Related papers: Controlling Several Atoms in a Cavity
Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent…
We develop aspects of geometric control theory on Lie groups G which may be infinite dimensional, and on smooth G-manifolds M modelled on locally convex spaces. As a tool, we discuss existence and uniqueness questions for differential…
A three-level atom in the $\Lambda$-configuration coupled to a microcavity is studied. The two transitions of the atom are assumed couple to different counterpropagating mode pairs in the cavity. We analyze the dynamics both, in the…
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…
In quantum control, quantum speed limits provide fundamental lower bounds on the time that is needed to implement certain unitary transformations. Using Lie algebraic methods, we link these speed limits to symmetries of the control…
In this paper we consider the two atoms Tavis--Cummings model and give an explicit form to the solution of this model which will play a central role in quantum computation based on atoms of laser--cooled and trapped linearly in a cavity. We…
An input-output model of a two-level quantum system in the Heisenberg picture is of bilinear form with constant system matrices, which allows the introduction of the concepts of controllability and observability in analogy with those of…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
Cavity quantum electrodynamics of multipartite systems is studied in depth, which consist of an arbitrary number of emitters in interaction with an arbitrary number of cavity modes. The governing model is obtained by taking the full…
The increasing level of experimental control over atomic and optical systems gained in the past years have paved the way for the exploration of new physical regimes in quantum optics and atomic physics, characterised by the appearance of…
Cavity quantum electrodynamics offers the possibility to observe and control the motion of few or individual atoms, enabling the realization of various quantum technological tasks such as quantum-enhanced metrology or quantum simulation of…
An overview and synthesis of results and criteria for open-loop controllability of Hamiltonian quantum systems obtained using Lie group and Lie algebra techniques is presented. Negative results for open-loop controllability of dissipative…
This paper considers a two-level atom interacting with two cavity modes with equal frequencies. Applying a unitary transformation, the system reduces to the analytically solvable Jaynes-Cummings model. For some particular field states,…
The paper discusses the single-mode Jaynes-Cummings model with time dependent parameters. Solvable models for two-level systems are utilized to consider the changes in the photon distribution affected by the passage of atoms through the…
Supersymmetry allows one to build a hierarchy of Hamiltonians that share the same spectral properties and which are pairwise connected through common superpotentials. The iso-spectral properties of these Hamiltonians imply that the dynamics…
In this paper, we show how to use the analysis of the Lie algebra associated with a quantum mechanical system to study its dynamics and facilitate the design of controls. We give algorithms to decompose the dynamics and describe their…
In this paper, a model by which we study the interaction between a motional three-level atom and two-mode field injected simultaneously in a bichromatic cavity is considered; the three-level atom is assumed to be in a $\Lambda$-type…
We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that…
We revisit the mathematical formulation of the famous Jaynes-Cummings-Paul Hamiltonian, which describes the interaction of a two-level atom with a single mode of an electromagnetic cavity reservoir. We rigorously show that under the…
The applications of geometric control theory methods on Lie groups and homogeneous spaces to the theory of quantum computations are investigated. These methods are shown to be very useful for the problem of constructing an universal set of…