Polarization-selective four-wave mixing in a degenerate multi-level system.

This paper describes the first observation of polarization-selective four-wave mixing signals in conventional coupling-probe spectroscopy, specifically, saturation absorption spectroscopy in 85Rb atoms. The four-wave mixing signal is induced by two counter-propagating laser beams in a degenerate multi-level atomic system, involving the F g = 3 → F e = 2 , 3 , and 4 transitions of the 85Rb D2 line. Consequently, the four-wave mixing signals copropagating along the probe beam induce polarization rotation of a linearly polarized probe beam. To distinguish these four-wave mixing signals from the resulting probe beam, we detect the polarization components orthogonal to the polarization direction of the input probe beam, depending on the linear polarization angles between the probe and coupling beams. The experimental findings demonstrate excellent agreement with theoretical results.

Analytical solutions for irradiance of principal and subsidiary maxima in multiple-slit diffraction.

This paper presents analytical solutions for the irradiance of principal and subsidiary maxima in multiple-slit diffraction with arbitrary slit numbers. By analytically solving the equation for the principal and subsidiary maxima, the irradiance of the principal and subsidiary maxima can be obtained up to the twelfth order in a / d , where a is the width of each slit and d is the separation between two adjacent slits.

Electromagnetically induced absorption in Rb atoms with circular polarization of laser beams: Effects of neighboring transitions.

We have studied the effects of neighboring transitions on electromagnetically induced absorption (EIA) and electromagnetically induced transparency (EIT) in the D2 transition line in Rb atoms with respect to the same circular polarization configurations ( σ + - σ + ) of coupling and probe lasers. Spectra for the open F g = 2 → F e = 2 transition of 87Rb and the F g = 3 → F e = 2 and 3 transitions of 85Rb exhibit EIA, resulting from the neighboring effect of F g = 2 → F e = 3 and F g = 3 → F e = 4 transitions, respectively. In contrast, EIT is observed for the open F g = 2 → F e = 1 transition of 87Rb, which indicates greater hyperfine energy splittings of 87Rb and weaker neighboring effects than those of 85Rb. Based on the theoretical results, we can confirm that EIT in the case of F g > F e for 87Rb for the same circular polarization configuration transforms into EIA due to the magnitude of the neighboring effects with a decrease in the hyperfine energy splittings.

Effects of neighboring transitions on the mechanisms of electromagnetically induced absorption and transparency in an open degenerate multilevel system.

In this study, optical Bloch equations with and without neighboring hyperfine states near the degenerate two-level system (DTLS) in the challenging case of [Formula: see text]Rb D2 transition, which involves the Doppler broadening effect, are solved. The calculated spectra agree well with the experimental results obtained based on the coupling-probe scheme with orthogonal linear polarizations of the coupling and probe fields. The mechanisms of electromagnetically induced absorption (electromagnetically induced transparency) for the open [Formula: see text] and 3 transitions (open [Formula: see text] and 3 transitions) are determined to be the effect of the strong closed [Formula: see text] transition line (strong closed [Formula: see text] transition line); this finding is based on a comparison between the calculated absorption profiles of the DTLS without neighboring states and those of all levels with neighboring states, depending on the coupling and probe power ratios. Furthermore, based on the aforementioned comparison, the crucial factors that enhance or reduce the coherence effects and lead to the transformation between electromagnetically induced absorption and electromagnetically induced transparency, are (1) the power ratios between the coupling and probe beams, (2) the openness of the excited state, and (3) effects of the neighboring states due to Doppler broadening in a real atomic system.

Observation of the ponderomotive effect in non-valence bound states of polyatomic molecular anions.

