Quantum phase transitions and cat states in cavity-coupled quantum dots

We study double quantum dots coupled to a quasistatic cavity mode with high mode-volume compression allowing for strong light-matter coupling. Besides the cavity-mediated interaction, electrons in different double quantum dots interact with each other via dipole-dipole (Coulomb) interaction. There is a first-order cavityinduced ferroelectric quantum phase transition when the attractive dipolar interaction is smaller than the critical value defined by the energy splitting in DQDs and a smooth transition, otherwise. We show that, in the smooth transition region, both the ground and the first excited states of an array of double quantum dots are cat states. Such states are actively discussed as high-fidelity qubits for quantum computing, and thus our proposal provides a platform for semiconductor implementation of such qubits. We also calculate gauge-invariant observables such as the net dipole moment, the optical conductivity, and the absorption spectrum beyond the semiclassical approximation. The results are robust against cavity losses and variations of system parameters.