Coherent Population Trapping

We discuss the differences between two well-studied and related phenomena-coherent population trapping (CPT) and electromagnetically induced transparency (EIT). Many differences between the two-such as the effect of power in the beams, detuning of the beams from resonance, and the use of vapor cells filled with buffer gas-are demonstrated experimentally. The experiments are done using magnetic sublevels of the 1 → 1 transition in the D2 line of 87 Rb.

We use the technique of coherent population trapping (CPT) to access the ground hyperfine interval (clock transition) in 133 Cs. The probe and control beams required for CPT are obtained from a single compact diode lasers system. The phase coherence between the beams, whose frequency difference is the clock frequency, is obtained by frequency modulating the laser with an electro-optic modulator (EOM). The EOM is fiber coupled and hence does not require alignment, and the atoms are contained in a vapor cell. Both of these should prove advantageous for potential use as atomic clocks in satellites.

Optical magnetometers have reached sensitivities that make them interesting candidates for the measurement of weak magnetic fields also outside physics laboratories. In order to overcome problems with stray magnetic fields a common solution with existing magnetometers is to operate a pair of them in a gradiometer configuration: one sensor measures the signal plus the stray fields, while the other one is mounted such that it is only influenced by the stray fields. In the difference signal the stray fields cancel. We have constructed such a gradiometer consisting of two sensors based on coherent population trapping (CPT) resonances in a thermal cesium vapor. Using a magnetic bias field the intrinsically scalar CPT magnetometer can be turned into a true vector magnetometer that is insensitive to magnetic fields perpendicular to a chosen measurement direction. We describe how to align and calibrate the gradiometer. Stray field suppression by more than two orders of magnitude has been achieved, limited by the sensitivity of the magnetometer. This makes possible the detection of picotesla flux density changes in a weakly shielded or even unshielded environment.

High-contrast coherent population trapping signals were observed on the Cs D 1 line by use of a bichromatic linear polarized light (lin‖lin field). A maximum absorption contrast of about 10% was obtained. This was nearly twice as high as that measured with the standard configuration of bichromatic circularly polarized light (σ -σ field). The results are compared with density matrix calculations of 4 and 5 level systems.

We report on the fabrication of millimetersized vapor cells and their performance in atomic clocks based on coherent population trapping (CPT). We discuss two fabrication techniques. The first one is based on hollow-core pyrex fibers, fused with a CO 2 laser or micro-torch, and the second one involves anodic bonding of micro-machined silicon wafers to pyrex. Key aspects of the discussion are the performance of the cell in frequency references, the potential for further miniaturization of the cells and the ability to manufacture them on a large scale with reproducible performance.

We demonstrate a microfabricated atomic clock physics package based on coherent population trapping (CPT) on the D 1 line of 87 Rb atoms. The package occupies a volume of 12 mm 3 and requires 195 mW of power to operate at an ambient temperature of 200 °C. Compared to a previous microfabricated clock exciting the D 2 transition in Cs [1], this 87 Rb clock shows significantly improved short-and long-term stability. The instability at short times is 4 × 10 -11 / τ 1/2 and the improvement over the Cs device is due mainly to an increase in resonance amplitude. At longer times (τ > 50 s), the improvement results from the reduction of a slow drift to -5 x 10 -9 / day. The drift is most likely caused by a chemical reaction of nitrogen and barium inside the cell. When probing the atoms on the D 1 line, spinexchange collisions between Rb atoms and optical pumping appear to have increased importance compared to the D 2 line.

The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte-Carlo methods. We study here an advanced version of familiar Markov-chain Monte-Carlo (MCMC) algorithms that sample from target distributions defined as change of measures from Gaussian laws on general Hilbert spaces. Such a model structure arises in several contexts: we focus here at the important class of statistical models driven by diffusion paths whence the Wiener process constitutes the reference Gaussian law. Particular emphasis is given on advanced Hybrid Monte-Carlo (HMC) which makes large, derivative-driven steps in the state space (in contrast with local-move Random-walk-type algorithms) with analytical and experimental results. We illustrate it's computational advantages in various diffusion processes and observation regimes; examples include stochastic volatility and latent survival models. In contrast with their standard MCMC counterparts, the advanced versions have mesh-free mixing times, as these will not deteriorate upon refinement of the approximation of the inherently infinite-dimensional diffusion paths by finite-dimensional ones used in practice when applying the algorithms on a computer.

