Optimal population inversion of a single dissipative two-level system

Fang-Yu Hong, Shi‐Jie Xiong, Yang Xiang

Hamza Jirari, Ning Wu

A. Ruschhaupt, Xi Chen, Daniel Alonso +1 more

We examine the stability versus different types of perturbations of recently proposed shortcuts to adiabaticity to speed up the population inversion of a two-level quantum system. We find the optimally robust processes by using invariant-based engineering of the Hamiltonian. Amplitude noise and systematic errors require different optimal protocols.

Alon Padan, Haim Suchowski

We present a novel approach for analytically reducing a family of time-dependent multi-state quantum control problems to two-state systems. The presented method translates between related n 2 -state systems and two-state systems, such that the former undergo complete population inversion (CPI) if and only if the latter reach specific states. For even n , the method translates any two-state CPI scheme to a family of CPI schemes in n 2 -state systems. In particular, facilitating CPI in a four-state system via real time-dependent nearest-neighbors couplings is reduced to facilitating CPI in a two-level system. Furthermore, we show that the method can be used for operator control, and provide conditions for producing several universal gates for quantum computation as an example. In addition, we indicate a basis for utilizing the method in optimal control problems.

J. Oreg, F. T. Hioe, Joseph H. Eberly

Ebrahim Ghasemian, Mohammad Kazem Tavassoly

Abstract In this paper we consider a system consisting of a number of two-level atoms in a Bose–Einstein condensate (BEC) and a single-mode quantized field, which interact with each other in the presence of two different damping sources, i.e. cavity and atomic reservoirs. The reservoirs which we consider here are thermal and squeezed vacuum ones corresponding to field and atom modes. Strictly speaking, by considering both types of reservoirs for each of the atom and field modes, we investigate the quantum dynamics of the interacting bosons in the system. Then, via solving the quantum Langevin equations for such a dissipative BEC system, we obtain analytical expressions for the time dependence of atomic population inversion, mean atom as well as photon number and quadrature squeezing in the field and atom modes. Our investigations demonstrate that for modeling the real physical systems, considering the dissipation effects is essential. Also, numerical calculations which are presented show that the atomic population inversion, the mean number of atoms in the BEC and the photons in the cavity possess damped oscillatory behavior due to the presence of reservoirs. In addition, non-classical squeezing effects in the field quadrature can be observed especially when squeezed vacuum reservoirs are taken into account. As an outstanding property of this model, we may refer to the fact that one can extract the atom–field coupling constant from the frequency of oscillations in the mentioned quantities such as atomic population inversion.