We investigate local three-body correlations for bosonic particles in three and one dimensions as a function of the interaction strength. The three-body correlation function g(3) is determined by measuring the three-body recombination rate in an ultracold gas of Cs atoms. In three dimensions, we measure the dependence of g(3) on the gas parameter in a BEC, finding good agreement with the theoretical prediction accounting for beyond-mean-field effects. In one dimension, we observe a reduction of g(3) by several orders of magnitude upon increasing interactions from the weakly interacting BEC to the strongly interacting Tonks-Girardeau regime, in good agreement with predictions from the Lieb-Liniger model for all strengths of interaction.
We combine theory and experiment to investigate five-body recombination in an ultracold gas of atomic cesium at negative scattering length. A refined theoretical model, in combination with extensive laboratory tunability of the interatomic interactions, enables the five-body resonant recombination rate to be calculated and measured. The position of the new observed recombination feature agrees with a recent theoretical prediction and supports the prediction of a family of universal cluster states at negative $a$ that are tied to an Efimov trimer.
Three-body recombination is a phenomenon common in atomic and molecular collisions, producing heating in the system. However, we find the cooling effect of the three-body recombination of a 6Li Fermi gas near its s-wave narrow Feshbach resonance. Such counter-intuitive behavior is explained as follows, the threshold energy of the quasi-bounded Feshbach molecule acts as the knife of cooling, expelling the scattering atoms with selected kinetic energy from the trap. When the threshold energy happens to be larger than 3/2kBT, each lost atom in the three-body recombination process has more than 3k…
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 experimentally measure, and theoretically analyze the three-atom recombination rate, $L_3$, around a narrow $s$ wave magnetic Feshbach resonance of $^6$Li-$^6$Li at 543.3 Gauss. By examining both the magnetic field dependence and especially the temperature dependence of $L_3$ over a wide range of temperatures from a few $μ$K to above 200 $μ$K, we show that three-atom recombination through a narrow resonance follows a universal behavior determined by the long-range van der Waals potential, and can be described by a set of rate equations in which three-body recombination proceeds via successi…
The system of four identical bosons with large two-boson scattering length is described using momentum-space integral equations for the four-particle transition operators. The creation of Efimov trimers via ultracold four-boson recombination is studied. The universal behavior of the recombination rate is demonstrated.
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…
The dimer-atom-atom recombination process in the system of four identical bosons with resonant interactions is studied. The description uses the exact Alt, Grassberger and Sandhas equations for the four-particle transition operators that are solved in the momentum-space framework. The dimer-dimer and atom-trimer channel contributions to the ultracold dimer-atom-atom recombination rate are calculated. The dimer-atom-atom recombination rate greatly exceeds the three-atom recombination rate.
The different resonant regimes that can be achieved by using a magnetic Feshbach resonance are analyzed with a separable two-channel model. Emphasis is put on the case of narrow resonances in a region of intermediate detuning where a shallow dimer exists and an approximate law including the background scattering length for the three-body recombination rate is derived.
We reveal a significant spin-exchange pathway in the three-body recombination process for ultracold lithium-7 atoms near a zero-crossing of the two-body scattering length. This newly discovered recombination pathway involves the exchange of spin between all three atoms, which is not included in many theoretical approaches with restricted spin structure. Taking it into account, our calculation is in excellent agreement with experimental observations. To contrast our findings, we predict the recombination rate around a different zero-crossing without strong spin-exchange effects to be two orders…
We study entropy generation in a one-dimensional (1D) model of bosons in an optical lattice experiencing two-particle losses. Such heating is a major impediment to observing exotic low temperature states, and "simulating" condensed matter systems. Developing intuition through numerical simulations, we present a simple empirical model for the entropy produced in this 1D setting. We also explore the time evolution of one and two particle correlation functions, showing that they are robust against two-particle loss. Because of this robustness, induced two-body losses can be used as a probe of sho…
We study three-body recombination in two dimensions for systems interacting via short-range two-body interactions in the regime of large scattering lengths. Using the adiabatic hyperspherical representation, we derive semi-analytical formulas for three-body recombination in both weakly and deeply bound diatom states. Our results demonstrate the importance of long-range corrections to the three-body potentials by showing how they alter the low-energy and scattering length dependence of the recombination rate for both bosonic and fermionic systems, which exhibit suppressed recombination if compa…
