We compare the behavior of absorption and of resonance fluorescence spectra in an extremely thin Rb vapor cell as a function of the ratio of L / , with L the cell thickness ͑L ϳ 150-1800 nm͒ and the wavelength of the Rb D 2 line ͑ = 780 mn͒. The Dicke-type coherent narrowing [G. Dutier et al., Europhys. Lett. 63, 35 (2003)] is observed only in transmission measurements, in the linear regime, with its typical collapse and revival, which reaches a maximum for L = ͑2n +1͒ /2 (n integer). It is shown not to appear in fluorescence, whose behavior-amplitude, and spectral width, is more monotonic with L. Conversely, at high-intensity, the sub-Doppler saturation effects are shown to be the most visible in transmission around L = n.

We describe a method of selective generation and study of polarization moments of up to the highest rank κ = 2F possible for a quantum state with total angular momentum F . The technique is based on nonlinear magneto-optical rotation with frequency-modulated light. Various polarization moments are distinguished by the periodicity of light-polarization rotation induced by the atoms during Larmor precession and exhibit distinct light-intensity and frequency dependences. We apply the method to study polarization moments of 87 Rb atoms contained in a vapor cell with antirelaxation coating. Distinct ultra-narrow (1-Hz wide) resonances, corresponding to different multipoles, appear in the magnetic-field dependence of the optical rotation. The use of the highest-multipole resonances has important applications in quantum and nonlinear optics and in magnetometry.PACS numbers: PACS 32.80. Bx,95.75.Hi High-rank polarization moments (PM) and associated high-order coherences have recently drawn attention (see [1,2,3,4,5,6,7,8] While signatures of high-order PM were detected in several experiments [3,4,5,6,8], the methods used in these investigations are not sufficiently selective and/or do not allow real-time manipulation of particular multipoles. Here we describe a method, based on nonlinear optical rotation with frequency-modulated light (FM NMOR) [16], by which one can selectively induce, control, and study any possible multipole moment. Applying the method to 87 Rb atoms in a paraffin-coated cell [17,18], we have verified the expected power and spectral dependences of the resonant signals and obtained a quantitative comparison of relaxation rates for the even-rank moments.The density matrix in the M, M ′ representation for a state with total angular momentum F can be decomposed into PM of rank κ = 0 . . . 2F , uncoupled under rotations, with components q = −κ . . . κ: with surfaces for which the distance to the origin in a given direction is proportional to the probability of finding the projection M = F along this direction. (a): "pure" quadrupole κ = 2, q = 0; (b): κ = 4, q = 0 hexadecapole; (c): same as in (b), but rotated by π/2 around the x-axis; (d): the average of (b) and (c), which has a 4-fold symmetry with respect to rotations aroundx. In all cases, the minimum necessary amount of ρ (0) 0 was added to ensure that all sublevel populations are non-negative [20]. Probability surfaces (a) and (d) rotating aroundx-directed magnetic field with the Larmor frequency correspond to the polarization states produced in this experiment.is uniquely associated with the highest PM for a given state, e.g., the quadrupole moment (κ = 2) for F = 1, or the hexadecapole (κ = 4) for F = 2. The method introduced here exploits the different axial symmetries of the PM (2-fold and 4-fold for the quadrupole and hexadecapole, respectively; Fig. 1) to selectively create and detect them (see also [3,4,5,6]).While multipole moments of rank κ ≤ 2 can be easily generated and detected with weak light (since a photon has spin one), higher-ra...

A low-light-power theory of nonlinear magneto-optical rotation of frequency-modulated light resonant with a J = 1 → J ′ = 0 transition is presented. The theory is developed for a Doppler-free transition, and then modified to account for Doppler broadening and velocity mixing due to collisions. The results of the theory are shown to be in qualitative agreement with experimental data obtained for the rubidium D1 line.

We propose a mechanism for producing Fock states on demand leaking from a single mode optical cavity interacting with a single atom and a laser pulse. The number of photons can be chosen, as it is determined by the Zeeman substructure of the ground state of the atom and its initial state. The deterministic generation of a free-propagating Fock state of 1 ≤ n ≤ 2F photons is achieved, when a circularly polarized laser pulse completely transfers the atomic population between Zeeman sublevels of the ground hyperfine state F through far-detuned Raman scattering thus producing linearly polarized cavity photons. We describe analytically the evolution of optical field taking into account the spontaneous losses and the cavity damping. We demonstrate the possibility of production of Fock-state with different numbers of photons by using different transitions of the same atom. We show also that this technique provides a deterministic source of a train of identical multiphoton Fock-states, if a sequence of left-and right-circularly polarized laser pulses is applied. The resulting states have potential applications in quantum computation and simulation.

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We present a mechanism to produce indistinguishable single-photon pulses on demand from an optical cavity. The sequences of two laser pulses generate, at the two Raman transitions of a four-level atom, the same cavity-mode photons without repumping of the atom between photon generations. Photons are emitted from the cavity with near-unit efficiency in well-defined temporal modes of identical shapes controlled by the laser fields. The second order correlation function reveals the single-photon nature of the proposed source. A realistic setup for the experimental implementation is presented. [5], is to have single photon pulses with well-defined identical shapes, frequency and polarization, as these schemes based on photoninterference effects are very sensitive to the parameters of SP pulses and their repetition rate. A good source has to ensure a pure SP state without mixture from both the multi-photon and zero-photon states, as well as to prevent the entanglement between the photons which degrades the purity of the SP state. Since the individual photons are usually emitted during the spontaneous decay of atomic systems, the SP sources must be immune to the environmental effects that induce the dephasing of atomic transitions. Most of the schemes proposed earlier to produce single photons on demand from solid state single emitters [6], organic molecules [7,8], and quantum dots [9,10] are confronted with this difficulty. Besides, they do not offer a high efficiency because of the isotropic nature of fluorescence that prevents to collect the photons, not to mention the spectral dephasing and inhomogeneity of solid-state emitters. Deterministic sources of single photons are realized also in cold atomic ensembles with feedback circuit [11,12]. But these schemes are not suitable to generate SP train with an arbitrary repetition rate because of strong temporary bounds caused by the feedback and write-read processes.At present, all the requirements mentioned above can be achieved together with a Λ-type atom trapped in highfinesse optical cavities [13][14][15][16], where the single photons are generated via vacuum-stimulated Raman scattering of a classical laser field into a cavity mode. These systems * Electronic address: yumal@ipr.sci.am not only provide a strong interaction between a photon and an atom, but also support very high collection efficiency due to the fact that the photons leave the cavity through one mirror with a transmissivity incomparably larger than that of the opposite one. By carefully adjusting the parameters of the laser pulse one can also easily control the waveform of output single photons. However, the main disadvantage of these schemes is the necessity to use a repumping field to transfer the population of the atom to its initial state after the generation of a cavity photon and only then to generate the next one. In this Letter we propose a scheme featuring a double Raman atomic configuration, which is able to deterministically generate a stream of identical SP pulses without using the repump...

We propose a method that enables efficient frequency conversion of quantum information based on recently demonstrated strong parametric coupling between two single-photon pulses propagating in a slow-light atomic medium at different group velocities. We show that an incoming singlephoton state is efficiently converted into another optical mode in a lossless and shape-conserving manner. The persistence of initial quantum coherence and entanglement within frequency conversion is also demonstrated. We first illustrate this result for the case of small frequency difference of converted photons, and then discuss the modified scheme for conversion of photon wavelengths in different spectral ranges. Finally we analyze the generation of a narrow-band single-photon frequency-entangled state.