Universal Pseudo-<inline-formula><tex-math><?CDATA ${\mathscr{P}}{\mathscr{T}}$?></tex-math> <mml:math> <mml:mrow> <mml:mi mathvariant='script'>P</mml:mi> <mml:mi mathvariant='script'>T</mml:mi> </mml:mrow> </mml:math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ctp_70_3_303_ieqn1.gif"/></inline-formula>-Antisymmetry on One-Dimensional Atomic Optical Lattices<xref rid="ctp_70_3_303fn1" ref-type="fn">*</xref><fn id="ctp_70_3_303fn1"><label>*</label><p>Support from National Basic Research Program of China under Grant No. 2014CB921403, National Natural Science Foundation of China under Grant Nos. 11534002, U1730449 and U1530401</p></fn>

Universal Pseudo-

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-Antisymmetry on One-Dimensional Atomic Optical Lattices**

Support from National Basic Research Program of China under Grant No. 2014CB921403, National Natural Science Foundation of China under Grant Nos. 11534002, U1730449 and U1530401

Wang Xin^{1, †}, Sun Chang-Pu^{1, 2}

(Color online) (a) Diagram of the four-level N configuration (4-zigzag), into which the atoms are driven by a weak probe field Ω_p and two moderate coupling field Ω_c and Ω_d. (b) An ensemble of cold ⁸⁷Rb atoms forming 1D optical lattice by being trapped at the bottom of periodically distributed dipole traps along z direction. The spatial period of the dipole trap distribution (and therefore the spatial period of atom distribution) is a. Within each dipole trap, we assume the atoms to be in Gaussian distribution, with σ being the standard deviation, as described by Eq. (17).