Abstract
Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for both cases, under strong repulsion, atomic spatial localization at extemporaneously created sites, forming quantum molecular magnetic structures with non-itinerant character. These findings usher future theoretical and experimental explorations into the highly correlated behavior of ultracold strongly repelling fermionic atoms in higher dimensions, beyond the fermionization physics that is strictly applicable only in the 1D case. The results for four atoms are well described with finite Heisenberg spin-chain and cluster models. The numerical simulations of three fermionic atoms in symmetric DWs reveal the emergent appearance of coupled resonating 2D Heisenberg clusters, whose emulation requires the use of a t–J-like model, akin to that used in investigations of high Tc superconductivity. The highly entangled states discovered in the microscopic and model calculations of controllably detuned, asymmetric, DWs suggest three-cold-atom DW quantum computing qubits.
Highlights
The unparalleled experimental advances and control achieved in the field of ultracold atoms have rekindled an intense interest in emulating magnetic behavior using ultracold atoms in optical traps [1, 2]
To date the theoretical studies of magnetism of a few ultracold atoms have mainly addressed [17, 18, 19, 20, 21, 22] strictly one-dimensional systems trapped within a single well, where the fermionization theory [23, 24, 25] can assist in inventing analytic forms for the correlated many-body wave functions
Heisenberg Hamiltonians are given in Eqs. (B.4) and (C.1), respectively; note that they have different matrix elements. The similarities between these two cases arise from the fact that the spin eigenfunctions onto which the CI wavefunctions map have the same group structure, differing only in the coefficients of their components [see, e.g., Eq (A.2) in Appendix A]; the multiplicity of the four fermions spin eigenfunctions onto which the CI spectrum maps is six
Summary
The unparalleled experimental advances and control achieved in the field of ultracold atoms have rekindled an intense interest in emulating magnetic behavior using ultracold atoms in optical traps [1, 2]. The associated mapping between the many-body wave function and the spin eigenfunctions [31] for N = 3 and N = 4 electrons confined in single and double semiconductor quantum dots has been predicted in previous studies [11, 12] to occur through the formation of quantum molecular structures in the regime of strong long-range Coulombic repulsion. We note that the related three-electron system in semiconductor double quantum dots has recently attracted a major attention in conjunction with the fabrication and implementation of pulse-gated fast hybrid qubits for solid-state-based quantum computing [47, 48] These advances and the fascinating physics of double-welltrapped three ultracold fermionic atoms that we uncover, and in particular the high degree of entanglement predicted by us for strong interatomic repulsion (see Sections 3, 4, and 5) and the very slow decoherence in such traps, suggest future exploration of this system as a robust ulracold 3-atom DW qubit. Appendix E discusses the mathematics of the more general t − J model for 3 localized fermions in the case of a double trap with symmetric wells
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
