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arXiv:1112.3722 · Physical Review A

Two-body and three-body spin substructures serve as building blocks in small spin-3 condensates

Bao Cheng-guang

Published Apr 19, 2012• 1 citation
arXivHTMLPDF

Abstract

It is found that stable few-body spin structures, pairs and triplexes in the spin space, may exist as basic constituents in small spin-3 condensates, and they play the role of building blocks when the parameters of interaction fall in particular domains. A specific method is designed to find these constituents.
DOI
10.1103/physreva.85.043616

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We have found a stable spin-structure of N [Formula: see text] 3 system in which three spin-3 atoms are trapped and coupled to total spin S [Formula: see text] 3. We have proved that a pair of this structure is nearly an exact solution for N [Formula: see text] 6 systems in a very broad district in the parameter-space. Comparing with the well-known singlet pairs, this pair is a more promising candidate to serve as a building block for large N systems with spin-3 atoms. This is because the spin-structure of the latter can be modified depending on the interactions to reduce the energy while the singlet pairs can not. In fact, we have proved that, for a specific set of strengths (a point in the parameter-space) the product state based on this pair is an exact solution of the N-body Hamiltonian. Thus, in the neighborhood of this point, the product state will appear as an approximate solution. However, how broad this neighborhood would be remains to be clarified.
Abstract Optical trapping techniques allow for the formation of bosonic condensates with internal degrees of freedom, so-called spinor condensates. Mean-field models of spinor condensates highlight the sensitivity of the quantum phases of the system to the relative strength of the two-body interaction in the different spin-channels. Such a description captures the regime where these interactions are weak. In the opposite and largely unexplored regime of strongly correlated spinor condensates, three-body interactions can play an important role through the Efimov effect, producing possible novel phases. Here, we study the three-body spinor problem using the hyperspherical adiabatic representation for spin-1, -2 and -3 condensates in the strongly-correlated regime. We characterize the Efimov physics for such systems and the relevant three-body mean-field parameters. We find that the Efimov effect can strongly affect the spin dynamics and three-body mean-field contributions to the possible quantum phases of the condensate through universal contributions to scattering observables.
Spinor condensates have proven to be a rich area for probing many-body phenomena richer than that of an ultracold gas consisting of atoms restricted to a single spin state. In the strongly correlated regime, the physics controlling the possible novel phases of the condensate remains largely unexplored, and few-body aspects can play a central role in the properties and dynamics of the system through manifestations of Efimov physics. The present study solves the three-body problem for bosonic spinors using the hyperspherical adiabatic representation and characterizes the multiple families of Efimov states in spinor systems as well as their signatures in the scattering observables relevant for spinor condensates. These solutions exhibit a rich array of possible phenomena originating in universal few-body physics, which can strongly affect the spin dynamics and three-body mean-field contributions for spinor condensates. The collisional aspects of atom-dimer spinor condensates are also analyzed, and effects are predicted that derive from Efimov physics.
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Abstract The spin-textures of trapped medium-body cold systems of spin-4 atoms with the interaction dominated by the attractive λ = 4 channel (the two interacting spins are coupled to 4) have been studied via an exact diagonalization of the spin-dependent Hamiltonian under the single spatial mode approximation. Particle number N (3 ≤ N ≤ 13) is assumed. The eigenstates have been analyzed to find out the details of spin-structures and the inherent excitation modes, and the relation between all of them. The emphasis is to find out how the spectra depend on N. We found that the singlet-triplets (a 3-body subsystem where the three spins are coupled to zero) and various excited triplets are basic constituents and all the eigenstates are composed of them. For low-lying states, only a few particles are involved in the excitation modes, while the other particles would 3-by-3 keep themselves in singlet-triplets.