Equivalent classes of closed three-level systems

Published versio

Slow Light in Doppler Broadened Two level Systems

We show that the propagation of light in a Doppler broadened medium can be slowed down considerably eventhough such medium exhibits very flat dispersion. The slowing down is achieved by the application of a saturating counter propagating beam that produces a hole in the inhomogeneous line shape. In atomic vapors, we calculate group indices of the order of 10^3. The calculations include all coherence effects.Comment: 6 pages, 5 figure

Theory of weak continuous measurements in a strongly driven quantum bit

Continuous spectroscopic measurements of a strongly driven superconducting qubit by means of a high-quality tank circuit (a linear detector) are under study. Output functions of the detector, namely, a spectrum of voltage fluctuations and an impedance, are expressed in terms of the qubit spectrum and magnetic susceptibility. The nonequilibrium spectrum of the current fluctuations in the qubit loop and the linear response function of the driven qubit coupled to a heat bath are calculated with Bloch-Redfield and rotating wave approximations. Backaction effects of the qubit on the tank and the tank on the qubit are analyzed quantitatively. We show that the voltage spectrum of the tank provides detailed information about a frequency and a decay rate of Rabi oscillations in the qubit. It is found that both an efficiency of spectroscopic measurement and measurement-induced decoherence of the qubit demonstrate a resonant behaviour as the Rabi frequency approaches the resonant frequency of the tank. We determine conditions when the spectroscopic observation of the Rabi oscillations in the flux qubit with the tank circuit can be considered as a weak continuous quantum measurement.Comment: 28 page

Polariton Analysis of a Four-Level Atom Strongly Coupled to a Cavity Mode

We present a complete analytical solution for a single four-level atom strongly coupled to a cavity field mode and driven by external coherent laser fields. The four-level atomic system consists of a three-level subsystem in an EIT configuration, plus an additional atomic level; this system has been predicted to exhibit a photon blockade effect. The solution is presented in terms of polaritons. An effective Hamiltonian obtained by this procedure is analyzed from the viewpoint of an effective two-level system, and the dynamic Stark splitting of dressed states is discussed. The fluorescence spectrum of light exiting the cavity mode is analyzed and relevant transitions identified.Comment: 12 pages, 9 figure

Approach to the semiconductor cavity QED in high-Q regimes with q-deformed boson

The high density Frenkel exciton which interacts with a single mode microcavity field is dealed with in the framework of the q-deformed boson. It is shown that the q-defomation of bosonic commutation relations is satisfied naturally by the exciton operators when the low density limit is deviated. An analytical expression of the physical spectrum for the exciton is given by using of the dressed states of the cavity field and the exciton. We also give the numerical study and compare the theoretical results with the experimental resultsComment: 6 pages, 2 figure

Decoherence in trapped ions due to polarization of the residual background gas

We investigate the mechanism of damping and heating of trapped ions associated with the polarization of the residual background gas induced by the oscillating ions themselves. Reasoning by analogy with the physics of surface electrons in liquid helium, we demonstrate that the decay of Rabi oscillations observed in experiments on 9Be+ can be attributed to the polarization phenomena investigated here. The measured sensitivity of the damping of Rabi oscillations with respect to the vibrational quantum number of a trapped ion is also predicted in our polarization model.Comment: 26 pdf pages with 5 figures, http://www.df.ufscar.br/~quantum

Quantum trajectory approach to stochastically-induced quantum interference effects in coherently-driven two-level atoms

Stochastic perturbation of two-level atoms strongly driven by a coherent light field is analyzed by the quantum trajectory method. A new method is developed for calculating the resonance fluorescence spectra from numerical simulations. It is shown that in the case of dominant incoherent perturbation, the stochastic noise can unexpectedly create phase correlation between the neighboring atomic dressed states. This phase correlation is responsible for quantum interference between the related transitions resulting in anomalous modifications of the resonance fluorescence spectra.Comment: paper accepted for publicatio

Resonance fluorescence of a trapped three-level atom

We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are $\Lambda$--shaped and driven at two-photon resonance by a pair of lasers, which cool the center--of--mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser--cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb--Dicke limit). We use the spectral decomposition of the Liouville operator of the master equation for the atomic density matrix and apply second order perturbation theory. We find that the spectrum of resonance fluorescence is composed by two narrow sidebands -- the Stokes and anti-Stokes components of the scattered light -- while all other signals are in general orders of magnitude smaller. For very low temperatures, however, the Mollow--type inelastic component of the spectrum becomes visible. This exhibits novel features which allow further insight into the quantum dynamics of the system. We provide a physical model that interprets our results and discuss how one can recover temperature and cooling rate of the atom from the spectrum. The behaviour of the considered system is compared with the resonance fluorescence of a trapped atom whose internal transition consists of two-levels.Comment: 11 pages, 4 Figure

An algebraic approach to the Tavis-Cummings problem

An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on polynomially deformed su(2), i.e. su_n(2), algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N-atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of N atoms in a resonator is found to result from collective effects.Comment: 13 pages, 7 figure

Coherent information analysis of quantum channels in simple quantum systems

The coherent information concept is used to analyze a variety of simple quantum systems. Coherent information was calculated for the information decay in a two-level atom in the presence of an external resonant field, for the information exchange between two coupled two-level atoms, and for the information transfer from a two-level atom to another atom and to a photon field. The coherent information is shown to be equal to zero for all full-measurement procedures, but it completely retains its original value for quantum duplication. Transmission of information from one open subsystem to another one in the entire closed system is analyzed to learn quantum information about the forbidden atomic transition via a dipole active transition of the same atom. It is argued that coherent information can be used effectively to quantify the information channels in physical systems where quantum coherence plays an important role.Comment: 24 pages, 7 figs; Final versiob after minor changes, title changed; to be published in Phys. Rev. A, September 200