Fundamental Models in the Light–Matter Interaction: Quantum Phase Transitions and the Polaron Picture

Abstract

The light–matter interaction not only is ubiquitous in nature but also can be simulated in various artificial systems. Besides the tunability of artificial quantum systems, the experimental access to the ultra‐strong and even deep‐strong couplings has brought a regime with novel phenomenology. Theoretically the finding of the integrability for the quantum Rabi model (QRM) has attracted tremendous attention to the study of the QRM and its extensions which are fundamental models of the light–matter interaction. With the continuing enhancements of coupling strengths, a most fascinating phenomenon of these light–matter models is that they can exhibit few‐body quantum phase transitions (QPTs), while a full understanding of these QPTs is a challenge. The polaron picture is a method capable of analyzing these fundamental models in the entire coupling regime and extracting the essential physics behind the QPTs. A review of its extensive applications on the fundamental light–matter models is presented, with discussions on the phase diagrams and QPT‐related features. The universality of critical exponent of the anisotropic QRM as well as the possibility of QPTs in A2 terms are also addressed.

Hidden Single‐Qubit Topological Phase Transition without Gap Closing in Anisotropic Light‐Matter Interactions

“…After the afore-mentioned unconventional TPT in increasing the anisotropy from the QRM line, we also find a transition from phase squeezing (PS) to amplitude squeezing (AS) in the gapped phase. We can apply the variational polaron picture [5,24,46] to facilitate the analysis for such a PS/AS transition. The terminologies of polaron and antipolaron were first used in light-matter interactions based on coherent-state expansion for each wave packet.…”

“…So far we have analyzed by standing in the positive-𝜆 regime, the analysis is similar for the negative-𝜆 regime by the mapping to momentum space in Equation (5). A panorama over full parameter space can be obtained by the phase diagram of ⟨a † a † ⟩ = (⟨ x2 ⟩ − ⟨p 2 ⟩)∕2 multiplied by the parity P, as shown in Figure 6a,c.…”

“…Such a coupling‐driven displacement leads to a composite state of the qubit and induced photons, analogous to a polaron in condensed matter that is a composite state of an electron and phonons induced from deviation of the local atom from its lattice site. [ 5,24 ] In such a picture the transition in the QRM is essentially a splitting of wave packets represented by polarons and antipolarons displaced in directions respectively the same as and opposite to the potential. [ 24 ] A final wave‐packet position does not fully follow the displacement of the potential, but has a renormalized displacement at $$\zeta g_{z}^{\prime }$$ instead.…”

“…[27,31,34] One of the most fascinating phenomena in enhancing the coupling is the possible onset of few-body phase transitions. [5,[23][24][25]31,33,34,65] When phase transitions traditionally lie in the thermodynamic limit in condensed matter, the QRM possesses a few-body quantum phase transition [23][24][25] in the low-frequency limit, that is, 𝜔∕Ω → 0 relatively to the atomic level splitting Ω, which replaces the thermodynamic limit in a finite system. [31,43] On the other hand, it was also suggested that whether the transition should be termed quantum or not is a matter of taste by considering the negligible quantum fluctuations in the photon vacuum state.…”

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

“…Indeed, under standard assumptions, critical protocols can achieve the Heisenberg scaling—a quadratic growth of parameter-estimation precision—both with respect to the number of probes and with respect to the measurement time. Furthermore, a recent theoretical work [ 15 ] demonstrated that the optimal limits of precision can be achieved using finite-component phase transitions [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 ], which are criticalities that take place in quantum optical systems where the thermodynamic limit is replaced by a scaling of the system parameters [ 20 , 29 , 30 , 31 , 32 , 33 , 34 ]. Critical quantum sensors can then also be implemented with controllable small-scale quantum devices, without requiring the control of complex many-body systems.…”