det…
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 f…
The universal properties of charged particles are modified by the presence of a long-range Coulomb interaction. We investigate the modification of Efimov universality as a function of the Coulomb strength using the Gaussian expansion method. The resonant short-range interaction is described by Gaussian potentials to which a Coulomb potential is added. We calculate binding energies and root mean square radii for the three- and four-body systems of charged particles and present our results in a generalised Efimov plot. We find that universal features can still be discerned for weak Coulomb inter…
Efimov physics is a universal phenomenon arising in quantum three-body systems. For systems with resonant two-body interactions, Efimov predicted an infinite series of three-body bound states with geometric scaling symmetry. These Efimov states were first observed in cold Cs atoms and have since been reported in a variety of atomic systems. While theories predict non-universal behavior for narrow Feshbach resonances, experiments on Efimov resonances are so far consistent with predictions based on universal theories. Here we directly compare the Efimov spectra in a $^6$Li-$^{133}$Cs mixture nea…
The low-energy spectrum of three particles interacting via nearly resonant two-body interactions in the Efimov regime is set by the so-called three-body parameter. We show that the three-body parameter is essentially determined by the zero-energy two-body correlation. As a result, we identify two classes of two-body interactions for which the three-body parameter has a universal value in units of their effective range. One class involves the universality of the three-body parameter recently found in ultracold atom systems. The other is relevant to short-range interactions that can be found in …
The mass-imbalanced three-body recombination process that forms a shallow dimer is shown to possess a rich Efimov-Stückelberg landscape, with corresponding spectra that differ fundamentally from the homonuclear case. A semi-analytical treatment of the three-body recombination predicts an unusual spectra with intertwined resonance peaks and minima, and yields in-depth insight into the behavior of the corresponding Efimov spectra. In particular, the patterns of the Efimov-Stückelberg landscape are shown to depend inherently on the degree of diabaticity of the three-body collisions, which strongl…
We study the universality of the three-body parameters for systems relevant for ultracold quantum gases with positive $s$-wave two-body scattering lengths. Our results account for finite-range effects and their universality is tested by changing the number of deeply bound diatomic states supported by our interaction model. We find that the physics controlling the values of the three-body parameters associated with the ground and excited Efimov states is constrained by a variational principle and can be strongly affected by $d$-wave interactions that prevent both trimer states from merging into…
Bosonic dimer-dimer scattering is studied near the unitary limit using momentum-space equations for the four-particle transition operators. The impact of the Efimov effect on the dimer-dimer scattering observables is explored and a number of universal relations is established with high accuracy. The rate for the creation of Efimov trimers via dimer-dimer collisions is calculated.
We study three-atom inelastic scattering in ultracold \textsuperscript{39}K near a Feshbach resonance of intermediate coupling strength. The non-universal character of such resonance leads to an abnormally large Efimov absolute length scale and a relatively small effective range $r_e$, allowing the features of the \textsuperscript{39}K Efimov spectrum to be better isolated from the short-range physics. Meticulous characterization of and correction for finite temperature effects ensure high accuracy on the measurements of these features at large-magnitude scattering lengths. For a single Feshba…
We calculated, using seven realistic 4He-4He potentials in the literature, the Efimov spectra of the 4He trimer and tetramer and analyzed the universality of the systems. The three-(four-)body Schroedinger equations were solved fully nonadiabatically with the high-precision calculation method employed in our previous work on the 4He trimer and tetramer [Phys. Rev. A 85, 022502 (2012); 85, 062505 (2012)]. We found the following universality in the four-boson system: i) The critical scattering lengths at which the tetramer ground and excited states couple to the four-body threshold are independe…
We report on the observation of triatomic Efimov resonances in an ultracold gas of cesium atoms. Exploiting the wide tunability of interactions resulting from three broad Feshbach resonances in the same spin channel, we measure magnetic-field dependent three-body recombination loss. The positions of the loss resonances yield corresponding values for the three-body parameter, which in universal few-body physics is required to describe three-body phenomena and in particular to fix the spectrum of Efimov states. Our observations show a robust universal behavior with a three-body parameter that st…
We measure the critical scattering length for the appearance of the first three-body bound state, or Efimov three-body parameter, at seven different Feshbach resonances in ultracold 39K atoms. We study both intermediate and narrow resonances, where the three-body spectrum is expected to be determined by the non-universal coupling of two scattering channels. We observe instead approximately the same universal relation of the three-body parameter with the two-body van der Waals radius already found for broader resonances, which can be modeled with a single channel. This unexpected observation su…
This dissertation presents theoretical investigations of universality and finite-range corrections in few- and many-boson systems. The main focus is on ultra-cold atomic gases seen both from the three-body, many-body, and mean-field perspective. Topics include corrections to Efimov physics, the N-body Efimov effect, two-body correlations in condensates and higher-order interactions in mean-field BECs.
