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Vacuum fluctuation at audio frequencies is very important and interesting in many research fields, such as the gravitational wave detection, ultra-weak magnetic field measurement, and the research of quantum metrology, etc. Since the generation of squeezed light in 1985, most of the squeezed light have been generated and measured at radio frequencies (～MHz) as there has not been much technical noise at higher frequencies. In the Michelson-interferometer-based gravitational wave detection, the detection band has frequencies from a few to tens of thousands Hz. Measuring vacuum noise at such low frequencies is a challenge since we have to stabilize and control all the audio noises and the interferences from a variety of mechanical and electronic noises, therefore a very high classical noise suppression is needed when the measurement time increases. In order to measure the squeezed light of low frequencies, the standard vacuum noise at audio frequencies must be measured. In this paper, a balanced homodyne detection system for measuring the low-frequency quantum vacuum noises is reported. It is not trivial to extend the detected frequency to very low analysis frequencies. Through a self-made self-subtraction balanced homodyne configuration, which can eliminate the DC component of each photocurrent from the photodiode and the classical common-mode technical noise, the standard vacuum noise has been detected. The linearity of the vacuum noise power has been validated by varying the local oscillator power, showing that the saturation power of light incidence is about 3.2 mW. When the incident-light power is 400 W, the standard vacuum noise is 11 dB higher than the electronic noise at 80 Hz. In the regime of about 80 Hz to 400 kHz, the linearity of the standard noise power as a function of incident laser power is verified. However, when the measurement is carried out at even lower frequencies, for example, 50 Hz, we may encounter some excess and non-stationary noises and find that the measured noise power is not proportional to the incident light power any more. These non-stationary noises are the main technical obstacle at low frequencies. The average common mode rejection ratio in the test frequency range from 10 Hz to 400 kHz is 55 dB and its maximum 63 dB at 100 Hz is obtained, implying a high suppression of the technical noise. This self-made homodyne vacuum noise detector can be widely used for precision measurement in quantum metrology and quantum optics.
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Keywords:
- low frequency /
- quantum vacuum noise /
- balanced homodyne detection /
- common mode rejection ratio
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[2] Goda K, Miyakawa O, Mikhailov E E, Saraf S, Adhikari R, McKenzie K, Ward R, Vass S, Weinstein A J, Mavalvala N 2008 Nat. Phys. 4 472
[3] Chelkowski S 2007 Ph. D. Dissertation (Hannover: Gottfried Wilhelm Leibniz Universitt)
[4] Koschorreck M, Napolitano M, Dubost B, Mitchell M W 2010 Phys. Rev. Lett. 104 093602
[5] Wolfgramm F, Cer A, Beduini F A, Predojević A, Koschorreck M, 2010 Phys. Rev. Lett. 105 053601
[6] Horrom T, Singh R, Dowling J P, Mikhailov E E 2012 Phys. Rev. A 86 023803
[7] Banaszek K, Demkowicz-Dobrzański R, Walmsley I A 2009 Nat. Photon. 3 673
[8] Slusher R E, Hollberg L W, Yurke B, Mertz J C, Valley J F 1985 Phys. Rev. Lett. 55 2409
[9] Mehmet M, Ast S, Eberle T, Steinlechner S, Vahlbruch H, Schnabel R 2011 Opt. Express 19 25763
[10] Zhang T C, Zhang J X, Xie C D, Peng K C 1998 Acta Phys. Sin. 7 340 (Overseas Edition)
[11] Zhang T C, Li T Y, Effenterre D V, Xie C D, Peng K C 1998 Acta Phys. Sin. 47 1498 (in Chinese) [张天才, 李廷鱼, Effenterre D V, 谢常德, 彭堃墀 1998 47 1498]