Coherent population trapping is studied in 87 Rb in a buffer gas. Experimental results are reported on the contrast of the field independent hyperfine resonance line and on its linewidth. A physical model, which includes an optical pumping process that traps atoms in a Zeeman sublevel of the ground state, is developed. The model explains the general behavior of the experimental observations.

The paper summarizes the relative advantages and disadvantages of coherent population trapping (CPT) or intensity optical pumping (IOP) for the implementation of a passive atomic frequency standard using the isotope 87 Rb. This paper outlines the basic principles common to both CPT and IOP when using laser optical pumping, and makes explicit their similarities and their differences. This paper describes experimental results obtained in the same cell on the characteristics of the CPT and IOP 87 Rb-hyperfine-resonance line. The measurements showed that the signal contrast is larger in CPT than in IOP for the same resulting line width; the light shift is smaller in CPT than in IOP, and is easier to control; in principle, a passive frequency standard based on CPT has a smaller size than that based on IOP, due to the absence of a microwave cavity. Conclusions on overall expectations for the future of such frequency standards are drawn.

An all-optical microwave frequency standard based on coherent population trapping (CPT) in 85 Rb is developed. The CPT resonances are detected by an ordinary edge-emitting diode laser in a simple optical setup. A buffer-gas mixture is carefully optimized to yield a narrow linewidth and a reduced temperature dependence of the resonance frequency. With the developed system we are able to measure ultranarrow optically induced hyperfine CPT resonances at Ͻ20 Hz, which is in good agreement with the linewidth calculated from experimental parameters. The frequency of an RF-signal generator has been stabilized to the CPT resonance between the two m F ϭ 0 magnetic sublevels. The relative frequency stability (square root of Allan variance) follows a slope of 3.5 ϫ 10 Ϫ11 Ϫ1/2 (1 s Ͻ Ͻ 2000 s). The best stability of 6.4 ϫ 10 Ϫ13 is reached at an integration time of ϭ 2000 s. This stability is sufficient for many high-precision applications. Frequencyshift measurements were made to evaluate the frequency dependencies on the operation parameters.

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Coherent population trapping (CPT) of metalalkali atoms is an interesting technique for the development of compact atomic frequency references; it relies on the excitation of the atoms by two phase-coherent laser fields. We describe the design and operation of an innovating dual-frequency laser source dedicated to Cs CPT atomic clocks, based on the direct dual-frequency and dual-polarization operation of an opticallypumped semiconductor laser at 852 nm. The phase noise of beatnote generated by the laser source is at maximum of -90 dBrad²/Hz with active stabilization, and the relative intensity noise (RIN) has been measured at -115 dB/Hz. It would potentially results in a clock frequency stability of 1.6 .10 -12 at 1 second, limited by the laser RIN. With proper adjustments in the laser and clock set-up, we target a stability of 3.10 -13 at 1 second.

Electromagnetically induced transparency and coherent population trapping were observed in a hot (1000 K) calcium vapor embedded into an electrical gas discharge. Unexpectedly large transparencies (of up to 70%) were observed under very unfavorable conditions: probe wavelength shorter than the coupling wavelength, and coupling Rabi frequency significantly smaller than the residual Doppler linewidth of the two photon transition. We developed

Ce travail de thèse effectué dans le cadre d’un contrat CIFRE-Défense porte sur l’étude des sources d’instabilité de fréquence d’une horloge atomique basée sur le piégeage cohérent de population. L’objectif est de démontrer une stabilité de fréquence d’horloge de l’ordre de 10-13 tau-1/2 jusque 10 000 s. Une cellule de vapeur de césium est utilisée avec un schéma d’excitation à fort contraste en utilisant des polarisations linéaires croisées et avec une interrogation impulsionnelle de type Ramsey. Un chapitre d’abord consacré aux sources de bruit à court terme présente les travaux réalisés pour réduire le bruit de phase et le bruit de puissance laser, limitant tous deux les performances de l’horloge à 1 s d’intégration. L’optimisation de la chaine micro-onde avec un nouvel oscillateur local, et la réalisation d’un asservissement de puissance performant ont permis d’améliorer la stabilité de fréquence à 2,3x10-13 à 1 s. L’analyse des fluctuations des paramètres de fonctionnement (pui...

