Quantum dynamics in photonic crystals

Employing a recently developed method that is numerically accurate within a model space simulating the real-time dynamics of few-body systems interacting with macroscopic environmental quantum fields, we analyze the full dynamics of an atomic system coupled to a continuum light field with a gapped spectral density. This is a situation encountered, for example, in the radiation field in a photonic crystal, whose analysis has so far been confined to limiting cases due to the lack of suitable numerical techniques. We show that both atomic population and coherence dynamics can drastically deviate from the results predicted when using the rotating-wave approximation, particularly in the strong-coupling regime. Experimental conditions required to observe these corrections are also discussed.

Figure 1

Comparison between t-DMRG (solid black), Heisenberg (dashed red), and Piessens (blue dots) solutions for ${\left|A\left(t\right)\right|}^2$, for the parameters $\alpha =1$, ${\omega }_0=100$, gap-edge frequency ${\omega }_b=5$, ${\omega }_c=800$, and $\Delta =1$. Time is in units of $1/{\alpha }^2$.

Figure 2

Excited-state population dynamics for the RWA (filled plot markers) and full Hamiltonian (empty plot markers). For these data $\alpha =1$, ${\omega }_0=100$, ${\omega }_b=5$, and ${\omega }_c=800$. Time is in units of $1/{\alpha }^2$.

Figure 3

Stationary-state atomic population for the RWA (red squares) and the complete Hamiltonian (blue dots) as a function of $\Delta$. The initial state is a fully excited system, and we have used $\alpha =1$, ${\omega }_0=100$, ${\omega }_b=5$, and ${\omega }_c=800$.

Figure 4

Time evolution of the absolute values of the coherence $\langle {\sigma }_x\left(t\right)\rangle$ for RWA (filled plot markers) and the full Hamiltonian (empty plot markers). For these data $\alpha =1$, ${\omega }_0=100$, ${\omega }_b=5$, and ${\omega }_c=800$. Time is in units of $1/{\alpha }^2$.

Figure 5

Frequency of coherence oscillations using the RWA (red squares) and the complete Hamiltonian (blue dots) as a function of $\Delta$ for an initially prepared superposition of ground and excited states. Parameters are $\alpha =1$, ${\omega }_0=100$, ${\omega }_b=5$, and ${\omega }_c=800$.