Sensitivity of atom based on slow light propagation and rotary photon drag: an efficient and secure model for quantum-based sensors in Internet of Things

In Fig. 1, the proposed sensors and network model are shown. The proposed model has entities: Quantum-based sensors, sender-side quantum-based IoT devices, Receiver-side quantum-based IoT devices, quantum security providers, quantum keys and state detectors, and quantum towers. The detail and work process of every entity is explained as follow:All the above-mentioned entities are to be used case of our designed scheme. At first, the quantum-based sensors use our photon drag investigation by exploiting the force exerted on particles due to the light gradient to efficiently sense and monitor the environment. This sensing data then transfers to the receiver-side quantum-based IoT devices, this transfer will be possible through a quantum tower and optical switching. To make this transfer efficient, the proposed photon drag technique is a very efficient solution to boost the performance of optical switching. Our photon drag exerts a force on the atoms that are used to manipulate the position and move the atoms, which provides higher bandwidth compared to traditional ones, enables the transfer of bulk data, makes possible HD-streaming, and can handle data from multiple sources, at the same time.

For long-distance communications, an intermediate quantum tower is used to transfer data. Our technique the scattering cross-section is an efficient solution for efficient and reliable long-distance communications. The scattering cross-section refers to the phenomenon describing the interaction between electromagnetic waves and particles/atoms, that reduces the blockage of signals, increases its propagation, handles multi-path fading, and reduces to avoid conjunction. Strong security is a highlighted issue in any quantum-based communication, a quantum security provider is used to manage the security. The quantum security provider provides keys for secure communication. These keys will be a combination of the photons, to verify and validate keys through quantum states, quantum keys and state detectors are used. Our proposed cross-sectional sensitivity investigation is utilized to increase security. The cross-sectional sensitivity of atoms in the context of quantum-based IoT refers to the ability of atoms to detect and respond to external influences with high precision that boosts up security and makes efficient quantum key distribution and detection process.

As illustrated in Fig. 2, our suggested model consists of a two-level atomic medium coupled with a single-mode cavity. Dielectric slabs of a thickness \(d_1\) and an inter-slab space of \(d_2\) make up the walls. The ground state of the two-level atoms is labelled as \(\left| 1\right\rangle\) while the excited state as \(\left| 2\right\rangle\). A probe field having Rabi frequency \(\Omega _p\), that makes an angle \(''\theta "\) with the normal is shined from one side of the cavity. Strong control field having Rabi frequency \(\Omega _c\) is driven normally from a single side of the cavity. Considering the ground state at zero energy level, the Hamiltonian under dipole and rotatory wave approximation is then given by Arif et al. (2021)

