Contrary to the long-held belief that phase transitions occur only in the thermodynamic limit of infinite number of constituents, we have recently discovered that finite-component systems of coupled spins and bosons may exhibit all the hallmarks of the quantum phase transition [1,2] in a closed system and the dissipative phase transition in an open quantum system . In this talk, I will introduce the notion of finite-component system phase transitions in both closed and open quantum systems and show how the simultaneously large spin-boson coupling strength and detuning lead to the thermodynamic limit of infinite excitations. I will focus on a few paradigmatic models in quantum optics such as the quantum Rabi model and the Jaynes-Cummings model and its open-system versions. A theoretical proposal for a trapped-ion experiment to realize the quantum phase transition of the quantum Rabi model  will be discussed; moreover, how the motional cooling of an ion could achieve a controlled emergence of the dissipative phase transition from the quantum phase transition .
 M.-J. Hwang, R. Puebla, and M. B. Plenio, Phys. Rev. Lett. 115, 180404 (2015).
 M.-J. Hwang and M. B. Plenio, Phys. Rev. Lett. 117, 123602 (2016).
 M.-J. Hwang, P. Rabl, and M. B. Plenio, arXiv:1708.08175 (2017)
 R. Puebla, M.-J. Hwang, J. Casanova, and M. B. Plenio, Phys. Rev. Lett. 118, 073001 (2017).