Multi-species Systems in Optical Lattices by Fernanda Pinheiro

Author:Fernanda Pinheiro
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.33)

which computes population imbalance between the different orbital states arises as a natural candidate for characterizing sensitivity of the system with respect to R. When , all the particles occupy only orbital states, and in the same way, when all the particles occupy only orbital states. The case of recovers the symmetric lattice, that is characterized by the equal sharing of population among the different orbitals. We remark, however, that since the trap defines an effective size for the system that is fixed by , the sensitivity under variations of R is expected to depend strongly on the values of the trap frequency.14 This is illustrated in Fig. 4.8, where the behavior of around is compared for different values of . In particular, since the range of becomes smaller for larger systems, this implies that qualitative properties of the ground state are expected to change more abruptly with increasing systems sizes. We also verified numerically that increases with increasing values of the interaction strength , which confirms the picture that the orbital order parameters are coupled by interactions.

Fig. 4.8The parameter for measuring population imbalance as a function of the lattice asymmetry parameter, R, and for different values of the trapping frequency. Here and . The vertical dashed lines are used to denote the typical sizes of the transition region where atoms coexist in the two orbital states. In particular, smaller values of are associated with smaller values of . This means that the transition becomes sharper as the system’s size increases (Reprinted from Ref. [1])

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