[12] Dong R F, Zhang J X, Zhang T C, Zhang J, Xie C D, Peng K C 2001 Acta Phys. Sin. 50 462 (in Chinese) [董瑞芳, 张俊香, 张天才, 张 靖, 谢常德, 彭堃墀 2001 50 462]
[13] Zhou Q Q, Liu J L, Zhang K S 2010 Acta Sin. Quantum Opt. 16 152 (in Chinese) [周倩倩, 刘建丽, 张宽收 2010 量子光学学报 16 152]
[14] Wang J J, Jia X J, Peng K C 2012 Acta Opt. Sin. 31 0127001 (in Chinese) [王金晶, 贾晓军, 彭堃墀 2012 光学学报 31 0127001]
[15] McKenzie K 2008 Ph. D. Dissertation (Canberra: Australian National University)
[16] Vahlbruch H, Chelkowski S, Danzmann K, Schnabel R 2007 New J. Phys. 9 371
[17] Vahlbruch H 2008 Ph. D. Dissertation (Hannover: The Albert Einstein Institute and the Institute of Gravitational Physics of Leibniz Universitt Hannover)
[18] Stefszky M S, Mow-Lowry C M, Chua S S Y, Shaddock D A, Buchler B C, Vahlbruch H, Khalaidovski A, Schnabel R, Lam P K, McClelland D E 2012 Class. Quantum Grav. 29 145015
[19] Dwyer S E 2013 Ph. D. Dissertation (Cambridge: Massachusetts Institute of Technology)
[20] The LIGO Scientific Collaboration 2011 Nat. Phys. 7 962
[21] Stefszky M S 2012 Ph. D. Dissertation (Canberra: Australian National University)
[22] Rogalski A (translated by Zhou H X, Cheng Y F) 2014 Infrared Detectors (Beijing: China Machine Press) pp47, 48 (in Chinese) [罗格尔斯基 A 著 (周海宪, 程云芳 译) 2014 红外探测器(北京: 机械工业出版社)第47, 48页]
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[1] Caves C M 1981 Phys. Rev. D 23 1693
[2] Goda K, Miyakawa O, Mikhailov E E, Saraf S, Adhikari R, McKenzie K, Ward R, Vass S, Weinstein A J, Mavalvala N 2008 Nat. Phys. 4 472
[3] Chelkowski S 2007 Ph. D. Dissertation (Hannover: Gottfried Wilhelm Leibniz Universitt)
[4] Koschorreck M, Napolitano M, Dubost B, Mitchell M W 2010 Phys. Rev. Lett. 104 093602
[5] Wolfgramm F, Cer A, Beduini F A, Predojević A, Koschorreck M, 2010 Phys. Rev. Lett. 105 053601
[6] Horrom T, Singh R, Dowling J P, Mikhailov E E 2012 Phys. Rev. A 86 023803
[7] Banaszek K, Demkowicz-Dobrzański R, Walmsley I A 2009 Nat. Photon. 3 673
[8] Slusher R E, Hollberg L W, Yurke B, Mertz J C, Valley J F 1985 Phys. Rev. Lett. 55 2409
[9] Mehmet M, Ast S, Eberle T, Steinlechner S, Vahlbruch H, Schnabel R 2011 Opt. Express 19 25763
[10] Zhang T C, Zhang J X, Xie C D, Peng K C 1998 Acta Phys. Sin. 7 340 (Overseas Edition)
[11] Zhang T C, Li T Y, Effenterre D V, Xie C D, Peng K C 1998 Acta Phys. Sin. 47 1498 (in Chinese) [张天才, 李廷鱼, Effenterre D V, 谢常德, 彭堃墀 1998 47 1498]
[12] Dong R F, Zhang J X, Zhang T C, Zhang J, Xie C D, Peng K C 2001 Acta Phys. Sin. 50 462 (in Chinese) [董瑞芳, 张俊香, 张天才, 张 靖, 谢常德, 彭堃墀 2001 50 462]
[13] Zhou Q Q, Liu J L, Zhang K S 2010 Acta Sin. Quantum Opt. 16 152 (in Chinese) [周倩倩, 刘建丽, 张宽收 2010 量子光学学报 16 152]
[14] Wang J J, Jia X J, Peng K C 2012 Acta Opt. Sin. 31 0127001 (in Chinese) [王金晶, 贾晓军, 彭堃墀 2012 光学学报 31 0127001]
[15] McKenzie K 2008 Ph. D. Dissertation (Canberra: Australian National University)
[16] Vahlbruch H, Chelkowski S, Danzmann K, Schnabel R 2007 New J. Phys. 9 371
[17] Vahlbruch H 2008 Ph. D. Dissertation (Hannover: The Albert Einstein Institute and the Institute of Gravitational Physics of Leibniz Universitt Hannover)
[18] Stefszky M S, Mow-Lowry C M, Chua S S Y, Shaddock D A, Buchler B C, Vahlbruch H, Khalaidovski A, Schnabel R, Lam P K, McClelland D E 2012 Class. Quantum Grav. 29 145015
[19] Dwyer S E 2013 Ph. D. Dissertation (Cambridge: Massachusetts Institute of Technology)
[20] The LIGO Scientific Collaboration 2011 Nat. Phys. 7 962
[21] Stefszky M S 2012 Ph. D. Dissertation (Canberra: Australian National University)
[22] Rogalski A (translated by Zhou H X, Cheng Y F) 2014 Infrared Detectors (Beijing: China Machine Press) pp47, 48 (in Chinese) [罗格尔斯基 A 著 (周海宪, 程云芳 译) 2014 红外探测器(北京: 机械工业出版社)第47, 48页]
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