Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator's Wave Functions
Lu Hai-Liang, Fan Hong-Yi · Communications in Theoretical Physics · 2007
We reveal that the two-variable Hermite function h m , n , which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator's wave functions. The Schmidt decomposition of h m , n is derived. It also turns out that h m , n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S ( r ) H m , n (μ a 1 † ,μ a 2 † )|00⟩, which is the minimum uncertainty state for sum squeezing, in ⟨η| representation is calculated.