Positive and negative subnatural-width resonances ͑SNWR͒ were observed in the absorption and fluorescence of rubidium vapor under excitation by two copropagating optical waves with variable frequency offset. The two optical fields resonantly couple Zeeman sublevels, belonging to the same ground-state hyperfine level ͑GSHL͒, to an intermediate excited state. The SNWR present opposite signs depending on which GSHL participates in the interaction with the two optical waves. For both Rb isotopes an increase in the transparency with reduced fluorescence occurs for the lower GSHL while the absorption and fluorescence are increased for the upper GSHL. The influence of external magnetic field, polarization, and intensity of applied optical fields on the SNWR is examined. The narrowest observed resonance has a width of 10 kHz ͑full width at half maximum͒. The origin of the SNWR is discussed in terms of coherent processes involving ground-state Zeeman sublevels. ͓S1050-2947͑98͒06703-1͔
A large increase in atomic absorption due to coherent interaction with resonant radiation is predicted for a closed transition between two degenerate atomic levels verifying 0ϽF g ϽF e (F g and F e are the total angular momentum of the ground and the excited levels, respectively͒. In good agreement with the theoretical prediction, a total absorption enhancement by a factor 1.7 was obtained on the D 2 line of 85 Rb in a vapor cell experiment. ͓S1050-2947͑99͒04106-2͔
Steep dispersion of opposite signs in driven degenerate two-level atomic transitions have been predicted and observed on the D2 line of 87 Rb in an optically thin vapor cell. The intensity dependence of the anomalous dispersion has been studied. The maximum observed value of anomalous dispersion (dn/dν ≃ −6× 10 −11 Hz −1 ) corresponds to a negative group velocity Vg ≃ −c/23000. 42.50. Gy, 32.80.Qk, 42.62.Fi, Investigations of coherent effects in resonant media, namely coherent population trapping (CPT) and electromagnetically induced transparency (EIT) [1,2], which can dramatically modify the absorptive and dispersive properties of an atomic vapor, have caused a rebirth of interest in the problem of light propagation through a dispersive medium. In the last decade, the study of the dispersive properties of coherently prepared media was always under attention due to fundamental and practical interest.An ultra-large index of refraction in coherently prepared resonant gas was predicted [3] and a refractive index variation as large as ∆n ≈ 1 × 10 −4 was demonstrated in a dense Rb vapor [4]. It was also shown that a coherently driven medium exhibits large dispersion [5]. A high normal dispersion (up to dn/dν ≃ 1 × 10 −11 Hz −1 ) was measured on the Cs D 2 line in a vapor cell [6] and in an atomic beam [7]. Recently, extremely slow light group velocity (17 m/s) associated with normal dispersion was demonstrated in an ultracold atomic sample [8]. However, the same order of magnitude of group velocity (90 m/s) was observed in a hot dense vapor cell [9].All these investigations were carried on alkaline atoms where the absorption is strongly suppressed and dispersion is steep and normal (D ≡ dn/dν > 0) due to CPT between the two ground state hyperfine levels (Λ scheme). However, atomic coherence among Zeeman sublevels belonging to the same ground-state hyperfine level can led not only to usual EIT, but also to an absorption enhancement named as electromagnetically induced absorption (EIA) [10,11]. Since EIT/EIA effects in degenerate two-level systems can produce a significant variation in the absorption with subnatural width, one can predict a large absolute value of dispersion in this case. Notice that at resonance dispersion would be normal (D > 0) for EIT and anomalous (D < 0) for EIA. In both cases the absolute value of the dispersion can be several orders of magnitude greater than for a linear medium. In this letter we present the first observation of steep anomalous and normal dispersion in coherently prepared degenerate two-level atomic system.Refractive index and dispersion were analyzed with the model recently used to study subnatural EIA resonances [12]. In this model, two monochromatic optical fields, a drive field and a weak probe field with amplitudes E d , E p and frequencies ω d , ω p respectively are incident on motionless two-level atoms with resonance frequency ω 0 and electric dipole moment µ. The atomic levels are degenerate. The configuration is closed. The spontaneous decay rate is Γ. Finite interact...
