In previous incoherent light-controlled schemes,^[21–27] bulk materials or optical resonators were excited by strong light to change their dielectric coefficients to control the transmission of weak signals, or multi-level atoms are strongly excited by the gate photons to initialize atoms in some special superposition to generate light controlling. These constructions are so complicated that a dedicated atomic energy structure is needed, and their nonlinearities are only generated by controlling light beams. Even in the recent coherent light-controlled systems,^[20,28–30] optical nonlinear performances only come from optical interference, while the atomic saturation nonlinearities induced by light are omitted.

In this work, we introduce light controlling into a simple two-level system, which will simplify the light-controlled setup greatly. Unlike previous work, this work takes into consideration both atomic nonlinearity and optical interference. As shown in our model, light scattering is dependent on total atomic nonlinear parameter x and optical interference. It suggests that a light can be manipulated not only by the intensity of another light, but also by its relative phase, which provides an approach to controlling strong light with weak light after careful design.

For simplicity, we restrict our discussion in the resonant case by setting Δ = 0 and fixing k₁ + k₂ = 8 to present the strong coupling throughout this work, and examine the scattering property of port 2 without loss of generality. In this case, r-component and t-component interfere destructively or constructively when b_in and c_in are in-phase or anti-phase, respectively. Coupling strength is normalized by setting γ_at ≡ 1 and all of the light intensities are normalized by the nonlinear coherent perfect absorption intensity I_ncpa = k₁ (1 − 1/P²)/8.

We first show the reflected property controlled by a weak coherent in-phase light. The difference between reflected light beams with and without a controlling light b_in is shown in Fig. 2(a), where reflected output intensity I_cout = |c_out|² increases with the increase of input intensity I_cin constantly when controlling light does not exist (I_bin = 0), while it drops to zero followed by a sustaining increase to match the case of I_bin = 0 when b_in exists (I_bin = 1). The reflected light shows an evident difference when controlling light is turned on. To explain such a difference, atomic saturation nonlinear factors (x, x₁, x₂, and x_coh) are also plotted in Fig. 2(b). Atomic nonlinearity only comes from I_cin when I_bin does not exist (x = x₂), while it is strengthened when I_bin exists (x = x₁ + x₂ + x_coh) since x_coh > 0.

Fig. 2.

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	Fig. 2. Optically controllable reflection by in-phase controlling light in symmetrical coupling system. (a) Icout versus Icin with and without in-phase controlling light bin = 1. (b) Nonlinear factor versus Icin in the presence of in-phase controlling light. Here, normalized parameters are set to be γat ≡ 1, k1 = k2 = 4, Δ = 0, and ϕ = 0.

The physics of controllable reflection originates from the enhancement of atomic nonlinearity and destructive interference. A larger nonlinear factor x results in a smaller t-component and a larger anti-phase r-component when ϕ = 0. They interfere destructively, which makes I_cout a remarkable decline at first. Specially, at the point of I_bin = I_cin = 1, the completely destructive interference swallows any output, which is called the nonlinear perfect photon absorption.^[38,40] In the following discussion, we will show that the transmission is also controlled by weak control light as expected.

As mentioned above, transmission is also controlled at a weak-intensity level, where b_in is specified as in-coming light or signal, c_in the bias or controlling filed, and c_out the out-coming light.

The transmitted curves of I_cout versus I_bin for controlling light I_cin = 0, 1/4, 1/2, 1, and 2 in the in-phase case ϕ = 0 are presented in Fig. 3(a), which shows an optically controllable switch-like behavior. As shown in the figure, I_cout increases steadily with I_bin increasing, which makes light easily propagate from port 1 to port 2 due to the dipole-induced transmission when I_cin does not exist (I_cin = 0). However, the destructive interference leads I_cout to sharply decrease followed by a slight increase when I_cin exists (I_cin = 1/4, 1/2, 1, and 2). Especially for the case of I_cin = 1, light transportation is almost blocked when |b_in|² > 0.62, which can be explained as self-matching-induced-block in the following discussion.

Fig. 3.

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Fig. 3. Optically controllable switch and self-matching-induced-block by in-phase controlling light in symmetrical coupling system. Panel (a) shows curves of Icout versus Ibin in the presence of in-phase controlling field cin. Panel (b) shows optical block property of switch and its scheme is plotted in Fig. 1(b). Panel(c) shows Ibin-dependent scattering property for |r2|2 and |t12 2. Panel (d) indicates Ibin-dependent self-matching amplitudes of r2cin and t12bin in the presence of in-phase controlling light Icin = 1.

