Abstract

It has been demonstrated in recent years that the interaction of a squeezed field with atomic systems leads to a number of very interesting phenomena. For example, three-level atoms can exhibit total population inversion when interacting with a squeezed field^[1-2]. However, this effect is sensitive to the number of squeezed modes coupled to the atoms. An inversion can be observed in free-space only when more than 50% of the modes are squeezed^[1]. In practice, the output of present sources of squeezed light can couple only to a small fraction of the modes enveloping the atoms. In this paper we propose a possible solution to this problem suggesting coupling the squeezed modes to the atoms in an optical cavity of small dimension, as this could be used to reduce the relative coupling of unsqueezed modes. In our model we have a microscopic Fabry-Perot cavity with two plane mirrors separated by half a wavelength. The first is a perfectly reflecting mirror located at z=0, and the second a partially transmitting lossless mirror has a real reflectivity R and is located at z=L. The squeezed field with an intensity N is propagating in z direction normal to the mirrors and is focused at a point r_s = (0,0,L/2). A three-level atom with the three states |1>, |2>, |3> in the ladder configuration is located at r= (r_x, 0, L/2). The transition frequencies of |2> → |1> and |3> → |2> are ω₁ and ω₂, respectively, with ω₁ – ω₂ = Δ, and the corresponding natural linewidths are γ₁ and γ₂. We assume the carrier frequency ω₀ of the squeezed field to be such that the condition 2ω₀ = ω₁ + ω₂ is satisfied. Stationary population in the state |3> is shown in Fig. 1 as a function of r_x/L for R=0.99, N = 0.2, the squeezed field propagation over the angle θ = 30°, and different γ₂/γ₁. These graphs show that almost the total population inversion (ρ₃₃ = 0.94) can be achieved when the ratio γ₂/γ₁ is much smaller than 1, and when the atom is at the point where squeezed field is focused. The present analysis of the total population inversion can be experimentally verified using, for example, absorption spectroscopy techniques. Because the absorption from the ground and the middle states is proportional to population differences ρ₂₂ – ρ₁₁ and ρ₃₃ - ρ₂₂, respectively, one can model these experiments by monitoring the absorption of a weak probe beam. Fig. 2 shows the absorption spectrum for the same parameters as in Fig. 1, Δ = 10γ₁, and r_x/L = 0. For γ₂ = γ₁ the spectrum exhibits positive values at Δ and negative values at-Δ indicating that there is a population inversion between |3> and |2>. As the ratio γ₂/γ₁ decreases the amplitude of the peak at Δ decreases and vanishes for small γ₂/γ₁. This fact indicates that there is no population in states |1> and |2> and only the state |3> is populated.

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