Cooperative states and resonance fluorescence II

In the Stark states representation the spectrum of cooperative resonance fluorescence of one, two and three two-level atoms in the limit of high Rabi frequency has been found to consist of the harmonics ω₀ and $\text{ω}{}_0\text{± 2Ω}{}_0$, with the ratio of their intensities tending to unity as the number of atoms increases.     

Cooperative two-photon resonance fluorescence of a three-level atom

We have calculated the Green function describing the physical process where a three level atom interacts with a strong pump field as well as with a weak perturbing signal field in the limit of high photon densities. The theory is then used to describe the cooperative two-photon resonance fluorescence which occurs when the sum of the two atomic transition frequencies is nearly twice the frequency of the pump field. Our atomic system is equivalent to a two-level atom when the degeneracy of the ground state is removed by a Stark field. The excitation spectrum has been found to consist of new bands and sidebands which exist only in the presence of the Stark field. The resonance process which occurs when the Stark splitting is in the neighbourhood of the energy shift induced by the laser field has been discussed in detail.     

Cooperative effects in the two atom resonance fluorescence spectrum

We consider the resonance fluorescence spectrum of two similar interacting atoms in the limit of high photon densities. The excitation spectrum of the symmetric modes contains two sidebands in addition to the usual three peaks which are analogous to those of the isolated atom. These two new sidebands are due entirely to the cooperative behaviour of the two atoms and vanish when the atoms are far apart. The energy shifts and spectral widths for these two sidebands are two and five times larger than those for the isolated atom respectively. The probability of occurrence of these sidebands depends on the parameters V_AB/Ω and γ²₀/Ω², where V_AB is the dipole-dipole interaction energy, γ₀ is the spontaneous emission probability and Ω is the Rabi frequency. The asymmetric broadening of both sidebands depends on the parameter γ₀/Ω. The possibility to measure the dipole-dipole energy through the observation of these sidebands is discussed.     

Atomic state reduction and energy balance relation in spectrally resolved resonance fluorescence

The paper is devoted to a study of properties of the reduced atomic state directly after detection of a resonance fluorescence photon that passed through a spectral (Fabry–Perot) filter. We establish the energy balance relation for the reduced state and discuss its observable consequences.     

Non-markovian resonance fluorescence

The power spectrum of a strong field resonance fluorescence is derived from non-markovian Bloch equations. It is shown that the Mollow spectrum is modified by non-markovian corrections. The main feature of the non-markovian behavior is a nonsymmetric power spectrum even at exact resonance. The magnitude of the non-markovian asymmetry depends on the power of the driving light.     

Two-photon resonance fluorescence

The excitation spectrum of a two-level atom interacting with a strong electromagnetic field is considered when the atomic transition frequency is nearly twice the frequency of the laser field. The spectral function consists of four Lorentzian lines describing: the central line peaked near the two-photon resonance, two sidebands peaked at the high and low frequency regions respectively and the one-photon frequency mode. In the limit of high photon densities, the low frequency photon mode is induced by the pump field which removes the singularity occurring at the two-photon resonance frequency.     

Cooperative and interference effects in the resonance fluorescence of two identical three-level atoms at high photon densities

The excitation spectrum of two identical three-level atoms is considered when a strong electromagnetic field operates resonantly between two levels of the atoms. While undergoing the transition into the excited state, the atoms interact through their dipole-dipole interaction and radiate to each other as well, and subsequently, they decay radiatively into another excited state. For such a system, the spectral functions are calculated describing the cooperative and interference spectra for the symmetric and antisymmetric modes arising from the decay of the atoms from one excited state into another. In the absence of the pump field, the spectral function for the symmetric modes consists of two peaks, which are described by Lorentzian lines peaked at the frequencies ω = ω₂₃ + V_AB and ω = ω₂₃ ? V_AB and having spectral widths of the order of γ⁰₂₁ + γ⁰₂₃ and γ⁰₂₃, respectively, where ω₂₃ is the transition frequency between the two excited states, V_AB is the dipole-dipole interaction and $\text{1}\text{2}\text{γ}{}^0{}_{21}$ is the natural width for a photon spontaneously emitted from the 2 → 1 transition of an isolated atom. The splitting of the central peak for the transition in question and the broadening of the spectral widths are due entirely to the dipole-dipole and radiative interactions between the atoms. The spectral function for the antisymmetric modes describes a stable mode at the frequency ω = ω₂₃ ? V_AB, which has a delta-function distribution, and a Lorentzian line peaked at the frequency ω = ω₂₃ + V_AB and has a spectral width of the order of γ⁰₂₁. In the presence of the pump field, the spectral function for the symmetric modes contains, in addition to the central peaks, two pairs of sidebands, one pair of which is induced by the pump field with an energy shift equal to $\text{Ω}{}_{\mathrm{<mtext>a</mtext>}}\text{/√2}$, while the other pair of sidebands is due to the dipole-dipole interaction between the atoms; the probability of occurrence of the latter pair of sidebands is proportional to $\text{V}{}_{\mathrm{AB}}\text{/Ω}{}_{\mathrm{<mtext>a</mtext>}}$, while the induced energy shift is equal to $\text{3Ω}{}_{\mathrm{<mtext>a</mtext>}}\text{/√2}$, where $\text{√2Ω}{}_{\mathrm{<mtext>a</mtext>}}$ is the induced by the laser field energy shift (Rabi frequency) for a single two-level atom. The spectral widths for both pairs of sidebands are of the order of γ⁰₂₁ + γ⁰₂₃. The excitation spectrum of the antisymmetric modes consists of, in addition to the central peaks, a pair of stable sidebands, which have delta-function distributions, and two pairs of sidebands, which are similar but sharper than those for the symmetric modes. Detail comparisons are given between the one- and two-atom excitation spectra for the systems under investigation.     