We develop a full multichannel spin model in momentum space to investigate three-body recombination of identical alkali-metal atoms colliding in a magnetic field. The model combines the exact three-atom spin structure and realistic pairwise atom-atom interactions. By neglecting the interaction between two particles when the spectating particle is not in its initial spin state we arrive at an approximate model. With this approximate model we achieve excellent agreement with the recent precise measurement of the ground Efimov resonance position in potassium-39 close to 33.58 G [Chapurin $et$ $al…
The simplest model for itinerant ferromagnetism, the Stoner model, has so far eluded experimental observation in repulsive ultracold fermions due to rapid three-body recombination at large scattering lengths. Here we show that a ferromagnetic phase can be stabilised by imposing a moderate optical lattice. The reduced kinetic energy drop upon formation of a polarized phase in an optical lattice extends the ferromagnetic phase to smaller scattering lengths where three-body recombination is small enough to permit experimental detection of the phase. We also show, using time dependent density func…
A general method to study classical scattering in $n$-dimension is developed. Through classical trajectory calculations, the three-body recombination is computed as a function of the collision energy for helium atoms, as an example. Quantum calculations are also performed for the $J^Π$ = $0^{+}$ symmetry of the three-body recombination rate in order to compare with the classical results, yielding good agreement for $E\gtrsim$ 1 K. The classical threshold law is derived and numerically confirmed for the Newtonian three-body recombination rate. Finally, a relationship is found between the quantu…
Three-body recombination is a prime example of the fundamental interaction between three particles. Due to the complexity of this process it has resisted a comprehensive description. Experimental investigations have mainly focussed on the observation of corresponding loss rates without revealing information on the reaction products. Here, we provide the first general experimental study on the population distribution of molecular quantum states after three-body recombination in a non-resonant regime. We have developed a highly sensitive detection scheme which combines photoionization of the mol…
We report on measurements of three-body recombination rates in an ultracold gas of $^7$Li atoms in the extremely nonuniversal regime where the two-body scattering length vanishes. We show that the rate is well defined and can be described by two-body parameters only: the scattering length $a$ and the effective range $R_e$. We find the rate to be energy independent, and, by connecting our results with previously reported measurements in the universal limit, we cover the behavior of the three-body recombination in the whole range from weak to strong two-body interactions. We identify a nontrivia…
We investigate three-boson recombination of equal mass systems as function of (negative) scattering length, mass, finite energy, and finite temperature. An optical model with an imaginary potential at short distance reproduces experimental recombination data and allows us to provide a simple parametrization of the recombination rate as function of scattering length and energy. Using the two-body van der Waals length as unit we find that the imaginary potential range and also the potential depth agree to within thirty percent for Lithium and Cesium atoms. As opposed to recent studies suggesting…
Motivated by recent experimental progresses, we investigate few-body properties of interacting spinless bosons nearby a d-wave resonance. Using the Skorniakov-Ter-Martirosion (STM) equations, we calculate the scattering length between an atom and a d-wave dimer, and we find that the atom-dimer scattering length is positive and is much smaller the result from the mean-field approximation. We also reveal unique properties of the three-body recombination rate for a degenerate Bose condensate nearby the d-wave resonance. We find that the total recombination rate is nearly a constant at the quasi-b…
We discuss the impact of a finite effective range on three-body systems interacting through a large two-body scattering length. By employing a perturbative analysis in an effective field theory well suited to this scale hierarchy we find that an additional three-body parameter is required for consistent renormalization once range corrections are considered. This allows us to extend previously discussed universal relations between different observables in the recombination of cold atoms to account for the presence of a finite effective range. We show that such range corrections allow us to simu…
Systems of three particles show a surprising feature in their bound state spectrum: a series of geometrically scaled states, known as Efimov states. These states have not yet been observed directly, but many recent experiments show indirect evidence of their existence via the so-called recombination process. The theories that predict the Efimov states also predicts either resonant enhancement of the recombination process or suppression by destructive interference, depending on the sign of the interaction between the particles. The theories predict universal features for the Efimov states, for …
We study three-body recombination in an ultracold Bose-Fermi mixture. We first show theoretically that, for weak inter-species coupling, the loss rate is proportional to Tan's contact. Second, using a 7 Li/ 6 Li mixture we probe the recombination rate in both the thermal and dual superfluid regimes. We find excellent agreement with our model in the BEC-BCS crossover. At unitarity where the fermion-fermion scattering length diverges, we show that the loss rate is proportional the 4/3 power of the fermionic density. Our results demonstrate that impurity-induced losses can be used as a quantitati…
