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.
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.
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.
We investigate the performance of the super-resolving quantum lidar with the entangled coherent states of light in the presence of loss and noise, especially in the noisy case. An exact analytical expression of the output signal has been derived with the binary-outcome photon counting measurements. Numerical results show that the resolution of our scheme with parity detection is √N (N) times enhanced relative to that of the coherent-state strategy with the same (intensity) detection in the lossless and noiseless cases. The influences of phase diffusion on resolution and sensitivity have been analyzed and discussed. It is found that the super-resolution emerges in the whole diffusion rate regions, whereas the super-sensitivity just exists in the high and low diffusion rate regimes. Comparisons are made with the well known N00N states, the results show that the entangled coherent states performs better resolution and sensitivity than those of the N00N scheme in the whole diffusion regimes. In addition, the effects of photon loss on resolution and sensitivity have also been studied. The phase sensitivity can beat the shot noise limit and the resolution is much better than the Rayleigh diffraction limit in the whole loss regions. Finally, the zero-nonzero photon counting measurement gives much worse sensitivity than that of the parity detection, which is just opposite from the case as demonstrated in a recent coherent-light Mach-Zehnder experiment.
Abstract Quantum sensing has drawn considerable attention as a means to overcome the fundamental limitations in classical sensing. In practice, however, quantum sensing has been strongly constrained by the photon loss, the achievable photon number N in N00N states, and by a finite squeezing level in squeezed states. These limitations are particularly critical to photon-loss-sensitive applications such as LiDAR as well as to general sensing platforms that require large effective N, such as ring-laser gyroscopes. Recently, fundamentally different sensing platforms have been reported to overcome both classical and quantum constraints in a practical regime. One such approach exploits the coherence de Broglie wavelength (CBW) realized in an anti-symmetrically coupled Mach-Zehnder interferometer (MZI) architecture. Here, a pure quantum mechanical analysis of the CBW is presented for a loss-free sensing mechanism of superresolution with enhanced sensitivity. A proof-of-principle demonstration of CBW is also presented.
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.
Here we are investigating the enhancement in phase sensitivity and resolution in Mach-Zehnder interferometer (MZI) based quantum LiDAR. We are using multi-photonic state (MPS), superposition of four coherent states [1], as the input state and binary outcome parity photon counting measurement and binary outcome zero-nonzero photon counting measurement as the measurement schemes. We thoroughly investigate the results in lossless as well as in lossy cases. We found enhancement in resolution and phase sensitivity in comparison to the coherent state and even coherent superposition state (ECSS) based quantum LiDAR. Our analysis shows that MPS may be an alternative nonclassical resource in the field of quantum imaging and quantum sensing technologies, like in quantum LiDAR.
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.