Three-Body Interacting Bosons in Free Space

Abstract

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 threebody one. The mechanism can be implemented for dipolar bosons in the bilayer configuration with tunneling or in an atomic system by using radio-frequency fields to couple two hyperfine states. One can then aim to observe a purely three-body interacting gas, dilute self-trapped droplets, the paired superfluid phase, Pfaffian state, and other exotic phenomena.PACS numbers: 34.50. 05.30.Jp, The Feshbach resonance technique, which allows for tuning the two-body interaction to any value, has been a major breakthrough in the field of quantum gases [1]. Reaching strongly interacting regimes by using this method is proven successful in two-component fermionic mixtures [2] because of the naturally built-in mechanism of suppression of local three-body inelastic processes [3]: the Pauli principle prohibits three fermions to be close to each other as at least two of them are identical. Essentially the same mechanism is responsible for the repulsion between weakly bound molecules in this system ensuring the mechanical stability. Bosons, having no such protection, are much more fragile. A Bose-Einstein condensate (BEC) collapses in free space even for infinitesimally weak attraction [4] not to mention devastating recombination losses close to resonance [5,6].A repulsive three-body force can stabilize the system and induce nontrivial many-body effects. A weakly interacting BEC with two-body attraction (coupling constant g 2 < 0) and three-body repulsion (g 3 > 0) is predicted to be a droplet, the density of which in the absence of external confinement and neglecting the surface tension is flat and equals n = −3g 2 /2g 3 [7][8][9]. For a strong (beyond mean-field) two-body attraction the spinless Bose gas can pass from the atomic to paired superfluid phase via an Ising-type transition with peculiar topological properties [10][11][12]. However, the mechanical stability of the system requires repulsive few-body interactions [13] or other stabilizing mechanisms [14]. Few-body forces are also important for quantum Hall problems: the exact ground state of bosons in the lowest Landau level with a repulsive three-body contact interaction is the Pfaffian state [15] also known as the weak-pairing phase and characterized by non-Abelian excitations [16]. Interestingly, a finite range of the three-body interaction breaks the pairing [17]. On the other hand, there may be a transition from the weak-to strong-pairing Abelian phase [18], presumably driven by varying g 2 .Most proposals for generating effective three-body interactions deal with lattice systems [19][20][21][22][23][24]. In free space, since three-body effects are significant when g 3 n is of order g 2...

Three-boson bound states in two dimensions

“…53 All these approaches involve several numerical integrations over unbounded spaces or kernel inversion, some of them are limited to s-wave resonant scattering. The hyperspherical method has been used for fewbody problems in two dimensions, [36][37][38][39][40][41] with the usual approach of representing states as a sum of many hyperspherical harmonics. Our paper therefore provides an alternative approach to the quantum three-body problems, simple and efficient, involving only direct root finding and evolving of a first-order ordinary differential equation to an intermediate length scale (for example, the divergence behavior showing the existence of bound state is already clear at a relatively small length scale r ∼ 20 in Fig.…”

“…Usually, the angular part of four dimensional vector is represented in terms of hyperspherical coordinates in the literature, [35][36][37][38][39][40][41][42][43] but the resulting algorithms have slow convergence and the number of states scales as the square of the number of levels included. Here we adopt the Hopf coordinates, which gives faster convergence and number of states proportional to the number of levels included (see Appendix A ):…”

ShieldingΣ2ultracold dipolar molecular collisions with electric fields

“…For molecules formed by a STIRAP process such as RbSr, it would be interesting to study whether the molecules can be formed directly at the shielding electric field in theñ = 1 rotational state, so to protect directly the molecules during their formation. Finally, this mechanism looks also promising for shielding three-body collisions of dipolar molecules which might play a significant role in dense dipolar Bose-Einstein Condensates and might have implications for many-body physics [48].…”

Stable Dilute Supersolid of Two-Dimensional Dipolar Bosons

“…Three-body forces are ubiquitous and arise naturally in effective field theories when one integrates out some of the high-energy degrees of freedom in the system [33]. In particular, our model can be realized for dipoles in the bilayer geometry with interlayer tunneling [34]. Tracing out the degree of freedom associated with the layer index one obtains an effective single-layer model in which g 2 and g 3 can be independently controlled by tuning the interlayer tunneling amplitude.…”