We have studied the three-body recombination rates on both sides of the interspecies d-wave Feshbach resonance in the $^{85}$Rb\,-$^{87}$Rb-$^{87}$Rb system using the $R$-matrix propagation method in the hyperspherical coordinate frame. Two different mechanisms of recombination rate enhancement for positive and negative $^{85}$Rb\,-$^{87}$Rb d-wave scattering lengths are analyzed. On the positive scattering length side, the recombination rate enhancement occurs due to the existence of three-body shape resonance, while on the negative scattering length side, the coupling between the lowest entr…
We study three-body recombination of fully spin-polarized ${}^6$Li atoms that are interacting resonantly in relative p-waves. Motivated by a recent experiment, we focus on negative scattering volumes where three atoms recombine into a deep dimer and another atom. We calculate the three-body recombination rate using a Faddeev equation derived from effective field theory. In particular, we study the magnetic field and temperature dependences of the loss rate and use the recombination data to determine the effective range of the p-wave atom-atom interaction. We also predict the existence of a sha…
We investigate three-body recombination rates into deep dimers in cold atomic gases with large scattering length within hyper-spherical adiabatic zero-range approach. We derive closed analytic expressions for the rates for one- and two-species gases. Although the deep dimers are beyond the zero-range theory the latter can still describe the recombination into deep dimers by use of one additional short-range absorption parameter. The recombination rate, as function of the scattering length, retains the known universal behavior --- the fourth power trend with characteristic log-periodic peaks --…
We consider three-body recombination into deep dimers in a mass-imbalanced two-component atomic gas. We use an optical model where a phenomenological imaginary potential is added to the lowest adiabatic hyper-spherical potential. The consequent imaginary part of the energy eigenvalue corresponds to the decay rate or recombination probability of the three-body system. The method is formulated in details and the relevant qualitative features are discussed as functions of scattering lengths and masses. We use zero-range model in analyses of recent recombination data. The dominating scattering len…
First-order phase transition in atom-molecule quantum degenerate mixtures with coherent three-body recombination
Missouri University of Science and Technology（密苏里科技大学）；Ben-Gurion University of the Negev（内盖夫本古里安大学）；Harvard & Smithsonian（哈佛大学与史密森尼学会）；University of Chicago（芝加哥大学）
A very recently method for classical trajectory calculations for three-body collision [J. Pérez-Ríos, S. Ragole, J. Wang and C. H. Greene, J. Chem. Phys. {\bf 140}, 044307 (2014)] has been applied to describe ion-neutral-neutral ternary processes for low energy collisions: 0.1 mK - 10 mK. As a result, a threshold law for the three-body recombination cross section is obtained and corroborated both, experimentally and numerically. The derived threshold law predicts the formation of weakly bound dimers, with binding energies comparable to the collision energy of the collisional partners. In this …
Three-body recombination in quantum gases is traditionally associated with heating, but it was recently found that it can also cool the gas. We show that in a partially condensed three-dimensional homogeneous Bose gas three-body loss could even purify the sample, that is, reduce the entropy per particle and increase the condensed fraction $η$. We predict that the evolution of $η$ under continuous three-body loss can, depending on small changes in the initial conditions, exhibit two qualitatively different behaviours - if it is initially above a certain critical value, $η$ increases further, wh…
We investigate three-body recombination loss across a Feshbach resonance in a gas of ultracold 7Li atoms prepared in the absolute ground state and perform a comparison with previously reported results of a different nuclear-spin state [N. Gross et.al., Phys. Rev. Lett. 103 163202, (2009)]. We extend the previously reported universality in three-body recombination loss across a Feshbach resonance to the absolute ground state. We show that the positions and widths of recombination minima and Efimov resonances are identical for both states which indicates that the short-range physics is nuclear-s…
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…
We report on high-resolution Feshbach spectroscopy on a degenerate, spin-polarized Fermi gas of $^{161}$Dy atoms, measuring three-body recombination losses at low magnetic field. For field strength up to 1\,G, we identify as much as 44 resonance features and observe plateaus of very low losses. For four selected typical resonances, we study the dependence of the three-body recombination rate coefficient on the magnetic resonance detuning and on the temperature. We observe a strong suppression of losses with decreasing temperature already for small detunings from resonance. The characterization…
We investigate the three-body properties of two identical "up" fermions and one distinguishable "down" atom interacting in a strongly confined two-dimensional geometry. We compute exactly the atom-dimer scattering properties and the three-body recombination rate as a function of collision energy and mass ratio m_up/m_down. We find that the recombination rate for fermions is strongly energy dependent, with significant contributions from higher partial waves at low energies. For m_up < m_down, the s-wave atom-dimer scattering below threshold is completely described by the scattering length. Furt…
We study Efimov resonances via three-body loss in an ultracold two-component gas of fermionic $^6$Li and bosonic $^{133}$Cs atoms close to a Feshbach resonance at 843~G, extending results reported previously [Pires \textit{et al.}, Phys. Rev. Lett. 112, 250404 (2014)] to temperatures around 120~nK. The experimental scheme for reaching lower temperatures is based upon compensating the gravity-induced spatial separation of the mass-imbalanced gases with bichromatic optical dipole traps. We observe the first and second excited Li-Cs-Cs Efimov resonance in the magnetic field dependence of the thre…
