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In this paper, we study the spatial noise fluctuations of the density distribution of non-interacting 6Li ultracold Fermi gases. For ideal ultracold Fermi gases, the Fermi-Dirac statistics governs its quantum distribution. The suppression of density fluctuations at low temperature, due to Pauli exclusion principle, is observed in a large cloud of fermions. To clearly reveal the density noise fluctuations of the ideal Fermi gases, other noises, such as the background noise, imaging laser noise, CCD photon counting noise, are greatly suppressed. The noise fluctuation shows a sub-Poissonian statistics in excess of 10,000 atoms per spin state. The dependence of the spatial atom noise fluctuation on the quantum degeneracy is also investigated by changing the temperature of the degenerated Fermi gases. The Fermi gases with lower temperature exhibit larger suppression of the noise fluctuations. The results may have great applications in measuring the temperature of strongly correlated many-body physics and observing the phase transition of incompressible quantum phases.
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Keywords:
- ideal Fermi gas /
- 6Li quantum degenerate Fermi gas /
- Pauli suppression /
- density fluctuations
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图 1 成像光路示意图. 其中符号的含义为FC: 光纤耦合头, PBS: 偏振分束器, F1—F4: 透镜, OB: 5×成像物镜, CCD: 电荷耦合器件.
Figure 1. Imaging setup for noise measurements. The meaning of each symbol: FC: Fiber Collimator, PBS: polarization beam splitter, F1–F4: lens, OB: 5× imaging objective, CCD: charge coupled device.
图 2 原子OD随成像光光强的变化关系. 蓝点为实验数据, 红线为高斯公式拟合结果
Figure 2. The relationship between atomic OD and imaging light intensity. The blue point is the experimental data, and the red line is the fitting result of Gaussian formula.
图 3 不同温度下原子数涨落Var(N)与平均原子数
$\left\langle N \right\rangle $ 的关系. 红色为高温${T=}{0.7}{{T}}_{\rm{F}}$ , 蓝色为低温${T=}{0.3}{{T}}_{\rm{F}}$ , 红色虚线是对高温数据密度较低时的拟合, 斜率为0.55, 这个数值反映了系统真实的散射截面为理论值的55%Figure 3. The relationship between the fluctuation of atomic number and the average atomic number at different temperatures. Red is high temperature
${T=}{0.7}{{T}}_{\rm{F}}$ , blue is low temperature${T=}{0.3}{{T}}_{\rm{F}}$ , red dotted line is the fitting of high temperature data with low density, and the slope is 0.55, which reflects that the real scattering cross section of the system is 55% of the theoretical value.
图 4 不同温度下原子密度与密度涨落的比较 (a)
${T}{=}{0.}{3}{{T}}_{\rm{F}}$ ; (b)${T}{=}{0.7}{{T}}_{\rm{F}}$ . 图中左侧为原子密度分布, 右侧为密度涨落Figure 4. Comparison of atomic density and density fluctuation at different temperatures: (a)
${T}{=}{0.}{3}{{T}}_{\rm{F}}$ ; (b)${T}{=}{0.7}{{T}}_{\rm{F}}$ . In figure (a) (b), the distribution of atomic density is on the left, and the density fluctuation is on the right.
图 5 不同温度下原子密度与密度涨落的空间分布. 图中红线为原子密度分布, 蓝线为密度涨落分布
Figure 5. Spatial distribution of atomic density and density fluctuation at different temperatures. The red line is the atomic density distribution and the blue line is the density fluctuation distribution.
图 6 密度涨落Var
$ (N)/\langle N\rangle $ 随温度的变化. 其中虚线为理论计算, 蓝点为实验测量结果, 此时BIN = 8Figure 6. Density fluctuation with temperature. The blue point is the experimental result, where BIN = 8 and the dotted line is the theoretical curve.
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[1] Zheng H, Bonasera A 2011 Phys. Lett. B 696 178
Google Scholar
[2] Zheng H, Giuliani G, Bonasera A 2012 Nucl. Phys. A 892 43
Google Scholar
[3] Sanner C, Su E J, Huang W, Keshet A, Gillen J, Ketterle W 2012 Phys. Rev. Lett. 108 240404
Google Scholar
[4] Sanner C, Su E J, Keshet A, Huang W, Gillen J, Gommers R, Ketterle W 2011 Phys. Rev. Lett. 106 010402
Google Scholar
[5] Altman E, Demler E, Lukin M D 2004 Phys. Rev. A 70 013603
Google Scholar
[6] Bruun G M, Syljuåsen O F, Pedersen K G L, Andersen B M, Demler E, Sørensen A S 2009 Phys. Rev. A 80 033622
Google Scholar
[7] Singh V P, Mathey L 2014 Phys. Rev. A 89 053612
Google Scholar
[8] Guarrera V, Fabbri N, Fallani L, Fort C, Stam V D, Inguscio M 2008 Phys. Rev. Lett. 100 250403
Google Scholar
[9] Petrov D S, Salomon C, Shlyapnikov G V 2004 Phys. Rev. Lett. 93 090404
Google Scholar
[10] DeMarco B, Papp B S, Jin D S 2001 Phys. Rev. Lett. 86 5409
Google Scholar
[11] Sanner C, Su E J, Keshet A, Gommers R, Shin Y, Huang W, Ketterle W 2010 Phys. Rev. Lett. 105 040402
Google Scholar
[12] Müller T, Zimmermann B, Meineke J, Brantut J, Esslinger T, Moritz H 2010 Phys. Rev. Lett. 105 040401
Google Scholar
[13] Chen X W, Liu Z Q, Kong X M 2014 Chin. Phys. B 23 026701
Google Scholar
[14] 袁都奇 2016 物理学报 65 180302
Google Scholar
Yuan D Q 2016 Acta Phys. Sin. 65 180302
Google Scholar
[15] 刁鹏鹏, 邓书金, 李芳, 武海斌 2019 物理学报 68 046702
Google Scholar
Diao P P, Deng S J, Li F, Wu H B 2019 Acta Phys. Sin. 68 046702
Google Scholar
[16] Esteve J, Trebbia J B, Schumm T, Aspect A, Westbrook C I, Bouchoule I 2006 Phys. Rev. Lett. 96 130403
Google Scholar
[17] Armijo J 2012 Phys. Rev. Lett. 108 225306
Google Scholar
[18] Whitlock S, Ockeloen C F, Spreeuw R J C 2010 Phys. Rev. Lett. 104 120402
Google Scholar
[19] Esteve J, Gross C, Weller A, Giovanazzi S, Oberthaler M K 2008 Nature 455 1216
Google Scholar
[20] Itah A, Veksler H, Lahav O, Blumkin A, Moreno C, Gordon C, Steinhauer J 2010 Phys. Rev. Lett. 104 113001
Google Scholar
[21] Tobias W G, Matsuda K, Valtolina G, Marco L D, Li J, Ye J 2020 Phys. Rev. Lett. 124 033401
Google Scholar
[22] Jördens R, Strohmaier N, Günter K, Moritz H, Esslinger T 2008 Nature 455 204
Google Scholar
[23] Werner F, Parcollet O, Georges A, Hassan S R 2005 Phys. Rev. Lett. 95 056401
Google Scholar
[24] Deng S, Diao P, Yu Q, Wu H 2015 Chin. Phys. Lett. 32 052401
Google Scholar
[25] Deng S, Shi Z, Diao P, Yu Q, Zhai H, Qi R, Wu H 2016 Science 353 371
Google Scholar
[26] Bruun M, Clark C W 2000 Phys. Rev. A 61 061601(R)
Google Scholar
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