Steering Matter Wave Superradiance with an Ultranarrow-Band Optical Cavity

A superfluid atomic gas is prepared inside an optical resonator with an ultranarrow bandwidth on the order of the single photon recoil energy. When a monochromatic off-resonant laser beam irradiates the atoms, above a critical intensity the cavity emits superradiant light pulses with a duration on the order of its photon storage time. The atoms are collectively scattered into coherent superpositions of discrete momentum states, which can be precisely controlled by adjusting the cavity resonance frequency. With appropriate pulse sequences the entire atomic sample can be collectively accelerated or decelerated by multiples of two recoil momenta. The instability boundary for the onset of matter wave superradiance is recorded and its main features are explained by a mean field model.

Figure 1

(a) A pump beam with frequency ${\omega }_p$ impinges upon a BEC inside a high finesse resonator. (b) Relevant momentum states coupled to the BEC by scattering photons from the pump beam. The black tuples $(n,m)$ below the filled gray disks denote the momenta of the respective momentum class along the $y$ and $z$ directions in units of $\hslash k$. The single numbers above the disks indicate the kinetic energy of the respective momentum class in units of the recoil energy. The colored numbers upon the arrows indicate the kinetic energy transfer associated with the respective scattering process.

Figure 2

(a) The intracavity photon number $N_p$ is plotted versus the effective detuning ${\delta }_{\mathrm{eff}}/2\pi$ and the strength of the pump beam ${ϵ}_p/E_{\mathrm{rec}}$. The pump strength ${ϵ}_p$ is linearly increased from 0 to $3E_{\mathrm{rec}}$ in 2 ms. As explained in the text, the signal within the dashed white circle is due to trap dynamics. (b) The excitation rate ${\gamma }_{\mathrm{exc}}$ characterizing the exponential instability is plotted versus ${\delta }_{\mathrm{eff}}/2\pi$ and ${ϵ}_p/E_{\mathrm{rec}}$. (c) Mean field simulation of the intracavity photon number for the pump strength ramp applied in (a).

Figure 3

The blue solid traces show the intensity leaking out of the cavity, while the pump strength is ramped [as in Fig. 2] from 0 to $3E_{\mathrm{rec}}$ in 2 ms (as indicated by the red dashed traces) with negative detuning ${\delta }_{\mathrm{eff}}/2\pi =-12\mathrm{kHz}$ in (a) and positive detuning ${\delta }_{\mathrm{eff}}/2\pi =23\mathrm{kHz}$ in (b), respectively. The insets numbered 1 to 6 in (a) and 1 to 8 in (b) show (single shot) momentum spectra taken at times marked by the black arrows. The green dashed dotted lines indicate the noise floor of the light detection. For momentum spectra taken at late times in the pump strength ramp, the higher order momentum components are decelerated at the trap edge, which explains the compression of these spectra along the horizontal axis.

Figure 4

The blue solid traces shows the intracavity intensity for a sequence of two pump pulses with 350 and $160\mu \mathrm{s}$ durations and detunings ${\delta }_{\mathrm{eff}}/2\pi =-31\mathrm{kHz}$ and ${\delta }_{\mathrm{eff}}/2\pi =-16\mathrm{kHz}$ as indicated by the red dashed line. The pump strength was ${ϵ}_p=2.5E_{\mathrm{rec}}$ and ${ϵ}_p=2.9E_{\mathrm{rec}}$, respectively. The insets show momentum spectra at different times indicated by black arrows.