Experimental Observation of One-Dimensional Superradiance Lattices in Ultracold Atoms

We measure the superradiant emission in a one-dimensional (1D) superradiance lattice (SL) in ultracold atoms. Resonantly excited to a superradiant state, the atoms are further coupled to other collectively excited states, which form a 1D SL. The directional emission of one of the superradiant excited states in the 1D SL is measured. The emission spectra depend on the band structure, which can be controlled by the frequency and intensity of the coupling laser fields. This work provides a platform for investigating the collective Lamb shift of resonantly excited superradiant states in Bose-Einstein condensates and paves the way for realizing higher dimensional superradiance lattices.

Figure 1

Band structure of the superradiance lattice in BEC. (a) In the superradiance lattice, the pump laser populates $|e_0⟩$, which is a superradiant state and coupled to other collective states. Among these states, only $|e_1⟩$ is superradiantly coupled to the ground states and its directional emission is measured. (b) The atoms dressed by the standing wave have different energies of their eigenstates $|\pm ⟩=(|e⟩\pm |m⟩)/\sqrt{2}$ at different positions. The excitation probabilities of the BEC atoms at different positions is plotted for two different pump frequencies. The total excitation probabilities are proportional to the density of states of a tight-binding model of collectively excited states.

Figure 2

Experimental configuration of the 1D superradiance lattice in BEC. (a) Energy diagram of the $5^2{S}_{1/2}-5^2{P}_{1/2}$ transition of ${}^{87}\mathrm{Rb}$. (b) The experimental geometry and the laser configuration. The three planes in the figure are the plane of the two coupling beams, the plane of the probe-superradiant beams, and the equal intensity plane of the coupling beams. (c) EIT spectrum by measuring the remaining atoms with only one coupling laser. The power of each coupling laser is $200\mu \mathrm{W}$ and on resonance (${\mathrm{\Delta }}_c=0$). The power of the probe laser is $25\mu \mathrm{W}$. (d) Intensity of the superradiant scattering with a pair of coupling lasers. Each of the coupling lasers is $200\mu \mathrm{W}$ and the other parameters are the same as in (c). The data points are simply connected.

Figure 3

Superradiant emission spectra for different intensities and detunings of the coupling laser. (a1)–(a4) The intensity of the coupling laser are (a1) 50, (a2) 100, (a3) 200, and (a4) $400\mu \mathrm{W}$. The coupling laser is on resonance and the power of the probe light is $25\mu \mathrm{W}$. (b1)–(b4). The detunings of the coupling laser are (b1) ${\mathrm{\Delta }}_c=-10$, (b2) 0, (b3) 10, and (b4) 20 MHz. The powers of each coupling laser and the probe laser are 200 and $25\mu \mathrm{W}$. The data points are simply connected with black lines and the red curves are the theoretical fitting.

Figure 4

Superradiant emission spectra for different incident angles of the incident probe beam. The deviation of the angle of the probe beam from $\varphi =132°$ are (a) $-0.9°$, (b) $-0.3°$, (c) 0°, (d) 0.3°, and (e) 0.6°. The powers of each coupling laser is $200\mu \mathrm{W}$. The power of the probe light is $25\mu \mathrm{W}$. ${\mathrm{\Delta }}_c=0$. The data points are simply connected with black lines and the red curve is the theoretical fitting.