Time-resolved interplay between superradiant and subradiant states in superradiance lattices of Bose-Einstein condensates

Measuring Zak phase in room-temperature atoms

“…A weak probe field propagating in direction couples the ground state to the excited state . The excited state is also coupled to a metastable state by two strong counter-propagating light fields, forming a 1D bipartite superradiance lattice 23 – 25 . The absorption spectra of the probe field are used to obtain the Zak phases of the superradiance lattices.…”

“…1e ). is the tight-binding Hamiltonian of the RM superradiance lattices 23 – 25 (we set and see Materials and Methods): where and are the Rabi frequencies of the co-propagating and counter-propagating coupling fields, and with being the coupling field frequency and being the transition frequency between states and . Here is the creation operator of the timed-Dicke state 26 with wave vector ( is an integer) and ( ) being the probe (coupling) field wave vector amplitude, the index labels the th atom at the position , is the total number of atoms within the velocity range where satisfies the Maxwell distribution and is the decay rate of the state (we neglect the decay of the hyperfine ground state ).…”

“…We reconstruct the Zak phases of the Rice-Mele (RM) model through the anti-crossing between the WSLs in a 1D tight-binding lattice 23 – 25 of timed Dicke states 26 : i.e., single-photon collective excitations of an ensemble of atoms (here is the position of the th atom with the ground state and an excited state ), which can be created by coherent laser fields that transfer momentum to the atoms. We introduce multiple laser fields to couple to another atomic state such that timed Dicke states with discrete values form a momentum-space tight-binding lattice, which is coined the superradiance lattice.…”