A single three-level atom with the ground state strongly coupled to an excited state and weakly coupled to a third intermediate state exhibits a telegraph signal of fluorescent emission when driven by laser light at the strong coupling frequency. The ``on'' periods correspond to normal resonance fluorescence, whereas the ``off'' periods correspond to the atom being ``shelved'' in the intermediate state. Such a system has interesting statistical properties. The photon statistics during the ``on'' periods correspond to two-level behavior and are close to Poisson in nature. However, the photon number distribution of a succession of ``on'' periods exhibits Bose-Einstein statistics. Thus the three-level system can exhibit both ``quiet'' and ``noisy'' behavior. The mathematical connection between the two cases is established, and an atomic beam experiment is described which records a mixture of the two statistical extremes. The composition of the mixture is varied, and the data are shown to be well represented by an analysis based upon the model developed.
A single three-level atom with the ground state strongly coupled to an excited state and weakly coupled to a third intermediate state exhibits a telegraph signal of fluorescent emission when driven by laser light at the strong coupling frequency. The on'' periods correspond to normal resonance fluorescence, whereas the off'' periods correspond to the atom being shelved'' in the intermediate state. Such a system has interesting statistical properties. The photon statistics during the on'' periods correspond to two-level behavior and are close to Poisson in nature. However, the photon number distribution of a succession of on'' periods exhibits Bose-Einstein statistics. Thus the three-level system can exhibit both quiet'' and ``noisy'' behavior. The mathematical connection between the two cases is established, and an atomic beam experiment is described which records a mixture of the two statistical extremes. The composition of the mixture is varied, and the data are shown to be well represented by an analysis based upon the model developed.
Abstract We discuss the statistics of emission of photons by a single atom or ion illuminated by a laser beam at the frequency of quasi-resonance between two energy levels, a situation that corresponds to real experiments. We extend this to the case of two laser beams resonant with the energy differences between two excited levels and the ground state (three level atom in V-configuration). We use a novel approach to this type of problem by considering a Kolmogorov equation for the probability distribution of the atomic state, which takes into account first the deterministic evolution of this state under the effect of the incoming laser beam and second the random emission of photons during the spontaneous decay of the excited state(s) to the ground state. This approach yields solvable equations in the two level atom case. For the three level atom case we set the problem and clearly define its frame. The results obtained are valid in both opposite limits of rare and frequent spontaneous decay, compared to the period of the optical Rabi oscillations due to the interaction between resonant excitation and atomic levels. Our analysis gives access to various statistical properties of the fluorescence light, including one showing that its fluctuations in time are not invariants under time reversal. This result makes evident the fundamentally irreversible character of quantum measurements, represented here by the emission of photons of fluorescence.
An experimental technique which permits the study of single three-level atoms prior to quantum jumps to a shelving state has been used to study the second-order photon statistics of laser-excited barium atoms. Measured values of Mandel's Q parameter agree with the theory derived for two-level atoms. This result illustrates the extent to which the presence of additional levels can be ignored in certain systems: Although the third level in this system is responsible for the quantum jumps, prior to each jump the system's behavior is within experimental errors, exactly like that of a two-level atom. The negative values of Q obtained for a range of laser intensities demonstrate the sub-Poisson character of the emission.
Statistics of fluorescence photons emitted by a single two-level atom interacting with a continuous wave laser field are analyzed. The photon-counting distribution is calculated for the so-called intermediate fluorescence photons, i.e., those counted during the time interval between instants at which photons are emitted. The result is a sub-Poissonian (narrower than Poisson) distribution, which agrees with experimental observations. This intermediate-photon distribution is used to calculate the average number of fluorescence photons, the second factorial moment of the photon-counting distribution, and Mandel’s Q parameter commonly used to evaluate the deviation of photon statistics from the Poisson distribution. The theoretical expressions obtained for moments of the intermediate-photon distribution are different from well-known Mandel’s formulas.
