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Journal of Modern Optics

Phase control of electromagnetically induced transparency in a double-Λ system

Arno Huss, Eugeny Korsunsky, Laurentius Windholz

Published Jan 1, 2002• 33 citations
Publisher

Abstract

It is experimentally demonstrated that the effect of electromagnetically induced transparency (EIT) can be controlled through the radiation phases. Corresponding investigations are performed by exciting a sodium atomic vapour by four-frequency laser radiation in a double-Λ configuration. In such a system the nonabsorbing (dark) state, responsible for EIT, is created only for particular values of the relative radiation phase. This phase dependency is confirmed using three different methods of phase control. Additionally, the relative phase is set at defined values in order to adjust the medium to a fixed transmission behaviour.

DOI
10.1080/09500340110087200

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European Quantum Electronics Conference (EQEC)•Apr 12, 2005•0 citations
It is experimentally demonstrated that the effect of electromagnetically induced transparency (EIT) can be controlled through the radiation phases. Corresponding investigations are performed by exciting a sodium atomic vapour by four-frequency laser radiation in a double-Λ configuration. In such a system the nonabsorbing (dark) state, responsible for EIT, is created only for particular values of the relative radiation phase. This phase dependency is confirmed using three different methods of phase control. Additionally, the relative phase is set at defined values in order to adjust the medium to a fixed transmission behaviour.
We theoretically investigate a double-Λ electromagnetically induced transparency (EIT) system. The property of the double-Λ medium with a closed-loop configuration depends on the relative phase of the applied laser fields. This phase-dependent mechanism differentiates the double-Λ medium from the conventional Kerr-based nonlinear medium, e.g., EIT-based nonlinear medium discussed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)], which depends only on the intensities of the applied laser fields. Steady-state analytical solutions for the phase-dependent system are obtained by solving the Maxwell-Bloch equations. In addition, we discuss efficient all-optical phase modulation and coherent light amplification based on the proposed double-Λ EIT scheme.
We study a double-Λ atomic scheme that interacts with four laser light beams so that a closed loop of radiation-induced transitions is formed. When specific relations for field phases, frequencies and amplitudes are satisfied, coherent superpositions (the so-called ‘dark states’) can be formed in a double-Λ, which leads to the well-known effect of electromagnetically induced transparency (EIT). If the interaction scheme in a double-Λ system is such that a closed loop is formed, the relative phase of the laser light fields becomes very important. We analyze here the effect of the lasers' relative phase on the EIT in double-Λ configuration of levels. The theoretical study of interactions of lasers with a double-Λ atomic scheme is commonly conducted by solving the optical Bloch equations (OBEs). We use here a perturbative method for solving OBEs, where the interaction of lasers with double-Λ is considered a perturbation. An advantage of the perturbative method is that it generally produces simpler solutions, and analytical expressions can be obtained. We present analytical expressions for the lower-order corrections of the EIT signal. Our results show that the EIT by the perturbative method can be approximated by the sum of products of complex Lorentzians. Through these expressions, we see in what way the relative phase affects the overall EIT profile.
We report on an investigation of electromagnetically induced transparency (EIT) in sodium vapour. In our experiment, sodium atoms are excited on the D1-line with laser radiation containing two components with a frequency difference close to that of the two hyperfine ground states of sodium (1.772 GHz). Such an excitation leads to coherent trapping of atomic population in “dark” superpositional states, which dramatically reduces the absorption of light. A frequency transparency window is measured to have a subnatural width, which is a clear indication of coherent population trapping. Dependence of EIT on laser frequencies and intensities, on the magnetic field strength as well as on the temperature of the sodium vapour is studied.
In this paper, we study the formation of two electromagnetically induced transparency (EIT) windows in a four-level lambda atomic system with Doppler broadening. The depth and the width of the EIT windows are easily changed by adjusting the intensity of the controlling laser fields. Meanwhile, the position of the EIT windows is also easily shifted by changing the frequency of the laser fields. In particular, by turning on or off one of the two coupling laser fields, the probe field response can be switched between one or two EIT window regimes, i.e., it is possible to switch between absorption and transparency regimes, and vice versa. In addition, our analytical model also allows one to investigate the influence of temperature (or Doppler width) on EIT windows, which is necessary for experimental observations as well as related applications at room temperature.
The effect of the relative phase on the spectral linewidth of electromagnetically induced transparency is studied in a Λ-type three-level configuration coupled by double coupling fields and the result is presented in this paper. We show that the relative phase between the double coupling fields has a great degree of influence on the spectral width of electromagnetically induced transparency window. The linewidth can be controlled by changing the relative phase. Particularly, as the double coupling fields have opposite phases, the linewidth of EIT window can be extremely narrow distinctly.
Summary form only given. The destructive quantum interference of resonantly excited transitions within a lambda-system in case of two photon resonance leads to a medium, which is coherently prepared in a superpositional dark state. The corresponding distinct enhancement of radiation transmission is well known as electromagnetically induced transparency. Interaction of quantized fields with such a medium yields a correlation of quantum phase fluctuations of the fields even for independent cw lasers. The experiments are done on the Na D/sub 1/ line by means of a temperature stabilized sodium vapor cell. One frequency component is modulated by a broad spectrum of phase fluctuations of about 50 MHz width by means of an electrooptical phase modulator driven by a noise generator. A transfer of noise to the other frequency components within a lambda- or a closed double-lambda transition scheme during transmission through the dark state medium is observed using the heterodyne spectroscopy. The verified exponential decay of the width of the beat signal in dependence on the medium optical density proofs the noise transfer and hence the correlation of phase fluctuations between the corresponding frequency components. This behaviour as well as the different limits of decay for lambda- (towards the transparency linewidth) and closed double-lambda (towards zero) scheme is in good qualitative agreement with the theory.