2005/07/21 by Avner Fleischer, Nimrod Moiseyev
Engineering · Mathematics · Physics and Astronomy · #Adiabatic process #Adiabatic quantum computation #Adiabatic theorem #Advanced Fiber Laser Technologies #Classical mechanics #Hamiltonian (control theory) #Hermitian matrix #Laser-Matter Interactions and Applications #Mathematical physics #Mathematics #Physics #Quantum #Quantum computer #Quantum mechanics #Scaling #Terahertz technology and applications #physics.atom-ph
paper · pdf · doi:10.1103/physreva.72.032103
arxiv created 2005/07/21 · openalex publication_date 2005/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the conventional quantum mechanics (i.e., Hermitian quantum mechanics) the adiabatic theorem for systems subjected to time-periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone, R. Ketzmerik, and W. Kohn, Phys. Rev. A 56, 4045 (1997)]. Here with the help of the (t,t^\ensuremath') formalism combined with the complex scaling method we derive an adiabatic theorem for open systems and provide an analytical criterion for the validity of the adiabatic limit. The use of the complex scaling transformation plays a key role in our derivation. As a numerical example we apply the adiabatic theorem we derived to a one-dimensional model Hamiltonian of Xe atom which interacts with strong, monochromatic sine-square laser pulses. We show that the generation of odd-order harmonics and the absence of hyper-Raman lines, even when the pulses are extremely short, can be explained with the help of the adiabatic theorem we derived.