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Spin noise spectroscopy (SNS) is a new kind of Faraday rotation technique, which does not need spin injection to generate polarized spin. This method uses a linearly polarized laser to detect the spontaneous spin fluctuation in a thermal equilibrium state. However, the signal of spontaneous spin fluctuation is so weak (~V) in the thermal equilibrium system that a big signal-noise ratio (SNR) is often demanded. Here, we report on the build-up and improvement of a spin noise spectrum measurement system. A home-made field-programmable gate array (FPGA) based data-acquisition card with real-time fast Fourier transform (DAC-FFT) is used to improve the SNR of the SNS measurement system. The reduction of intrinsic noise in the experimental system is discussed in detail. Both the dependence of background noise and the dependence of spin noise on the intensity of probe laser are analyzed. We find that the background noise is proportional to the intensity of the probe laser, while the spin noise signal shows square dependence on probe laser intensity. The spin noise indeed comes from the spontaneous spin fluctuation as experimentally confirmed via an acousto-optic modulator (AOM) inserted in the measurement system. The measurement performances of two FPGA based DAC-FFTs (the 8-bit FFTsDAC1 and the 12-bit FFTsDAC2, respectively) are compared. Several factors are found to affect the SNR of the system, including the measurement efficiency and the acquisition resolution. The FFTsDAC2 has longer single acquisition time and faster data transmission speed (with USB 3.0) than the FFTsDAC1, when the total measurement time is set to be the same, the effective measurement time realized in FFTsDAC2 is longer than in FFTsDAC1. With better measurement efficiency and sampling depth and longer single acquisition time, the FFTsDAC2 has a better SNR and finer frequency resolution with a much narrower full width at half maximum (FWHM) value. Moreover, the simulations of the measurement process show the effect of the single acquisition time on the FWHM of spin noise peak, further clarifying the reason why the spin noise spectrum measured by FFTsDAC2 is more accurate.
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Keywords:
- spin noise spectroscopy /
- background noise /
- Faraday rotation /
- data-acquisition card with real-time fast Fourier transforms
[1] Mller G M, Oestreich M, Rmer M, Hbner J 2010 Physica E 43 569
[2] Crooker S A, Cheng L, Smith D L 2009 Phys. Rev. B 79 035208
[3] Aleksanfrov E B, Zapassky V S 1981 JETP 81 132
[4] Crooker S A, Rickel D G, Balatsky A V, Smith D L 2004 Nature 431 49
[5] Oestreich M, Rmer M, Haug R J, Hgele D 2005 Phys. Rev. Lett. 95 216603
[6] Rmer M, Hbner J, Oestreich M 2007 Rev. Sci. Instrum. 78 103903
[7] Crooker S A, Brandt J, Sandfort C, Greilich A, Yakovlev D R, Reuter D, Wieck A D, Bayer M 2010 Phys. Rev. Lett. 104 036601
[8] Mller G M, Rmer M, Hbner J, Oestreich M 2010 Appl. Phys. Lett. 97 192109
