Light-Induced Coherence in an Atom-Cavity System

We demonstrate a light-induced formation of coherence in a cold atomic gas system that utilizes the suppression of a competing density wave (DW) order. The condensed atoms are placed in an optical cavity and pumped by an external optical standing wave, which induces a long-range interaction mediated by photon scattering and a resulting DW order above a critical pump strength. We show that the light-induced temporal modulation of the pump wave can suppress this DW order and restore coherence. This establishes a foundational principle of dynamical control of competing orders analogous to a hypothesized mechanism for light-induced superconductivity in high-$T_c$ cuprates.

Figure 1

Bose-Einstein condensed rubidium atoms are held inside an optical cavity by a magnetic trap. An optical standing wave with frequency ${\omega }_p$ and strength ${ϵ}_p$ (red arrows) pumps the atoms. A second weaker optical standing wave at frequency ${\omega }_m={\omega }_p+{\delta }_m$ and strength ${ϵ}_m$ (blue arrows) produces an amplitude modulation of the pump wave at the difference frequency ${\delta }_m/2\pi$.

Figure 2

(a) Time sequence for pump and modulation beams. (b) The intracavity photon number $N_p$ is recorded versus time for three final values of the modulation strength $M$. (c) The intracavity photon number $N_p$ is plotted versus the final modulation strength $M$ and time, with the pump strength and the modulation strength ramped up according to (a). (d) Momentum spectra recorded after 2 ms of modulation according to the traces shown in (b). The dashed gray, white, and red circles illustrate the locations of the incoherent fraction, the occupation of the BEC mode $(0,0)\hslash k$, and the atoms in the $(1,1)\hslash k$ momentum mode, respectively (see text). (e) The number of atoms $N_{00}$ in the BEC mode (black squares) and the number $N_{\mathrm{inc}}$ of incoherent atoms. (f) The fraction $F_1$ of atoms in the first excited momentum modes at $(\pm 1,\pm 1)\hslash k$ (open circles) and the intracavity photon number (red squares) after 2 ms of modulation are plotted versus $M$. Because we do not make assumptions about possible systematic contributions, the error bars show the standard deviations for typically 100 repeated individual measurements. The number of atoms initially prepared in the BEC was $N_a=6.5\times {10}^4$, and the modulation frequency was ${\delta }_m/2\pi =50\mathrm{kHz}$.

Figure 3

(a) Time sequence for pump and modulation beams with ${\delta }_{\mathrm{eff}}/2\pi =-38\mathrm{kHz}$ and ${\delta }_m/2\pi =50\mathrm{kHz}$. In (b)–(e) MF (red traces) and TW calculations (black traces) are superimposed. (b) shows the intracavity photon number $N_p$. (c)–(e) show the corresponding relative populations of the zero momentum BEC mode (c), the first excited $(1,1)\hslash k$ mode (d), and the $(2,0)\hslash k$ mode (e). (f) shows the condensate fraction $F_c$ defined as the largest eigenvalue of the single-particle density matrix (see text). For all plots (a)–(f) the modulation strength is $M=0.4$. (g) and (h), MF calculations of the population of the BEC mode [black squares in (g)], the fraction $F_1$ of atoms in the $(\pm 1,\pm 1)\hslash k$ modes [blue triangles in (f)], and the intracavity photon number $N_p$ [(red squares in (h)] after 10 ms of modulation. The white disks compare calculations based on a TW approximation.