First we point out that such an optical block can be used to fabricate an optically controlled switch whose scheme is shown in Fig. 1(b). The switch is optically controllable by turning the in-phase coherent controlling light I_cin = 1 on or not. When controlling light is turned off (I_cin = 0), light can propagate from port 1 to port 2 easily, while light transmission is blocked when controlling light is turned on (I_cin = 1). Contrast ratio C = 10 × log₁₀(I_{cout − cin = 0} / I_{cout − cin = 1}) is defined to characterize the property of optical switch, where I_{cout − cin = 0} and I_{cout − cin = 1} represent outputting intensities I_cout for I_cin = 0 and I_cin = 1, respectively. As shown in Fig. 3(b), contrast ratio C is easy to exceed 30 dB in the range of 0.62 < | b_in|² < 4. The infinite C for I_bin = 1 is the consequence of nonlinear perfect photon absorption.^[38,40]

Next, we figure out that the physics behind the switch is self-matching-induced-block, that is, the quasi-completely destructive interference of the self-matched r-component and t-component makes almost nothing output. When controlling light is switched on (I_cin = 1), |r₂|² increases while |t₁₂|² decreases constantly with the increasing of |b_in|² due to atomic saturation nonlinearity, and it leads the amplitudes of r component and t component (i.e., r₂c_in and t₁₂b_in) to match each other adaptively in a wide range (as shown in Figs. 3(c) and 3(d)). Such the self-matched two components are the consequence of the single atom saturation nonlinearity induced by the two light beams. As r- and t-components are antiphase, their quasi-completely destructive interference presents almost no I_cout finally.

Until now, all the setups of light amplification are performed in a multi-level system. So there comes a question, i.e., does an optical transistor exist in a two-level system? To our interest, optically controllable transistor-like behavior is uncovered when two coherent anti-phase beams enter into the asymmetrical coupling setup and the broken spatial symmetry takes effect.

The curves of I_cout versus I_bin are calculated at a series of bias light beams (I_cin = 0, 1/2, 1, 3/2, and 2) for the antiphase case ϕ = π in the asymmetrical coupling setups (k₁ = 6, k₂ = 2, and k₁ = 7, k₂ = 1). In the presence of nonzero bias light (I_cin = 1/2, 1, 3/2, and 2), I_cout presents a nonzero background when I_bin = 0. After removing the background intensity, we plot the curves of transmitted intensities versus incident intensity in Figs. 4(a) and 4(c), which clearly show that a slight amplification occurs in a proper regime. As shown in the figure, when bias light does not exist (I_cin = 0), transmitted intensity is less than incident intensity since part energy is reflected and absorbed. However, when I_cin is switched on (I_cin = 1/2, 1, 3/2, and 2), part of bias light c_in is reflected into c_out to supply the transmitted light, and their constructive interference makes amplification ratio I_cout / I_bin > 1 finally.

Fig. 4.

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Fig. 4. Transport property of optical transistor by anti-phase controlling light in asymmetrical coupling system. Panels (a) and (c) show that Icout versus Ibin is dependent on the presence of antiphase bias field Icin. Light amplification regime is restricted by the gray dotted line of Icout = Ibin. Panels (b) and (d) display optical transistor regime and its amplification ratio. Scheme of optical transistor is shown in Fig. 1(c).

The asymmetric atom–nanowire setup can be used to realize a single-atom optical transistor and the scheme is shown in Fig. 1(c). Although the light amplification ratio is not high, we really show optical amplification can occur in the single two-level system. Optical transistor regime and the amplification ratio in the present asymmetric setups are shown in Figs. 4(b) and 4(d). The larger the value of k₁/k₂, the wider the the transistor regime is. Only in the transistor regime does the amplification ratio exceed 100%.

In the core of present light amplification a weak signal b_in is used to disturb the scattering of a strong bias light c_in for supplying the output light, and brocken spatial symmetry takes effect. In the asymmetrical coupling setup of k₁ > k₂, we achieve critical power P₁ < P₂ which indicates that a weaker b_in can produce a much considerable atomic saturation nonlinearity to perturb the scattering of c_in. The harder the spatial symmetry is broken (corresponding to the larger of k₁/k₂), the wider the transistor regime is. As ϕ = π, the r- and t-components are in-phase, and their constructive interference makes light amplified without gain medium.

It is feasible to fabricate such an atom-waveguide coupling system with the present technology by carefully designing it. Atom interacts with metal nanowire through surface plasmons propagating thereon, where interaction strength is enhanced greatly. Recently, a strong coupling system containing a single emitter and a nanowire has been proposed.^[12,41,42] Atom–light coupling strength relates to the shape and material of nanowire and the distance between them. For example, consider a scheme where a fixed 20-nm-radius silver nanowire (ε_Ag = −50 + 0.6i) embedded in the host material with index n = 1.414, couples with an emitter 10 nm far from the nanowire with emission wavelength of 1000 nm, and P is about 37.^[39] Adopting such a scheme, it is not difficult to adjust P to 8 by changing the atomic position since we take k₁ + k₂ = 8 in our discussion.

However, the setup of a single atom interacting with two individual nanowires has not been reported experimentally so far. The main challenge of the fabrication is how to exclude their direct interaction between two nanowires while they both strongly coupled with the imbedded atom. Two nanowires should be close enough to the atom to generate strong atom–nanowire coupling, while they should be far enough away to exclude their direct coupling. Therefore, two nanowires should be placed properly (such as vertically) to exclude their direct coupling and only interact with the imbedded atom. The other challenge is how to manipulate a single atom between two nanowires. Although few-atom transference and manipulation has been realized recently by the technology of magneto–optical trapping, it is still very difficult to trap and fix a single atom between two nanowires. Therefore, great efforts are still needed to construct such an atom–nanowires coupling system.