(a) Proposed experimentally-feasible setup that an ensemble of ultracold six-level atoms interacts with two quantized cavity fields and two pairs of Raman lasers. A couple of orthogonally placed cavities C_a and C_b are arranged in a specific plane, and a guided magnetic field B is applied along one of the two cavities (see, for example, C_a) to fix a quantized axis and split the Zeeman sublevels of the atomic ensemble. Both the cavity modes and Raman lasers propagated in C_a (C_b) are assumed to be right-handed circularly polarized (linearly polarized along the guided magnetic field B). (b) Energy-level structure and their transitions induced by two photon modes and two pairs of Raman lasers. For ⁸⁷Rb atom, the detailed levels can be chosen as |0⟩ → 5S_1/2 |F = 1,m_F = 0⟩, |1⟩ → 5S_1/2 |F = 2,m_F = 0⟩, |r₁⟩ → 5P_1/2 |F = 1,m_F = 0⟩, |s₁⟩ → 5P_3/2 |F = 1,m_F = 0⟩, |r₂⟩ → 5P_1/2 |F = 1,m_F = −1⟩, and |s₂⟩ → 5P_3/2 |F = 1,m_F = −1⟩. In such an arrangement, the transitions labeled by the red lines (blue lines) are thus π transitions (σ⁻ transitions).