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Acta Physica Sinica

Influence of atmospheric scintillation on entangled coherent states quantum interferometric radar

Yichong Ren, Shu Wang, Rao Rui-zhong, Xikui Miao

Published Jan 1, 2018• 4 citations
Publisher

Abstract

Much interest has been aroused in quantum metrology such as quantum interferometric radar, due to its application in sub-Raleigh ranging and remote sensing. Generally, the quantum signal emitted by quantum radar will be affected by atmosphere medium. For instance, both atmospheric loss and atmospheric scintillation seriously affect the sensitivity and resolution of quantum radar. In fact, the effects of atmospheric loss on the sensitivity and resolution of quantum interferometric radar have been investigated thoroughly and completely in the past decades. However, the investigation about the influence of atmospheric scintillation is lacking until now. To realize practical quantum interferometric radar, the perturbation coming from turbulent atmosphere must be considered, thus it is necessary to investigate how the atmospheric scintillation affects the performance of quantum radar.In this paper, the influence of intensity fluctuation which is caused by atmospheric scintillation on the performance of quantum interferometric radar with entangled coherent states (ECS) is thoroughly investigated. We first introduce the physical model of quantum interferometric radar, and the dynamic evolution of quantum light field in atmosphere is obtained by solving the master equation of dissipation channel. Considering the dissipation and fluctuation caused by atmospheric scintillation, we regard the turbulent atmosphere as so-called dissipation-fluctuation channel. Moreover, according to classical statistical theory of turbulence, we derive the explicit expression of probability distribution of transmission coefficient P(T), this probability distribution of transmission cofficient, which is determined by average transmission coefficient TD and scintillation index βD2 plays a crucial role in the studying of atmospheric scintillation.The results of investigation show that atmospheric scintillation leads to the degradation of the sensitivity and resolution of ECS quantum interferometric radar at lower atmospheric loss. Under the higher lossy condition of atmosphere, atmospheric scintillation can greatly enhance the performance of quantum interferometric radar. Furthermore, the critical atmospheric transmission coefficient which determines the lower and higher loss of atmosphere keeps increasing with the increase of average photon number per pulse. Increasing the atmospheric scintillation, rather than introducing noise and degrading the performance of quantum radar, can improve the sensitivity and resolution.This anomalous phenomenon can be explained only by quantum decoherence theory. As is well known, the supersensitivity and super-resolution of quantum radar are based on the nonlocal characteristic of quantum light field, while the dissipation process will induce decoherence that leads to the loss of nonlocal characteristic, and finally degrades the performance of quantum radar. However, there have been several researches indicating that the dissipation-fluctuation channel can alleviate the decoherence effect and maintain the nonlocal characteristic of quantum light field compared with pure dissipation channel. For the evolution of quantum light field in dissipation medium, the loss of amplitude plays a crucial role at a lower loss, while the decoherence will play a dominant role at a higher loss. Consequently, the fluctuation may induce extra noise and degrade the performance of quantum radar at lower loss. For higher loss, the fluctuation can prevent the decoherence process and maintain the quantum characteristic of light field, thus the atmospheric scintillation finally improves the sensitivity and resolution of quantum radar.

