Remote Individual Addressing of Quantum Emitters with Chirped Pulses

We propose to use chirped pulses propagating near a band gap to remotely address quantum emitters. We introduce a particular family of chirped pulses that dynamically self-compress to subwavelength spot sizes during their evolution in a medium with a quadratic dispersion relation. We analytically describe how the compression distance and width of the pulse can be tuned through its initial parameters. We show that the interaction of such pulses with a quantum emitter is highly sensitive to its position due to effective Landau-Zener processes induced by the pulse chirping. Our results propose pulse engineering as a powerful control and probing tool in the field of quantum emitters coupled to structured reservoirs.

Figure 1

(a) Quantum emitters embedded in an electromagnetic waveguide. A time-dependent driving applied at the origin of the coordinate system creates a chirped self-compressing electromagnetic pulse. At a time $t_f$ the pulse becomes compressed at a distance $d_f$ from the origin, reaching a minimum width ${\sigma }_f$. Inset: Quadratic dispersion relation of the waveguide. The distribution of the pulse wave number along $z$ is centered around $k_0=2\pi /{\lambda }_0$. (b) Spatial profile of the electric field of the chirped pulse at different times. The electric field is normalized by its maximum value $E_{\max }={\max }_{d,t}E(d,t)$. (c) Mean frequency $\overline{\omega }$ and standard deviation $S_{\omega }$ (defined in the text) of the electric field pulse as a function of the compression width ${\sigma }_f$. Parameters used: ${\omega }_0/{\omega }_c=1.005$, $d_f/{\lambda }_0=7.5$, ${\sigma }_f/{\lambda }_0=0.21$, $\varphi =0$.

Figure 2

(a) Excited state population of a qubit of frequency ${\omega }_q={\omega }_0$ as a function of time for different positions of the qubit. We choose ${\omega }_0/{\omega }_c=1.005$, $\mathrm{\Gamma }/{\omega }_0={10}^{-6}$, $d_f/{\lambda }_0=18$, ${\sigma }_f/{\lambda }_0=0.35$, ${\mathrm{\Omega }}_0/{\omega }_c=0.038$, and $\varphi =0$. (b) Ground-state population of the qubit as a function of the on-axis distance $d$ from the origin, for different values of $d_f$ and ${\sigma }_f$ (see inset) and at a time $\tau (d)=2t_f+\eta d/v$ (see main text). For (b) we fix ${\omega }_0/{\omega }_c=1.005$ and ${\mathrm{\Omega }}_0/{\omega }_c=0.038$ (${\mathrm{\Omega }}_0/{\omega }_c=0.030$) for the curves with ${\sigma }_f/{\lambda }_0=0.35$ (${\sigma }_f/{\lambda }_0=0.5$).

Figure 3

Population of the internal states of an oscillator with anharmonicity $\alpha /{\omega }_q=-0.05$ interacting with the pulse as a function of the distance $d$ to the center of the waveguide, at a time $\tau (d)=2t_f+\eta d/v$, such that $t_f\ll \tau (d)\ll {\mathrm{\Gamma }}^{-1}$ with $\mathrm{\Gamma }/{\omega }_q={10}^{-6}$. Parameters used: ${\omega }_q/{\omega }_c={\omega }_0/{\omega }_c=1.005$, $d_f/{\lambda }_0=18$, ${\sigma }_f/{\lambda }_0=0.35$, ${\mathrm{\Omega }}_0/{\omega }_c=0.038$, $\varphi =0$.