Cooperativity and Ultrastrong Coupling in Terahertz Metasurfaces

The interaction of cavity photons with an emitter material is usually characterized by two standard parameters: cooperativity (C), which describes the degree of coherence of the coupling, and the normalized coupling strength (η). Both are functions of the coupling rate which itself is proportional to the dipole moment. The large dipole moment is a key factor in strong-light matter coupling. We demonstrate that the coupling rate of a localized surface plasmon resonance (LSPR) ensemble with the first-order surface lattice resonance (SLR) exhibit a square-root dependence on the density of the metasurface (MS) unit cells (N atoms). Therefore there is a collective interaction of an ensemble of dipoles, also known as Dicke cooperativity, at ambient temperature.<br/>The MS is based on an array of silver (Ag) four-gap split-ring resonators (SRRs) deposited on a 50.8-µm-thick flexible polyimide substrate. Upon increasing the lattice constant of the array from 275 μm to 400 μm and keeping the remaining geometrical parameters constant, the measured transmission spectra exhibit a transparency window between the two transmission minima. This behavior, known as lattice-induced transparency, is analogous to vacuum-Rabi splitting which leads to a quantum level repulsion or an anti-crossing effect, a clear signature of strong coupling. As the capacitive split gap is decreased from 35 µm to 5 nm, a blueshift and detuning of the polaritonic curves occurs, which is accompanied by a gradual enhancement of the normalized coupling strength. Thus, increasing the capacitance of the metamaterial resonator increases the Rabi frequency.<br/>In this artificial matter-matter system, we simultaneously achieve high cooperativity of C = 37 and a normalized coupling strength of η= 0.15. These values indicate that the system reaches the ultrastrong coupling (USC) regime. This also shows that the advantage of using MS-based plasmonic systems is the ability to localize strong fields within small split-gaps when excited by an incident light and dramatically enhance the nonlinear response. The ground state of a system in the USC regime is a highly entangled two-mode squeezed state, which can be used for efficient protocols of quantum state generation, ultrafast two qubit quantum gates, protected quantum computation, and quantum memories with dramatically enhanced coherence times. This room-temperature technology serves as a convenient quantum emulator of the dynamics of a qubit with a giant dipole moment coherently driven by a single bosonic field.