Cooperative Resonance Fluorescence Research Articles

Squeezing in cooperative resonance fluorescence.

Cooperative effects on squeezing in resonance fluorescence from a finite number N of atoms are examined. Analytical expressions for the spectrum of squeezing and a quantity Q(T) related to the photon-counting statistics of the squeezed states are presented for N=1 and 2. These expressions are obtained by invoking the high-field approximation of the relevant master equation. The analytical results are supplemented by the numerical solutions of the exact master equation for N\ensuremath{\le}10. It is shown that for intense fields or large detunings, squeezing in resonance fluorescence is predominantly due to the quantum nature of the sidebands of the Mollow triplet. As a manifestation of cooperative effects, squeezing present in the total as well as the sideband radiation increases with the number of atoms. This is further confirmed from the behavior of the photon-statistics function Q(T).

Commutator version of the evolution operator and cooperative resonance fluorescence (CRF)

A generalisation of a commutator version of the evolution operator method to the CRF problem has been given. The effect of amplifying the ( omega a+or-2 Omega ) harmonics has been confirmed and their intensity ratio has been shown to be highly dependent on the initial atomic level populations.

Higher Harmonics in Cooperative Resonance Fluorescence

In the Stark representation, in third-order perturbation theory with respect to fluorescence, it is shown that probability of the ωa + 4Ω harmonic emission in the cooperative fluorescence of two two-level atoms is small and proportional to γ2 / Ω2, Ω2 / ω2 a, contributions to this probability from non-resonant processes being of the order of γ2 / ω2 a.

Effect of Detuning on Squeezing in Two-atom Resonance Fluorescence

The exact steady-state solution is presented for the reduced atomic density operator describing the cooperative resonance fluorescence from a system of two atoms separated by an arbitrary distance in an off-resonance laser field, with the dipole-dipole near-field interaction between the atoms included. It is shown that the destructive effect of the dipole-dipole interaction on the formation of squeezing in two-atom resonance fluorescence found recently by Ficek et al. can be compensated to a very large extent by an appropriate choice of the detuning between the laser frequency and the single-atom transition frequency.

Dipole-dipole stability in cooperative resonance fluorescence

Dipole-dipole stability in cooperative resonance fluorescence

Cooperative Resonance Fluorescence from Two Atoms Experiencing Different Driving Fields

The inclusion of the coupling of the antisymmetric state to the driving field, if the atoms are in inequivalent positions, can change the steady-state total scattering intensity as a function of field strength from one monotonically approaching the saturation intensity 2 n to one which at first runs through a maximum above 2 n at intermediate field strengths. Moreover, under suitable conditions the scattering spectrum can exhibit three distinct peaks, and depending on the detuning, photon bunching and antibunching can occur in the scattered radiation.

Sidebands in cooperative resonance fluorescence in collections of N three-level atoms in strong excitation laser fields

It is shown that, in addition to an Autler-Townes doublet, the resonance fluorescence spectrum of N three-level atoms consists of sidebands separated by three pump Rabi frequencies and much reduced in intensity to the symmetrically-located central doublet. The sidebands are due to cooperative atomic interaction.

Cooperative states and resonance fluorescence III

It has been shown that cooperative fluorescence takes place if γ ≫ R and turns into “single-atom” fluorescence when λ ≪ R. For two and three two-level atoms the cooperative effect leads to narrowing of the fluorescence lines and to increasing of the sideband intensities.

Power Broadening and Two-photon Correlations in Two-atom Resonance Fluorescence

The cooperative resonance fluorescence radiation from two atoms separated by an arbitrary distance and driven by a coherent laser field is studied, taking into account the dipole-dipole near-field interaction. The steady-state total scattering intensity, as a function of laser frequency and field strength, differs considerably from the single-atom one for sufficiently small distances. Photon bunching and antibunching occur in the scattered radiation depending on the laser frequency. Practically a full antibunching effect is found, especially if the laser is tuned to resonance with a transition frequency of the two-atom system. This is in contrast to a recent result of Agarwal et al., who studied the two-atom system but neglected the frequency splitting due to the dipole-dipole near-field interaction.

