Recent experiments with single atomic ions isolated in electromagnetic traps have demonstrated abrupt changes in observed fluorescence intensities, which have been interpreted as evidence for quantum jumps as the atom changes energy levels. This presents the seeming paradox of discontinuously changing observables from a system whose dynamical evolution is governed by the continuous optical Bloch equations. In this paper I present an analysis of the dynamics of a model three-level atom interacting with two laser fields in terms of the dressed states of the atom-laser system. These dressed states are eigenstates of a Hamiltonian which includes laser-atom interactions, and thus they simplify the discussion of the time evolution of the combined laser-atom system. This dressed-state description is particularly useful in the regime in which both laser intensities are strong enough to saturate their respective transitions. I calculate the radiative lifetimes of the different species of dressed states and the branching ratios for decay to other dressed states, and demonstrate the consequences of these quantities for the observed fluorescence pattern. The calculated duration of bright and dark periods shows a pronounced dependence on the detunings of the lasers.
Recent experiments with single atomic ions isolated in electromagnetic traps have demonstrated abrupt changes in observed fluorescence intensities, which have been interpreted as evidence for quantum jumps as the atom changes energy levels. This presents the seeming paradox of discontinuously changing observables from a system whose dynamical evolution is governed by the continuous optical Bloch equations. In this paper I present an analysis of the dynamics of a model three-level atom interacting with two laser fields in terms of the dressed states of the atom-laser system. These dressed states are eigenstates of a Hamiltonian which includes laser-atom interactions, and thus they simplify the discussion of the time evolution of the combined laser-atom system. This dressed-state description is particularly useful in the regime in which both laser intensities are strong enough to saturate their respective transitions. I calculate the radiative lifetimes of the different species of dressed states and the branching ratios for decay to other dressed states, and demonstrate the consequences of these quantities for the observed fluorescence pattern. The calculated duration of bright and dark periods shows a pronounced dependence on the detunings of the lasers.
The statistics of spontaneous photon emission times in single atom resonance fluorescence are investigated through the radiative cascade of the dressed atom. The delay function which gives the distribution of the delays between two successive emissions is calculated for a coherent as well as an incoherent laser excitation. For a two-level atom, various signals that reflect the fluorescence intensity (average value, photon counting, fluctuation spectrum, etc.) are reviewed by this method. For a three-level atom, this approach is applied to the analysis of the recently observed phenomenon of intermittent fluorescence and quantum jumps.>
Complete density-matrix equations and a one-photon counting probability are used to examine the photon statistics of fluorescence light of a single three-level atom, weakly coupled to an external cavity of low Q value. The internal structure of the atom is supposed to be characterized by a weak and a strong transition. The strong transition is coherently driven by an external laser field, whereas no external field is acting on the weak transition. In free space the system exhibits quantum jumps. By placing the atom within the mirrors of an external cavity, tuned close to the transition frequency of the two upper levels, modifications in the quantum jump behavior of the atom are shown due to a modified spontaneous decay rate between the two states. In particular, it is demonstrated that the effect of the cavity is to modify the repetition rate of quantum jumps into the metastable dark state and the average duration of bright periods of fluorescence, whereas the average duration of dark periods is not changed in first order of the spontaneous decay rates involved. In view of current experiments in our laboratory a quantitative analysis is presented for the special case of a single indium ion located between the mirrors of a high-order symmetric confocal cavity.
The dressed atom approach provides a tool to investigate the dynamics of an atom-laser system by fully retaining the quantum nature of the coherent mode. In its standard derivation, the internal atom-laser evolution is described within the rotating-wave approximation, which determines a doublet structure of the spectrum and the peculiar fluorescence triplet in the steady state. However, the rotating wave approximation may fail to apply to atomic systems subject to femtosecond light pulses, light-matter systems in the strong-coupling regime or sustaining permanent dipole moments. This work aims to demonstrate how the general features of the steady-state radiative cascade are affected by the interaction of the dressed atom with propagating radiation modes. Rather than focusing on a specific model, we analyze how these features depend on the parameters characterizing the dressed eigenstates in arbitrary atom-laser dynamics, given that a set of general hypotheses is satisfied. Our findings clarify the general conditions in which a description of the radiative cascade in terms of transition between dressed states is self-consistent. We provide a guideline to determine the properties of photon emission for any atom-laser interaction model, which can be particularly relevant when the model should be tailored to enhance a specific line. We apply the general results to the case in which a permanent dipole moment is a source of low-energy emission, whose frequency is of the order of the Rabi coupling.
