We investigate two-component boson systems by using their two individual average sizes and the distance between their centers as coordinates. We use zero-range interactions and include only relative $s$ waves. An effective potential is computed and discussed as a function of particle numbers and interaction strengths. Efimov conditions of two very large scattering lengths can arise if one component is a binary molecule. The corresponding atom-molecule interaction can then exhibit chaotic behavior. We present static and dynamic properties of an atom-molecule two-component system. We discuss the possible atom-molecule oscillations when all atoms are identical. The atomic number is then used as a collective coordinate and the cranking mass is computed. The collective oscillation frequency is estimated and compared with the trap frequency and the three-body recombination rate.
We investigate two-component boson systems by using their two individual average sizes and the distance between their centers as coordinates. We use zero-range interactions and include only relative s waves. An effective potential is computed and discussed as a function of particle numbers and interaction strengths. Efimov conditions of two very large scattering lengths can arise if one component is a binary molecule. The corresponding atom-molecule interaction can then exhibit chaotic behavior. We present static and dynamic properties of an atom-molecule two-component system. We discuss the possible atom-molecule oscillations when all atoms are identical. The atomic number is then used as a collective coordinate and the cranking mass is computed. The collective oscillation frequency is estimated and compared with the trap frequency and the three-body recombination rate.
We investigate two-component boson systems consisting of atoms and binary bound molecules of the same atoms. We assume that a coherent superposition of atomic and molecular Bose?Einstein condensates is formed in a non-stationary state leading to oscillations between the two condensates. To facilitate the formulation, we first give analogies in neutrino oscillations applicable for two states of one particle. We then extend to many non-interacting particles in an external field treated in the mean-field approximation as for collective motion of finite systems. We then go beyond the mean field and provide a framework for interacting particles and correlated wavefunctions. The atom?molecule oscillation frequency is dominated by the molecular binding energy when the atom?atom scattering length is substantially smaller than the oscillator trap length. Comparable scattering lengths can completely change the oscillation frequency. The damping time of the oscillations decreases with atom number and scattering lengths, although a large increase can occur for special combinations of the different interactions.
The effective potential is computed for two boson systems in one trap as a function of their two individual hyperadii and the distance between their centers. Zero-range interactions are used and only relative s-states are included. Existence and properties of minima are investigated as a function of these three collective coordinates. For sufficiently strong repulsion stable structures are found at a finite distance between the centers. The relative center of masses motion corresponds to the lowest normal mode. The highest normal mode is essentially the breathing mode where the subsystems vibrate by scaling their radii in phase. The intermediate normal mode corresponds to isovector motion where the subsystems vibrate by scaling their radii in opposite phase. Stability conditions are established as substantially more restrictive than in mean-field computations.
The effective potential is computed for two boson systems in one trap as a function of their two individual hyperadii and the distance between their centers. Zero-range interactions are used and only relative s-states are included. Existence and properties of minima are investigated as a function of these three collective coordinates. For sufficiently strong repulsion stable structures are found at a finite distance between the centers. The relative center of masses motion corresponds to the lowest normal mode. The highest normal mode is essentially the breathing mode where the subsystems vibrate by scaling their radii in phase. The intermediate normal mode corresponds to isovector motion where the subsystems vibrate by scaling their radii in opposite phase. Stability conditions are established as substantially more restrictive than in mean-field computations.
Two-component Fermi and Bose gases with infinitely large interspecies s-wave scattering length as exhibit a variety of intriguing properties. Among these are the scale invariance of two-component Fermi gases with equal masses, and the favorable scaling of Efimov features for two-component Bose gases and Bose-Fermi mixtures with unequal masses. This paper builds on our earlier work [Phys. Rev. Lett. 105, 170403 (2010)] and presents a detailed discussion of our studies of small unequal-mass two-component systems with infinite as in the regime where three-body Efimov physics is absent. We report on nonuniversal few-body resonances. Just like with two-body systems on resonance, few-body systems have a zero-energy bound state in free space and a diverging generalized scattering length. Our calculations are performed within a nonperturbative microscopic framework and investigate the energetics and structural properties of small unequal-mass two-component systems as functions of the mass ratio $\ensuremath{\kappa}$, and the numbers N1 and N2 of heavy and light atoms. For purely attractive Gaussian two-body interactions, we find that the (N1,N2)=(2,1) and (3,1) systems exhibit three-body and four-body resonances at mass ratios $\ensuremath{\kappa}=12.314(2)$ and 10.4(2), respectively. The three- and four-particle systems on resonance are found to be large. It seems feasible that the features discussed in this paper can be probed experimentally with present-day technology.
Abstract 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 length is usually related to the non-equal two-body systems. We account for temperature smearing which tends to wipe out the higher-lying Efimov peaks. The range and the strength of the imaginary potential determine positions and shapes of the Efimov peaks as well as the absolute value of the recombination rate. The Efimov scaling between recombination peaks is calculated and shown to depend on both scattering lengths. Recombination is predicted to be largest for heavy–heavy–light systems. Universal properties of the optical parameters are indicated. We compare to available experiments and find in general very satisfactory agreement.
We study the wave function φ(3) of three identical bosons scattering at zero energy, zero total momentum, and zero orbital angular momentum in two dimensions, interacting via short-range potentials with a finite two-body scattering length a. We derive asymptotic expansions of φ(3) in two regimes: the 111-expansion, where all three pairwise distances are large, and the 21-expansion, where one particle is far from the other two. In the 111-expansion, the leading term grows as ln3(B/a) at large hyperradius B=(s12+s22+s32)/2. At order B−2ln−3(B/a), we identify a three-body parameter D with dimension of length squared, which we term the three-body scattering area. This quantity should be contrasted with the three-body scattering area previously studied for infinite or vanishing two-body scattering length. If the two-body interaction is attractive and supports bound states, D acquires a negative imaginary part, and we derive its relation to the probability amplitudes for the production of two-body bound states in three-body collisions. Under weak modifications of the interaction potentials, we derive the corresponding shift of D in terms of φ(3) and the changes of the two-body and three-body potentials. We also study the effects of D and φ(3) on three-body and many-body physics, including the three-body ground-state energy in a large periodic volume, the many-body energy and the three-body correlation function of the dilute two-dimensional Bose gas, and the three-body recombination rates of two-dimensional ultracold atomic Bose gases.