I am wondering if anybody can help me to find any good textbooks, articles, or other publications from which I can learn about two-mode-squeezed states.
I understand the concept of the squeezed state well enough, but I am having a hard time finding anything about two-mode squeezed states.
Chapter 7 of the book "Quantum Optics" by Gerry and Knight (published by Cambridge University Press) is decidated to quadrature squeezing. Section 7.2 contains a discuss of two-mode squeezing.
The frontmatter for this book is openly available. Quoting from this:
This text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first- and second-year graduate students.
The book review published in American Journal of Physics is also openly available, stating that "this book may be the most accessible quantum optics book for" upper-level undergraduates and beginning graduate students.
Squeezing is realized in quantum optics through operators of the type $\hat a^\dagger \hat b^\dagger$, $\hat a\hat b$ and their commutator. The set closes on $su(1,1)$ but most of the mathematics - especially if you are interested in squeezing the boson vacuum $\vert 0\rangle$ - actually only requires patient use of raising and lowering operators. If you have experience with creation and destruction operators, you can bypass much of the more technical quantum optics stuff of the early chapters of Gerry and Knight and dive in directly to chapter 7, going back to the early chapters only if needed.
I would suggest the very informative review "Squeezed Light", by A. I. Lvosky (arXiv:1401.4118v2 [quant-ph] 28 Jul 2016), and "A pedestrian introduction to coherent and squeezed states", by Bijan Bagchi, Rupamanjari Ghosh and Avinash Khare (arXiv:2004.08829v4 [quant-ph] 6 Jul 2020) who also give great explanation about two-mode squeezing.