Correlations between the emission of photons from an excited three-level atom with one transition more strongly driven than the other are studied. Antibunching, anticorrelation, and superbunching are exhibited in the four possible configurations: ``vee'' (V), ``lambda'' (\ensuremath{\Lambda}), and two cascades with the upper or lower transition strongly driven. We pay particular attention to the projection of the atom into particular states by the measurement of fluorescence, and its significance for detecting quantum jumps in the weak transition by observing the fluorescence from the strong transition. For incoherent excitation we find that cross antibunching (the anticorrelation between emissions of different types of photons) manifests itself as prolonged periods of darkness. For the V and the cascade configuration with a strongly driven lower transition, these periods herald the emission of a weak-transition photon; for the other cascade and the \ensuremath{\Lambda} configuration the periods are heralded by the emission of a weak-transition photon. For on-resonance coherent excitation, dark periods are extremely infrequent for the former two configurations, and are extremely long or infinite for the latter two.
A theoretical study is made of the steady-state intensity and squeezing properties of the fluorescent light from a three-level-atom system in a ladder configuration, which is subject to spontaneous-emission decay to the electromagnetic-field vacuum. Two cases are examined: in the equispaced (ES) level case, the two atomic transition frequencies are nearly equal and two photon absorption processes occur from a single coherent laser field that couples both transitions and has a small detuning from each; in the non- equispaced (NES) level case, the atomic transition frequencies are rather different and two photon absorption processes occur from two coherent laser fields, each coupled to a single transition and in near resonance with it. In both cases, a situation of small two-photon detuning occurs. Optical Bloch equations for the atomic density matrix in rotating frames are given and matrix expressions for determining the steady-state populations and coherences are obtained. Analytic expressions are also given for special cases. The fluorescent intensity is obtained from the populations of the intermediate and upper states, with the normally ordered variance (NOV) for quadrature components of the fluorescent field involving, in addition, the atomic coherences. The fluorescent intensities are shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases.In both cases, the fluorescent intensities show the well known resonances from the upper state at zero two-photon detuning and from the intermediate state at zero one-photon detuning for the lower transition. However, further resonances are also found. The intermediate-state intensity displays a resonance at zero two-photon detuning. Also, the upper-state intensity shows a resonance at zero one-photon detuning for the upper transition, but only for the NES case; evidently, the transfer rate from upper to lower transition coherences destroys this resonance for the ES case. The time-averaged NOV is also shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases. For the ES case, the quadrature frequency is chosen as the single laser frequency and for the NES case, it is chosen as either the average of the two laser frequencies or the lower transition laser frequency. Squeezing occurs near zero two-photon detuning for both ES and NES cases, though only for the quadrature frequency equal to the average laser frequency in the latter case. It also occurs near zero detuning for the lower transition for both cases, though only for the quadrature frequency equal to the lower transition laser frequency in the NES case. The squeezing minima show a splitting effect for large Rabi frequencies corresponding to two-photon or one-photon Rabi splitting of the dressed atom levels for the situation near two-photon or one-photon resonance, respectively. The large squeezing near two-photon resonance for moderate Rabi frequencies and large one-photon detuning corresponds to essentially pure three-level squeezing, while that near one-photon resonance for weak Rabi frequencies involves two-level squeezing.
Abstract This thesis presents an investigation into the quantum characteristics of fluorescence emitted by a two-level atom placed in the electromagnetic vacuum and driven by a classical coherent field. The theoretical analysis employs the Jaynes–Cummings model together with the master-equation formalism commonly used to describe open quantum systems. Within this framework, the work examines key nonclassical fea tures such as photon antibunching, sub-Poissonian statistics, and quantum regression. Particular emphasis is given to resonance fluorescence and the influence of weak and strong driving fields on the coherence properties of the emitted radiation. The master equation is solved in the long-time limit to obtain the evolution of relevant atomic expectation values, which are subsequently used to study population dynamics, mean photon behavior, and spectral features of the fluorescence signal. The study also highlights the role of vacuum fluctuations in spontaneous emission and their impact on the quantum behavior of the atom, ultimately providing insights into the generation of coherent and nonclassical light from driven atomic systems and their relevance to quantum communication and quantum information technologies. Keywords: Fluorescence, Jaynes–Cummings model, Photon statistics, Quantum optics, Two-level atom