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缀饰态的几何相位特征及其分布状态研究

立庆任, 永放李, 兆华王, 瑞琼马, 蕾王, 百宏李

Published Feb 1, 2010• 0 citations

Abstract

Suter等人 [9] 利用核磁共振方法在实验中证明了三能级系统中的A-A相拓扑不变性.2003 年Tian小组首次在可见光范围内利用光子回波技术, 在钡原子中实现了对几何相位的测量 [10] .次年该小组又在二能级系统中实现了对几何相位的操控 [11] .2003 年Du等人 [12] 利用核磁共振方法实现了对混合态几何相位的观测. 2006 年Ghosh和Kumar利用核磁共振效应测量了光场混合态的几何相位 [ 1 3 ] .以上的实验研究都是采用核磁共振和光子回波的方法(统称为回波方法). 然而, 由于回波方法具有一定的局限性, 因而克服其不足之处、研究探索测量几何相位的新方法有着重要的科学意义.通常测量几何相位所采用的回波方法是利用π脉冲技术实现时间反演, 从而实现对几何相位的测量.这种方法的不足之处有: (ⅰ) 若原子系统在含时外场非共振作用下, 例如强高斯脉冲光场, 如图 1 所示, 这时几何相位 ( ) π (1 cos ( )) t t γ θ = ± -中的θ 是时间的函数, 与制备量子态的外场有关.对于不同时刻的t, cos(θ (t))不同, 因此几何相位会随时间变化.对于这种情况, 利用回波技术是无法实现对几何相位的精确测量.(ⅱ) 不能直接从探测信号中获取几何相位信息, 而是通过已知的脉冲面积和所完成的周期演化方式确定几何相位.(ⅲ) 实验中对光场的控制技术和对信号检测技术的要求较高.回波技术要求作用的脉冲场之间要有时序和脉冲面积的控制.

DOI: 10.1360/2010-40-1-47

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Suter等人 [9] 利用核磁共振方法在实验中证明了三能级系统中的A-A相拓扑不变性.2003 年Tian小组首次在可见光范围内利用光子回波技术, 在钡原子中实现了对几何相位的测量 [10] .次年该小组又在二能级系统中实现了对几何相位的操控 [11] .2003 年Du等人 [12] 利用核磁共振方法实现了对混合态几何相位的观测. 2006 年Ghosh和Kumar利用核磁共振效应测量了光场混合态的几何相位 [ 1 3 ] .以上的实验研究都是采用核磁共振和光子回波的方法(统称为回波方法). 然而, 由于回波方法具有一定的局限性, 因而克服其不足之处、研究探索测量几何相位的新方法有着重要的科学意义.通常测量几何相位所采用的回波方法是利用π脉冲技术实现时间反演, 从而实现对几何相位的测量.这种方法的不足之处有: (ⅰ) 若原子系统在含时外场非共振作用下, 例如强高斯脉冲光场, 如图 1 所示, 这时几何相位 ( ) π (1 cos ( )) t t γ θ = ± -中的θ 是时间的函数, 与制备量子态的外场有关.对于不同时刻的t, cos(θ (t))不同, 因此几何相位会随时间变化.对于这种情况, 利用回波技术是无法实现对几何相位的精确测量.(ⅱ) 不能直接从探测信号中获取几何相位信息, 而是通过已知的脉冲面积和所完成的周期演化方式确定几何相位.(ⅲ) 实验中对光场的控制技术和对信号检测技术的要求较高.回波技术要求作用的脉冲场之间要有时序和脉冲面积的控制.

文章介绍了王力军等人的光脉冲在反常色散介质中传播实验的测量结果,说明了实验测量的不完全性,因而它不可能在是否超光速的问题上给出明确的答案.文章还介绍了近一年来相应的理论研究工作.文章作者依据物理概念和理论研究结果论证了该实验所得的负群速度本身并不超光速;如果把负群速度看成是某种能量的传播,那么超光速出现在负群速度开始时的瞬间,因而它是超距作用,违反能量守恒或动量守恒.因此,负群速度只是表观速度,能流的研究结果也证明了这一点.这就是说,该实验并没有观察到超光速传播.

Robert Aaron Tseglin's New Retrocausal Calculus COMPREHENSIVE A+B MAX Rigorous — Part A Solid Mathematics + Part B Physical Mapping — DOI Chain 10.5281/zenodo.23376206 → 23403697 FINAL —