For a three-level atom in the ssV configuration (i.e., having two excited states each dipole-coupled to a common ground state), we have found a particular linear combination of bare-atom states in which Rabi oscillations and their associated collapses and revivals do not occur. Moving to a dressed-state picture, we discover that this particular linear combination state is just that dressed state which is decoupled from all the field modes. It is a dressed state for which the transition dipole moments with the other dressed states are zero. The existence of this decoupled dressed state depends on the tuning of the dressing laser field, which in turn depends on the bare-atom excited-state dipole moments and energy-level separation. When we include spontaneous emission, the population decays from the other dressed states into this decoupled state and remains coherently trapped there, producing a system that experiences no dynamical behavior. This is exact for \ensuremath{\delta}-function photon statistics (i.e., if there is no intensity uncertainty). The trapping becomes less perfect as the photon statistics are allowed to have a greater bandwidth. Also, if the applied field is tuned incorrectly, the spontaneous realignment of the atomic state amplitudes does not result in a totally decoupled dressed state, and the dynamics proceed normally.
A strongly driven $(\ensuremath{\Omega}\ensuremath{\gg}\ensuremath{\gamma})$ two-level atom relaxes towards an equilibrium state $\ensuremath{\rho}$ which is almost completely mixed. One interpretation of this state is that it represents an ensemble average, and that an individual atom is at any time in one of the eigenstates of $\ensuremath{\rho}$. The theory of Teich and Mahler [Phys. Rev. A 45, 3300 (1992)] makes this interpretation concrete, with an individual atom jumping stochastically between the two eigenstates when a photon is emitted. The dressed-atom theory is also supposed to describe the quantum jumps of an individual atom due to photoemissions. But the two pictures are contradictory because the dressed states of the atom are almost orthogonal to the eigenstates of $\ensuremath{\rho}$. In this paper we investigate three ways of measuring the field radiated by the atom, which attempt to reproduce the simple quantum jump dynamics of the dressed state or Teich and Mahler models. These are spectral detection (using optical filters), two-state jumps (using adaptive homodyne detection), and orthogonal jumps (another adaptive homodyne scheme). We find that the three schemes closely mimic the jumps of the dressed-state model, with errors of order $\frac{3}{4}(\ensuremath{\gamma}/\ensuremath{\Omega}{)}^{2/3},$ $\frac{1}{4}(\ensuremath{\gamma}/\ensuremath{\Omega}{)}^{2}$, and $\frac{3}{4}(\ensuremath{\gamma}/\ensuremath{\Omega}{)}^{2}$, respectively. The significance of this result to the program of environmentally induced superselection is discussed.
This paper is concerned with two rather basic phenomena: the incoherent fluorescence spectrum of an atom driven by an intense laser field and the coupling of the atom to the (empty) modes of the radiation field. The sum of the many-photon processes gives rise to the inelastic part of the atomic fluorescence, which, for a two-level system, has a well-known characteristic three-peak structure known as the Mollow spectrum. From a theoretical point of view, the Mollow spectrum finds a natural interpretation in terms of transitions among laser-dressed states which are the energy eigenstates of a second-quantized two-level system strongly coupled to a driving laser field. As recently shown, the quasi-energies of the laser-dressed states receive radiative corrections which are nontrivially different from the results which one would expect from an investigation of the coupling of the bare states to the vacuum modes. In this article, we briefly review the basic elements required for the analysis of the dynamic radiative corrections, and we generalize the treatment of the radiative corrections to the incoherent part of the steady-state fluorescence to a three-level system consisting of 1S, 3P and 2S states.