Multimode quantum squeezing generation via multiple four-wave mixing processes within a single atomic vapor cell

Multimode quantum squeezing plays an essential role in the fields of quantum metrology and quantum information. In this paper, we first construct a three- and four-mode energy-level cascaded four-wave mixing system in a single <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>85</mml:mn> </mml:mrow> </mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">R</mml:mi> <mml:mi mathvariant="normal">b</mml:mi> </mml:mrow> </mml:mrow> </mml:math> vapor, and then analyze the quantum properties of the produced states, including the covariance matrix and the intensity squeezing with 11 possible Hamiltonians. In addition, the dressing field is applied to modulate the nonlinear susceptibility and the multimode quantum states. Our scheme allows active modulation of the quantum states integrated within the generation step, without the need for any post-operation of the optics. The mode number of the states also can be extended using more pump fields and the dressing effect. Our study provides a promising candidate to generate multimode quantum states and multimode quantum squeezing within a quantum device involved in the construction of practical quantum networks.