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Journal of Modern Optics

Effect of the Dipole-dipole Interaction on the Pure Two-atom Squeezed State

Z. Ficek

Published Dec 1, 1993• 7 citations
Publisher

Abstract

The influence of the dipole-dipole interaction on the final atomic state of a two-atom system driven by a coherent laser field and damped by a broad-band squeezed vacuum is discussed. It is shown that in the absence of a coherent laser field the final atomic state is independent of the dipole-dipole interaction and can be the pure two-atom squeezed state only if detuning of the squeezed vacuum field from atomic resonance is equal to zero. In the presence of a coherent laser field, the final atomic state depends on the dipole-dipole interaction. As the latter increases, the final atomic state shifts from a mixed state to the pure two-atom squeezed state. However, this happens only if the driving field and the squeezed field frequencies are tuned to the atomic transition frequency. For the driving field and the squeezed vacuum field frequencies detuned from atomic resonance the system decays into a mixed state irrespective of the dipole-dipole interaction between the atoms.

DOI
10.1080/09500349314552371

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The influence of the dipole-dipole interaction on the final atomic state of a two-atom system driven by a coherent laser field and damped by a broad-band squeezed vacuum is discussed. It is shown that in the absence of a coherent laser field the final atomic state is independent of the dipole-dipole interaction and can be the pure two-atom squeezed state only if detuning of the squeezed vacuum field from atomic resonance is equal to zero. In the presence of a coherent laser field, the final atomic state depends on the dipole-dipole interaction. As the latter increases, the final atomic state shifts from a mixed state to the pure two-atom squeezed state. However, this happens only if the driving field and the squeezed field frequencies are tuned to the atomic transition frequency. For the driving field and the squeezed vacuum field frequencies detuned from atomic resonance the system decays into a mixed state irrespective of the dipole-dipole interaction between the atoms.
We report exact results concerning the effect of dipole-dipole interaction (dispersion forces) on dynamic and steady-state characteristics of squeezing in the emitted fluorescent field from two identical coherently driven two-level atoms. The atomic system is subjected to three different damping baths in particular the normal vacuum, a broad band thermal field and a broad band squeezed vacuum. The atomic model is the Dicke model, hence possible experiments are most likely to agree with theory when performed on systems of Rydberg atoms making microwave transitions. The presence of dipole-dipole interaction can enhance squeezing for realizable values of the various parameters involved.
The authors investigate the dipole-dipole interaction role in the resonance fluorescence of two identical two-level atoms, which are confined to a region much smaller than the resonant wavelength and which are damped by a squeezed vacuum. The spectrum consists of seven or five lines, depending on the relative phase between the driving field and the squeezed vacuum, whereas the spectrum without the dipole-dipole interaction displays three lines. The widths of these lines depend on the parameters of the squeezed vacuum and can be subnatural or supernatural depending on the phase. The central line and additional sidebands at double the Rabi frequency can have intensities larger than in the normal vacuum but the intensities of lines at one Rabi frequency are always less than in the normal vacuum.
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.
We study the near-resonant dipole-dipole interaction between two atoms in a broadband squeezed vacuum. We show that this ``vacuum'' modifies the rate of spontaneous emission of the atoms so that it may depend not merely on their relative position, as is normally the case, but also on their center-of-mass position. The explicit form of this latter dependence is a function of the way squeezing is achieved. We also show that in contrast to the spontaneous decay rate, squeezed vacua do not modify the dipole-dipole potential between the atoms as compared to its usual form. Finally, we develop a Monte Carlo wave-function description of the interaction between atoms with an arbitrary internal structure and a squeezed vacuum and apply this formalism to the case of off-resonant excitation of the atoms. We find that in addition to the usual light shift, the squeezed vacuum results in an additional contribution to the effective potential governing the evolution of the atomic ground states. \textcopyright{} 1996 The American Physical Society.
The relaxation process of a single two-level atom driven by an intense resonant coherent field is studied in the presence of a broadband squeezed vacuum field. Generalized forms for the self-field operator and the field-dependent damping coefficients are derived. In the steady state, positive atomic inversion (~5%) is shown for some range of the phase of the squeezed vacuum field. The squeezing-induced enhanced and asymmetric coherence (i.e.?non-zero dispersive atomic polarization) induces profound asymmetry in the side-bands of the Mollow fluorescent spectrum and the absorptive?dispersive spectra near the Rabi side-band frequencies. The case of two and three cooperative atoms, instead of a single atom, shows (i)?positive atomic inversion in the steady state for larger interval of the squeeze phase parameter and more enhanced extrema for the atomic polarization components and (ii) the extra side peaks in the fluorescent spectrum become asymmetric and of dispersive-like profile. Dressed-state analysis in the single-atom case with the field-dependent decay process in the presence of the squeezed vacuum field is presented and shows that the inequality of the (field-dependent) decay rates of the dressed states leads to more positive inversion in the dressed states as compared with the normal vacuum case.