Two-atom two-photon resonance fluorescence

The excitation spectrum arising from the interaction between two identical two-level atoms, one of which is excited in the presence of a strong electromagnetic field (pump field), is investigated when the atomic transition frequency is nearly twice the frequency of the pump field. The excitation spectrum consists of those describing the symmetric and antisymmetric modes, respectively. The spectral functions for the symmetric and antisymmetric modes are derived and discussed in detail. The possibility to measure directly the magnitude of the dipole-dipole interaction energy is discussed.     

Classical and quantum mechanical resonance fluorescence

We study resonance fluorescence from a two-level atom illuminated by coherent and incoherent light. Especially, we treat the case of an intense incoherent component which is broad band and chaotic in character.New insights into the phenomenon of resonance fluorescence are obtained by constructing certain analogies with the precession of a classical (Bloch) vector around a classical stochastic field. The analogies are based on a representation of the density operator of the two-level atoms as a diagonal mixture of directed angular momentum states.As long as the whole light field is an imposed one the weight function of the mixture mentioned above describes a random sequence of rotations of the Bloch vector and obeys a simple Fokker Planck equation. If, however, the incoherent component of the light field acts as a zero- or finite temperature heat bath, the equation of motion for the weight function is no longer a Fokker Planck equation. Nontheless, we find the exact solution and calculate the correlation functions relevant to a discussion of the spectrum and of antibunching effects.     

Cooperative effects in optical double resonance

A theory of optical double resonance which takes into account the cooperative interactions among atoms is formulated. The analytical result for the double resonance spectra in the conventional situation when the probe field is weak, is given. The changes in the nature of the spectra as one sweeps from cooperative to single atom branch are discussed. The cooperative interaction is shown to reduce considerably the asymmetry of the Autler-Towne's doublet.     

Spectrum of squeezing in resonance fluorescence

The spectral squeezing in resonance fluorescence from a two-level atom is calculated. It is shown that for resonance excitation optimum squeezing is obtained for near resonant frequencies of the fluorescent light. An operational definition of the spectrum of squeezing is given based on a discussion of possible experimental configurations.     

Quantum beats in two-photon resonance fluorescence

The two-photon resonance fluorescence spectrum of a three-level atom is shown to consist of the low frequency modes in addition to the high frequency ones in the limit of high photon densities. The spectral function for the low frequency modes consists of two lorentzian lines describing: the peak occuring at the renormalized beat frequency Δ₊ and that of the zero-photon excitation at the frequency Δ_-, where Δ_±=Δ-3Ω²/2ω_a±Ω²u/2ω_a, u²=1+(2Δω_a/Ω ²)². Here, 2Δ is the energy splitting between the two excited states, ω_a is the photon energy of the pump field and Ω is the Rabi frequency. The peak at the renormalized beat frequency Δ₊ occurs provided that the condition (2Δω_a/Ω²)² > 1 is satisfied. The two-photon laser spectroscopy is expected to be a useful tool for the observation of the low frequency modes in question.     

Nuclear resonance fluorescence in121Sb

Usingγ quanta from a⁵⁶Co source, resonance fluorescence from a 3,452 keV level in¹²¹Sb was observed. Four deexcitingγ transitions were identified. The profile of theγ emission line, investigated by means of a high speed centrifuge, yields with a novel variety of Doppler shift analysis a lifetime of τ_4,298=(110±50)fs for theγ emitting 4,298 keV level in⁵⁶Fe. The lifetime of the 3,452 keV level was determined to beτ _3,452 =(200±100)fs.     

Sideband entanglement in collective resonance fluorescence

We examine the quantum correlation between the Mollow sidebands in the collective resonance fluorescence from a strongly driven ensemble of two-level atoms. By using the criterion proposed by Shchukin and Vogel, we show that non-Gaussian entanglement exists between the two separated sidebands. The responsible mechanism is traced to the spontaneous parametric process, in which the nonclassical correlation is established. This suggests that the collective resonance fluorescence provides a continuous source for the non-Gaussian entangled light and thus has great potentials for various applications in quantum information and quantum computation.     

Two-time photon correlations in resonance fluorescence

The factorization formula for the two-time intensity correlation of the fluorescence produced by a two-level atom in a coherent field is generalized for an arbitrary quantum state of the field. The formula is then applied to a Fock state.     

Cooperative and interference effects in the resonance fluorescence of two identical three-level atoms at high photon densities: II. Numerical results

Numerical calculations are presented for the excitation spectrum of two identical three-level atoms interacting with a strong resonant laser field. The atoms interact through their dipole-dipole interaction and radiate to each other as well. The spectrum of the symmetric and antisymmetric modes due to the radiative decay from the higher to the lower excited state of the interacting atoms is considered without and with taking into account the effects of the strong pumping process. In the absence of strong pumping, the dipole-dipole interaction in the spectrum of the symmetric modes gives rise to an asymmetric doublet whose ratio of intensities is 2:1, while the spectrum of the antisymmetric modes consists of two peaks one of which represents a stable mode indicating the trapping of a photon between the atoms and a radiative one which has a lifetime one-half that of the isolated atom. In the presence of strong pumping, asymmetries due to the dipole-dipole interaction arise enhancing certain peaks while diminishing the intensity of others and a new pair of sidebands is induced as well. The computed spectra are presented graphically for different values of the Rabi frequencies and the dipole-dipole interaction, respectively.