The control field is detuned from the probe field, and atomic transition frequency \(\omega _{21}\) by an amount \(\delta =\omega _{21}-\omega _c\) and \(\Delta _a=\omega _{p}-\omega _c\), respectively. Similarly, the detuning of cavity mode \(\upsilon\) and probe field from atomic transition frequency is given by \(\Delta _c=-(\omega _{21}-\upsilon )\) and \(\Delta _p=\omega _{21}-\omega _p\), respectively. Whereas, \(\omega _c\) and \(\omega _p\) are the angular frequencies of the control and probe fields, respectively. In the above equation, G is the coupling strength between the system and cavity mode, \(a^\dag (a)\) are the creation and annihilation operators for the cavity mode. The a is the lowering operator for the atomic decays between states of the proposed atomic model while \(a^\dag\) is the raising operator for these decays. Furthermore, \(\sigma _{ij}\) is the operator for atomic transition while \(\Omega _{c,p}\) are the Rabi frequencies of the driving fields. The parameter \(\varrho\) having the dimensions of frequency is the strength of the atom cavity coupling, given in explicit form as \(\varrho =\mu _{21} \zeta _V/\hbar\), where \(\mu _{21}\) is the transition dipole moment and \(\zeta _V=[(\hbar \upsilon )/2\hbar \epsilon _0 V]^{1/2}\) is the strength of vacuum field over the volume \(''V"\) of the cavity. To study the dynamics and equation of motion for the proposed system, we use the following master equation (Arif et al. 2021).Where \(\hbar\) is reduced plank constant, \(\rho\) is the density matrix operator and \(\gamma\) is the damping rate. Using Eqs. (1) and (2), we obtained the following equations which describe the dynamics of the population, as well as polarization.Where, \(\overset{\cdot }{\rho }_{21}=\overset{\cdot }{\rho }^*_{12}\), \(\overset{\cdot }{\rho }_{11}=-\overset{\cdot }{\rho }_{22}\) and n is the number of photons in the cavity mode. The exact steady-state solutions of the above equations are obtained by applying the following possible solutions to each of them.We have used the rotating wave approximation, assuming that the detuning between the atomic transition frequency \(\delta\) and the cavity frequency is much larger than the decay rate \(\gamma\) of the atomic states. In the above equation, \(\rho ^0_{uv}\) is the steady state solution under atom coupling with \(\Omega _c\) and \(\delta\). The preceding two terms describe the steady-state solution in the presence of coupled probe field. Utilizing this equation and comparing constants and coefficients of the exponential yields twelve coupled equations; the first order coherence \(\rho ^-_{21}\) in \(\Omega _p\) is given by:The terms in the above equations are given below.WhereTo access the susceptibility in terms of position-dependent Rabi frequency of the control driving field \(\Omega _c(kx,ky)\), we define the induced polarization in terms of susceptibility and electric probe field of amplitude \(E_p\) as \(p=\epsilon _0\chi _eE_p\) and in terms of the probe field coherence \(\rho _{21}\), it is given by \(p=2N\mu _{21}\rho _{21}\), where N is the atomic density. Comparing these relations, while assuming \(\rho ^-_{21}=\rho _{21}\) the susceptibility of the intra-cavity medium becomes:where \(\beta =\frac{2N|\mu _{21}|^2}{\epsilon _0\hbar }\). The refractive index is calculated by \(n_r= 1+2\pi Re(\chi )\).

The group index is written as:The velocity at which, information is transferred along a wave is the group velocity. The group velocity in terms of group index is written as:

The delay time is the difference of time taken by a light beam in a medium to the time taken in vacuum for the same length L, i-e \(t_d=t_m-t_v\). In context of group index, it can be written as:

The rotary photo drag is written as:The cross-sectional area of a particle is written as:Here, d is the diameter of a spherical particle, while \(\lambda\) is wavelength of light denoted by \(\lambda =2\pi c/\omega\).

The scattering cross-sectional sensitivity is written as:

We investigated the rotary photon drag to \(\theta _d=\pm 5\) micro radian. This effect of photon drag is used in sensing, energy harvesting, and optical switching in IoT. In optical switching, an external field (mostly a laser beam) exerts a force on the atoms, which is used for the manipulation of the position as well as the movement of these atoms. On the basis of this property, optical switches (re-configurable optics) are made for the IoT devices used for the control and modulation of signals dynamically. The use of photon drag in optical switching, and its work process in IoT is illustrated in Fig. 7.

In wired/wireless communication for IoT, optical switching provides higher bandwidth, compared to traditional ones. This enables the transfer of bulk data among IoT devices. It also makes possible HD-streaming as well as can handle data from multiple sources, at the same time. Further, the delay time is also minimized and the communication in IoT is made real-time.

The scattering cross-section of \(0.1\times 10^21\) \(m^2\) is measured. In quantum, the scattering cross-section refers to the phenomenon describing the interaction between electromagnetic waves and particles/atoms. As a result of this interaction, many phenomena occur such as interference of signals, reflection, or signal attenuation. Hence, this phenomenon greatly affects the efficiency as well as the reliability of communication in IoT, based on quantum. To counter the problem of signal interference, this effect is used as shown in Fig. 8. It reduces the blockage of signals and increases its propagation. Using the diversity technique of scattering cross-section, the effect of multi-path fading is reduced to avoid conjunction.

We measured the maximum cross-sectional sensitivity of \(S_\sigma =0.4\times 10^{-19}m^2/n_r\). For the communication in IoT to be secure, the cross-sectional sensitivity of atoms plays a major role as it enables the sensors to detect with high precision. In quantum-based IoT, it is the ability of atoms/quantum systems to precisely detect external influences and respond to them. The atoms are considered as the basis for quantum sensors for the measurement of temperature, pressure, magnetic as well as electric field at the quantum level which manipulate the atom’s quantum states. Further, quantum-based cryptography, like quantum key distribution (QKD) enables secure communication channels, having high resistance to eavesdroppers, as provided by Fig. 9.