All-Electromagnetic Control of Broadband Quantum Excitations Using Gradient Photon Echoes

A broadband photon echo effect in a three level $\mathrm{\Lambda }$-type system interacting with two laser fields is investigated theoretically. Inspired by the emerging field of nuclear quantum optics which typically deals with very narrow resonances, we consider broadband probe pulses that couple to the system in the presence of an inhomogeneous control field. We show that such a setup provides an all-electromagnetic-field solution to implement high bandwidth photon echoes, which are easy to control, store and shape on a short time scale and, therefore, may speed up future photonic information processing. The time compression of the echo signal and possible applications for quantum memories are discussed.

Figure 1

(a) $\mathrm{\Lambda }$-type three level system. The blue (red) arrow depicts the control (probe) laser field which drives the transition $|2⟩\to |3⟩$ ($|1⟩\to |3⟩$). (b) All-electromagnetic photon echo setup. Blue translucent Gaussian beam depicts the spatial profile of the control field. The control Rabi frequency ${\mathrm{\Omega }}_c$ is displayed by the blue raising curve on the side of the green cube. The array of short green arrows shows the position-dependent evolution of ${\rho }_{21}$ along the $z$ axis. (c) Position-dependent ATS. The energy splitting becomes larger due to the focusing of the control field, as shown by the projection of the ATS at different positions $z$ on the vertical plane. The red Gaussian curve depicts the Fourier transform of a broadband incident probe pulse.

Figure 2

(a) Probe spectra considering Gaussian control fields with different parameters $\beta$ (see text). Green solid, red dashed and blue dotted lines illustrate the scattered probe signals for $\beta =1$, 2, and 4, respectively. (b) Photon echo effect. The echoes of the scattered probe fields at around $3.6\mu \tau$ are induced by adding a $\pi$ phase shift to the control field at around $1.8\mu \tau$. All time spectra are presented in units of the lifetime $\tau$ of the excited state $|3⟩$, e.g., $\mu \tau ={10}^{-6}\tau$.

Figure 3

Modulation of probe echo signal on the time scale of (a) $\mu \tau$ and (b) $0.1\tau$. Blue dashed-dotted lines depict control and red solid lines probe fields, respectively. The duration of the probe echo signals is proportional to $|{\mathrm{\Omega }}_c{|}^{-1}$. Further parameters are (a) $\xi ={10}^6$ and $\beta =4$ and (b) $\xi =10$ and $\beta =4\times {10}^{-5}$, where the values of $\beta$ correspond to control field unity on the axis.

Figure 4

(a) Contour plot of the storage efficiency $R(\xi ,\zeta )$ for a linear control field intensity ${\mathrm{\Omega }}_c(z)=\zeta \mathrm{\Gamma }z/L$. Yellow cross indicates the parameter set $(\xi ,\zeta )=(2000,1000)$ used in (b) and (c) to demonstrate storage, retrieval and generation of a broadband pulse via photon echo. (b) around 80% of the incident probe (green dashed line) with a duration of $\kappa =5\times {10}^{-3}\tau$ are stored as target quantum coherence. By switching ${\mathrm{\Omega }}_c\to -{\mathrm{\Omega }}_c$ at $0.16\tau$, an echo signal (red solid line) with a duration of $5\times {10}^{-3}\tau$ is emitted. (c) switching ${\mathrm{\Omega }}_c\to -2{\mathrm{\Omega }}_c$ (blue dashed-dotted line) releases a shorter echo signal with a duration of $2.5\times {10}^{-3}\tau$. Red arrows on the abscissa and blue arrows on the ordinate indicate the echo peak times and the control field intensity, respectively.