An ensemble of N noninteracting spins being in thermal equilibrium and coupled to the resonant mode of a lossless microwave cavity is studied as the function of the spin temperature τ. Near τ = 0 the system is known to be in a coupled spin-photon state that manifests itself by the splitting of the cavity mode (vacuum Rabi splitting). The cavity emission spectrum is simulated for arbitrary τ. A critical temperature τ C = ω S √N/2, where ω S is the spin excitation energy, is related to the destruction of the strong coupling regime as a consequence of thermal excitations arising within the spin ensemble.
Abstract The strong coupling regime is essential for efficient transfer of excitations between states in different quantum systems on timescales shorter than their lifetimes. The coupling of single spins to microwave photons is very weak but can be enhanced by increasing the local density of states by reducing the magnetic mode volume of the cavity. In practice, it is difficult to achieve both small cavity mode volume and low cavity decay rate, so superconducting metals are often employed at cryogenic temperatures. For an ensembles of N spins, the spin–photon coupling can be enhanced by N N through collective spin excitations known as Dicke states. For sufficiently large N the collective spin–photon coupling can exceed both the spin decoherence and cavity decay rates, making the strong-coupling regime accessible. Here we demonstrate strong coupling and cavity quantum electrodynamics in a solid-state system at room-temperature. We generate an inverted spin-ensemble with N ~ 1015 by photo-exciting pentacene molecules into spin-triplet states with spin dephasing time T2∗∼3 T 2 * ~ 3 μs. When coupled to a 1.45 GHz TE01δ mode supported by a high Purcell factor strontium titanate dielectric cavity ( Vm∼0.25 V m ~ 0.25 cm3, Q ~ 8,500), we observe Rabi oscillations in the microwave emission from collective Dicke states and a 1.8 MHz normal-mode splitting of the resultant collective spin–photon polariton. We also observe a cavity protection effect at the onset of the strong-coupling regime which decreases the polariton decay rate as the collective coupling increases.
Magnetic resonance can be used as a testbed for observing, demonstrating, and studying fundamental concepts of quantum cavity interaction with a two-level system at the microwave regime. Such experiments are mostly carried out at low cryogenic temperatures with spin systems that are embedded in a high-quality (Q-factor) superconducting cavity. For example, recent work has shown that under such conditions, and in a regime of high cooperativity and strong collective coupling between an electron spin system and a microwave cavity, multiple spin echoes are observed. These echoes have been analysed as signatures of coherent quantum effects; namely, the photons in the cavity can excite the spin system, which in turn can excite the cavity itself and so on. In this work we show that the use of a unique tailor-made moderate Q cavity in conjunction with diamond crystals having large concentrations of nitrogen vacancy (NV) centers makes it possible to observe such non-linear quantum phenomenon, even at room temperature. A key requirement of our experiments is that the spin system’s thermodynamic (rather than the physical) temperature is cooled to a few K, while high cooperativity and/or strong coupling are not a necessary prerequisite for such observations. The observation of meaningful microwave cavity quantum effects even at room temperature could lead to applications such as quantum memories and quantum sensing.