Complete eigenstates of identical qubits arranged in regular polygons

We calculate the energy eigenvalues and eigenstates corresponding to coherent single and multiple excitations of an array of N identical qubits or two-level atoms (TLA's) arranged on the vertices of a regular polygon. We assume only that the coupling occurs via an exchange interaction which depends on the separation between the qubits. We include the interactions between all pairs of qubits, and our results are valid for arbitrary distances relative to the radiation wavelength. To illustrate the usefulness of these states, we plot the distance dependence of the decay rates of the n=2 (biexciton) eigenstates of an array of 4 qubits, and tabulate the biexciton eigenvalues and eigenstates, and absorption frequencies, line widths, and relative intensities for polygons consisting of N=2,...,9 qubits in the long-wavelength limit.Comment: Added a figure showing how these results can be used to compute deviations from "equal collective decoherence" approximation

Cavity induced modifications to the resonance fluorescence and probe absorption of a laser-dressed V atom

A cavity-modified master equation is derived for a coherently driven, V-type three-level atom coupled to a single-mode cavity in the bad cavity limit. We show that population inversion in both the bare and dressed-state bases may be achieved, originating from the enhancement of the atom-cavity interaction when the cavity is resonant with an atomic dressed-state transition. The atomic populations in the dressed state representation are analysed in terms of the cavity-modified transition rates. The atomic fluorescence spectrum and probe absorption spectrum also investigated, and it is found that the spectral profiles may be controlled by adjusting the cavity frequency. Peak suppression and line narrowing occur under appropriate conditions.Comment: 12 pages, 10 postscript figures, to be appeared in Phys. Rev.

Resonance fluorescence and Autler-Townes spectra of a two-level atom driven by two fields of equal frequencies

We study the effects of driving a two-level atom by two intense field modes that have equal frequencies but are otherwise distinguishable; the intensity of one mode is also assumed to be greater than that of the other. We calculate first the dressed states of the system, and then its resonance fluorescence and Autler-Townes absorption spectra. We find that the energy spectrum of the doubly dressed atom consists of a ladder of doublet continua. These continua manifest themselves in the fluorescence spectrum, where they produce continua at the positions of the Mellow sideband frequencies omega(L)+/-2 Omega of the strong field, and in the Autler-Townes absorption spectrum, which becomes a two-continuum doublet

Initial-Phase Spectroscopy as a Control of Entangled Systems

We introduce the concept of initial-phase spectroscopy as a control of the dynamics of entangled states encoded into a two-atom system interacting with a broadband squeezed vacuum field. We illustrate our considerations by examining the transient spectrum of the field emitted by two systems, the small sample (Dicke) and the spatially extended (non-Dicke) models. It is found that the shape of the spectral components depends crucially on the relative phase between the initial entangled state and the squeezed field. We follow the temporal evolution of the spectrum and show that depending on the relative phase a hole burning can occur in one of the two spectral lines. We compare the transient behavior of the spectrum with the time evolution of the initial entanglement and find that the hole burning can be interpreted as a manifestation of the phenomenon of entanglement sudden death. In addition, we find that in the case of the non-Dicke model, the collective damping rate may act like an artificial tweezer that rotates the phase of the squeezed field.Comment: 20 pages, 9 figure

Resonance fluorescence spectrum of a two-level atom driven by a bichromatic field in a squeezed vacuum

The steady-state resonance fluorescence spectrum of a two-level atom driven by a bichromatic field in a broadband squeezed vacuum is studied. When the carrier frequency of the squeezed vacuum is tuned to the frequency of the central spectral line, anomalous spectral features, such as hole burning and dispersive profiles, can occur at the central line. We show that these features appear for wider, and experimentally more convenient, ranges of the parameters than in the case of monochromatic excitation. ?he absence of a coherent spectral component at the central line makes any experimental attempt to observe these features much easier. We also discuss the general features of the spectrum. When the carrier frequency of the squeezed vacuum is tuned to the first odd or even sidebands, the spectrum is asymmetric and only the sidebands an sensitive to phase. For appropriate choices of the phase the linewidths or only the odd or even sidebands can be reduced. A dressed-stale interpretation is provided

Quantum interference in a driven two-level atom

We show that a dynamical suppression of spontaneous emission, predicted for a three-level atom [S.-Y. Zhu and M. O. Scully, Phys. Rev. Lett. 76, 388 (1996)] can occur in a two-level atom driven by st polychromatic field. We find that the quantum interference, responsible for the cancellation of spontaneous emission, appears between different channels of transitions among the dressed states of the driven atom. We discuss the effect for bichromatic and trichromatic (amplitude-modulated) fields and fmd that these two cases lead to the cancellation of spontaneous emission in different parts of the fluorescence spectrum. Our system has the advantage of being easily accessible by current experiments. [S1050-2947(99)50712-9]

Gain without population inversion in V-type systems driven by a frequency-modulated field

We obtain gain of the probe field at multiple frequencies in a closed three-level V-type system using frequency modulated pump field. There is no associated population inversion among the atomic states of the probe transition. We describe both the steady-state and transient dynamics of this system. Under suitable conditions, the system exhibits large gain simultaneously at series of frequencies far removed from resonance. Moreover, the system can be tailored to exhibit multiple frequency regimes where the probe experiences anomalous dispersion accompanied by negligible gain-absorption over a large bandwidth, a desirable feature for obtaining superluminal propagation of pulses with negligible distortion.Comment: 10 pages + 8 figures; To appear in Physical Review

Transition from antibunching to bunching for two dipole-interacting atoms

It is known that there is a transition from photon antibunching to bunching in the resonance fluorescence of a driven system of two two-level atoms with dipole-dipole interaction when the atomic distance decreases and the other parameters are kept fixed. We give a simple explanation for the underlying mechanism which in principle can also be applied to other systems. PACS numbers 42.50.Ar, 42.50FxComment: Submitted to Phys. Rev. A; 15 pages Latex + 4 figure

Bichromatic electromagnetically induced transparency in cold rubidium atoms

In a three-level atomic system coupled by two equal-amplitude laser fields with a frequency separation 2$\delta$, a weak probe field exhibits a multiple-peaked absorption spectrum with a constant peak separation $\delta$. The corresponding probe dispersion exhibits steep normal dispersion near the minimum absorption between the multiple absorption peaks, which leads to simultaneous slow group velocities for probe photons at multiple frequencies separated by $\delta$. We report an experimental study in such a bichromatically coupled three-level $\Lambda$ system in cold $^{87}$Rb atoms. The multiple-peaked probe absorption spectra under various experimental conditions have been observed and compared with the theoretical calculations.Comment: RevTex, 4 pages, 6 figures, Email address: [email protected]

Interference pattern with a dark center from two atoms driven by a coherent laser field

In a recent paper Meyer and Yeoman [Phys. Rev. Lett. 79, 2650 (1997)] have shown that the resonance fluorescence from two atoms placed in a cavity and driven by an incoherent field can produce an interference pattern with a dark center. We study the fluorescence from two coherently driven atoms in free space and show that this system can also produce an interference pattern with a dark center. This happens when the atoms are in nonequivalent positions in the driving: field, i.e., the atoms experience different intensities and phases of the driving field. We discuss the role of the interatomic interactions in this process and find that the interference pattern with a dark center results from the participation of the antisymmetric state in the dynamics of the driven two-atom system