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European Quantum Electronics Conference (EQEC)

Correlation of phase fluctuations in electromagnetically induced transparency

Arno Huss, Roland Lammegger, Laurentius Windholz

Published Apr 12, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1109/eqec.2003.1314220

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Correlation of phase fluctuations in electromagnetically induced transparency

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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.

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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.
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.
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 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.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.
It is known that cross correlation between the random intensity fluctuations of two lasers forming electromagnetically induced transparency (EIT) exhibits a transition from correlation to anticorrelation. We study the linewidth behavior of this transition and have found the linewidth is below the (effective) coherence lifetime limit and is limited only by competing noises. We established a numerical model which reveals the linewidth dependence on laser linewidth and laser power. Our experiments using lasers with different linewidth showed results in qualitative agreement with the model. This result is useful for quantum optics using EIT and may also have applications in spectroscopy and precision measurements.