Controlling correlations of a polaritonic Luttinger liquid by engineered cross-Kerr nonlinearity

TL;DR

This paper investigates how engineered cross-Kerr nonlinearity in a superconducting circuit lattice influences the correlation properties of polaritons, effectively controlling the Luttinger liquid behavior and correlation decay.

Contribution

It introduces a method to control polariton correlations via cross-Kerr nonlinearity, deriving an effective Luttinger liquid model from a multiconnected Jaynes--Cummings lattice.

Findings

Cross-Kerr nonlinearity reduces compressibility of the polariton mode.

Enhancement of the Luttinger parameter $K_{+}$ leads to slower decay of correlations.

Effective single-component Luttinger liquid description is valid in certain regimes.

Abstract

We study correlation properties of polaritons at zero temperature in a multiconnected Jaynes--Cummings (MCJC) lattice on a superconducting circuit quantum electrodynamics platform with engineered cross-Kerr nonlinearity that mimics attractive nearest-neighbour interaction. A multi-connected Jaynes--Cummings lattice is a one-dimensional lattice constructed from alternating qubits and resonators with different left and right couplings. The nearest-neighbour interaction or cross-Kerr coupling is implemented dispersively through ladder-type qutrits between each nearest neighboring pair of resonator modes. Projecting onto the lower-polaritonic manifold, we derive an extended two-mode (bipartite) Bose--Hubbard-like model featuring on-site and attractive nearest-neighbor interactions. Employing a continuum bosonization approach, we express the Hamiltonian in terms of symmetric ($+$) and antisymmetric ($-$) collective modes. In the regime where the ($-$) sector acquires a finite gap, one can reduce the system to an effective single-component Luttinger liquid model for the $+$ sector. The cross-Kerr term reduces the compressibility of the ($+$) mode, thereby enhancing the corresponding Luttinger parameter $K_{+}$, resulting in the slower algebraic decay of single-particle correlations, $G(x)\propto|x|^{-1/(4K_{+})}$.