Superradiance Lattice

We show that the timed Dicke states of a collection of three-level atoms can form a tight-binding lattice in momentum space. This lattice, coined the superradiance lattice (SL), can be constructed based on electromagnetically induced transparency (EIT). For a one-dimensional SL, we need the coupling field of the EIT system to be a standing wave. The detuning between the two components of the standing wave introduces an effective uniform force in momentum space. The quantum lattice dynamics, such as Bloch oscillations, Wannier-Stark ladders, Bloch band collapsing, and dynamic localization can be observed in the SL. The two-dimensional SL provides a flexible platform for Dirac physics in graphene. The SL can be extended to three and higher dimensions where no analogous real space lattices exist with new physics waiting to be explored.

Figure 1

(a) The real space configuration and the internal atomic states of a 1D bipartite SL in momentum space. An EM plane wave mode ${\mathbf{k}}_p$ collectively excites the transition from $|g⟩$ to $|e⟩$. The standing wave formed by modes ${\mathbf{k}}_1$ and ${\mathbf{k}}_2$ couples the transition between $|e⟩$ and $|m⟩$. (b) The 1D bipartite SL in momentum space. The red (blue) circles represent the $|m_{\mathbf{k}}⟩$ ($|e_{\mathbf{k}}⟩$) states. The solid (dashed) lines represent the interaction via mode ${\mathbf{k}}_1$ (${\mathbf{k}}_2$). The distance between the adjacent sites is $|{\mathbf{k}}_1|$ and the direction of ${\mathbf{k}}_1$ is defined to the right.

Figure 2

(a) The dispersion relation of a 1D SL. (b) The DOS of the SL (black solid) and the standing wave coupled EIT absorption spectrum (red dash). $\gamma =0.06{\mathrm{\Omega }}_1$, ${\gamma }^{\prime }=0$. Assuming that each eigenstate has a finite lifetime, the DOS is Lorentzian broadened with width $0.01{\epsilon }_{\max }$ to fit with the EIT absorption spectrum.

Figure 3

The absorption spectra of a 1D SL in an oscillating force. (a) Absorption spectra as a function of detuning ${\mathrm{\Delta }}_p$ and the amplitude-frequency ratio of the effective oscillating force $f$. ${\delta }_1={\delta }_2=0$. The band collapses at the Bessel function zeros $J_0(f)=0$ for $f=2.4$ and 5.5. (b) Absorption spectra for ${\delta }_1=-{\delta }_2={\nu }_d$. The band collapses at the Bessel function zeros $J_1(f)=0$ for $f=3.8$ and 7.0. The other parameters are ${\mathrm{\Omega }}_1={\mathrm{\Omega }}_2=6\gamma$, ${\nu }_d=12\gamma$, $\gamma =1$, and ${\gamma }^{\prime }=0.001$.

Figure 4

(a) The honeycomb structure of the 2D SL. Timed Dicke states with $|e⟩$ and $|m⟩$ correspond to the two sublattices. The three bonds to the nearest neighbors correspond to the three coupling fields. (b) The DOS of graphene (blue dash) and the absorption spectrum of the 2D SL (red solid). The Rabi frequencies of the three coupling fields are all $20\gamma$. $\gamma =1$, ${\gamma }^{\prime }=0.001$. Correspondingly, the nearest-neighbor hopping coefficients are set as 20.