DOI
10.7498/aps.67.20172401

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Much interest has been aroused in quantum metrology such as quantum interferometric radar, due to its application in sub-Raleigh ranging and remote sensing. Generally, the quantum signal emitted by quantum radar will be affected by atmosphere medium. For instance, both atmospheric loss and atmospheric scintillation seriously affect the sensitivity and resolution of quantum radar. In fact, the effects of atmospheric loss on the sensitivity and resolution of quantum interferometric radar have been investigated thoroughly and completely in the past decades. However, the investigation about the influence of atmospheric scintillation is lacking until now. To realize practical quantum interferometric radar, the perturbation coming from turbulent atmosphere must be considered, thus it is necessary to investigate how the atmospheric scintillation affects the performance of quantum radar.In this paper, the influence of intensity fluctuation which is caused by atmospheric scintillation on the performance of quantum interferometric radar with entangled coherent states (ECS) is thoroughly investigated. We first introduce the physical model of quantum interferometric radar, and the dynamic evolution of quantum light field in atmosphere is obtained by solving the master equation of dissipation channel. Considering the dissipation and fluctuation caused by atmospheric scintillation, we regard the turbulent atmosphere as so-called dissipation-fluctuation channel. Moreover, according to classical statistical theory of turbulence, we derive the explicit expression of probability distribution of transmission coefficient P(T), this probability distribution of transmission cofficient, which is determined by average transmission coefficient TD and scintillation index βD2 plays a crucial role in the studying of atmospheric scintillation.The results of investigation show that atmospheric scintillation leads to the degradation of the sensitivity and resolution of ECS quantum interferometric radar at lower atmospheric loss. Under the higher lossy condition of atmosphere, atmospheric scintillation can greatly enhance the performance of quantum interferometric radar. Furthermore, the critical atmospheric transmission coefficient which determines the lower and higher loss of atmosphere keeps increasing with the increase of average photon number per pulse. Increasing the atmospheric scintillation, rather than introducing noise and degrading the performance of quantum radar, can improve the sensitivity and resolution.This anomalous phenomenon can be explained only by quantum decoherence theory. As is well known, the supersensitivity and super-resolution of quantum radar are based on the nonlocal characteristic of quantum light field, while the dissipation process will induce decoherence that leads to the loss of nonlocal characteristic, and finally degrades the performance of quantum radar. However, there have been several researches indicating that the dissipation-fluctuation channel can alleviate the decoherence effect and maintain the nonlocal characteristic of quantum light field compared with pure dissipation channel. For the evolution of quantum light field in dissipation medium, the loss of amplitude plays a crucial role at a lower loss, while the decoherence will play a dominant role at a higher loss. Consequently, the fluctuation may induce extra noise and degrade the performance of quantum radar at lower loss. For higher loss, the fluctuation can prevent the decoherence process and maintain the quantum characteristic of light field, thus the atmospheric scintillation finally improves the sensitivity and resolution of quantum radar.
There has been aroused much interest in quantum metrology such as quantum radar, due to its applications in sub-Raleigh ranging and remote sensing. For quantum radar, the atmospheric absorption and diffraction rapidly degrade any actively transmitted quantum states of light, such as N00N and MM' states. Thus for the high-loss condition, the optimal strategy is to transmit coherent state of light, which can only provide sensitivity at the shot-noise limit but suffer no worse loss than the linear Beer's law for classical radar attenuation. In this paper, the target detection theory of quantum interferometric radar in the presence of photon loss is thoroughly investigated with the model of Mach-Zehnder interferometer, and the dynamic evolution of the quantum light field in the detecting process is also investigated. We utilize the parity operator to detect the return signal of quantum interferometric radar with coherent-state source. Then we compare the detection result of quantum radar with that of classical radar, which proves that the quantum radar scheme that employs coherent radiation sources and parity operator detection can provide an N-fold super-resolution, which is much below the Rayleigh diffraction limit; besides, the sensitivity of this scheme can also achieve the shot-noise-limit. Also, we analyze the effect of atmospheric attenuation on the performance of quantum radar, and find that the sensitivity is seriously influenced by atmospheric attenuation:only when the reference beam and the detection beam have the same transmissivity, will the sensitivity increase monotonically with increasing the photon number per pulse N, otherwise it first increases and then decreases with increasing N. Further, the sensivity is directly proportional to 1/N for the first case. In conclusion, we investigate the effects of atmospheric absorption on the resolution and sensitivity of quantum radar, and find that one can overcome the harmful effects of atmospheric attenuation by adjusting the transmissivity of reference beam to the atmospheric transmittance.
Quantum Sensors like Quantum Radar and Lidar based on the interference of non-classical states can achieve super-sensitivity beyond the Standard Quantum Limit (SQL). But as the photons transporting in atmosphere, the environmental interaction causes quantum de-coherence and results in the reduction of super-sensitivity range of the quantum sensors. The most significant effect of atmospheric transmission is photon loss along with phase fluctuation. In this letter, we introduce both the photon loss and phase fluctuation by adding a fictitious beam splitter in the signal arm of Mach- Zehnder interferometer (MZI). The density matrix with N00N and M&M' entangled states being the input states under the condition of photon loss and phase fluctuation is given respectively. Then as the optimal detection schemes parity operator is used as the detector and the formula of the sensitivity is derived. The super-sensitivity range of M&M’ and N00N states with de-coherence are simulated. As a consequence, with high photon loss M&M’ states shows the better phase sensitivity than N00N states but the N00N state is better when the loss is smaller than 20%. And with pure phase fluctuations N00N states get the longer range. M&M’ states is sensitive to the transmittance difference between two arms of the interferometer.
