Quantitative sufficient conditions for adiabatic approximation

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.

An upper bound for the adiabatic approximation error

In this paper, we derive an upper bound for the adiabatic approximation error, which is the distance between the exact solution to a Schrodinger equation and the adiabatic approximation solution. As an application, we obtain an upper bound for 1 minus the fidelity of the exact solution and the adiabatic approximation solution to a SchrOdinger equation.

Adiabatic approximation in PT-symmetric quantum mechanics

In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics,which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.

An upper bound for the generalized adiabatic approximation error with a superposition initial state

The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr6dinger equation （SE） by choosing a single eigenstate of the Hamiltonian as the initial state. The superposition principle of quantum states enables us to mathematically discuss the exact solution to the SE starting from a superposition of two different eigenstates of the time-dependent Hamiltonian H（0）. Also, we can construct an approximate solution to the SE in terms of the corresponding instantaneous eigenstates of H（t）. On the other hand, any physical experiment may bring errors so that the initial state （input state） may be a superposition of different eigenstates, not just at the desired eigenstate. In this paper, we consider the generalized adiabatic evolution of a quantum system starting from a superposition of two different eigenstates of the Hamiltonian at t = 0. A generalized adiabatic approximate solution （GAAS） is constructed and an upper bound for the generalized adiabatic approximation error is given. As an application, the fidelity of the exact solution and the GAAS is estimated.

Dynamics of two arbitrary qubits strongly coupled to a quantum oscillator

Using adiabatic approximation, a two arbitrary qubits Rabi model has been studied in ultra-strong coupling. The analytical expressions of the eigenvalues and the eigenvalues are obtained. They are in accordance with the numerical determined results. The dynamical behavior of the system and the evolution of entanglement have also been discussed. The collapse and revival phenomena has garnered particular attention. The influence of inconsistent coupling strength on them is studied. These results will be applied in quantum information processing.

Dynamical and Geometric Phases of a Two Energy-Level Bose-Einstein Condensate Interacting with a Laser Field

By using of the invariant theory, we study a two energy-level Bose-Einstein condensate interacting with a timedependent laser field, the dynamical and geometric phases are given respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.

Non-frozen process of heavy-ion fusion reactions at deep sub-barrier energies

The hindrance in heavy-ion fusion reactions a deep sub-barrier energies is investigated using the double folding model with a hybrid method between the frozen and adiabatic density approximations.In this method,the density distributions of the projectile and the target depend closely on the distance between them.As the distance decreased,the half-density radii of the colliding nucle gradually increased to the half-density radius of the compound nucleus.The total potential based on this non-frozen approximation generates a slightly shallower pocket and becomes more attractive inside the pocket compared to that obtained from the frozen approximation.A damping factor was used to simulate the decline of the coupled channel effects owing to the density rearrangement of the two colliding nuclei.The calculated fusion cross-sections and astrophysical S factors at the deep sub-barrier energies are both in good agreement with the experimental data for the medium-heavyNi+Ni and medium-lightMg+Si mass systems.In addition,it was concluded that the apparent maximum of the S factors most likely appears in fusion systems with strong coupling effects.

Evolution of entanglement between qubits ultra-strongly coupling to a quantum oscillator

We investigate the dynamics of two qubits coupled with a quantum oscillator by using the adiabatic approximation method. We take account of the interaction between the qubits and show how the entanglement is affected by the interaction parameter. The most interesting result is that we can prolong the entanglement time or improve the entanglement degree by using an appropriate interaction parameter. As the generation and preservation of entanglement of qubits are crucial for quantum information processing, our research will be useful.