Relation between atomic coherent-state representation, state multipoles, and generalized phase-space distributions

The relationship between the atomic coherent-state representation of Arecchi et al. [Phys. Rev. A 6, 2211 (1972)] and the state multipoles is established. The state multipoles are used to develop a theory of generalized phase-space distributions for angular momentum (collective atomic) systems. The general theory for angular momentum systems is shown to have many features in common with the general theory for boson systems [Phys. Rev. D 2, 2161 (1970)]. These generalized phase-space distributions contain as a special case the coherent-state representation of Arecchi et al. The applications of the generalized phase-space distributions and state multipoles to the dynamical problems and to the calculation of multitime correlations are given. State-multipole techniques are used to give a brief discussion of the master equation describing cooperative resonance fluorescence.

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 ω 0 and ω 0± 2Ω 0 , with the ratio of their intensities tending to unity as the number of atoms increases.

Cooperative state and resonance fluorescence

Using the exact solution of the Schrödinger equation for a system of N two-level atoms driven by a strong resonant field, the spectrum of cooperative resonance fluorescence consisting of the (ω 0 + mΩ)-harornics has been found.

Analytical and numerical results for the steady state in cooperative resonance fluorescence

The cooperative resonance fluorescence steady state is discussed within the context of an operator master equation which conserves total pseudospin. Emphasis throughout is on quantum fluctuations and their significance in relation to a background of factorised dynamics. Atom-atom correlations are shown to play a fundamental role for systems driven beyond the linear regime. Use of the atomic coherent state representation yields a Fokker-Planck description closely allied to the dynamics for a classical angular momentum oscillator. For intense incident fields the quantum-mechanical steady state is understood in terms of diffusion both around and between classical trajectories on the Bloch sphere. In the limit of infinite systems simple closed-form expressions for steady-state features are derived. Coherent and incoherent fluorescent intensities are obtained together with the second-order correlation function for fluorescent light. Specific features are illustrated by numerical results for systems of from two to fifty atoms.

Observables and moments of cooperative resonance fluorescence

The moments of the fluorescent radiation of a ${J}^{2}$-invariant, cooperative fluorescent group of atoms are calculated exactly. Both photon bunching and antibunching can occur in the fluorescent radiation. All finite-order moments have a critical-point behavior at ${\ensuremath{\Omega}}_{c}=J\ensuremath{\gamma}$ in the cooperative limit of $J\ensuremath{\rightarrow}\ensuremath{\infty}$. The maximum normalized intensity correlation is 6/5 which shows greatly reduced intensity fluctuations compared to noncooperative resonance fluorescence. Enhanced antibunching in all the fluorescent correlation functions occurs in the threshold region.

Multiple sidebands in cooperative resonance fluorescence: Exact semiclassical results

Multiple sidebands in cooperative resonance fluorescence: Exact semiclassical results

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 resonance fluorescence and atomic interactions

The effect of interatomic interaction on cooperative resonance fluorescence in the case of well separated components is discussed. It is shown that for two atoms the new components appear both in the emission spectrum and in the intensity correlation function. An increase of the number of interacting atoms leads to an increase in the number of additional spectral components.

Additional Sidebands in Cooperative Resonance Fluorescence

Additional Sidebands in Cooperative Resonance Fluorescence

Photon statistics and absorption spectrum in cooperative resonance fluorescence

Analytic results for the absorption spectrum in cooperative resonance fluorescence are presented. An initial broad-band absorption spectrum on the cooperative branch develops a sharp spike as the instability point is approached. The usual one-atom absorption spectrum is regained on the non-cooperative branch. The photon statistics of the scattered light are studied through a calculation of the second-order correlation function g(2)(0). On the cooperative branch the value of g(2)(0) is unity reflecting the coherent scattering from the cooperative atomic state. On the non-cooperative branch the value of g(2)(0) jumps to two, reflecting the incoherent scattering from independently scattering atoms.

Hysteresis in the spectrum for cooperative resonance fluorescence

Hysteresis in the spectrum for cooperative resonance fluorescence