We study theoretically several aspects of the dynamics of coherent atom-molecule conversion in spin-1 Bose-Einstein condensates. Specifically, we discuss how for a suitable dark-state condition the interplay of spin-exchange collisions and photoassociation leads to the stable creation of an atom- molecule pairs from three initial spin-zero atoms. This process involves two two-body interactions and can be intuitively viewed as an effective three-body recombination. We investigate the relative roles of photoassociation and of the initial magnetization in the \resonant" case where the dark state …
We study the recombination process of three atoms scattering into an atom and diatomic molecule in heteronuclear mixtures of ultracold atomic gases with large and positive interspecies scattering length at finite temperature. We calculate the temperature dependence of the three-body recombination rates by extracting universal scaling functions that parametrize the energy dependence of the scattering matrix. We compare our results to experimental data for the 40K-87Rb mixture and make a prediction for 6Li-87Rb. We find that contributions from higher partial wave channels significantly impact th…
We investigate universal behavior in the recombination rate of three bosons close to threshold. Using the He-He system as a reference, we solve the three-body Schrödinger equation above the dimer threshold for different potentials having large values of the two-body scattering length $a$. To this aim we use the hyperspherical adiabatic expansion and we extract the $S$-matrix through the integral relations recently derived. The results are compared to the universal form, $α\approx 67.1\sin^2[s_0\ln(κ_*a)+γ]$, for different values of $a$ and selected values of the three-body parameter $κ_*$. A g…
We investigate finite-range effects in systems with three identical bosons. We calculate recombination rates and bound state spectra using two different finite-range models that have been used recently to describe the physics of cold atomic gases near Feshbach resonances where the scattering length is large. The models are built on contact potentials which take into account finite range effects; one is a two-channel model and the other is an effective range expansion model implemented through the boundary condition on the three-body wave function when two of the particles are at the same point…
A zero range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parametrizes the three-body boundary condition while the scattering length enters the Bethe-Peierls boundary condition. The model is solved exactly at zero energy for any value of the scattering length, positive or negative. From this solution, an analytical expression for the rate of three-body recombination to the universal shallow dimer is extracted.
When quantum particles are confined into lower dimensions, an effective three-body interaction inevitably arises and may cause significant consequences. Here we study bosons in one dimension with weak two-body and three-body interactions, predict the existence of two three-body bound states when both interactions are attractive, and determine their binding energies as universal functions of the two-body and three-body scattering lengths. We also show that an infinitesimal three-body attraction induces an excited bound state only for 3, 39, or more bosons. Our findings herein have direct releva…
Ultracold atoms offer valuable opportunities where interparticle interactions can be controlled at will. In particular, by extinguishing the two-body interaction, one can realize unique systems governed by the three-body interaction, which is otherwise hidden behind the two-body interaction. Here we study one-dimensional bosons with a weak three-body attraction and show that they form few-body bound states as well as a many-body droplet stabilized by the quantum mechanical effect. Their binding energies relative to that of three bosons are all universal and the ground-state energy of the dilut…
The relationship between natural orbitals, one-body coherences and two-body correlations is explored for bosonic many-body systems of definite parity with two occupied single-particle states. We show that the strength of local two-body correlations at the parity-symmetry center characterizes the number state distribution and controls the structure of non-local two-body correlations. A recipe for the experimental reconstruction of the natural orbital densities and quantum depletion is derived. These insights into the structure of the many-body wave-function are applied to the predicted quantum-…
When the binding energy of a two-body system goes to zero the two-body system shows a continuous scaling invariance governed by the large value of the scattering length. In the case of three identical bosons, the three-body system in the same limit shows the Efimov effect and the scale invariance is broken to a discrete scale invariance. As the number of bosons increases correlations appear between the binding energy of the few- and many-body systems. We discuss some of them as the relation between the saturation properties of the infinite system and the low-energy properties of the few-boson …
Correlation properties in ultracold Fermi gas with negative scattering length and its impact on the three-body recombination is analyzed. We find that Cooper pairing enhances the recombination rate in contrast to the decrease of this rate accompanying Bose-Einstein condensation in a Bose gas. This trend is characteristic for all interval of temperatures T<Tc.