In this paper we discuss the recent discovery of the universality of the three-body parameter (3BP) from Efimov physics. This new result was identified by recent experimental observations in ultracold quantum gases where the value of the s-wave scattering length, $a=a_-$, at which the first Efimov resonance is created was found to be nearly the same for a range of atomic species --- if scaled as $a_-/r_{\rm vdW}$, where $r_{\rm vdW}$ is the van der Waals length. Here, we discuss some of the physical principles related to these observations that emerge from solving the three-body problem with v…
We provide an exact solution of the Efimov spectrum in ultracold gases within the standard two-channel model for Feshbach resonances. It is shown that the finite range in the Feshbach coupling makes the introduction of an adjustable three-body parameter obsolete. The solution explains the empirical relation between the scattering length a_- where the first Efimov state appears at the atom threshold and the van der Waals length l_vdw for open channel dominated resonances. There is a continuous crossover to the closed channel dominated limit, where the scale in the energy level diagram as a func…
Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by a continuous-scale invariance, which is broken to a discrete one when three or more particles come into play. This symmetry induces a universal behavior for different systems, independent of the details of the underlying interaction, rooted in the smallness of the ratio $\ell/a_B \ll 1$, where the length $a_B$ is associated to the binding energy of the two-body system $E_2=\hbar^2/m a_B^2$ and $\ell$ is the natural length given by the interaction range. Efimov physics refers to this u…
Universality is a powerful concept in physics, allowing one to construct physical descriptions of systems that are independent of the precise microscopic details or energy scales. A prime example is the Fermi gas with unitarity limited interactions, whose universal properties are relevant to systems ranging from atomic gases at microkelvin temperatures to the inner crust of neutron stars. Here we address the question of whether unitary Bose systems can possess a similar universality. We consider the simplest strongly interacting Bose system, where we have an impurity particle ("polaron") reson…
We perform precise studies of two- and three-body interactions near an intermediate-strength Feshbach resonance in $^{39}\mathrm{K}$ at $33.5820(14)\thinspace$G. Precise measurement of dimer binding energies, spanning three orders of magnitude, enables the construction of a complete two-body coupled-channel model for determination of the scattering lengths with an unprecedented low uncertainty. Utilizing an accurate scattering length map, we measure the precise location of the Efimov ground state to test van der Waals universality. Precise control of the sample's temperature and density ensure…
Physics is said to be universal when it emerges regardless of the underlying microscopic details. A prominent example is the Efimov effect, which predicts the emergence of an infinite tower of three-body bound states obeying discrete scale invariance when the particles interact resonantly. Because of its universality and peculiarity, the Efimov effect has been the subject of extensive research in chemical, atomic, nuclear and particle physics for decades. Here we employ an anisotropic Heisenberg model to show that collective excitations in quantum magnets (magnons) also exhibit the Efimov effe…
The Efimov effect is the only experimentally realized universal phenomenon that exhibits the renormalization-group limit cycle with the three-body parameter parametrizing a family of universality classes. Recent experiments in ultracold atoms have unexpectedly revealed that the three-body parameter itself is universal when measured in units of an effective range. By performing an exact functional renormalization-group analysis with various finite-range interaction potentials, we demonstrate that the onset of the renormalization-group flow into the limit cycle is universal, regardless of short-…
We study the interspecies scattering properties of ultracold Li-Cs mixtures in their two energetically lowest spin channels in the magnetic field range between 800 G and 1000 G. Close to two broad Feshbach resonances we create weakly bound LiCs dimers by radio-frequency association and measure the dependence of the binding energy on the external magnetic field strength. Based on the binding energies and complementary atom loss spectroscopy of three other Li-Cs s-wave Feshbach resonances we construct precise molecular singlet and triplet electronic ground state potentials using a coupled-channe…
Recent measurements of Efimov resonances in a number of ultracold atom species have revealed an unexpected universality, in which three-body scattering properties are determined by the van der Waals length of the two-body interaction potential. To investigate whether this universality extends to heteronuclear mixtures, we measure loss rate coefficients in an ultracold trapped gas of $^{40}$K and $^{87}$Rb atoms. We find an Efimov-like resonance in the rate of inelastic collisions between $^{40}$K$^{87}$Rb Feshbach molecules and $^{87}$Rb atoms. However, we do not observe any Efimov-related res…
We explore the properties of weakly bound bosonic states in the strongly interacting regime. Combining a correlated-Gaussian (CG) basis set expansion with a complex scaling method, we extract the energies and structural properties of bosonic cluster states with $N\le6$ for different two-body potentials. The identification of five- and six-body resonances attached to an excited Efimov trimer provides strong support to the premise of Efimov universality in bosonic systems. Our study also reveals a rich structure of bosonic cluster states. Besides the lowest cluster states which behave as bosonic…
We investigate theoretically and experimentally the heteronuclear Efimov scenario for a three-body system that consists of two bosons and one distinguishable particle with positive intraspecies scattering lengths. The three-body parameter at the three-body scattering threshold and the scaling factor between consecutive Efimov resonances are found to be controlled by the scattering length between the two bosons, approximately independent of short-range physics. We observe two excited-state Efimov resonances in the three-body recombination spectra of an ultracold mixture of fermionic $^6 $Li and…