We have undertaken a development effort to produce a prototype chip-scale atomic clock (CSAC). The design goals include short-term stability, 2 / 1 10 y 10 6) (− − × < τ τ σ , with a total power consumption of less than 30 mW and overall device volume < 1 cm 3. The stringent power requirement dominates the physics package architecture, necessarily dictating a small (< 1 mm 3) volume gaseous atomic ensemble interrogated by a low-power semiconductor laser. At PTTI 2002 and PTTI 2003, we reported on laboratory experiments that underlie the fundamental architecture of our CSAC, based on interrogation of the cesium D1 transition by the technique of coherent population trapping (CPT). In the past year, the development effort has shifted from fundamental research and feasibility investigation to engineering and prototype development. In this paper, we report on the design of a rugged and compact physics package that is expected to exceed the ultimate performance and power requirements of the CSAC.

and Nuc. Sc. Div. @ LBNL-A recently identified alkene based anti-relaxation coating exhibit Zeeman relaxation times in excess of 60 s in alkali vapor cells (two orders of magnitude longer than in paraffin coated cells). The long relaxation times, motivate revisiting the long-standing question of what is the mechanism underlying wall-collision induced relaxation and renew interest in applications of alkali vapor cells to secondary frequency standards. We measure the Zeeman relaxation time, and the width and frequency shift of the clock resonance, in 85 Rb and 87 Rb vapor cells with alkene anti-relaxation coating. We compare the results with those in paraffin coated cells. We find that the frequency shift is slightly larger than for paraffin coated cells. However we observe that the Zeeman relaxation rate appears to be a linear function of the hyperfine frequency shift, whereas a linear dependence was not observed in paraffin coated cells. To shed light on this result we propose a model describing different Zeeman relaxation mechanisms of alkene and alkane cell-wall coatings.

We investigate experimentally and theoretically the coherent population trapping ͑CPT͒ effect occurring in 87 Rb D 1 line due to the interaction with linearly polarized laser light ͑linʈ lin CPT͒. In this configuration, the coherence is strongly influenced by the structure of the excited state; consequently, the quantum interference between dark states is an essential feature of this interaction scheme. We study the linʈ lin CPT resonance as a function of the laser optical detuning. The comparison between experimental and theoretical results allows us to quantify the contribution from different dark states to the total signal. Based on these results, we investigate the signal depending on both the pressure broadening of the optical transition and the laser linewidth, and we find in which conditions the laser linewidth does not degrade the linʈ lin CPT resonance.

We propose a novel approach to all-optical frequency standard design, based on a counterintuitive combination of the coherent population trapping effect and signal discrimination at the maximum of absorption for the probe radiation. The short-term stability of such a standard can achieve the level of 10 −14 / √ τ. The physics beyond this approach is dark resonance splitting caused by interaction of the nuclear magnetic moment with the external magnetic field.

A universal mechanism destroying coherence in a ⌳ system driven by two resonant laser fields due to four-photon interactions is analyzed theoretically. It is shown that this mechanism gives rise to novel spectral structures in resonance fluorescence. The ''dark resonance'' in absorption ͑dispersion͒ spectra is affected as well. ͓S1050-2947͑98͒09411-6͔

We observe a surprising plateau in the decay of pulse-echo amplitude measured for quantum vibrational states in a 1D optical lattice, indicating a long-lived component of the coherence. We present a hypothesis for the origin of the plateau in the decay, and develop a 2D pump-probe spectroscopy technique to test this model. In our 1D lattice, atoms are free to move in the transverse directions with thermal velocities about 3 cm/s. Although the intrinsic decoherence time is expected to be of the order of 50 ms, this transverse drift through the spatially inhomogeneous laser ...

database and to 1.47 for the characters database. However, it must be noted that in our case only two parameters are used to characterise each BP. Some examples of retrieval results are shown in Figs. 2-4. It can be appreciated that recognition is successful even when additional BPs appear, like in the square and elliptic shapes. (CICYT), under Project No. TlC098-0562. We would also like to thank F.S. Chang and S.Y. Chen, from Yuan-Ze University (Republic of China), for their help and for providing the databases used in this work.

