For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld inva...For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.展开更多
By using the Lewis-Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent A-type Jaynes Cummings model. We lind that, compared with the dynamical phases, th...By using the Lewis-Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent A-type Jaynes Cummings model. We lind that, compared with the dynamical phases, the geometric phases in a cycle case are independent of the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. It is pointed out that the geometric phases in a cycle ease can be measured under the case of a stronger time-dependent photon field and a stronger coupling photon-atom system. On the other hand, the geometric phases of the model may be measured in the composition of cold atoms.展开更多
Two linear In this letter, we prove the following conclusions by introducing a function Fn（t）： （1） If a quantum system S with a time-dependent non-degenerate Hamiltonian H（t） is initially in the n-th eigenstate...Two linear In this letter, we prove the following conclusions by introducing a function Fn（t）： （1） If a quantum system S with a time-dependent non-degenerate Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values Fn（t） for all t are always on the circle centered at 1 with radius 1; （2） If a quantum system S with a time-dependent Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain c-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values F,（t） for all t are always outside of the circle centered at 1 with radius 1-ε. Moreover, some quantitative sufficient conditions for the state of the system at time t to remain ε-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor are established. Lastly, our results are illustrated by a spin-half particle in a rotating magnetic field.展开更多
Considering time-dependence of both interactions and external potential,we analytically study the collisional behaviors of two bright solitons in Bose-Einstein condensates by using Darboux transformation.It is found t...Considering time-dependence of both interactions and external potential,we analytically study the collisional behaviors of two bright solitons in Bose-Einstein condensates by using Darboux transformation.It is found that for a closed external potential,the soliton-soliton distance is decreased with nonlinearly increased interactions,while the amplitude of each soliton increases and its width decreases.For linearly increased interactions but nonlinearly decreased external potential,especially,the atom transfer between two solitons is observed,different from previous theory of no atom transfer in solitons collision in a fixed external potential.In addition,it is shown that the collisional type,such as head-on,"chase",or collision period between two solitons,can be controlled by tuning both interactions and external potential.The predicted phenomena can be observed under the condition of the current experiments and open possibilities for future application in atoms transport.展开更多
文摘For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.
基金supported by the Beijing NSF under Grant No.1072010supported by Scientific Creative Platform Foundation of Beijing Municipal Commission of Education under Grant No.PXM2008_ 014224_067420
文摘By using the Lewis-Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent A-type Jaynes Cummings model. We lind that, compared with the dynamical phases, the geometric phases in a cycle case are independent of the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. It is pointed out that the geometric phases in a cycle ease can be measured under the case of a stronger time-dependent photon field and a stronger coupling photon-atom system. On the other hand, the geometric phases of the model may be measured in the composition of cold atoms.
基金supported by the National Natural Science Foundation of China(Grant No. 11171197)the IFGP of Shaanxi Normal University(Grant No. 2011CXB004)the FRF for the Central Universities(Grant No. GK201002006)
文摘Two linear In this letter, we prove the following conclusions by introducing a function Fn（t）： （1） If a quantum system S with a time-dependent non-degenerate Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values Fn（t） for all t are always on the circle centered at 1 with radius 1; （2） If a quantum system S with a time-dependent Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain c-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values F,（t） for all t are always outside of the circle centered at 1 with radius 1-ε. Moreover, some quantitative sufficient conditions for the state of the system at time t to remain ε-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor are established. Lastly, our results are illustrated by a spin-half particle in a rotating magnetic field.
基金Supported by National Natural Science Foundation of China under Grant Nos.51032002 and 11074212Foundation for the Author of National Excellent Doctoral Dissertation of China under Grant No.200726+1 种基金the key Project of the National HighTechnology Research and Development Program ("863" Program) of China under Grant No.2011AA050526Hunan Provincial Innovation Foundation for Postgraduate under Grant No.CX2010B254
文摘Considering time-dependence of both interactions and external potential,we analytically study the collisional behaviors of two bright solitons in Bose-Einstein condensates by using Darboux transformation.It is found that for a closed external potential,the soliton-soliton distance is decreased with nonlinearly increased interactions,while the amplitude of each soliton increases and its width decreases.For linearly increased interactions but nonlinearly decreased external potential,especially,the atom transfer between two solitons is observed,different from previous theory of no atom transfer in solitons collision in a fixed external potential.In addition,it is shown that the collisional type,such as head-on,"chase",or collision period between two solitons,can be controlled by tuning both interactions and external potential.The predicted phenomena can be observed under the condition of the current experiments and open possibilities for future application in atoms transport.