The ponderomotive force on molecular systems has rarely been observed hitherto, despite potentially being extremely useful for the manipulation of the molecular properties. Here, the ponderomotive effect in the non-valence bound states has been experimentally demonstrated, for the first time to the best of our knowledge, giving great promise for the manipulation of polyatomic molecules by the dynamic Stark effect. Entire quantum levels of the dipole-bound state (DBS) and quadrupole-bound state (QBS) of the phenoxide (or 4-bromophenoxide) and 4-cyanophenoxide anions, respectively, show clear-cut ponderomotive blue-shifts in the presence of the spatiotemporally overlapped non-resonant picosecond control laser pulse. The quasi-free electron in the QBS is found to be more vulnerable to the external oscillating electromagnetic field compared to that in the DBS, suggesting that the non-valence orbital of the former is more diffusive and thus more polarizable compared to that of the latter.

Magnetic-field enhanced modulation transfer spectroscopy: theory and experiment.

We herein present a theoretical and experimental study on magnetic-field enhanced modulation transfer spectroscopy (MTS) for the 5S1/2 (F = 1) → 5P3/2 (F' = 0, 1, and 2) transitions of 87Rb atoms. The density matrix equations are solved numerically to obtain the MTS spectra and an excellent agreement is found between the experimental and calculated results. In particular, the enhancement of the MTS signal for the F = 1 → F' = 0 transition in the presence of the magnetic field is directly verified based on the comparison of the results calculated by neglecting with those calculated including the Zeeman coherences in the F = 1 ground state. The unexpected behaviors of the F = 1 → F' = 1 transition are also examined.

Four-wave mixing in a ladder configuration of warm 87Rb atoms: a theoretical study.

We present a theoretical study of the four-wave mixing (FWM) spectra of 5S1/2 - 5P3/2 - 5D5/2 ladder-type transitions of 87Rb atoms. The density matrix equations are solved by considering all the magnetic sublevels to calculate the FWM signals in the atomic vapor cell. These results are subsequently compared with the experimental results. We observe that the FWM signal propagating exactly opposite to the driving field is measured experimentally. Additionally, we demonstrate the effects of optical depth, laser linewidths, and the coupling field power on the FWM spectra. Finally, the origin of the dispersive-like FWM signal is investigated by intentionally varying the intrinsic atomic properties.

Double-Electromagnetically-Induced-Transparency Ground-State Cooling of Stationary Two-Dimensional Ion Crystals.

We theoretically and experimentally investigate double-electromagnetically-induced transparency (double-EIT) cooling of two-dimensional ion crystals confined in a Paul trap. The double-EIT ground-state cooling is observed for ^{171}Yb^{+} ions with a clock state, for which EIT cooling has not been realized like many other ions with a simple Λ scheme. A cooling rate of n[over ¯][over ˙]=34(±1.8) ms^{-1} and a cooling limit of n[over ¯]=0.06(±0.059) are observed for a single ion. The measured cooling rate and limit are consistent with theoretical predictions. We apply double-EIT cooling to the transverse modes of two-dimensional (2D) crystals with up to 12 ions. In our 2D crystals, the micromotion and the transverse mode directions are perpendicular, which makes them decoupled. Therefore, the cooling on transverse modes is not disturbed by micromotion, which is confirmed in our experiment. For the center of mass mode of a 12-ion crystal, we observe a cooling rate and a cooling limit that are consistent with those of a single ion, including heating rates proportional to the number of ions. This method can be extended to other hyperfine qubits, and near ground-state cooling of stationary 2D crystals with large numbers of ions may advance the field of quantum information sciences.

Experimental Observation of the Autler-Townes Splitting in Polyatomic Molecules.

Autler-Townes (AT) splitting has been experimentally observed in the optical transition between the zero-point levels of S1 and S0 for supersonically cooled 2-methoxythiophenol, 2-fluorothiophenol, and 2-chlorothiophenol. This is the first experimental observation of the light-dressed quantum states of polyatomic molecules (N > 3) in the electronic transition. In the resonance-enhanced ionization process involving the optically coupled states, if Rabi cycling is ensured within the nanosecond laser pulse, AT splitting is clearly observed for the open system for which the excited-state lifetime is shorter than hundreds of picoseconds. Semiclassical optical Bloch equations and a dressed-atom approach based on the three-level atomic model describe the experiment quite well, giving deep insights into the light-matter interaction in polyatomic molecular systems.

Linewidth in saturated absorption spectroscopy for two-level atoms: an empirical formula.

