We apply a general formalism for the separation of rapid and slow time scales in linear evolution equations to three-state atoms with a strong and a weak radiative transition. This leads to an expression for the intensity correlation function that constitutes a good approximation on both time scales. This result can also be translated into an expression for the waiting-time distribution for the next photon emission after a previous one. The slow evolution is expressed in two rate constants, which determine the statistical distribution for dark and bright periods in the fluorescent emission. The result is applied to various configurations of the radiative couplings between the three states.
We apply a general formalism for the separation of rapid and slow time scales in linear evolution equations to three-state atoms with a strong and a weak radiative transition. This leads to an expression for the intensity correlation function that constitutes a good approximation on both time scales. This result can also be translated into an expression for the waiting-time distribution for the next photon emission after a previous one. The slow evolution is expressed in two rate constants, which determine the statistical distribution for dark and bright periods in the fluorescent emission. The result is applied to various configurations of the radiative couplings between the three states.
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.
For pt.I see Phys. Rev. A, vol.37, p.4303 (1988). The principle of wavefunction collapse by non-detection of photons leads to simple but rigorous expressions for the average dark and bright periods, T D and T B , of intermittent quantum jump fluorescence from a V-configuration three-level atom. Here further consequences of this principle are explored, including: the derivation of some new correlation functions which exhibit the physical characteristics of extended dark and bright periods; the expressions for T D and T B when one transition is driven coherently and the other incoherently; and a general expression for the characteristic time to be sure that a quantum jump has occurred for any type of driving field.
We consider a three-level atomic system driven strongly on one transition and weakly on the other. The excited state on the weak transition is assumed to be metastable. We give an analysis of the fluorescence from the strong transition in terms of the elementary probability density p[0,t)(t1,t2,..., tn) which gives us the probability density that exactly n photons are emitted at times t1,t2,...,tn by the atom in the time interval [0,t). We show that p[0,t) essentially factorizes into products of conditional densities c\ifmmode \tilde{}\else \~{}\fi{}(\ensuremath{\tau}) that, given a photon is emitted at time zero, the next photon emission occurs at time \ensuremath{\tau}. This enables a simulation of the individual photon emissions to be given which shows directly the existence of prolonged dark windows in the fluorescence corresponding to the shelving of the electron in the metastable state or ``quantum jumps.''
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.>
A single-atom optical clock proposed over ten years ago utilizes an amplification scheme which only recently was recognized as a novel problem in quantum statistics. The atom, a three-state system, has two coupled transitions that are driven continuously by two external fields, one being an allowed transition (1\ensuremath{\leftrightarrows}3) and the other a forbidden transition (2\ensuremath{\leftrightarrows}3) where \ensuremath{\Vert}3〉 is the lowest state. It has been argued that the weak transition, which is difficult to detect, could be monitored by the presence or absence of spontaneous emission of the strong transition. Thus, when the atom is shelved in the metastable state \ensuremath{\Vert}2〉, the strong transition is extinguished, but when the atom executes a single quantum jump (2\ensuremath{\rightarrow}3), it triggers a succession of perhaps a million quantum jumps (macroscopic quantum jumps) in the strong transition, an amplification that can be detected easily. This intuitive argument for alternating bright and dark intervals assumes, however, that the atom is always in an eigenstate. Should the atom be in a superposition state, because of coherent excitation, one could imagine that the weak transition would merely reduce the intensity of the strong transition slightly. This issue is resolved, in favor of the first intuitive argument, by calculating the photon-counting statistics, the probability W(n,T) of observing precisely n photon-counting events in a collection T in a quantum-mechanically consistent way. The results cannot be described by classical statistics. A compact analytic form is obtained for W(n,T) by considering the entire hierarchy of correlation functions where the emission interval peaks sharply about a particular n with a Poisson distribution and can be comparable in length to the darkness interval (n=0) while the other values of n display vanishingly small probabilities.
We present a microscopic model for the so-called quantum jumps in three-level atoms with one transition between two levels being strongly driven and the third level being metastable. Our model is based on calculating the elementary probability density P(0,t)(t1, … , t n ) which gives the probability density that exactly n photons are emitted at times t1, … , t n by the atom in the time interval (0, t) on the strong transition. This enables us to calculate the conditional probabilities c ˜ ( τ ) that given a photon has emitted at τ = 0 the next photon emission occurs at time τ. This quantity is shown to be the sum of two exponentials which for sufficient differetial in the time scales describe the periods of light and darkness. Using this conditional probability it is possible to numerically simulate the individual photon emissions.