Aspects of Two-Level Systems under External Time Dependent Fields

We study the interaction of a two-level atom and two fields, one of them classical. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to neglect some terms in the rotated Hamiltonian. Then we solve a variation of the Schr\"odinger equation that models decoherence as the system evolves through intrinsic mechanisms beyond conventional quantum mechanics rather than dissipative in...

This paper generalizes some known solitary solutions of a time-dependent Hamiltonian in two ways: The time-dependent field can be an elliptic function, and the time evolution is obtained for a complete set of basis vectors. The latter makes it feasible to consider arbitrary initial conditions. The former makes it possible to observe a beating caused by the non-linearity of the driving field.

A remarkably simple result is found for the optimal protocol of drivings for a general two-level Hamiltonian which transports a given initial state to a given final state in minimal time. If one of the three possible drivings is unconstrained in strength the problem is analytically completely solvable. A surprise arises for a class of states when one driving is bounded by a constant $c$ and the other drivings are constant. Then, for large $c$, the optimal driving is of type b...

We describe some new exact solutions for two- and four-level systems. In all the cases, external fields have a restricted behavior in time. First, we consider two types of new solutions for one-spin equation, one of them is in a external magnetic field that acts during a finite time interval. A new solution for two interacting spins is found in the case when the field difference between the external fields in each spin vary adiabatically, vanishing on the time infinity. The l...

Quantum information is a useful resource to set up information processing. Despite physical components are normally two-level systems, their combination with entangling interactions becomes in a complex dynamics. Studied for piecewise field pulses, this work analyzes the modeling for quantum information operations with fields affordable technologically towards a universal quantum computation model.

Two-level systems are one of the most important quantum systems and they form the basis of quantum computers. We briefly look at the traditional approach to two-level systems with an external driving field as well as those subjected to noise. This project is aimed at studying two specific methods for obtaining analytic solutions for two-level systems. One of the methods enables us to obtain analytic solutions for driven time-dependent two-level systems while the other attempt...

We study the dynamics of a two-level quantum system interacting with an external electromagnetic field periodic and quasiperiodic in time. The quantum evolution is described exactly by the classical equations of motion of a gyromagnet in a time-dependent magnetic field. We prove that this classical system is integrable as a consequence of the underlying unitary quantum dynamics. As a consequence, for the periodic case: i) rigorous assessment of the validity of the rotating-wa...

We consider the problem of two-level system dynamics induced by the time-dependent field B={a(t)cos\omega t,a(t)sin\omega t,\omega_0}, with a(t) \sim cn(\nu t,k). The problem is exactly analytically solvable and we propose the scheme for constructing the solutions. For all field configurations the resonance conditions are discussed. The explicit solutions for N=1,2 we obtained coincide at \omega=0 in the proper parameter domain with predictions of the rotating wave approximat...

General features of nonlinear quantum mechanics are discussed in the context of applications to two-level atoms.

Transition probabilities for a class of two level systems described by explicitly time dependent Hamiltonians are considered. Provided only that the approach to the infinite time limit is non-trivial falling at least as fast as 1/t for large t, the transition probability takes a particularly simple form depending only on the value of Hamiltonian parameters in this limit.