We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU...We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.展开更多
Shortcut to adiabaticity(STA) is a speedway to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxili...Shortcut to adiabaticity(STA) is a speedway to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxiliary counterdiabatic fields or finding new Hamiltonians that own dynamical invariants to constraint the system into the adiabatic paths. In this paper,an efficient method is introduced to naturally cover the above two techniques with a unified Lie algebraic framework and neatly remove the design difficulties and loose assumptions in the two techniques. A general STA scheme for different potential expansions concisely achieves with the aid of squeezing transformations.展开更多
The system of the Hamiltonian involving a driving part,a single mode part,and a two-mode squeezedone and a two-mode coupled one is discussed using the Lewis-Riesenfeld invariant theory.The time evolution operatoris ob...The system of the Hamiltonian involving a driving part,a single mode part,and a two-mode squeezedone and a two-mode coupled one is discussed using the Lewis-Riesenfeld invariant theory.The time evolution operatoris obtained.When the initial state is a coherent state,the quantum fluctuation of the system is calculated,and it isdependent on the squeezed part and the two-mode coupled part,but not dependent on the driving one.展开更多
Based on the construction of supersymmetric generators, we use the Lewis-Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes-Cummings model. One of ...Based on the construction of supersymmetric generators, we use the Lewis-Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes-Cummings model. One of the advantages of this approach is that it can transform the hidden form, related to the chronological product, of the time evolution operator into an explicit expression. Moreover, the dynamical and statistics properties of physical quantities are obtained for the given initial states in the thermo Jaynes Cummings system.展开更多
Rashba effect in presence of a time-dependent interaction has been considered.Then time-evolution of such a system has been studied by using Lewis–Riesenfeld dynamical invariant and unitary transformation method.So a...Rashba effect in presence of a time-dependent interaction has been considered.Then time-evolution of such a system has been studied by using Lewis–Riesenfeld dynamical invariant and unitary transformation method.So appropriate dynamical invariant and unitary transformation according the considered system have been constructed as well as some special cases have come into this article which are common in physics.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056.
文摘We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11447025 and 11847308)。
文摘Shortcut to adiabaticity(STA) is a speedway to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxiliary counterdiabatic fields or finding new Hamiltonians that own dynamical invariants to constraint the system into the adiabatic paths. In this paper,an efficient method is introduced to naturally cover the above two techniques with a unified Lie algebraic framework and neatly remove the design difficulties and loose assumptions in the two techniques. A general STA scheme for different potential expansions concisely achieves with the aid of squeezing transformations.
基金National Natural Science Foundation of China under Grant Nos.10405006 and 10547106
文摘The system of the Hamiltonian involving a driving part,a single mode part,and a two-mode squeezedone and a two-mode coupled one is discussed using the Lewis-Riesenfeld invariant theory.The time evolution operatoris obtained.When the initial state is a coherent state,the quantum fluctuation of the system is calculated,and it isdependent on the squeezed part and the two-mode coupled part,but not dependent on the driving one.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174)
文摘Based on the construction of supersymmetric generators, we use the Lewis-Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes-Cummings model. One of the advantages of this approach is that it can transform the hidden form, related to the chronological product, of the time evolution operator into an explicit expression. Moreover, the dynamical and statistics properties of physical quantities are obtained for the given initial states in the thermo Jaynes Cummings system.
文摘Rashba effect in presence of a time-dependent interaction has been considered.Then time-evolution of such a system has been studied by using Lewis–Riesenfeld dynamical invariant and unitary transformation method.So appropriate dynamical invariant and unitary transformation according the considered system have been constructed as well as some special cases have come into this article which are common in physics.
