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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.
[1] Xiao H T, Liu K, Fan H Q 2014 J. Nat. Univ. Def. Technol. 36 140 (in Chinese) [肖怀铁, 刘康, 范红旗 2014 国防科技大学学报 36 140]
[2] Xu S L, Hu Y H, Zhao N X, Wang Y Y, Li L, Guo L R 2015 Acta Phys. Sin. 64 154203 (in Chinese) [徐世龙, 胡以华, 赵楠翔, 王阳阳, 李乐, 郭力仁 2015 物理学报 64 154203]
[3] Jiang T, Sun J 2014 J. CAEIT 9 10 (in Chinese) [江涛, 孙俊 2014 中国电子科学研究院学报 9 10]
[4] Giovannetti V, Lloyd S, Maccone L 2004 Science 306 1330
[5] Gao Y, Anisimov P M, Wildfeuer C F, Luine J, Lee H, Dowling J P 2010 J. Opt. Soc. Am. B 27 170
[6] Lanzagorta M 2010 Proc. SPIE 7727 77270K
[7] Bakut P A 1967 Radio. Eng. Electron. Phys. 12 1
[8] Helstrom C W 1976 Quantum Detection and Estimation Theory (New York: Academic Press) p95
[9] Jehle R E, Hudson D F 1992 US Patent 5 095 312 [1992-3-10]
[10] Kumar P, Grigoryan V, Vasilyev M 2007 Noise-Free Amplification: Towards Quantum Laser Radar (Snowmass: 14th Coherent Laser Radar Conference) p9
[11] Wasilousky P A, Smith K H, Glasser R, Burdge G L, Burberry L, Deibner B, Silver M, Peach R C, Visone C, Kumer P, Lim O, Alon G, Chen C H, Bhagwat A R, Manurkar P, Vasilyev M, Annamalai M, Stelmakh N, Dutton Z, Guha S, Chen J, Silva M, Kelly W, Shapiro J F, Nair R, Yen B J, Wong F N C 2011 Proc. SPIE 8163 816305
[12] Lloyd S 2008 Science 321 1463
[13] Tan S H, Erkmen B I, Giovannetti V, Guha S, Lloyd S, Maccone L, Pirnadola S, Shapiro J H 2008 Phys. Rev. Lett. 101 253601
[14] Guha S, Erkmen B I 2009 Phys. Rev. A 80 052310
[15] Lopaeva E D, Berchera I R, Degiovanni I P, Olivares S, Brida G, Genovese M 2013 Phys. Rev. Lett. 110 153603
[16] Dutton Z, Shapiro J H, Guha S 2010 J. Opt. Soc. Am. B 27 A63
[17] Nair R, Yen B J, Shapiro J H, Chen J, Dutton Z, Guha S, Silva M P 2011 Proc. SPIE 8163 816310
[18] Ekert A K, Rarity J G, Tapster P R, Palam G M 1992 Phys. Rev. Lett. 69 1293
[19] Allen E H, Karageorgis M 2008 US Patent 7375802 B2
[20] Smith J F 2010 Proc. SPIE 7702 p131
[21] Yurke B, McCall S L, Klauder J R 1986 Phys. Rev. A 33 4033
[22] Breuer H P, Francesco P 2002 The Theory of Open Quantum Systems (Oxford: Oxford University Press) pp161, 162
[23] Ren Y C, Fan H Y 2016 Acta Phys. Sin. 65 030301 (in Chinese) [任益充, 范洪义 2016 物理学报 65 030301]
[24] Howard C 1999 Statistical Methods in Quantum Optics 1: Master Equation and F-P Equation (Berlin Heidelberg: Springer-Verlag Press) p9
[25] Fan H Y, Hu L Y 2010 The Thermal Entanglement Entangled-State Representation of Open Quantum System (Shanghai: Shanghai Jiao Tong University Press) p91 (in Chinese) [范洪义, 胡利云 2010 开放量子系统退相干的纠缠态表象论(上海: 上海交通大学出版社) 第91页]
[26] Kok P, Braunstein S L, Dowling J P 2004 J. Opt. B 6 S811
[27] Kok P, Boto A N, Abarms D S, Williams C P, Braunstein S L, Dowling J P 2001 Phys. Rev. A 63 063407
[28] Knysh S, Smelyanskil V N, Durkin G A 2011 Phys. Rev. A 83 021804
[29] Lee T W, Huver S D, Lee H, Kaplan L, McCracken S B, Min C, Uskov D B, Wildfeuer C F, Veronis G, Dowling J P 2009 Phys. Rev. A 80 063803
[30] Resch K J, Pregnell K L, Prevedel R, Gilchrist A, Pryde G J, O'Brien J L, White A G 2007 Phys. Rev. Lett. 98 223601
[31] Huver S D, Wildfeuer C F, Dowling J P 2008 Phys. Rev. A 78 063828
[32] Wang Q, Hao L L, Zhang Y, Xu L, Yang C H, Yang X, Zhao Y 2016 Opt. Express 24 5045
[33] Jiang K, Lee H, Gerry C C, Dowling J P 2013 J. Appl. Phys. 114 193102
[34] Fan H Y 1992 Representation and Transformation Theory in Quantum Mechanics (Shanghai: Shanghai Scientific and Technical Publishers) p44 (in Chinese) [范洪义 1992 量子力学表象与变换论(上海: 上海科学技术出版社) 第44页]
[35] Distante E, Jezek M, Andersen U L 2013 Phys. Rev. Lett. 111 033603
[36] Feng X M, Jin G Y, Yang W 2014 Phys. Rev. A 90 013807