We report a theoretical study of the collisional ionization processes which occur under 2s → 2p excitation of lithium vapor excited with a nanosecond pulsed laser. The time evolution of the electron energy distribution function and the atomic ion density (Li +) as well as the molecular ion density (Li + 2) at dierent lithium vapor densities was investigated. The results show a nonlinear behavior of the energy spectra of the electrons created during the interaction of the laser with the lithium vapor. The nonlinear behavior results from superelastic collisions between the free electrons produced by collisional ionization and photoionization with Li(2p). The results also show that a competition exists between the collisional ionization and photoionization processes in producing the atomic ion and the molecular ions.

Ce travail de these effectue dans le cadre d’un contrat CIFRE-Defense porte sur l’etude des sources d’instabilite de frequence d’une horloge atomique basee sur le piegeage coherent de population. L’objectif est de demontrer une stabilite de frequence d’horloge de l’ordre de 1E-13 t^(-1/2) jusque 10 000 s. Une cellule de vapeur de cesium est utilisee avec un schema d’excitation a fort contraste en utilisant des polarisations lineaires croisees et avec une interrogation impulsionnelle de type Ramsey. Un chapitre d’abord consacre aux sources de bruit a court terme presente les travaux realises pour reduire le bruit de phase et le bruit de puissance laser, limitant tous deux les performances de l’horloge a 1 s d’integration. L’optimisation de la chaine micro-onde avec un nouvel oscillateur local, et la realisation d’un asservissement de puissance performant ont permis d’ameliorer la stabilite de frequence a 2,3E-13 a 1 s. L’analyse des fluctuations des parametres de fonctionnement (puis...

We discuss the differences between two well-studied and related phenomena-coherent population trapping (CPT) and electromagnetically induced transparency (EIT). Many differences between the two-such as the effect of power in the beams, detuning of the beams from resonance, and the use of vapor cells filled with buffer gas-are demonstrated experimentally. The experiments are done using magnetic sublevels of the 1 → 1 transition in the D2 line of 87 Rb.

Accurate measurements are presented of the rate of trap-loss-producing collisions between ultracold magneto-optically trapped Li atoms for a range of trap laser intensities and frequencies. Intensities from near the atomic saturation intensity to well above it are investigated. At low intensities, fine-structure-changing collisions cause trap loss with a rate constant of-10 ' cm /s. At sufficiently high intensity, the trap can be deep enough to effectively freeze out the dominant fine-structure-changing collisions as a loss mechanism, enabling an accurate comparison of the radiative escape loss rate with theory. At the lowest intensities of this radiative escape regime, the measured loss rates compare favorably with those calculated using an optical Bloch equation theory and a three-dimensional model of trap depth. However, the intensity dependence of the measured rates does not show the saturation predicted by the optical Bloch equation theory. It is shown that reliable knowledge of trap depth is necessary to accurately compare experiment with theory.

We demonstrate the excitation and low-noise differential detection of a coherent population trapping (CPT) resonance with two modulated optical fields with orthogonal circular polarizations. When a microwave phase delay of λ/4 is introduced in the optical path of one of the fields, the difference in the power transmitted through the cell in each polarization shows a narrow, dispersive resonance. The differential detection allows a high degree of suppression of laser-induced noise and will enable nearly shot-noise-limited operation of atomic frequency references and magnetometers based on CPT.

We present experimental data on collisions between excited He-atoms occurring in a magneto-optical trap (MOT) at a temperature of 1.1 mK. He(2 3 S)-atoms produced in a discharge are pre-cooled and trapped using the He(2 3 S)± He(2 3 P 2) transition for laser manipulation. Measurements of the Penning ionization rate as a function of the MOT-laser frequency are presented and theoretically analyzed. The analysis, based on a model which is presented in detail for the ®rst time, leads to a good understanding of the complex nature of optical collisions. Further, ®rst and preliminary measurements of the kinetic energy distributions of He 2-and He-ions formed by Penning ionization in optical collisions are presented.