We have studied relative-intensity fluctuations for a variable set of orthogonal elliptic polarization components of a linearly polarized laser beam traversing a resonant 87 Rb vapor cell. Significant polarization squeezing at the threshold level (-3dB) required for the implementation of several continuous variables quantum protocols was observed. The extreme simplicity of the setup, based on standard polarization components, makes it particularly convenient for quantum information applications.PACS numbers: 42.50. Lc,42.50.Ct,32.80.Qk In recent years, large attention has been given to the use of continuous variables for quantum information processing. A foreseen goal is the distribution of entanglement between distant nodes. For this, quantum correlated light beams are to interact with separate atomic systems in order to build quantum mechanical correlations between them [1,2].A particular kind of quantum correlation between two light beams occurs when the intensity difference between them has fluctuations smaller than the standard quantum limit (SQL), that is smaller than the fluctuations of the intensity difference of two coherent states of the same intensity. The two beams are said to present relative-intensity squeezing (RIS). RIS has been generated through different nonlinear optics techniques. One of the most successful is parametric down conversion in a nonlinear χ (2) crystal. Up to 9.7 dB RIS has been obtained with this method [3]. Such experiments require a relatively elaborate and expensive setup. The resulting light beams are spectrally broad and usually far detuned from convenient alkali atoms D transitions. An alternative approach has considered the use of four-wave mixing in atomic samples [4][5][6][7].Reduced relative-intensity fluctuations have been observed between light beams of different frequency. However, RIS can also occur between orthogonal polarization components of a single light beam. In such case, the field is said to be polarization squeezed [8,9] and the noise reduction is described in terms of squeezing of the fluctuations of one of the Stokes operators:Here a x , a y are the field destruction operators for the orthogonal linear polarizations x and y. Polarization squeezing has been produced via propagation in optical fibers [10,11], through the combination on a polarizing beam splitter of two quadrature squeezed light beams [12] and through the interaction of linearly polarized light with cold atoms inside an optical cavity [9,13].It has been recently demonstrated that the single passage of a linearly polarized pump beam through a few-cmlong atomic vapor cell results in squeezing of the polarization orthogonal to that of the pump (vacuum squeezing) [14][15][16][17] as a consequence of the nonlinear optics mechanism known as polarization self-rotation (PSR) [18][19][20]. Vacuum squeezing via PSR has been observed for the D1 [15][16][17] and D2 [14] transitions using 87 Rb vapor. As noted in [9], the existence of polarization squeezing can be inferred from these results.In this ...
We report on the generation of light carrying orbital angular momentum through Bragg diffraction into an electromagnetically induced coherence grating in a degenerate two-level system of cold cesium atoms. The induced Zeeman coherence grating is shown to contain the spatial phase structure of the incident beams. The exchange of phase information between a light beam with orbital angular momentum and a long-lived atomic coherence opens up the way to process quantum information encoded in a multidimensional state space.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations. 42.50. Gy, 32.80.Bx, 42.62.Fi
We report on the first spectroscopic observation of the rotational Doppler shift associated with light beams carrying orbital angular momentum. The effect is evidenced as the broadening of a Hanle/EIT coherence resonance on Rb vapor when the two incident Laguerre-Gaussian laser beams have opposite topological charges. The observations closely agree with theoretical predictions.PACS numbers: 42.50. Gy, 42.15.Dp, 32.70.Jz Light beams with twisted wavefronts, as is the case for the Laguerre-Gaussian (LG) modes, are known to carry orbital angular momentum (OAM) along their propagation direction. The properties of such modes have attracted considerable attention in recent years and a wide range of applications were suggested [1,2]. LG beams were used for atom trapping and cooling [3,4,5] and special attention was put on the application of LG beams for the exchange of orbital angular momentum between light and Bose-Einstein condensates [6,7,8,9]. Some of us have demonstrated that OAM can be recorded in the position dependent population and coherence of a cold atom sample [10], and transferred between internal atomic states. In addition, the generation of new fields with OAM via non-linear wave mixing in coherently prepared cold atoms was observed [11]. Quite recently, the use of photons in LG modes, was suggested for quantum information processing. The state of such a photon lies in a multi-dimensional Hilbert space, describing the total (intrinsic plus orbital) angular momentum, in which quantum computation with improved efficiency should be possible [12]. Entanglement between pairs of photons in modes with OAM was recently reported [13].The interaction of a moving atom with a LG field raises the fundamental question of the Doppler effect [14]. As an atom moves across the helicoidal wavefronts of the LG mode, it experiences, in addition to the usual Doppler shift related to the velocity in the light propagation direction (and a small shift associated to radial motion in a curved wavefront), a most intriguing frequency shift, the so called rotational Doppler effect (RDE) associated to the azimuthal velocity. To date, the RDE has only been observed interferometrically. The RDE results in frequency shift when the light beam is rotated around its propagation axis [15]. Such shift was observed in [16,17] using millimeter-waves. In the optical domain, a frequency shift in the field generated by a rotating plate was observed in [18]. A different approach, used in [19], relates the RDE to the asymmetric interferometric spatial pattern occurring in the superposition of a Gaussian and a LG modes. In this work we present the first experimental demonstration of the RDE arising directly from the interaction of LG light beams with an atomic sample.Laguerre-Gaussian modes are usually identified with two integer numbers: l and p [20]. The topological charge l corresponds to the phase variation (in units of 2π) of the field along a loop encircling the optical axis. The integer p + 1 corresponds to the number of maxima of the field...
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