# Multifunctional logic gates based on resonance transmission in the structure of plasmonic atoms

Figure 2 reveals the reflection spectrum of our hybrid structure while SP touches the Rb atoms with a modular energy equal to the energy of the ultrafine Rb transitions. Based on the large damping rate of plasmons, we ignore changes in SP energy in a narrow range of Rb D1 ultrafine transitions. The results clearly show the transmission of incoming light at a wavelength equal to any high-resolution atomic transmission. The fact is that all the incoming photons after passing through the prism windows couple to the plasmonic mode and are damped in different channels especially by ohmic damping in the metallic film. Photons transmitted to our plasmonic damping scape structure by resonant coupling of ultrafine atom transitions. The resonance physical behavior of the coupled atom-SP system proves that the resonant transmission (EIT-like) system of our proposed hybrid structure operates on an EIT-based filter platform for a band-pass filter with line FWHM, equal to atomic transitions. Also, we believe that any physical change that leads to a reasonable reduction in atomic transmission line width, such as selective reflection, or plasmonic saturation absorption will be used in conjunction with SP to achieve narrower band-pass filters, taking advantage of the coupling model.

To analyze the tunability of the combined behavior of the coupled atom-permeability-SPP, we performed spectroscopic measurements in two steps; Firstly under the SP mode energy shift and secondly by modulating the quantum state of the Rb atoms by applying an external AC magnetic field. To change the SP energy formed at the metal-dielectric interface in the Kretschmann configuration, the easiest way is to change the angle of incidence of the laser light (Supplementary Information S1-S2). Figure 2a represents the measurements made under all stationary experimental conditions where the angles of incidence of the photons changed only around the SP resonance angle. Figure 1b clearly shows a sharp change in the results of the system associated with changes in the angle of incidence for a wavelength equal to 52s1/2–52s1/2 Atomic transformations of 85Rb counterpart. While changing the angle of incidence of the laser light changes the SP power, the coupling system switches from Fano to EIT and vice versa. We conclude that the filter behavior changes from a band-pass filter to an absorbing line filter. It occurs because a large change in the angle of incidence causes the plasmonic mode to be overthrown and the optical field near the SP shifted to an evanescent dielectric prism field, so atomic absorption commonly occurs as evident in the last row of data.

SP modulation mechanisms will be used to fine-tune the atom-plasmon coupling to exploit a hybrid device such as the proposed filter. This includes a variety of engineered plasmonic structures available in published papers36. In addition to the effect of the angle change as presented, we examined the effect of an increase in the measurement probe temperature by possible methods on a single Au thin layer. We compare the result of measurement at 85 and 105 ° C. The harsh increase in temperature actually eliminates the atom-SP coupling state due to the increases in the ohmic damping of the Au film. In response, the rate of damping of the energy of photons (polaritons) in the SP mode exceeds the rate of energy exchange between the atom and the SP. With the elimination of the optical sensitivity associated with the coupled structure, the optical response of the atoms to the evanescent wave of total reflection from the prism became dominant and the resonant transmission behavior disappeared due to the collapse of the coupling state. (Supplementary information, page S-3).

As shown in the experimental part, the angle of incidence into an atom plasmonic cell clearly shows a resonant transmission of photons from the coupled structure through all the high-resolution transitions of the Rb atom. The transmittance is directly proportional to the amplitudes of both resonances in particular, the high-resolution atomic transition probability. Considering multiple lines of ultrafine absorption, with different levels of transmittance caused by Rb atoms, we propose the logical behavior of atom-SP coupling. To show the effects of the impressive parameters, we set the angle of incidence of the laser light on the prism at −0.5, −0.27, 0.17° (SP resonance off), 0° (SP resonance off) and 0.08, 0.17, and 0.29° (SP resonance off) and scored The intensity of the reflected laser light at the cut-off wavelengths (separation is marked as the x-axis of the results). To determine the measured angle of incidence we consider the angle of resonance SP, 2.25°, as the reference angle and for each angle of incidence we use $$\frac{\theta -2.25}{\theta +2.25}$$.