The entangled quantum radar applies the quantum information technology to the radar sensing network and detection system. The dynamic particle changes and optical attenuation caused by complex atmospheric environments will severely limit the traditional radar performance. Due to entanglement characteristics, the entangled optical quantum radar has better anti-stealth interference ability, stronger anti-turbulence properties, and higher spatial resolution which makes it promising in complex and high-attenuation environments. In addition, quantum radar based on the entangled light source can overcome the limitations of low imaging resolution and low confidentiality in traditional target detection. Therefore, high-precision positioning and high-resolution imaging are the research focus of the quantum radar sensing network. Based on this, we first design and optimize an optical path structure of the quantum entangled light source to obtain higher brightness entangled source which is suitable for complex atmospheric environments. Second, in response to the problem of low positioning accuracy in the traditional quantum radar, we design a new positioning optical path and propose a novel entangled optical quantum positioning method based on the photon scattering model. Third, to address the problems of low resolution and slow speed in traditional quantum radar imaging, we propose a new entangled light quantum imaging method based on two-phase coincidence counting. Finally, we conduct extensive experiments to evaluate the effectiveness of the proposed method in complex atmospheric environments and further provide possibilities for the entangled light source quantum radar sensing network.
A quantum entangled radar uses entangled photons instead of separate photons. It has been shown that for quantum entangled interferometers that the value of quantum entanglement deteriorates in an environment with attenuation. This paper introduces a correction method that allows the quantum radar to maintain excellent performance even when dealing with an environment with attenuation. The correction method is analogous to techniques used in adaptive optics to improve images. Correction approaches based on signal sources deliberately introduced into the environment and electromagnetic sources already present in the environment are considered. Closed form expressions for estimating the range error are derived for the cases when the radar uses N entangled photons for imaging or N separate imaging photons. Simulations of radar range error estimates for entangled and separate photon cases for propagation media with widely varying attenuation properties are provided. Comparisons of estimates with and without atmospheric correction are given. The atmospheric correction method extends the range of the beneficial effects of entanglement by a factor of 82, i.e. to 5000 km for a slowly varying propagation medium. For a propagation medium with 50 times as much variation, the atmospheric correction method offers super sensitivity for three times the range of the uncorrected case.
This work is to study the effects of charged sand/dust atmosphere on the performances of microwave quantum illumination (QI) radar. Based on Mie particle scattering theory, using a Monte Carlo method for simulating the physical process in which photon is scattered multiple times by discrete random distributed particles, the specific attenuation (dB/km) of microwave propagating in sand/dust atmosphere are analyzed under the conditions of varying atmospheric visibility and sand/dust particles with different charged quantities. It is indicated that the specific attenuation obtained by multiple scattering is smaller than that obtained based on Mie theory, for microwave propagating in charged sand/dust atmosphere. The smaller the atmospheric visibility, the greater the difference is, while the difference decreases gradually as the atmospheric visibility increases. Then, it is more reasonable to consider multiple scattering attenuation at lower atmospheric visibility. When sand/dust particle is charged, the specific attenuation is increased, however, this increase is not linear. According to quantum illumination radar theory, a beam splitter-based optical link model is used to simulate the sand/dust atmospheric channel. The effects of charged sand/dust atmosphere with different visibility on the detection error probability, signal-to-noise ratio, and maximum detection range for microwave quantum illumination radar are studied by using quantum radar equation and quantum detection error probability theory. The performances between QI radar and classical two-mode noise (TMN) radar are compared and analyzed. These results show that the performances of quantum illumination radar are improved with sand/dust atmospheric visibility increasing. When sand/dust particles are charged, the performances for QI radar are degraded due to attenuation increasing. The change in the performance is nonlinear with the variation of sand/dust carrying charge quantity. When visibility is high, increasing the signal frequency can improve the performance of quantum illumination radar, but when visibility is low, the gain of frequency increase is offset by the performance decline caused by attenuation increase. Therefore, it is not recommended to increase the frequency in such a case. The comparison with classical radar reveals that QI radar performs better under the condition of lower atmospheric visibility and lower average photon emission, but this advantage diminishes as the number of photons increases. In a word, these results show that the performances of QI radar are more significant at lower atmospheric visibility. Under higher visibility conditions, the QI system SNR can be improved by increasing frequency. The maximum detection range of the QI radar is significantly better than that of the classical TMN radar.
There has been much recent interest in quantum metrology for applications to sub-Raleigh ranging and remote sensing such as in quantum radar. For quantum radar, atmospheric absorption and diffraction rapidly degrades any actively transmitted quantum states of light, such as N00N states, so that for this high-loss regime the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the linear Beer's law for classical radar attenuation, and which provide sensitivity at the shot-noise limit in the returned power. We show that coherent radar radiation sources, coupled with a quantum homodyne detection scheme, provide both longitudinal and angular super-resolution much below the Rayleigh diffraction limit, with sensitivity at shot-noise in terms of the detected photon power. Our approach provides a template for the development of a complete super-resolving quantum radar system with currently available technology.