[9] Quirk M P, Garyantes M F, Wilck H C, Grimm M J 1988 IEEE Trans. Acoust., Speech, Signal Processing 36 1854
[10] Iglesias V, Grajal J, Snchez A, Vallejo M L 2015 IEEE Trans. Instrum. Meas. 64 338
[11] Shi P, Ma J, Qian X, Ji Y, Li W 2017 Acta Phys. Sin. 66 017201 (in Chinese)[史平, 马健, 钱轩, 姬扬, 李伟 2017 66 017201]
[12] Shannon C E 1949 Proc. IRE 37 10
[13] Demtrder W (translated by Ji Y) 2012 Laser Spectroscopy (4th Ed., Vol. 1) (Beijing:Science Press) pp162-163 (in Chinese)[戴姆特瑞德 著 (姬扬 译) 2012 激光光谱学:(原书第四版第1卷) (北京:科学出版社)第162163页]
[14] Horn H, Mller G M, Rasel E M, Santos L, Hbner J, Oestreich M 2011 Phys. Rev. A 84 043851
[15] Ma J, Shi P, Qian X, Li W, Ji Y 2016 Chin. Phys. B 25 117203
[16] Arimondo E, Inguscio M, Violino P 1977 Rev. Mod. Phys. 49 31
[17] Bize S, Sortais Y, Santos M S, Clairon A, Salomon C 1999 Europhys. Lett. 45 558
[18] Zhu Y S 2006 Probability and Statistics in Experimental Physics (2nd Ed.) (Beijing:Science Press) pp431-433 (in Chinese)[朱永生 2006 实验物理中的概率和统计(第二版)(北京:科学出版社) 第431433]
[19] Demtrder W (translated by Ji Y) 2012 Laser Spectroscopy (4th Ed., Vol. 1) (Beijing:Science Press) pp74-77 (in Chinese)[戴姆特瑞德 著(姬扬 译) 2012 激光光谱学 (原书第四版第1卷) (北京:科学出版社)第7477页]
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[1] Mller G M, Oestreich M, Rmer M, Hbner J 2010 Physica E 43 569
[2] Crooker S A, Cheng L, Smith D L 2009 Phys. Rev. B 79 035208
[3] Aleksanfrov E B, Zapassky V S 1981 JETP 81 132
[4] Crooker S A, Rickel D G, Balatsky A V, Smith D L 2004 Nature 431 49
[5] Oestreich M, Rmer M, Haug R J, Hgele D 2005 Phys. Rev. Lett. 95 216603
[6] Rmer M, Hbner J, Oestreich M 2007 Rev. Sci. Instrum. 78 103903
[7] Crooker S A, Brandt J, Sandfort C, Greilich A, Yakovlev D R, Reuter D, Wieck A D, Bayer M 2010 Phys. Rev. Lett. 104 036601
[8] Mller G M, Rmer M, Hbner J, Oestreich M 2010 Appl. Phys. Lett. 97 192109
[9] Quirk M P, Garyantes M F, Wilck H C, Grimm M J 1988 IEEE Trans. Acoust., Speech, Signal Processing 36 1854
[10] Iglesias V, Grajal J, Snchez A, Vallejo M L 2015 IEEE Trans. Instrum. Meas. 64 338
[11] Shi P, Ma J, Qian X, Ji Y, Li W 2017 Acta Phys. Sin. 66 017201 (in Chinese)[史平, 马健, 钱轩, 姬扬, 李伟 2017 66 017201]
[12] Shannon C E 1949 Proc. IRE 37 10
[13] Demtrder W (translated by Ji Y) 2012 Laser Spectroscopy (4th Ed., Vol. 1) (Beijing:Science Press) pp162-163 (in Chinese)[戴姆特瑞德 著 (姬扬 译) 2012 激光光谱学:(原书第四版第1卷) (北京:科学出版社)第162163页]
[14] Horn H, Mller G M, Rasel E M, Santos L, Hbner J, Oestreich M 2011 Phys. Rev. A 84 043851
[15] Ma J, Shi P, Qian X, Li W, Ji Y 2016 Chin. Phys. B 25 117203
[16] Arimondo E, Inguscio M, Violino P 1977 Rev. Mod. Phys. 49 31
[17] Bize S, Sortais Y, Santos M S, Clairon A, Salomon C 1999 Europhys. Lett. 45 558
[18] Zhu Y S 2006 Probability and Statistics in Experimental Physics (2nd Ed.) (Beijing:Science Press) pp431-433 (in Chinese)[朱永生 2006 实验物理中的概率和统计(第二版)(北京:科学出版社) 第431433]
[19] Demtrder W (translated by Ji Y) 2012 Laser Spectroscopy (4th Ed., Vol. 1) (Beijing:Science Press) pp74-77 (in Chinese)[戴姆特瑞德 著(姬扬 译) 2012 激光光谱学 (原书第四版第1卷) (北京:科学出版社)第7477页]
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