S=2\theta_H

V_T=|\cos\theta_H\cos(\theta_H/2)|

V_T(90°)=0

S_T=2.40

l_T=5e-8

m Certified 37-point Protocol

Comprehensive rigorous version combining Part A Solid Mathematics and Part B Physical Mapping. Part A: Unique bi-invariant Haar measure dμ_T=sin^2(S/2)dS on SU(2) ≅ S^3, Weyl Hall Thm 11.10, metric ds^2=dS^2/4+sin^2(S/2)dΩ^2, Hermitian momentum p=-iħ(d_S+1/2 cot(S/2)) in L^2([0,2π],sin^2(S/2)dS). Part B Maximum Proofs:B1 S=2θ_H mapping from photon polarization SU(2) Jones J_HWP=exp(i2θ_H σ_y) double cover, Pancharatnam-Berry holonomy S=∮A=2θ_H, BBO Type-II phase matching S_k=l_T^2 k^μ k_μ.B2 V_T=|cosθ_H cos(θ_H/2)| from Haar-weighted amplitude ψ(S)=√(dμ_T/dS) e^{iS/2}=sin(S/2)e^{iS/2}, integral ∫sin^2(S/2)cos(S/2-θ_H)=π cosθ_H cos(θ_H/2), V_T(90°)=0 vs QM flat 0.95, S_T=2.40 matches loophole-free average 2.40±0.03.B3 P_T=|exp(iS1)sin(S1/2)+exp(iS2)sin(S2/2)|^2 zero at 2πn erasing Gödel 1949 Tipler 1974 Morris-Thorne 1ly wormhole 10cm CTCs, deriving Born P∝sin^2(S/2). Falsifiable at Z~31 null Z=21.75 confirmation >20σ, certified protocol 37 points 0-180° step 5° cost €2500 $2700 without participation. Both outcomes publishable: null first bound l_T<1e-8m λ_c<35nm = 3 PRLs, confirmation first observation l_T=5e-8m = 2 Nature Physics. Closes DOI chain 23376206→23403697 FINAL. For PRL submission with certified CSV SHA256. Author: Robert Aaron Tseglin, Kefar HaNagid, Israel.

First 95% CL bound l_T < 10 nm on effective HWP-like retrocausal model V_T = |cosθ_H cos(θ_H/2)|, V_T(90°)=0, with SU(2) Haar measure dμ_T = sin²(S/2) dS, S=2θ_H [Hall Thm 11.10, Jones 1941]. This is v4 combining:1. Original retrocausal calculus derivation: Jones matrix J_HWP(θ_H), retrocausal projection ansatz A_T = <H|J_HWP|H>·cos(θ_H/2) → V_T = |cosθ_H cos(θ_H/2)|.2. Experimental test: 37 Bell visibility points flat V_exp = 0.95 ±0.03 from Kwiat 99.6%±0.3% [PRL 75, 4337 (1995)] to 2015 loophole-free tests [Hensen Nature 526, 682 (2015), Giustina PRL 115, 250401 (2015), Shalm PRL 115, 250402 (2015)]. No V=0 observed at 90°. Raw model excluded at Z_null = 31.7σ, χ²_T ~473 vs χ²_QM ~2.1, single point χ²=1002.8 at 90°.3. Suppression buffer: V_T,corr = V_QM [1 - (l_T/L_0)² (1-V_T)], L_0=1μm, V_QM=0.95. With l_T=10 nm, s=1e-4, V_corr=0.9499, χ²=1e-5 compatible. Bound l_T <1.0e-8 m 95% CL. THERMODYNAMIC PROOF OF BUFFER via Landauer Principle:E_L = k_B T ln2 = 2.87e-21 J [Landauer IBM J. 5, 183 (1961)].E_avail = ħc l_T / L_0², ħc=3.16e-26 J·m.At l_T=10 nm, L_0=1 μm: E_avail=3.16e-22 J, ratio E_L/E_avail = 9.08.Exact if L_0^derived = sqrt(ħc l_T / E_L) = 332 nm = typical HWP dielectric coating thickness — more physical than 1 μm.Thus buffer η = (l_T/L_0)²(1-V_T) = E_erase/E_avail derived as E_L/E_vac.Same quality as Landauer dark energy derivations ρ_Λ ~ c⁴/(G L_dS²) solving 1e122 CC discrepancy [Bekenstein PRD 7, 2333 (1973), Lloyd PRL 88, 237901 (2002), Gough Entropy 15, 4108 (2013)]. Classification: (i) σ derived, (ii) ∫dμ_T=π/2 derived SU(2) Haar, (iii) V_T derived from chosen Jones+SU(2) ansatz, (iv) (l_T/L_0)² inserted but now thermodynamically derived within factor 9.

双数态是量子相位估计问题中的有用资源，其作为马赫-曾德尔干涉仪输入态，可使得相位测量精度突破标准量子极限。然而，符合计数探测导致双数态的相位分布函数（即似然函数）出现多峰结构，出现相位模糊。针对这一问题，提出一种可消除相位模糊的简便方案，并对其有效性进行分析。该方案的核心是将N光子双数态和单光子分别注入干涉仪中，使得总的相位分布函数具有单峰结构，由此得到唯一最大似然估计量，该估计量的涨落在整个相位区间均优于标准量子极限。

Abstract We propose improved ring shaped like potential of the form, V(r, θ) = V(r) + (ħ 2 /2Mr 2 )[(β sin 2 θ + γ cos 2 θ + λ) / sin θ cos θ] 2 and its exact solutions are presented via the Nikiforov–Uvarov method. The angle dependent part V(θ) = (ħ 2 / 2 Mr 2 )[(β sin 2 θ + γ cos 2 θ + λ) / sin θ cos θ] 2 , which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.