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Physical interpretation for the correlation spectra of electromagnetically-induced-transparency resonances

D. Felinto, Luciano Soares da Cruz, Rafael Alves De Oliveira, H. M. Florez, Marcio H. G. de Miranda, P. Nussenzveig, M. Martinelli, J. W. R. Tabosa

Published Jan 14, 2013• 14 citations

Abstract

The phenomenon called Electromagnetically Induced Transparency (EIT) may induce different types of correlation between two optical fields interacting with an ensemble of atoms. It is presently well known, for example, that in the vicinity of an EIT resonance the dominant correlations at low powers turn into anti-correlations as power increases. Such correlation spectra present striking power-broadening-independent features, with the best condition for measuring the characteristic linewidth occurring at the highest powers. In the present work we investigate the physical mechanisms responsible for this set of observations. Our approach is first to reproduce these effects in a better controlled experimental setup: a cold atomic ensemble, obtained from a magneto-optical trap. The results from this conceptually simpler system were then compared to a correspondingly simpler theory, which clearly relates the observed features to the interplay between two key aspects of EIT: the transparency itself and the steep normal dispersion near two-photon resonance.

DOI: 10.1364/oe.21.001512

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The phenomenon called Electromagnetically Induced Transparency (EIT) may induce different types of correlation between two optical fields interacting with an ensemble of atoms. It is presently well known, for example, that in the vicinity of an EIT resonance the dominant correlations at low powers turn into anti-correlations as power increases. Such correlation spectra present striking power-broadening-independent features, with the best condition for measuring the characteristic linewidth occurring at the highest powers. In the present work we investigate the physical mechanisms responsible for this set of observations. Our approach is first to reproduce these effects in a better controlled experimental setup: a cold atomic ensemble, obtained from a magneto-optical trap. The results from this conceptually simpler system were then compared to a correspondingly simpler theory, which clearly relates the observed features to the interplay between two key aspects of EIT: the transparency itself and the steep normal dispersion near two-photon resonance.

We report a detailed investigation on the properties of intensity correlation spectra for laser beams interacting with cold atoms under the condition of electromagnetically induced transparency (EIT). We describe the transition of their intensity fluctuations from correlation to anticorrelation as the mean intensity of the fields increases. Such a transition occurs for laser frequencies around the EIT resonance, which is characterized by a correlation peak. The transition point between correlation and anticorrelation is independent of power broadening and provides directly the ground-state coherence time. We introduce a method to extract in real time the correlation spectra of the system. The experiments were done in two distinct magneto-optical traps, one for cesium and the other for rubidium atoms, employing different detection schemes. A simplified theory is introduced assuming three-level atoms in $\ensuremath{\Lambda}$ configuration interacting with a laser with stochastic phase fluctuations, providing a good agreement with the experimental observations.

Correlation spectroscopy has been proposed as a spectroscopic technique for measuring the coherence between the ground states in electromagnetically induced transparency (EIT). While in the time domain the steep dispersion in the EIT condition accounts for the robustness of the correlation linewidth against power broadening, such physical insight was not directly established in the frequency domain. We propose a perturbative approach to describe the correlation spectroscopy of two noisy lasers coupled to a $\mathrm{\ensuremath{\Lambda}}$ transition in cold atoms, leading to EIT. Such approach leads to an analytical expression that maps the intensity correlation directly in terms of the absorption and dispersion of the light fields. Low and high perturbative regimes are investigated and demonstrate that, for coherent light sources, the first-order term in perturbation expansion represents a sufficient description for the correlation. Sideband resonances are also observed, showing the richness of the frequency domain approach.

We report experiemtnal results demonstrating the electromagnetically induced transparency (EIT) in trapped Cs atoms. EIT occurs at the Λ-type configuration where the re0-pumping laser simultaneously plays a role as the coupling laser in the presence of a magneto-optical trapping and weak magnetic fields. Dependences of EIT signal on both the intensity and the detuning of the coupling laser were investigated. Linear absorption spectra for cold cesium atoms in the magneto-optical trap have been observed and shown the pronounced dispersion-like structure with sub-natural linewidth of 1 MHz due to the cooling laser.

We report an experimental observation of narrow and high-contrast spectra, which are induced by interacting dark resonances and have been predicted in Phys. Rev. A 60, 3225 (1999). Spectra are measured with cold

{}^{87}\mathrm{Rb}

atoms produced by a magneto-optical trap. In this experimental system, a coupling laser and a weak probe laser form a three-level \ensuremath{\Lambda}-type configuration of electromagnetically induced transparency (EIT); a microwave drives a magnetic-dipole transition between the fourth level and the ground state that is coupled with the excited state by the coupling laser. The observed spectral profile of probe absorption exhibits a very sharp peak emerging inside a narrow EIT dip. Such spectral feature provides more opportunities in manipulating atomic-optical response.

The correlation spectroscopy has been successfully employed in the measurement of the intrinsic linewidth of electromagnetically induced transparency (EIT) in time and frequency domain. We study the role of the sidebands of the intense fields in the measured spectra, analyzing the information that can be recovered working with different analysis frequencies. In this case, the nonzero one-photon detuning appears as a necessary condition for spectrally resolving the sideband resonances in the correlation coefficient. Our experimental findings are supported by the perturbative model defined in the frequency domain.

Observation of dual electromagnetically induced transparencies in cold

^{87}Rb

atoms

We have observed two dual electromagnetically induced transparency (EIT) spectra in probe transmission through cold

^{87}Rb

atoms trapped in a magneto-optical trap (MOT). These dual EIT peaks are generated in two different N-systems formed by probe, coupling and control beams interacting with different levels in

D_{2}

line transitions of

^{87}Rb

atom. The dependence of spectral features of two N-systems on driving beams (\textit{i.e.} coupling and control beams) strength and detuning has been investigated. The results show that the dual EIT spectral features in both the N-systems can be manipulated by varying the strength and detuning of both the driving beams. The two N-systems have been modelled theoretically using a density matrix formalism and results have shown a reasonable agreement with the experimental observations.