The results show an EIT-like transition at the SP resonance angle (Fig. Figure 3a shows the reflection normalized to the EIT-like reflection of laser light on ultrafine transitions at any angle of incidence. To investigate the possibility of multi-channel switching, we consider any single letter D1 Ultra-fine absorption lines for the Rb atom as a distinct gateway. In Figure 3a, four channels of blue and red colored wavelengths are highlighted. We will assign Booleans 0 or 1 depending on the value of the reflection intensity in each channel. A comparison of our results in Figure 3b shows a logic current “1010” after the resonance and a logic value of “0101” before the resonance angles. The change of symmetry of the logic state current results from the sweep of the angle of incidence around the resonant angle SP. The SP potential energy in the resonance angle is equal to the atomic transition energy, an increase or decrease in the angle of incidence leads to an increase or decrease in the SP energy related to the atomic transitions energy. The sign of the symmetry of the Fano line profile in each channel directly depends on the sign of the energy difference in the SP mode of the Rb transitions. The effect of forcing a change in the angle of incidence is not only the symmetry sign, but the value of the Fano line shape asymmetry is directly proportional to the difference between the energies of the paired modes16. This change prompts us to introduce an atom-SP hybrid structure as a photo switch that would change the logic state of the channels only by changing the angle of incidence around the SP resonance angle.

Here to investigate the performance of the proposed logic gate, we define the inputs of the system as the angles of incidence and wavelength separation. Figure 4 reveals the heatmap result, where the measured angle and wavelength are the first and second inputs, and the reflection intensity is the output channel. We assume that the angles of incidence lie in the range [−0.4, 0.4] degrees as logical input 0 and all other angles outside this range as one logical input. In addition, the frequency separation lines ν < 300 MHz, 0 and lines are assumed to be distinct as single logical states. In this way, we will build four logical input states 00, 01, 10 and 11, as in Figure 4.

The results show that our hybrid structure will act as an XNOR or NOR logic operator just by switching on the frequency of the incoming light and applying a change to the energy of the SP mode, here the change of the angle of incidence of the incoming light is used to control the SP modal energy, certainly the rate of change mechanically applied to the angle of incidence Quite less than the ideal SP atom-based switching system. The damping rate of the proposed structure for ultrafine Rb transitions (two pairs of GHz) and the lifetime of the SP output mode (femtosecond) will be the final limiting parameters on the ON-OFF switching rate of an SP atom-based logic gate.29,37.

As expected from the paired structures, the behavior of both sides is efficient in the behavior of the hybrid structure. So far, we have shown the effect of changes on the SP mode in the dual susceptibility of media coupled to the SP atom. Any perturbation in the quantum states of the Rb atom changes the working of the dual behavior as well.

The application of a magnetic field breaks up the degeneracy of ultrafine levels and divides them into subzeeman levels according to their quantum number. The amount of the applied magnetic field directly controls the amount of splitting and transition energy transitions between the quantum states. Therefore, the absorption spectrum of the D1 line of Rb vapor will be changed related to the strength and direction of the applied magnetic field. Thus, when the wavelength and angle of incidence of the incoming light are constant, the intensity of the resulting light can be controlled by applying a magnetic field. In fact, the magnetic field strength can play the role of the control signal in the proposed structure.

In our case, linearly polarized light fell on the gold-coated prism and the SP wave optically pumped sub-Zeemann levels, while the magnetic field was applied perpendicular to the direction of SP propagation. Implementation of frequency modulation technology, ultra-precise Rb transitions for Rb D1 The line has been completely dissolved. However, due to Doppler broadening, at low magnetic field strength (less than ~10 mT for Rb), it is not possible to spectral distinctions between permissible transitions between large numbers of magnetic sublevels. Therefore, instead of applying an external DC magnetic field, we studied the permeability of the coupled plasmonic atomic system, under magnetic field application, at the constant wavelength of the incoming light. A modified signal was obtained by recording the intensity of the light while the laser wavelength was kept at one of the ultrafine transitions and the AC magnetic field was applied to the Rb vapor (Fig. 5a). We recorded changes for three different 15 Hz AC magnetic fields with amplitudes of 5.9, 11.4 and 21.5 mT. The results showed that the modulation depth of the transmitted laser light was proportional to the strength of the applied magnetic field. Although in all cases the transmitted light was modulated at the same frequency, a small phase shift was observed in the results (Fig. 5b).

Our results also show the possibility of change in the transmittance and phase of our proposed gate through a difference in the amplitude of the applied AC magnetic field. As shown in Fig. 5b, the red dot shows phase changes in transmittance in a coupled atomic plasmonic structure and provides the possibility of phase modulation of the logic by changing the strength of the magnetic field. It is noteworthy that the cleavage-based Zeeman shift of the absorption line is not linearly related to the strength of the applied magnetic field. Therefore, we used the weak strength of the magnetic field to perform the modulation of light in a linear system. Figure 5c shows the relationship between the amplitude of the laser light modulated in the transmission from the coupled system and the strength of the applied magnetic field. Extrapolation of this figure indicated that the sensitivity of the amplitude modulation of the transmitted light to the magnetic field strength is on the order of 0.62 V/T.