In this thesis, we study light-matter interaction in the contexts of coherent population trapping (CPT) and the ac Stark effect in nanoparticles embedded (doped) in two important classes of reservoirs-photonic crystals and dispersive materials. These materials have gaps in their energy spectra and are studied widely due to their unusual optical properties and potential for novel applications. We consider that the reservoirs are doped with an ensemble of five-level nanoparticles, each with a single Λ core (consisting of a lower doublet and an upper energy level), which interact with both the host reservoir and external radiation fields. We have also included studies of cases where the nanoparticles interact with each other as well via dipole-dipole interaction (DDI), which is included in the mean field approximation. This only happens when the doping concentration is high (~ per cubic meter). In studying CPT, we have developed a novel technique of optical switching by devising a system whereby the doped nanoparticles become stable against absorption from the radiation field(s) i.e. they switch to their ground states. We have confirmed the occurrence of CPT in both types of reservoir and have also identified a number of important contrasting features which have markedly different utilities. Most significantly, we have found that the strength of the DDI between the nanoparticles plays a very important role in determining the conditions required for CPT in both materials. In studying the ac Stark effect in photonic crystals, we have used an ensemble of five-level nanoparticles, each with a single cascade core [ladder configuration], both with and without DDI. We found that, in the ac Stark regime, resonance tuning of the transitions within the nanoparticles, in relation to the band structure of these crystals, offers a new mechanism for switching the nanoparticle system from an inverted to a non-inverted state. Specifically, a doped nanoparticle can effectively become transparent to any radiation field tuned to the probed transition. Under DDI, we found that the absorption in the system decreases with increasing DDI strength. These findings have very exciting potential for applications in optical switching.

Hyperfine structure of the 852 nm 6 2 S1/2 →6 2 P3/2 (D2 line) transition in 133 Cs atoms has been investigated. Natural linewidth of the transition has been measured using saturated absorption spectroscopy. The measured value of linewidth is 5.09 MHz which is close to the literature value of 5.2 MHz. Such novel technique is easily realizable and useful for quick investigations of hyperfine structure of atomic samples in normal vapour cells.

When a three-level quantum system is irradiated by an intense coupling field resonant with one of the three possible transitions, the absorption peak of an additional probe field involving the remaining level is split. This process is known in quantum optics as the Autler-Townes effect. We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an "artificial atom" with a multilevel quantum structure. The spectroscopy peaks can be explained reasonably well by a simple three-level Hamiltonian model. Simulation of a more complete model (including dissipation, higher levels, and cross-coupling) provides excellent agreement with all the experimental data.

When a three-level quantum system is irradiated by an intense coupling field resonant with two of the three possible transitions, the resonant absorption of the system from its ground state by an additional radiation field is suppressed. This effect, where the population is trapped in the ground state, is known in quantum optics as "electromagnetically induced transparency". When the coupling field is detuned from resonance, the resonant absorption peak splits to form an "Autler-Townes doublet". We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an "artificial atom" with a multilevel quantum structure. These observations are qualitatively described by a simple model restricted to three energy levels. A full solution of the master equation including higher levels provides excellent agreement with all the experimental data.

Circular Rydberg states with n = 70 have been prepared in helium using a modified version of the crossed-fields method. This approach to the preparation of high-n circular Rydberg states overcomes limitations of the standard crossed-fields method which arise at this, and higher, values of n. The experiments were performed with atoms traveling in pulsed supersonic beams that were initially laser photoexcited from the metastable 1s2s 3 S1 level to the 1s73s 3 S1 level by resonanceenhanced two-color two-photon excitation in a magnetic field of 16.154 G. These excited atoms were then polarized using a perpendicular electric field of 0.844 V/cm, and transferred by a pulse of microwave radiation to the state that, when adiabatically depolarized, evolves into the n = 70 circular state in zero electric field. The excited atoms were detected by state-selective electric field ionization. Each step of the circular state preparation process was validated by comparison with the calculated atomic energy level structure in the perpendicular electric and magnetic fields used. Of the atoms initially excited to the 1s73s 3 S1 level, ∼ 80% were transferred to the n = 70 circular state. At these high values of n, ∆n = 1 circular-to-circular Rydberg state transitions occur at frequencies below 20 GHz. Consequently, atoms in these states, and the circular state preparation process presented here, are well suited to hybrid cavity QED experiments with Rydberg atoms and superconducting microwave circuits.

We have investigated the performance of a remote-detection sodium cell magnetometer using synchronous optical pumping with amplitude modulated light. The magnetometer is used to measure ambient geomagnetic field with high-sensitivity using backscattered resonance fluorescence.

We use mode locked lasers in a non-conventional way, as a sensor to perform intracavity measurements. To understand this new technique of intracavity phase interferometry (IPI), one should take a detailed look at the characteristics of the frequency comb and its sensitivity to its parent cavity. The laser cavity provides a means to perform phase interferometry while outside the cavity one can only observe amplitude intereference. Many physical quantities such as nonlinear index, Earth rotation, magnetic field, Fresnel drag, etc are converted to phase. IPI is performed by designing laser cavities in which two pulses circulate independently, generating two pulse trains that can have a phase difference that will be converted to frequency. We also explore repetition rate spectroscopy in Rb 87 by tailoring a laser wavelength, power and bandwidth. Coherent population trapping is observed when the laser repetition rate matches submultiples of hyperfine splitting.

