Collective theory for an interacting solid in a single-mode cavity

Abstract

We investigate the control of interacting matter through strong coupling to a single electromagnetic mode, such as the photon mode in a Fabry-Perot or split-ring cavity. For this purpose, we analyze the exact effective theory for the collective light-matter hybrid modes of a generic system of N transition dipoles within an interacting solid. The approach allows to predict properties of the coupled light-matter system from the nonlinear response functions of the uncoupled matter "outside the cavity". The limit of large N corresponds to a conventional macroscopic description based on the polarizability of matter. In this limit, the cavity does not affect the static ferroelectric response. Corrections, which are needed to understand finite size systems and to obtain the nonlinear light-matter response, can be obtained from the non-linear susceptibilities of the matter outside the cavity. The theory is benchmarked for the Dicke model, and for a quantum Ising model which serves as a minimal mean-field model for a quantum paraelectric material like SrTiO3.

Dynamical mean-field study of a photon-mediated ferroelectric phase transition

“…Apart from that, a conventional static mean-field approach, which often provides a reasonable starting point to get a qualitative understanding of a phase transition, does not capture the effect of the transverse field on the transition in the present case: The mean-field approximation replaces the induced interaction by a static and uniform self-consistent field; this mean field, however, vanishes, because the interactions between dipoles that are induced by the transverse field are zero in the static limit due to the positive-definite light-matter coupling. This fact also underlies the no-go theorems which exclude the condensation of hybrid light-matter modes due to the coupling to a single-cavity mode [25,31,35,36].…”

“…This value has been extracted from a fit of the mean-field result for the dielectric constant to experimental data for the paradigmatic quantum paraelectric material SrTiO 3 [34], which yields = 3.3 meV, α = 0.328 , and λ = 4024 (see Ref. [31]). For reference, the dielectric function obtained within the mean-field solution, which is given by (T ) = 1 + λ χ at 1−αχ at with the static susceptibility χ at = FIG.…”

“…In an extended solid, one would expect that the effect of light on the thermodynamic properties of matter arises not from the coupling to a single-cavity mode [31,32], but from a mode continuum. In a coplanar cavity setting, e.g., interactions within matter are mediated by photons with a continuous in-plane momentum.…”

Local Fluctuations in Cavity Control of Ferroelectricity

“…Recently, it has been argued that this may be done by instead shaping the environment of electromagnetic fluctuations through the use of optical cavities, resonators, and metamaterials [14,15]. Many systems have recently been proposed to be amenable to control in this way, including superconductors [6,[16][17][18], excitonic insulators [19], antiferromagnets [20,21], spin-liquids [22], quantum Hall fluids [23], and ferroelectrics [24][25][26][27][28], with a great deal more proposed to exhibit strong coupling between material and optical excitations [29]. Recent experiments on * jon.curtis.94@gmail.com the metal-insulator transition in 1T -TaS 2 even seem to have seen promising signatures of cavity control on the transition temperature [30].…”

“…Intrinsic SrTiO 3 is believed a quantum paraelectric (QPE) [36][37][38][39][40], lying right at the border of the ferroelectric phase, with long-range order suppressed by quantum fluctuations. Strain, chemical, and isotope substitution have all been shown to tip the system over the edge in to the ordered phase [37], and recently resonant optical excitation of the lattice [38,46] have also been shown to seemingly induce a transition into the ordered phase [47,48], making this a prime candidate for demonstrating cavity control over the phase diagram [24,25,27]. Previous theoretical investigations have largely been limited to single-mode, dipole coupling, and translationally invariant approximations.…”