Enhancing the optical cross section of quantum antenna

The classical radio-frequency antenna theory indicates that large cross sections can be realized through directional radiation. In this paper, a similar principle is applied in quantum systems, in which quantum antennas, constructed by a cluster of quantum two-level systems, explore the collective excitation of two-level systems to realize large directivity. Both the optical cross section and the coherent time can be dramatically enhanced in free space, far exceeding the case of a single two-level system.

Figure 1

(a) A classical dipole antenna made of metallic rods. (b) A Yagi-Uda antenna with three elements. The cross section increases as a result of the increased directivity of the radiation pattern. (c) The simplest quantum antenna is a TLS in the free space. (d) Three TLSs form an antenna with enhanced directivity and cross section.

Figure 2

The cross section of the photon incident angles with (a) $\theta =0$ and (b) $\theta =90$. (c) The cross-section spectra for incident angles from 0 to 90. (d) The cross section $\sigma \left(\theta ,\varphi \right)$ and directivities of three collective modes. The central column shows the complex excitation amplitudes of the constituent TLSs. The relative magnitude and phase of the complex excitation amplitudes $e_i$ are represented by the length and the direction of the blue arrows.

Figure 3

(a) The cross-section spectra for different inter-TLS spacing $d$. The incident angle is $\theta =0$. The values in the dashed box are multiplied by 20 times for easy visualization. (b) The cross sections $\sigma \left(\theta ,\varphi \right)$ for inter-TLS distances of $0.2\lambda$ and $4\lambda$, respectively. (c) The maximum cross section ${\sigma }_{\max }$ at different inter-TLS spacing $d$. It converges to the incoherent addition of $4.5{\sigma }_0$ when $d\gg \lambda$. (d) The lifetime of mode C as a function of the inter-TLS distance $d$.

Figure 4

(a) The maximum cross section of a quantum antenna increases with the number of TLSs. The insets show $\sigma \left(\theta ,\varphi \right)$ for 4-TLS and 5-TLS antennas (marked with red dots), respectively. (b) The maximum coherent time also increases with $N$, reaching over 1000 times of natural lifetime ${\tau }_0$.

Figure 5

(a) Schematic of a cluster of TLSs in free space. (b) Distribution of channels in the ${\mathit{k}}_{xy}$ space. The channels are discretized by $\mathrm{\Delta }k=2\pi /L$. The allowed channels are located within the circle with a radius of $k_0$. (c) Real-space bosonic creation operators. $c_{F/B,n}^{†}\left(\xi \right)$ creates a forward- or backward-moving photon at the location $\xi$ in the $n$ th channel. (d) Spatial single-photon wave functions in the $n$ th channel. The coefficients are the amplitudes of forward (green line) and backward (purple line) directions between the $m$ th and ($m$ +1)th TLSs in the $n\mathrm{th}$ channel, respectively.

Figure 6

The scattering cross section calculated with (red lines) and without (black solid lines) rotation-wave approximation for light incident from two different directions.

Figure 7

The TLSs arrangement along the $z$ axis and the dipole moment $\mathit{d}$ along the $x$ axis. ${\mathit{e}}_k$ is the polarization of the incident direction and is perpendicular to the incident direction. $\theta$ and $\phi$ are the polar and azimuthal angles of the incident photon.