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Quantum Optics Journal of the European Optical Society Part B

Squeezing in two-atom resonance fluorescence induced by two-photon coherences

Z. Ficek, R. Tanaś

Published Apr 1, 1994• 5 citations
Publisher

Abstract

We examine squeezing properties of resonance fluorescence from two interacting atoms. Previous theoretical analyses of this model have predicted squeezing on one-photon resonance. Here we show that it is possible to obtain squeezing in two-atom resonance fluorescence through two-photon transitions induced by a cooperative atomic interaction. The squeezing occurs near a two-photon resonance and is not sensitive to the duration of the detection time in comparison with the decay time of the subradiant state. Moreover, squeezing near a two-photon resonance is completely independent of the direction of observation in respect to the atomic axis and can be significantly larger than that previously found on one-photon resonance.

DOI
10.1088/0954-8998/6/2/005

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Optics Communications•Dec 1, 1998•4 citations
We examine squeezing properties of resonance fluorescence from two interacting atoms. Previous theoretical analyses of this model have predicted squeezing on one-photon resonance. Here we show that it is possible to obtain squeezing in two-atom resonance fluorescence through two-photon transitions induced by a cooperative atomic interaction. The squeezing occurs near a two-photon resonance and is not sensitive to the duration of the detection time in comparison with the decay time of the subradiant state. Moreover, squeezing near a two-photon resonance is completely independent of the direction of observation in respect to the atomic axis and can be significantly larger than that previously found on one-photon resonance.
Phase-sensitive squeezing in the resonance fluorescence of two-level atoms, that are coherently driven by a near-resonant laser field in free space, was observed recently (Lu et al 1998 Phys. Rev .L ett. 81 3635). This was accomplished via homodyne detection at a phase near ±45 ◦ relative to the driving field for strong off-resonant excitation of ‘long-lived’ atoms (where th ea tomic lifetime far exceeded the laser–atom interaction time, meaning that relaxation effects could be ignored). On the other hand, traditional theoretical predictions of phase-sensitive squeezing in the resonance fluorescence from two-level atoms have emphasized in- and out-of-phase (i.e., 0 ◦ and 90 ◦ ) quadratures, and weak, on-resonant excitation of ‘short-lived’ atoms (where the observation time for laser–atom interaction fa re xceeded the natural atomic lifetime, meaning that relaxation effects dominate). Here, we calculate the probability of a delayed-coincidence detection in the interference field of a fluorescing dipole with a local oscillator (LO). We show that, despite the strikingly different conditions in which squeezing occurs in short- and long-lived atoms, squeezing in both cases can be shown to arise from a joint detection of two photons which are related by a quantum jump in the following way: the first photodetection precipitates a quantum jump of the atom to the ground state, and the second measures the mean amplitude of the fluorescent field subsequent to the quantum jump.
We discuss the phase-sensitive noise properties of fluorescence emitted by three-level atoms coherently excited by two laser fields, using both undressed and dressed uncoupled-state representations. The occurrence of steady-state squeezing is found to be highly sensitive to relaxation processes between the two-photon resonant levels. For purely radiative decay from the upper level, and no lower-state relaxation, the population is susceptible to coherent population trapping. Near two-photon resonance, the atom is optically pumped into a nonabsorbing (trapped) superposition state, which, although it reduces upper-level population, also leads to an interference cancellation of dipole moments and to suppression of squeezing. Lower-level relaxation unbalances this interference and restores the squeezing to some extent. Transient squeezing is also predicted in the time-dependent fluorescence.
In this paper, we study cooperative two-photon transitions in a system of two (nonoverlapping) atoms for two processes: two-photon spontaneous emission and two-photon resonance fluorescence. Expressions are obtained for the energy shifts and decay rates due to the interaction of the atoms with and via the field. The altered decay rates signal the existence of superradiance and subradiance in the two-atom system. The energy shifts of the single-excitation states are found to be proportional to ${\mathit{R}}^{\mathrm{\ensuremath{-}}6}$ for small atomic separations R, and to ${\mathit{R}}^{\mathrm{\ensuremath{-}}2}$ for large separations.
The occurrence of steady-state squeezing in a coherently driven three-level atom of the \ensuremath{\Lambda} configuration is found to be highly sensitive to the detection process of the fluorescence field. We show that there is no steady-state squeezing when the two atomic transitions equally contribute to the detected fluorescence field. There is no squeezing even when only one of the two possible transitions contributes to the detected fluorescence field, if the decay rate of the contributing transition is smaller than or equal to the decay rate of the other transition. Squeezing may occur only when the decay rate of the transition that exclusively contributes to the detected fluorescence field is larger than the decay rate of the other transition. Moreover, when the squeezing attains its maximum value, pure two-level squeezing is involved. The system reduces to a two-level system in which both the basic three-level dynamics and the two-photon coherences are destroyed.
The authors present analytical and numerical results for resonance fluorescence produced by a two-level atom damped by a broad-band squeezed vacuum. Previous theoretical analyses of this model have assumed that the laser frequency and the carrier frequency of the squeezed vacuum are equal. The authors introduce a non-zero detuning between the laser frequency and the carrier frequency while maintaining resonance between the laser frequency and atomic resonance. In the absence of the driving field there is a squeezing threshold: above threshold the decay rate of the atomic polarization can be reduced, and below threshold a squeezing-induced two peak spectrum and frequency shift, which is analogous to the Bloch-Siegert shift, are predicted. In the presence of the driving field, the spectrum is asymmetric for Rabi frequencies smaller or comparable to the detuning of the squeezed vacuum. A symmetric spectrum is obtained for large Rabi frequencies. An interpretation is predicted by means of a dressed-state analysis. The authors find that for not too large Rabi frequencies a remarkably large population inversion can be induced in the dressed states, even at exact resonance of the driving field, provided that the laser frequency and carrier frequency are detuned. Moreover, for detection times larger than the inverse detuning, the spectrum is insensitive to the phase between the driving field and the squeezed vacuum, in marked contrast to the case of no detuning.
Interaction of single-mode coherent light with dipole-forbidden two-level atoms via non-resonant virtual level is studied in this paper. It is shown that, in the case of two-photon resonance fluorescence , the atomic system generates three bands of correlated photon pairs with the carrier frequencies ω k 0 , ω k 0 ± Γ , where Γ=[Ω 2 +(Δ/2) 2 ] 1/2 , 2Ω is the two-photon Rabi frequency and Δ is the detuning from the two-photon resonance. It is established that amplitude-squared squeezing occurs from the sidebands of the two-photon resonance fluorescence spectrum . When the atom number increases, the amplitude-squared squeezing also increases.