We present a detailed analysis of phase sensitivity for a nonlinear Ramsey interferometer, which utilize effective mean-field interaction of a two-component Bose-Einstein condensate in phase ac- cumulation. For large ...We present a detailed analysis of phase sensitivity for a nonlinear Ramsey interferometer, which utilize effective mean-field interaction of a two-component Bose-Einstein condensate in phase ac- cumulation. For large enough particle number N and small phase shift φ, analytical results of the Ramsey signal and the phase sensitivity are derived for a product coherent state θ, 0）. When collisional dephasing is absent, we confirm that the optimal sensitivity scales as 2/N3/2 for polar angle of the initial state θ = π/4 or 3π/4. The best-sensitivity phase satisfies different transcendental equations, depending upon the initial state and the observable being measured after the phase accumulation. In the presence of the collisional dephasing, we show that the N-3/2-scaling rule of the sensitivity maintains with spin operators jx and jy measurements. A slightly better sensitivity is attainable for optimal coherent state with θ = π/6 or 5π/6.展开更多
We investigate the dependence of the average parameter estimation precision （APEP）, which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state ｜θ0,φ0〉 in a one-axis...We investigate the dependence of the average parameter estimation precision （APEP）, which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state ｜θ0,φ0〉 in a one-axis twisting model. Jin et al. [New J. Phys. 11 （2009） 073049] found that the spin squeezing sensitively depends on the polar angle θ0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ0 in the vicinity of π/2 and a near- Heisenberg limit 2IN in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ0- π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEE展开更多
考虑理想弹塑性弯扭-Mohr-Coulomb-最大拉应力破坏准则,以及拉伸失效、压剪失效、转动屈服和扭转屈服4种失效模式,提出一种新的离散元弹塑性本构模型。该模型植入二次开发的三维颗粒流程序,通过数值试验研究宏细观参数关系,模拟Lac du B...考虑理想弹塑性弯扭-Mohr-Coulomb-最大拉应力破坏准则,以及拉伸失效、压剪失效、转动屈服和扭转屈服4种失效模式,提出一种新的离散元弹塑性本构模型。该模型植入二次开发的三维颗粒流程序,通过数值试验研究宏细观参数关系,模拟Lac du Bonnet(LDB)花岗岩试样压剪和拉伸强度试验。研究表明:颗粒转动弹塑性弯扭矩对宏观内摩擦角和黏聚力具有显著影响;宏观黏聚力随细观黏聚力和屈服弯扭矩增加而趋于恒定;宏观内摩擦角随屈服弯扭矩和细观摩擦系数增加而增加;岩石宏观单轴抗拉强度随细观极限拉应力的增加而趋于恒定;宏观弹性模量和泊松比主要受细观弹性模量和刚度比影响。弹塑性颗粒流本构模型模拟的LDB花岗岩的强度参数和变形参数,以及压拉强度比和裂缝分布与室内试验结果吻合较好。LDB花岗岩单轴压剪模拟试验在达到峰值应力前,试样内部裂缝以细观拉伸裂缝为主,从试样端部向中部发展成近似X状;在接近或超过峰值应力后,试样内部开始出现压剪裂缝、转动屈服裂缝和扭转屈服裂缝,从试样一端向另一端发展成单斜状,其倾角与宏观破坏倾角接近,发展成宏观压剪破坏面,从而揭示了宏观裂缝形成的细观机理。展开更多
文摘We present a detailed analysis of phase sensitivity for a nonlinear Ramsey interferometer, which utilize effective mean-field interaction of a two-component Bose-Einstein condensate in phase ac- cumulation. For large enough particle number N and small phase shift φ, analytical results of the Ramsey signal and the phase sensitivity are derived for a product coherent state θ, 0）. When collisional dephasing is absent, we confirm that the optimal sensitivity scales as 2/N3/2 for polar angle of the initial state θ = π/4 or 3π/4. The best-sensitivity phase satisfies different transcendental equations, depending upon the initial state and the observable being measured after the phase accumulation. In the presence of the collisional dephasing, we show that the N-3/2-scaling rule of the sensitivity maintains with spin operators jx and jy measurements. A slightly better sensitivity is attainable for optimal coherent state with θ = π/6 or 5π/6.
基金supported by the National Basic Research Program of China(Grant No.2012CB921602)the National Natural Science Foundation of China(Grant Nos.11025527 and 10935010)
文摘We investigate the dependence of the average parameter estimation precision （APEP）, which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state ｜θ0,φ0〉 in a one-axis twisting model. Jin et al. [New J. Phys. 11 （2009） 073049] found that the spin squeezing sensitively depends on the polar angle θ0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ0 in the vicinity of π/2 and a near- Heisenberg limit 2IN in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ0- π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEE
文摘考虑理想弹塑性弯扭-Mohr-Coulomb-最大拉应力破坏准则,以及拉伸失效、压剪失效、转动屈服和扭转屈服4种失效模式,提出一种新的离散元弹塑性本构模型。该模型植入二次开发的三维颗粒流程序,通过数值试验研究宏细观参数关系,模拟Lac du Bonnet(LDB)花岗岩试样压剪和拉伸强度试验。研究表明:颗粒转动弹塑性弯扭矩对宏观内摩擦角和黏聚力具有显著影响;宏观黏聚力随细观黏聚力和屈服弯扭矩增加而趋于恒定;宏观内摩擦角随屈服弯扭矩和细观摩擦系数增加而增加;岩石宏观单轴抗拉强度随细观极限拉应力的增加而趋于恒定;宏观弹性模量和泊松比主要受细观弹性模量和刚度比影响。弹塑性颗粒流本构模型模拟的LDB花岗岩的强度参数和变形参数,以及压拉强度比和裂缝分布与室内试验结果吻合较好。LDB花岗岩单轴压剪模拟试验在达到峰值应力前,试样内部裂缝以细观拉伸裂缝为主,从试样端部向中部发展成近似X状;在接近或超过峰值应力后,试样内部开始出现压剪裂缝、转动屈服裂缝和扭转屈服裂缝,从试样一端向另一端发展成单斜状,其倾角与宏观破坏倾角接近,发展成宏观压剪破坏面,从而揭示了宏观裂缝形成的细观机理。
