# Four-mode squeezed states: two-field quantum systems and the symplectic group $$\mathrm {Sp}(4,{\mathbb {R}})$$ Sp ( 4 ,

@article{Colas2021FourmodeSS, title={Four-mode squeezed states: two-field quantum systems and the symplectic group \$\$\mathrm \{Sp\}(4,\{\mathbb \{R\}\})\$\$ Sp ( 4 , }, author={Thomas Colas and Julien Grain and Vincent Vennin}, journal={The European Physical Journal C}, year={2021}, volume={82}, pages={1-32} }

We construct the four-mode squeezed states and study their physical properties. These states describe two linearly-coupled quantum scalar fields, which makes them physically relevant in various contexts such as cosmology. They are shown to generalise the usual two-mode squeezed states of single-field systems, with additional transfers of quanta between the fields. To build them in the Fock space, we use the symplectic structure of the phase space. For this reason, we first present a pedagogical…

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