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Physical Review A

Overtone generation in driven coherent media

Jonas Tidström, L. Mauritz Andersson

Published Jun 23, 2009• 0 citations
Publisher

Abstract

We observe overtone signal generation of a near-resonant bichromatic light field interacting with $^{85}\text{R}\text{b}$ on the Zeeman split $F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=1,2,3$ hyperfine transitions of the ${D}_{2}$ line at 780 nm. A nonperturbative theoretical model for electromagnetically induced transparency is developed in order to explain this phenomenon. Assuming a $\ensuremath{\Lambda}$ system, an explicit and convenient expression for the atomic coherence is derived from the Lindblad equation assuming a phase-damping channel. The light field state is parametrically varied through one beat note of the bichromatic field and the spatial properties are studied by numerically solving the coupled-wave equation. The polarization characteristics is analyzed on the Poincar\'e sphere, which together with field intensity analysis offers a simple explanation of the harmonic beating signal due to Stokes vector rotation around the Poincar\'e sphere and decoherence effects. The experimental data and theoretical analysis focus on the first and second harmonics, although many higher harmonics are present. A distinct and narrow minimum of the second-harmonic generation is measured on two-photon resonance.

DOI
10.1103/physreva.79.063832

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We observe overtone signal generation of a near-resonant bichromatic light field interacting with 85Rb^{85}\text{R}\text{b}85Rb on the Zeeman split F=2\ensuremath↔F\ensuremath′=1,2,3F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=1,2,3F=2\ensuremath↔F\ensuremath′=1,2,3 hyperfine transitions of the D2{D}_{2}D2​ line at 780 nm. A nonperturbative theoretical model for electromagnetically induced transparency is developed in order to explain this phenomenon. Assuming a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system, an explicit and convenient expression for the atomic coherence is derived from the Lindblad equation assuming a phase-damping channel. The light field state is parametrically varied through one beat note of the bichromatic field and the spatial properties are studied by numerically solving the coupled-wave equation. The polarization characteristics is analyzed on the Poincar'e sphere, which together with field intensity analysis offers a simple explanation of the harmonic beating signal due to Stokes vector rotation around the Poincar'e sphere and decoherence effects. The experimental data and theoretical analysis focus on the first and second harmonics, although many higher harmonics are present. A distinct and narrow minimum of the second-harmonic generation is measured on two-photon resonance.
In this thesis we study light-matter coherence phenomena related to the interaction of a coherent laser field and the so-called Λ-system, a three-level quantum system (e.g., an atom). We observe electromagnetically induced transparency (EIT), slow and stored light in hot rubidium vapor. For example, a 6 μs Gaussian pulse propagate at a velocity of ~1 km/s (to be compared with the normal velocity of 300 000 km/s). Dynamic changes of the control parameter allows us to slow down a pulse to a complete stop, store it for ~100 μs, and then release it. During the storage time, and also during the release process, some properties of the light pulse can be changed, e.g., frequency chirping of the pulse is obtained by means of Zeeman shifting the energy levels of the Λ-system. If, bichromatic continuous light fields are applied we observe overtone generation in the beating signal, and a narrow `dip' in overtone generation efficiency on two-photon resonance, narrower than the `coherent population trapping' transparency. The observed light-matter coherence phenomena are explained theoretically from first principles, using the Lindblad master equation, in conjunction with the Maxwell's equations. Furthermore, we analyze an optical delay-line based on EIT and show that there is in principle (besides decoherence) no fundamental limitation, but the usefulness today is scant. The combination of EIT and a photonic crystal cavity is inquired into, and we show that the quality value of a small resonator (area of 2.5λ×2.5λ with a missing central rod) can be enhanced by a factor of 500 due to the increased modal density close to two-photon resonance. Open system effects (decoherence effects) are thoroughly investigated using a coherence vector formalism, furthermore, a vector form of the Lindblad equation is derived. Specifically we find an open system channel that lead to slow light and gain.
Light propagating through an optically anisotropic resonant medium excites coherent Raman fields that propagate together with the original wave; the interference between the two fields generates the well-known Raman beats. We solve the coupled-wave equations for finite optical path lengths and show how the coherent exchange of energy between the two fields leads to interference effects that distort the observed signal for different detection schemes. Theoretical analysis is compared with experimental results from the Na D1 transition.
The interaction of a two-level system with a strong standing wave is examined by the probe field resonant to the adjacent transition in the $\ensuremath{\Lambda}$ configuration of Ar II. The known peak of electromagnetically induced transparency is observed in the absorption spectrum at the detuning of the probe field proportional to the detuning of the strong field. Along with it, the different structure has been found at the line center, independently of the strong-field frequency. The calculations clarify that the central structure is induced by the higher-order spatial harmonics of the atomic coherence induced at the probe transition. The effect results in steep frequency dependence of the refractive index at the line center.
Light propagation through an ensemble of ultracold Rydberg atoms in an electromagnetically-induced-transparency (EIT) configuration is studied. In strongly interacting Rydberg EIT media, nonlinear optical effects lead to a nontrivial dependence of the degree of probe-beam attenuation on the medium density and on its initial intensity. We develop a Monte Carlo rate equation model that self-consistently includes the effect of the probe-beam attenuation to investigate the steady state of the Rydberg medium driven by two laser fields. We compare our results to recent experimental data and to results of other state-of-the-art models for light propagation in Rydberg EIT media. We find that for low probe field intensities, our results match the experimental data best if a density-dependent dephasing rate is included in the model. At higher probe intensities, our model deviates from other theoretical approaches, because it predicts a spectral asymmetry together with line broadening. These are likely due to off-resonant excitation channels, which, however, have not been observed in recent experiments. Atomic motion and coupling to additional Rydberg levels are discussed as possible origins for these deviations.
We report on experimental and theoretical study of the nonlinear Faraday effect under conditions of electromagnetically induced transparency at the $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}\ensuremath{\rightarrow}5{D}_{5/2}$ two-photon transition in rubidium vapor. These transitions realize the inverted YYY model which combines the $\ensuremath{\Lambda}$ and ladder systems. Strong nonlinearity allowing for large rotation angles of a probe beam tuned to the $S\ensuremath{\rightarrow}P$ transition was obtained by creation of quantum superpositions of magnetic sublevels (Zeeman coherences) in the rubidium ground state ($\ensuremath{\Lambda}$ scheme). Additionally, electromagnetically induced transparency was accomplished in a ladder scheme by acting with a second strong coupling laser on the $P\ensuremath{\rightarrow}D$ transition. Under conditions of a two-photon resonance the rotation was significantly reduced, which is interpreted as a competition between the coherent processes. The effect was observed in sub-Gauss magnetic fields and could be used for efficient coherent control of generation of the ground-state coherences, e.g., for controlling the polarization state of the probe light.
The evolution of enhanced four-wave mixing based on Raman coherence as the probe intensity increases is observed experimentally in an 85 R b atomic vapor system. We propose that for a Doppler-broadened Λ -type level system, the generated anti-Stokes field from one-photon resonance will be suppressed by the dressed-states resonance and can be controlled by the probe intensity, which influences the effective transverse relaxation rate of Raman coherence. When the probe field is not so weak, the double resonance for dressed states will greatly suppress the anti-Stokes emission at the central frequency, and the signal peak will be split. We show that this phenomenon is a result of the destructive polarization interference between atoms with different velocities from the two types of resonance. Based on our model, we present a new, to the best of our knowledge, interpretation of four-wave mixing enhancement in the conventional Λ -type electromagnetically induced transparency system.