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Physical Review A

Geometry-dependent dynamics of two Λ -type atoms via vacuum-induced coherences

Jörg Evers, Martin Kiffner, Mihai Macovei, Christoph H. Keitel

Published Feb 6, 2006• 41 citations
Publisher

Abstract

The dynamics of a pair of atoms can significantly differ from the single-atom dynamics if the distance of the two atoms is small on a scale given by the relevant transition wavelengths. Here, we discuss two nearby three-level atoms in $\ensuremath{\Lambda}$ configuration, and focus on the dependence of the optical properties on the geometry of the setup. We find that in general transitions in the two atoms can be dipole-dipole coupled by interactions via the vacuum field even if their transition dipole moments are orthogonal. We give an interpretation of this effect and show that it may crucially influence the system dynamics. In particular, for a fixed setup of driving fields and detectors, the spatial orientation of the two-atom pair decides if the system reaches a true constant steady state or if it exhibits periodic oscillations in the long-time limit. As an example observable, we study the resonance fluorescence intensity, which is either constant or is modulated periodically in the long-time limit.

DOI
10.1103/physreva.73.023804

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The dynamics of a pair of atoms can significantly differ from the single-atom dynamics if the distance of the two atoms is small on a scale given by the relevant transition wavelengths. Here, we discuss two nearby three-level atoms in \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ configuration, and focus on the dependence of the optical properties on the geometry of the setup. We find that in general transitions in the two atoms can be dipole-dipole coupled by interactions via the vacuum field even if their transition dipole moments are orthogonal. We give an interpretation of this effect and show that it may crucially influence the system dynamics. In particular, for a fixed setup of driving fields and detectors, the spatial orientation of the two-atom pair decides if the system reaches a true constant steady state or if it exhibits periodic oscillations in the long-time limit. As an example observable, we study the resonance fluorescence intensity, which is either constant or is modulated periodically in the long-time limit.
The resonance fluorescence emitted by a system of two dipole-dipole interacting nearby four-level atoms in a $J=1/2\ensuremath{\leftrightarrow}J=1/2$ configuration is studied. This setup is the simplest realistic model system which provides a complete description of the (inter-atomic) dipole-dipole interaction for arbitrary orientation of the inter-atomic distance vector, and at the same time allows for intra-atomic spontaneously generated coherences. Our main interest is the interplay of both these different coupling mechanisms. We discuss different methods to analyze the contribution of the various vacuum-induced coupling constants to the total resonance fluorescence spectrum. These allow us to find a dressed state interpretation of the contribution of the different inter-atomic dipole-dipole couplings to the total spectrum. We further study the role of the spontaneously generated coherences, and identify two different contributions to the single-particle vacuum-induced couplings. We show that they have a noticeable impact on the total resonance fluorescence spectrum down to small inter-atomic distances, even though the dipole-dipole coupling constants then are much larger in magnitude than the the single-particle coupling constants. Interestingly, we find that the inter-atomic couplings can induce an effect of the intra-atomic spontaneously generated coherences on the observed spectra which is not present in single-atom systems.
Quantum interference and coherence effects in the interaction of atoms with the quantized electromagnetic field are investigated theoretically. A general master equation for the description of atom-field interactions is introduced. The interplay of the concepts of complementarity and interference in the time-energy domain are studied on the basis of the fluorescence light emitted by a single laser-driven atom, where the coherence of spontaneous processes gives rise to quantum interference in the spectrum of resonance fluorescence. The vacuum-induced dipole-dipole interaction in pairs of multi-level atoms is analyzed. It is shown that the interaction between orthogonal transition dipole moments of different atoms does not only influence the system dynamics crucially, but implies that the few-level approximation in general cannot be applied to near-degenerate Zeeman sublevels of the atomic level scheme. Potential applications of dipole-dipole interacting multi-level atoms for the implementation of decoherence-free subspaces and the generation of entanglement between atomic states are examined. The generation of an entangled state of the radiation field with a macroscopic number of photons is discussed on the basis of a single-atom laser.
We examine the gain spectrum of a coherently driven Λ-type atom with a pair of closely lying ground levels, where a single laser field drives both transitions from the upper state to the lower states simultaneously. The effects of vacuum-induced coherence among decay channels are taken into account. Gain spectra under various conditions are presented and analyzed. We show that the spectral structure and the gain amplitude of the probe are strongly influenced by the vacuum-induced coherence as well as the frequency separation between the two ground levels. We present an explanation to our numerical results by introducing dipole moments in the dressed-state representation.
We investigate the quantum dynamics of a quantum oscillator coupled with the most upper state of a three-level Λ-type system. The two transitions of the three-level emitter, possessing orthogonal dipole moments, are coherently pumped with a single or two electromagnetic field sources, respectively. We have found ranges for flexible lasing or cooling phenomena referring to the quantum oscillator’s degrees of freedom. This is due to asymmetrical decay rates and quantum interference effects leading to population transfer among the relevant dressed states of the emitter’s subsystem with which the quantum oscillator is coupled. As an appropriate system can be considered a nanomechanical resonator coupled with the most excited state of the three-level emitter fixed on it. Alternatively, if the upper state of the Λ-type system possesses a permanent dipole then it can couple with a cavity electromagnetic field mode which can be in the terahertz domain, for instance. In the latter case, we demonstrate an effective electromagnetic field source of terahertz photons.
In two nearby atoms, the dipole-dipole interaction can couple transitions with orthogonal dipole moments. This orthogonal coupling accounts for a number of interesting effects, but strongly depends on the geometry of the setup. Here, we discuss several setups of interest where the geometry is not fixed, such as particles in a trap or gases, by averaging over different sets of geometries. Two averaging methods are compared. In the first method, it is assumed that the internal electronic evolution is much faster than the change of geometry, whereas in the second, it is vice versa. We find that the orthogonal coupling typically survives even extensive averaging over different geometries, albeit with qualitatively different results for the two averaging methods. Typically, one- and two-dimensional averaging ranges modeling, e.g., low-dimensional gases, turn out to be the most promising model systems.
The dynamics of an atomic few-level system can depend on the phase of driving fields coupled to the atom if certain conditions are satisfied. This is of particular interest to control interference effects, which can alter the system properties considerably. In this article, we discuss the mechanisms of such phase control and interference effects in an atomic three-level system in the Λ configuration, where the upper state spontaneously decays into the two lower states. The lower states are coupled by a driving field, which we treat as quantized. This allows for an interpretation on the single photon level for both the vacuum and the driving field. By analysing the system behaviour for a driving field initially in non-classical states with only a few Fock number states populated, we find that even though the driving field is coupled to the lower states only, it induces a multiplet of upper states. Then interference occurs independently in three-level subsystems in the V configuration, each formed by two adjacent upper states and a single dressed lower state.