We investigate a system of dipolar bosons in an optical lattice with local two and three-body interactions. Using the mean-field theory approach, we obtain the ground state phase diagram of the extended Bose-Hubbard (EBH) model with both repulsive and attractive three-body interac- tions. We show that the additional three-body on-site interaction has strong effects on the phase diagram especially on the supersolid phase. Positive values of the three-body interaction lead to the enhancement of the gapped phases at densities larger than unity by reducing the supersolid region. However, a small a…
We study binary atomic boson-fermion mixtures confined in one dimensional box potentials by few-body theory with contact interactions and mean-field many-body theory with density-density interactions. A variety of correlations and structures arise as the inter- and intra- species interactions are tuned. Both few-body and many-body results show that miscible phase and three-chunk phase separation are directly observable in the density profiles. Meanwhile, two-chunk phase separation can be inferred from the few-body correlations and many-body density profiles. We present phase diagrams of select…
We develop the perturbation theory for bosons interacting via a two-body potential $V$ of vanishing mean value. We find that the leading nonpairwise contribution to the energy emerges in the third order in $V$ and represents an effective three-body interaction, the sign of which in most cases (although not in general) is anticorrelated with the sign of the long-range tail of $V$. Explicit results are obtained for a few particular two-body interaction potentials and we perform a detailed perturbative analysis of tilted dipoles in quasi-low-dimensional geometries.
The low-energy spectrum of $N$-boson clusters with pairwise zero-range interactions is believed to be governed by a three-body parameter. We study the ground state of $N$-boson clusters with infinite two-body $s$-wave scattering length by performing {\em{ab initio}} Monte Carlo simulations. To prevent Thomas collapse, different finite-range three-body regulators are used. The energy and structural properties for the three-body Hamiltonian with two-body zero-range interactions and three-body regulator are in much better agreement with the "ideal zero-range Efimov theory" results than those for …
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.
We analyse the ground-state properties of three-body constrained bosons in a one dimensional optical lattice with staggered hoppings analogous to the double well optical lattice. By considering attractive and repulsive on-site interactions between the bosons, we obtain the phase diagram which exhibits various quantum phases. Due to the double-well geometry and three-body constraint several gapped phases such as the Mott insulators and dimer/bond-order phases emerge at commensurate densities in the repulsive interaction regime. Attractive interaction leads to the pair formation which leads to t…
We consider the problem of a fixed impurity coupled to a small number $N$ of non-interacting bosons. We focus on impurity-boson interactions that are mediated by a closed-channel molecule, as is the case for tuneable interatomic interactions in cold-atom experiments. We show that this two-channel model can be mapped to a boson model with effective boson-boson repulsion, which enables us to solve the three-body ($N=2$) problem analytically and determine the trimer energy for impurity-boson scattering lengths $a>0$. By analysing the atom-dimer scattering amplitude, we find a critical scattering …
We propose a method of controlling two- and three-body interactions in an ultracold Bose gas in any dimension. The method requires us to have two coupled internal single-particle states split in energy such that the upper state is occupied virtually but amply during collisions. By varying system parameters one can switch off the two-body interaction while maintaining a strong three-body one. The mechanism can be implemented for dipolar bosons in the bilayer configuration with tunnelling or in an atomic system by using radio-frequency fields to couple two hyperfine states. One can then aim to o…
A Bose gas in a double well is investigated in the presence of single-particle, two-body and three-body asymmetric loss. The loss induces an interesting decay behavior of the total population as well as a possibility to control the dynamics of the system. In the noninteracting limit with asymmetric single-body dissipation, the dynamics of the populations can be obtained analytically. The general many-body problem requires, however, an adequate approximation. We use a mean-field approximation and the Bogoliubov back-reaction beyond mean-field truncation, which we extend up to three-body loss. B…
We investigate one-dimensional three-body systems composed of two identical bosons and one imbalanced atom (impurity) with two-body and three-body zero-range interactions. For the case in the absence of three-body interaction, we give a complete phase diagram of the number of three-body bound states in the whole region of mass ratio via the direct calculation of the Skornyakov-Ter-Martirosyan equations. We demonstrate that other low-lying three-body bound states emerge when the mass of the impurity particle is not equal to another two identical particles. We can obtain not only the binding ene…
A new narrow 3-atom loss resonance associated with an Efimov trimer crossing the 3-atom threshold has recently been discovered in a many-body system of ultracold 6Li atoms in the three lowest hyperfine spin states at a magnetic field near 895 G. O'Hara and coworkers have used measurements of the 3-body recombination rate in this region to determine the complex 3-body parameter associated with Efimov physics. Using this parameter as the input, we calculate the universal predictions for the spectrum of Efimov states and for the 3-body recombination rate in the universal region above 600 G where …