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[1] Xiao H T, Liu K, Fan H Q 2014 J. Nat. Univ. Def. Technol. 36 140 (in Chinese) [肖怀铁, 刘康, 范红旗 2014 国防科技大学学报 36 140]
[2] Xu S L, Hu Y H, Zhao N X, Wang Y Y, Li L, Guo L R 2015 Acta Phys. Sin. 64 154203 (in Chinese) [徐世龙, 胡以华, 赵楠翔, 王阳阳, 李乐, 郭力仁 2015 物理学报 64 154203]
[3] Jiang T, Sun J 2014 J. CAEIT 9 10 (in Chinese) [江涛, 孙俊 2014 中国电子科学研究院学报 9 10]
[4] Giovannetti V, Lloyd S, Maccone L 2004 Science 306 1330
[5] Gao Y, Anisimov P M, Wildfeuer C F, Luine J, Lee H, Dowling J P 2010 J. Opt. Soc. Am. B 27 170
[6] Lanzagorta M 2010 Proc. SPIE 7727 77270K
[7] Bakut P A 1967 Radio. Eng. Electron. Phys. 12 1
[8] Helstrom C W 1976 Quantum Detection and Estimation Theory (New York: Academic Press) p95
[9] Jehle R E, Hudson D F 1992 US Patent 5 095 312 [1992-3-10]
[10] Kumar P, Grigoryan V, Vasilyev M 2007 Noise-Free Amplification: Towards Quantum Laser Radar (Snowmass: 14th Coherent Laser Radar Conference) p9
[11] Wasilousky P A, Smith K H, Glasser R, Burdge G L, Burberry L, Deibner B, Silver M, Peach R C, Visone C, Kumer P, Lim O, Alon G, Chen C H, Bhagwat A R, Manurkar P, Vasilyev M, Annamalai M, Stelmakh N, Dutton Z, Guha S, Chen J, Silva M, Kelly W, Shapiro J F, Nair R, Yen B J, Wong F N C 2011 Proc. SPIE 8163 816305
[12] Lloyd S 2008 Science 321 1463
[13] Tan S H, Erkmen B I, Giovannetti V, Guha S, Lloyd S, Maccone L, Pirnadola S, Shapiro J H 2008 Phys. Rev. Lett. 101 253601
[14] Guha S, Erkmen B I 2009 Phys. Rev. A 80 052310
[15] Lopaeva E D, Berchera I R, Degiovanni I P, Olivares S, Brida G, Genovese M 2013 Phys. Rev. Lett. 110 153603
[16] Dutton Z, Shapiro J H, Guha S 2010 J. Opt. Soc. Am. B 27 A63
[17] Nair R, Yen B J, Shapiro J H, Chen J, Dutton Z, Guha S, Silva M P 2011 Proc. SPIE 8163 816310
[18] Ekert A K, Rarity J G, Tapster P R, Palam G M 1992 Phys. Rev. Lett. 69 1293
[19] Allen E H, Karageorgis M 2008 US Patent 7375802 B2
[20] Smith J F 2010 Proc. SPIE 7702 p131
[21] Yurke B, McCall S L, Klauder J R 1986 Phys. Rev. A 33 4033
[22] Breuer H P, Francesco P 2002 The Theory of Open Quantum Systems (Oxford: Oxford University Press) pp161, 162
[23] Ren Y C, Fan H Y 2016 Acta Phys. Sin. 65 030301 (in Chinese) [任益充, 范洪义 2016 物理学报 65 030301]
[24] Howard C 1999 Statistical Methods in Quantum Optics 1: Master Equation and F-P Equation (Berlin Heidelberg: Springer-Verlag Press) p9
[25] Fan H Y, Hu L Y 2010 The Thermal Entanglement Entangled-State Representation of Open Quantum System (Shanghai: Shanghai Jiao Tong University Press) p91 (in Chinese) [范洪义, 胡利云 2010 开放量子系统退相干的纠缠态表象论(上海: 上海交通大学出版社) 第91页]
[26] Kok P, Braunstein S L, Dowling J P 2004 J. Opt. B 6 S811
[27] Kok P, Boto A N, Abarms D S, Williams C P, Braunstein S L, Dowling J P 2001 Phys. Rev. A 63 063407
[28] Knysh S, Smelyanskil V N, Durkin G A 2011 Phys. Rev. A 83 021804
[29] Lee T W, Huver S D, Lee H, Kaplan L, McCracken S B, Min C, Uskov D B, Wildfeuer C F, Veronis G, Dowling J P 2009 Phys. Rev. A 80 063803
[30] Resch K J, Pregnell K L, Prevedel R, Gilchrist A, Pryde G J, O'Brien J L, White A G 2007 Phys. Rev. Lett. 98 223601
[31] Huver S D, Wildfeuer C F, Dowling J P 2008 Phys. Rev. A 78 063828
[32] Wang Q, Hao L L, Zhang Y, Xu L, Yang C H, Yang X, Zhao Y 2016 Opt. Express 24 5045
[33] Jiang K, Lee H, Gerry C C, Dowling J P 2013 J. Appl. Phys. 114 193102
[34] Fan H Y 1992 Representation and Transformation Theory in Quantum Mechanics (Shanghai: Shanghai Scientific and Technical Publishers) p44 (in Chinese) [范洪义 1992 量子力学表象与变换论(上海: 上海科学技术出版社) 第44页]
[35] Distante E, Jezek M, Andersen U L 2013 Phys. Rev. Lett. 111 033603
[36] Feng X M, Jin G Y, Yang W 2014 Phys. Rev. A 90 013807
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