第五章相干态和压缩态一、相干态二、压缩态三、相干态和压缩态的电磁场表示四、薛定谔猫态（作业）五、思考题20241020ygu@pku.edu.cn2
2 第五章 相干态和压缩态 一、相干态 二、压缩态 三、相干态和压缩态的电磁场表示 五、思考题（作业） 四、薛定谔猫态 20241020 ygu@pku.edu.cn
TheNobelPrize inPhysics2005RoyJ.GlauberBorn:1925,NewYork,NY,USADied:2018,Newton,MA, USAAffiliation:Harvard UniversityPrize motivation:"for his contribution to thequantum theory of optical coherence.""According to quantum physics, which was developed at the beginningofthe2Oth century,light andotherelectromagnetic radiation appear intheform of quanta,packets with fixed energies, whichcanbe describedasboth waves and as particles, photons.However, no real in-depth theory oflightbased on quantum theory existed before Roy Glauber establishedthefoundationforquantumopticsin 1963.Thisrequiredthedevelopment ofthe laser:Its concentrated and coherentlightgave rise tomore quantum physical phenomena than regular light."https://www.nobelprize.org/prizes/phvsics/2005/glauber/facts/3
3 The Nobel Prize in Physics 2005 Roy J. Glauber Born: 1925, New York, NY, USA Died: 2018, Newton, MA, USA Affiliation: Harvard University Prize motivation: "for his contribution to the quantum theory of optical coherence." “According to quantum physics, which was developed at the beginning of the 20th century, light and other electromagnetic radiation appear in the form of quanta, packets with fixed energies, which can be described as both waves and as particles, photons. However, no real in-depth theory of light based on quantum theory existed before Roy Glauber established the foundation for quantum optics in 1963. This required the development of the laser. Its concentrated and coherent light gave rise to more quantum physical phenomena than regular light.” https://www.nobelprize.org/prizes/physics/2005/glauber/facts/
压缩态1.0完美0.75压缩态AX20.5定义：相干态0.2500.750.250.51.0AX1相于态与理想压缩态都是符合最小测不准关系的量子态令Xi = (a + at)/2, X2 = (a-at)/(2i), [Xi, X2]=i/ 2 。测不准关系允许的范围为：14Xi4X1 ≥4相干态是4X1=4X2=1/2的量子态而压缩态则是4X1或4X2>1/2的量子态
4 l 相干态与理想压缩态都是符合最小测不准关系的量子态 l 令�! = (� + �")/2，�# = (� − �")/(2�)，[�!, �#]= � / 2 。 测不准关系允许的范围为： ��!��! ≥ 1 4 相干态是��! = ��# = 1/2的量子态 而压缩态则是��!或��# > 1/2的量子态 定义：
一、相干态1.相干态的几个侧面a）经典电流辐射b)平移的真空态—|α)=D(α)I0)ca的本征态—a[α)=αα)其中b)和c）的等价性可以推导（相干态的一个例子）a)经典电流辐射如果存在随时间变化的电流（，t），那么它辐射出的电磁场就是相干态在Maxwell方程组中，电流出现在VxH=D+j，以及Vj=atap中at5
5 一、相干态 1. 相干态的几个侧面 a) 经典电流辐射 b) 平移的真空态——|�⟩ = �(�)|0⟩ c) �的本征态——�|�⟩ = �|�⟩ 其中b)和c) 的等价性可以推导 a) 经典电流辐射（相干态的一个例子） l 如果存在随时间变化的电流 ⃗ �(� ⃗ ,�)，那么它辐射出的电磁场 就是相干态 l 在Maxwell方程组中，电流出现在∇×� = $% $& + ⃗ �，以及∇ = ⃗ � = − $' $&中
下面考虑电流与磁势的相互作用。在辐射规范下V.A= 0,Φ= 0于是磁矢势与电场、磁场的关系为aAE--9B = VxA,at从量子化电场=ZkekEkake-ivkt+i-T+H.c.可以得到量子化的磁矢势Zkletekae-it+i- + H.c.A(r,t) = -ikVk电流与磁矢势的相互作用（由于经典电流（，t）的存在而附加的能量可由如下哈密顿量给出：V(t) = [i(r,t) · A(r,t)d3r6
6 l 下面考虑电流与磁矢势的相互作用。在辐射规范下 ∇ = � ⃗ = 0,� = 0 于是磁矢势与电场、磁场的关系为 � = ∇×� ⃗ , � = − �� ⃗ �� 从量子化电场 C � = ∑( �(�(�(�)*+!&,*(-/⃗ + �. �.可以得到量 子化的磁矢势 � ⃗ � ⃗ ,� = −�I( 1 �( �(�(�(�)*+!&,*(-/⃗ + �. �. 电流与磁矢势的相互作用(由于经典电流⃗ �(� ⃗ ,�)的存在而 附加的能量)可由如下哈密顿量给出： � � = L ⃗ � (� ⃗ ,�) = � ⃗ � ⃗ ,� �0