We present a laser system for the generation and stabilization of continuous wave emission at 1.9 THz. The system is based on difference frequency generation (DFG) from a bicolor vertical external cavity surface emitting laser (VECSEL). The intracavity DFG process enables THz generation with milliwatt power level at room temperature with a clear quadratic dependence red on the intracavity power. The two colors are spectrally selected via an intracavity etalon while the laser cavity geometry is engineered to minimize mode competition between the two colors via spatial hole burning, improving the stability of the THz emission. The intensity noise of the THz output is further reduced by 16 dB/Hz with an active stabilization scheme. The origin of residual fluctuations is discussed and we found that the asymmetrical amplification of one color reduced the RIN even further, down to 21 dB/Hz, comparing to the free-running symmetrical lasing.

We present the first experimental observation of the Rabi splitting of Mossbauer resonance lines. A radio-frequency magnetic field is tuned to induce transitions between hyperfine sublevels of the Zeeman-split excited or ground state of Fe nuclei. The line splitting corresponding to the Rabi flopping &equency is observed using a magnetically soft FeNi absorber foil of composition with almost zero magnetostriction.

A new, efficient method to produce cold negative muon ions is proposed. The muonium atom is made up of an antimuon and an electron and is given the chemical symbol Mu. A second electron with binding energy or electron affinity of 0.75 eV makes the Muion, which is in many ways almost identical to the Hion that is used for charge-exchange injection into most proton particle accelerators. Muonium negative ions were observed in 1987 [1,2] by interaction of muons with a foil. Using the foil charge-exchange approach, the efficiency of transformation of muons to negative muonium ions has been very low ~10. However, by using a hot tungsten or palladium single crystal foil treated by cesium deposition, the production efficiency can be improved up to 50%. The process described here has surface muons focused onto a tungsten or palladium single crystal foil (that can be heated up to 2000 Celsius) and partially covered by a cesium layer up to minimal work function. The negative muon ions can be ...

This paper describes the fabrication of chip-scale alkali atom vapor cells, for use in highly miniaturized atomic frequency references, using silicon micromachining and anodic bonding technology. The cells consist of silicon cavities with internal volume ranging from a few mm3 to less than 1 mm3. The cells were filled with cesium and nitrogen buffer gas either by chemical reaction of cesium chloride and barium azide, or by direct injection of elemental miurn within a controlled anaerobic environment. Cesium optical absorption spectra were obtained from the cells, and coherent population trapping resonances with linewidths of about 1 kHz were measured.

We report on the fabrication of millimetersized vapor cells and their performance in atomic clocks based on coherent population trapping (CPT). We discuss two fabrication techniques. The first one is based on hollow-core pyrex fibers, fused with a CO 2 laser or micro-torch, and the second one involves anodic bonding of micro-machined silicon wafers to pyrex. Key aspects of the discussion are the performance of the cell in frequency references, the potential for further miniaturization of the cells and the ability to manufacture them on a large scale with reproducible performance.

We consider theoretically the expected performance of ultra-small vapor-cell frequency references with cell volumes below 1 mm3. The short-term stability is found to degrade as the size is reduced. The amount of degradation depends on whether a buffer gas or wall coating is used for the atomic confinement. Preliminary experimental results with all-optical excitation indicate that the atomic Q-factor behaves as expected.

A thermal vapor of three-level atoms irradiated by two copropagating laser beams of suitable frequencies exhibits the phenomenon of coherent population trapping, leading to an electromagnetically induced transparency ͑EIT͒. When a mirror reflects the beams back onto themselves one finds that depending on the position along the resulting standing wave the fluorescence intensity from the sample ͑cesium in our case͒ decreases ͑EIT͒ or even increases ͓electromagnetically induced absorption ͑EIA͔͒ with a period on the centimeter scale. An intuitive picture is based on the interference of coherent dark states but the explanation of the EIA effect requires consideration of Doppler effects in the thermal vapor. This allows for a quantitative comparison between experimental and calculated results.