Superradiance Lattice

Abstract

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. [31] in two-dimensional lattices. Nevertheless, the observation of these phenomena remains challenging. Novel types of lattices [32][33][34][35] provide new testing grounds for the rich physics mentioned above.In this Letter, we introduce the concept of the superradiance lattice (SL), a lattice in momentum space [36]. The conventional lattice has discrete translational symmetry in position space. The tight-binding model which allows electron hopping between nearest neighbours is diagonal in momentum space. The crystal momentum k is a good quantum number labelling each eigenstate. On the other hand, the SL corresponds to a tight-binding model in momentum space which has good quantum numbers r in position space. The dynamics of r in an SL is analogous to the dynamics of k in a real space lattice. We show that Bloch oscillations, Wannier Stark ladders and Bloch band collapsing can be observed in an SL based on electromagnetically induced transparency (EIT). The two-dimensional SL provides a tunable quantum optics model for Dirac physics in graphene.

Quantum scattering theory of a single-photon Fock state in three-dimensional spaces

“…These waves induce the radiative interactions among the TLSs. They are responsible for collective effects, such as the superradiant spontaneous emission [34][35][36][37][38].…”

Electromagnetically induced transparency with superradiant and subradiant states

“…Eq. (3) can be solved with the Floquet theorem [32,33] and the absorption is proportional to Imρ [0] +gg , the imaginary part of the zero frequency coherence (see Appendix C).…”

High-frequency light reflector via low-frequency light control

“…The physics of the reflection can be understood from the picture of the superradiance lattice [17], as shown in Fig. 5.…”

“…5. The probe field creates excitation |b kp from the ground state |G ≡ |c 1 , c 2 , ..., c N in a one-dimensional momentum space tight-binding lattice where the lattice sites are timed Dicke states connected by the two coupling fields Ω 1 and Ω 2 [17]. The excitation propagates along the lattice to |b −kp which is strongly coupled to the ground state |G due to the superradiance √ N enhancement, and consequently generates the reflected field.…”

“…This linear dependence between the order of the nonlinearity and the field strength will be confirmed in the following for both single photons and continuous wave probe fields. The hidden physics of this nonlinearity is envisioned and explained with a momentum space Fano lattice [16], the superradiance lattice [17]. Single photons-We first apply the idea to the backward retrieval of a single photon from a medium prepared at time t = 0 in the timed Dicke state of an ensemble of N atoms by absorption of a single probe photon,…”