Entanglement induced by spontaneous emission in spatially extended two-atom systems

The role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms has been investigated. Populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions are calculated and illustrated graphically. Calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. It is found that the ability of spontaneous emission to create transient entanglement relies on the absence of population in the collective symmetric state of the system. For the initial state of only one atom excited, entanglement builds up rapidly in time and reaches a maximum for parameter values corresponding roughly to zero population in the symmetric state. On the other hand, for the initial condition of both atoms excited, the atoms remain unentangled until the symmetric state is depopulated. A simple physical interpretation of these results is given in terms of the diagonal states of the density matrix of the system. We also study entanglement creation in a system of two non-identical atoms of different transition frequencies. It is found that the entanglement between the atoms can be enhanced compared to that for identical atoms, and can decay with two different time scales resulting from the coherent transfer of the population from the symmetric to the antisymmetric state. In addition, it was found that a decaying initial entanglement between the atoms can display a revival behaviour.

Quantum interference effects in a cavity QED system

We consider the effect of quantum interference on population distribution and photon statistics of a cavity field interacting with dressed states of a strongly driven three-level atom. We analyse three coupling configurations of the cavity field to the driven atom, with the cavity frequency tuned to the outer Rabi sideband, the inner Rabi sideband and the central frequency of the 'singly dressed' three-level atom. The quantum doubly dressed states for each configuration are identified and the population distribution and photon statistics are interpreted in terms of transitions among these dressed states and their populations. We find that the population distribution depends strongly on quantum interference and the cavity damping. For the cavity field tuned to the outer or inner Rabi sidebands the cavity damping induces transitions between the dressed states which are forbidden for the ordinary spontaneous emission. Moreover, we find that in the case of the cavity field coupled to the inner Rabi sideband the population distribution is almost Poissonian with a large average number of photons that can be controlled by quantum interference. This system can be considered as a one-atom dressed-state laser with controlled intensity.

Multilevel coherence effects in a two-level atom driven by a trichromatic field

We study the absorption and dispersion properties of a weak probe field monitoring a two-level atom driven by a trichromatic field. We calculate the steady-state linear susceptibility and find that the system can produce a number of multilevel coherence effects predicted for atoms composed of three and more energy levels. Although the atom has only one transition channel, the multilevel effects are possible because there are multichannel transitions between dressed states induced by the driving field. In particular, we show that the system can exhibit multiple electromagnetically induced transparency and can also produce a strong amplification at the central frequency which is not attributed to population inversion in both the atomic bare states and in the dressed atomic states. Moreover, we show that the absorption and dispersion of the probe field is sensitive to the initial relative phase of the components of the driving field. In addition, we show that the group velocity of the probe field can be controlled by changing the initial relative phases or frequencies of the driving fields and can also be varied from subluminal to superluminal. (C) 2003 Elsevier Science B.V. All rights reserved.

Simulating quantum interference in a three-level system with perpendicular transition dipole moments

We consider a three-level V-type atomic system with the ground state coupled by a laser field to only one of the excited states, and with the two excited states coupled together by a dc field. Although the dipole moments of the two dipole-allowed transitions are assumed perpendicular, we demonstrate that this system emulates to a large degree a three-level system with parallel dipole moments-the latter being a system that exhibits quantum interference and displays a number of interesting features. As examples, we show that the system can produce extremely large values for the intensity-intensity correlation function, and that its resonance fluorescence spectrum can display ultranarrow lines. The dressed states for this system are identified, and the spectral features are interpreted in terms of transitions among these dressed states. We also show that this system is capable of exhibiting considerable squeezing.

Stationary two-atom entanglement induced by nonclassical two-photon correlations

A system of two two-level atoms interacting with a squeezed vacuum field can exhibit stationary entanglement associated with nonclassical two-photon correlations characteristic of the squeezed vacuum field. The amount of entanglement present in the system is quantified by the well known measure of entanglement called concurrence. We find analytical formulae describing the concurrence for two identical and nonidentical atoms and show that it is possible to obtain a large degree of steady-state entanglement in the system. Necessary conditions for the entanglement are nonclassical two-photon correlations and nonzero collective decay. It is shown that nonidentical atoms are a better source of stationary entanglement than identical atoms. We discuss the optimal physical conditions for creating entanglement in the system; in particular, it is shown that there is an optimal and rather small value of the mean photon number required for creating entanglement.

Entangling two atoms via spontaneous emission

We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulae for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r(12) and interact with each other via the dipole-dipole interaction, and the antisymmetric state of the system is included throughout, even for small interatomic separations, in contrast to the small-sample model. It is shown that for sufficiently large values of the dipole-dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.

Fluctuations and single molecules

The fluorescence of single molecules coupled to a thermal bath is studied both experimentally and theoretically. The effect of different fluctuations on the coherence properties of resonance fluorescence is considered first. Coherence is measured in an interference experiment where a single molecule is used as a light source. A standard approach based on the optical Bloch equations apparently provides quite an accurate description of the interference experiment. Systems with long correlation times (where spectra are time dependent on any timescale) are considered next. It is shown that intensity-time-frequency correlation spectroscopy, which provides both high signal-to-noise ratio and high time resolution, is very suitable for such a case. The Bloch equations are further tested in an experiment where the shape of an excitation spectral line of a single molecule is accurately measured over six orders of magnitude of the exciting laser power. Significant deviations from the predictions of the Bloch equations are found. The role of critical parameters-the correlation time of the bath, the Rabi oscillation period, and the coupling constant between the bath and the molecule-is discussed. The paper also includes a short general introduction to the methodology of single-molecule studies.