Squeezing of Dirac's inverse operator in Fock space and the squeezed creation operator's eigenket

详细信息    查看全文

• 作者：Jun Zhou^a ; ^{zhj0064@mail.ustc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Hong-yi Fan^b ; Jun Song^a ; Ke-yue Wu^a ; Guo-zhu Pan^a ; Bo Zhang^a
• 关键词：0365&minus ; w ; 4250&minus ; p
• 刊名：Optik - International Journal for Light and Electron Optics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：127
• 期：2
• 页码：773-775
• 全文大小：234 K

文摘

By using the singular eigenvector (eigenket) of the creation operator a^† we study how Dirac's inverse operators are squeezed and what is the normally ordered expansion of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S003040261501387X&_mathId=si1.gif&_user=111111111&_pii=S003040261501387X&_rdoc=1&_issn=00304026&md5=cc39114d639093dfe526adf6f7f05a4f" title="Click to view the MathML source">(a^†coshλ+asinhλ)⁻¹class="mathContainer hidden">class="mathCode">${\left(a^{†}cosh\lambda +asinh\lambda \right)}^{-1}$. We find the rule for converting annihilator's eigenket to creator's eigenket is: class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S003040261501387X&_mathId=si2.gif&_user=111111111&_pii=S003040261501387X&_rdoc=1&_issn=00304026&md5=1fe100bd50febf42410cc5ce0ab64a41">class="imgLazyJSB inlineImage" height="22" width="108" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S003040261501387X-si2.gif">class="mathContainer hidden">class="mathCode">$e^z\to e^{-\frac{\partial }{\partial z^{*}}}\delta (z^{*}),$ where δ(z^*) is the Dirac's Delta function in contour integration form. We also derive the squeezed creation operator's eigenket and conclude that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S003040261501387X&_mathId=si3.gif&_user=111111111&_pii=S003040261501387X&_rdoc=1&_issn=00304026&md5=c4bfa5c098eb78cceb4d785de991662d" title="Click to view the MathML source">(a^†coshλ+asinhλ)⁻¹|0〉class="mathContainer hidden">class="mathCode">${\left(a^{†}cosh\lambda +asinh\lambda \right)}^{-1}|0〉$ is an excited squeezed state.