Aspects of Two-Level Systems under External Time Dependent Fields

Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics. Each of the sub-dynamics is shown to be brought into an exactly solvable form by appropriately engineering the magnetic fields and thus we obtain an exact time evolution of the compound system. Several physically relevant and interesting qu...

In this paper we study the time evolution of a class of two-level systems driven by periodic fields in terms of new convergent perturbative expansions for the associated propagator U(t). The main virtue of these expansions is that they do not contain secular terms, leading to a very convenient method for quantitatively studying the long-time behaviour of that systems. We present a complete description of an algorithm to numerically compute the perturbative expansions. In part...

In this paper we treat the 2--level system interacting with external fields without the rotating wave approximation and construct some approximate solutions in the strong coupling regime.

Finding the evolution of two level Hamiltonian is of great importance in quantum computation and quantum precision manipulation due to the requirement of quantum experiment control. However, the Schr\"odinger equation of an arbitrary time-dependent two level Hamiltonian is hardly solvable due to its non-commutativity Hamiltonian in different times. In this article, we expand and demonstrate an exact solution of Schr\"odinger equation respect to general two level systems with ...

We study the Schroedinger equation of a class of two-level systems under the action of a periodic time-dependent external field in the situation where the energy difference 2epsilon between the free energy levels is sufficiently small with respect to the strength of the external interaction. Under suitable conditions we show that this equation has a solution in terms of converging power series expansions in epsilon. In contrast to other expansion methods, like in the Dyson ex...

In this work, we derive exact solutions of a dynamical equation, which can represent all two-level Hermitian systems driven by periodic $N$-step driving fields. For different physical parameters, this dynamical equation displays various phenomena for periodic $N$-step driven systems. The time-dependent transition probability can be expressed by a general formula that consists of cosine functions with discrete frequencies, and, remarkably, this formula is suitable for arbitrar...

In the present article, we consider the so-called two-spin equation that describes four-level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general properties of the two-spin equation and show that the problem for certain external backgrounds can be identified with the problem of one spin in an appropriate background. This allows one to generate a number of exact solutions for two-spin equation...

In this paper we extend previous results on convergent perturbative solutions of the Schroedinger equation of a class of periodically time-dependent two-level systems. The situation treated here is particularly suited for the investigation of two-level systems exhibiting the phenomenon of (approximate) dynamical localisation. We also present a convergent perturbative expansion for the secular frequency and discuss in detail the particular case of monochromatic interactions (a...

We show how a laser driven two-level system including quantized external degrees of freedom for each state can be decoupled into a set of oscillator equations acting only on the external degrees of freedom with operator valued damping representing the detuning. We give a way of characterizing the solvability of this family of problems by appealing to a classical oscillator with time-dependent damping. As a consequence of this classification we (a) obtain analytic and represen...

Analytical solutions to the time-dependent Schrodinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm that generates an unlimited number of exact analytical solutions. We show that a general single-axis driving term and its corresponding evolution operator are determined by a single real function which is constrained only by a certain inequality and initial conditions...