We consider a system of three helium-4 atoms, which is so far the simplest realistic three-body system exhibiting the Efimov effect, in order to analyse deviations from the universal Efimov three-body spectrum. We first calculate the bound states using a realistic two-body potential, and then analyse how they can be reproduced by simple effective models beyond Efimov's universal theory. We find that the non-universal variations of the first two states can be well reproduced by models parametrized with only three quantities: the scattering length and effective range of the original potential, a…
Under certain circumstances, three or more interacting particles may form bound states. While the general few-body problem is not analytically solvable, the so-called Efimov trimers appear for a system of three particles with resonant two-body interactions. The binding energies of these trimers are predicted to be universally connected to each other, independent of the microscopic details of the interaction. By exploiting a Feshbach resonance to widely tune the interactions between trapped ultracold lithium atoms, we find evidence for two universally connected Efimov trimers and their associat…
We observe two consecutive heteronuclear Efimov resonances in an ultracold Li-Cs mixture by measuring three-body loss coefficients as a function of magnetic field near a Feshbach resonance. The first resonance is detected at a scattering length of $a_-^{(1)}=-320(10)~a_0$ corresponding to $\sim 7 $ ($\sim 3$) times the Li-Cs (Cs-Cs) van der Waals range. The second resonance appears at $5.8(1.0) a_-^{(1)}$ close to the unitarity-limited regime at the sample temperature of 450 nK. Indication of a third resonance is found in the atom loss spectra. The scaling of the resonance positions is close t…
We demonstrate the emergence of universal Efimov physics for interacting photons in cold gases of Rydberg atoms. We consider the behavior of three photons injected into the gas in their propagating frame, where a paraxial approximation allows us to consider them as massive particles. In contrast to atoms and nuclei, the photons have a large anisotropy between their longitudinal mass, arising from dispersion, and their transverse mass, arising from diffraction. Nevertheless, we show that in suitably rescaled coordinates the effective interactions become dominated by s-wave scattering near thres…
Ultracold atomic gases have recently become a driving force in few-body physics due to the observation of the Efimov effect. While initially observed in equal mass systems, one expects even richer few-body physics in the heteronuclear case. In previous experiments with ultracold mixtures of potassium and rubidium, an unexpected non-universal behavior of Efimov resonances was observed. In contrast, we measure the scattering length dependent three-body recombination coefficient in ultracold heteronuclear mixtures of $^{39}\mathrm{K}$-\87Rb and $^{41}\mathrm{K}$-\87Rb and do not observe any signa…
Analytical solution of the Schrödinger equation with $1/r^3$ and attractive $1/r^2$ potentials: Universal three-body parameter of mixed-dimensional Efimov states
University of Electro-Communications（电气通信大学）；Tohoku University（东北大学）
A new kind of "super-Efimov" states of binding energies scaling as $\ln|E_n|\sim-e^{3nπ/4}$ were predicted by a field theory calculation for three fermions with resonant $p$-wave interactions in two dimensions [Phys. Rev. Lett. \textbf{110}, 235301 (2013)]. However, the universality of these "super-Efimov" states has not been proved independently. In this Letter, we study the three fermion system through the hyperspherical formalism. Within the adiabatic approximation, we find that at $p$-wave resonances, the low energy physics of states of angular momentum $\ell=\pm1$ crucially depends on the…
Within the universal zero-range theory, we compute the three-body recombination rate to deep molecular states for two identical bosons resonantly interacting with each other and with a third atom of another species, in the absence of weakly bound dimers. The results allow for a quantitative understanding of loss resonances at finite temperature and, combined with experimental data, can be used for testing the Efimov universality and extracting the corresponding three-body parameters in a given system. Curiously, we find that the loss rate can be dramatically enhanced by the resonant heavy-heav…
We treat small trapped unequal-mass two-component Fermi gases at unitarity within a non-perturbative microscopic framework and investigate the system properties as functions of the mass ratio $κ$, and the numbers $N_{1}$ and $N_2$ of heavy and light fermions. While equal-mass Fermi gases with infinitely large interspecies s-wave scattering length $a_s$ are universal, we find that unequal mass Fermi gases are, for sufficiently large $κ$ and in the regime where Efimov physics is absent, not universal. In particular, the $(N_1,N_2)=(2,1)$ and $(3,1)$ systems exhibit three-body (3b) and four-body …
We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. T…
The universal aspects of atom-dimer elastic collisions are investigated within the framework of Faddeev equations. The two-body interactions between the neutral atoms are approximated by the separable potential approach. Our analysis considers a pure van der Waals potential tail as well as soft-core van der Waals interactions permitting us in this manner to address the universally general features of atom-dimer resonant spectra. In particular, we show that the atom-dimer resonances are solely associated with the {\it excited} Efimov states. Furthermore, the positions of the corresponding reson…
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 w…
Universality in Ionic Three-body Systems Near an Ion-atom Feshbach Resonance
University of Warsaw（华沙大学）；JILA, NIST, and the Department of Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校JILA、NIST和物理系）；Department of Physics, University of Massachusetts Boston（马萨诸塞大学波士顿分校物理系）