We present an empirical formula for linewidth in saturated absorption spectroscopy for two-level atoms with cycling transition lines, taking the coherence term in the Doppler-broadened limit into account. The full width at half-maximum is obtained as (1+(1+as0)b)γt, where s0 is the on-resonance saturation parameter, γt is the transverse decay rate, and a and b are the parameters that depend on γt. We find that as γt increases, a and b approach 1 and 1/2, respectively. These are the typical values in the case without the coherence term.

Coherence effects in electromagnetically induced transparency in V-type systems of 87Rb.

We present a theoretical and experimental study of electromagnetically induced transparency (EIT) in V-type systems of 87Rb atoms. We calculate accurate lineshapes of V-type EIT spectra by solving density matrix equations considering all the magnetic sublevels involved. The calculated spectra demonstrate consistency with the experimental results. We identify the coherence effect in the calculated EIT spectra, and determine that the coherence effect exists only in the cycling transition. We explain the reason for the suppression of the coherence effect in open transitions using an analytical calculation of the spectra for a simple V-type three-level atomic system.

Scaling of thermal hysteretic behavior in a parametrically modulated cold atomic system.

We observe the hysteresis of a spontaneous symmetry breaking (SSB) transition in a parametrically modulated magneto-optical trap by sweeping the total number of atoms and study thermal hysteretic behavior in the system by measuring the scaling exponent of hysteresis. It is shown that the relaxation time of the order parameter in the SSB transition becomes larger near the critical number. The scaling exponent of the hysteresis area with number sweeping rate is found to be 0.64±0.04, which is consistent with the value in the mean-field model.

Relationship between two- and three-photon coherence in a ladder-type atomic system.

We investigated the relationship between two- and three-photon coherence in terms of the transition routes and coupling field intensities in a Doppler-broadened ladder-type atomic system for the 5S(1/2)-5P(3/2)-5D(5/2) transition in (87)Rb atoms. Three-photon electromagnetically induced absorption (TPEIA) due to three-photon coherence was observed in the only transition route that exhibited a dominant two-photon coherence effect. We showed that two-photon coherence is a necessary condition for three-photon coherence phenomena. A comparison of the relative magnitudes of the electromagnetically induced transparency and TPEIA as a function of the coupling field intensity revealed that the increase of three-photon coherence was faster than that of two-photon coherence. Considering three-photon coherence in a Doppler-broadened ladder-type three-level atomic system, the relation between two- and three-photon coherence was numerically calculated.

Modulation transfer spectroscopy mediated by spontaneous emission.

We report the polarization dependence of the spectrum in modulation transfer spectroscopy for the transitions from the lower ground state (F(g) = 1) of (87)Rb atoms. We measured the spectra for the two polarization configurations where the carrier and probe beams were linearly polarized in parallel or perpendicular directions. The measured spectra were in excellent agreement with calculated results. The spectra were strongly dependent on the polarization configurations. In particular, the signal for parallel polarization configuration was generated via an incoherent process mediated by spontaneous emission.

Resonant two-photon absorption and electromagnetically induced transparency in open ladder-type atomic system.

We have experimentally and theoretically studied resonant two-photon absorption (TPA) and electromagnetically induced transparency (EIT) in the open ladder-type atomic system of the 5S(1/2) (F = 1)-5P(3/2) (F' = 0, 1, 2)-5D(5/2) (F″ = 1, 2, 3) transitions in (87)Rb atoms. As the coupling laser intensity was increased, the resonant TPA was transformed to EIT for the 5S(1/2) (F = 1)-5P(3/2) (F' = 2)-5D(5/2) (F″ = 3) transition. The transformation of resonant TPA into EIT was numerically calculated for various coupling laser intensities, considering all the degenerate magnetic sublevels of the 5S(1/2)-5P(3/2)-5D(5/2) transition. From the numerical results, the crossover from TPA to EIT could be understood by the decomposition of the spectrum into an EIT component owing to the pure two-photon coherence and a TPA component caused by the mixed term.

Lineshapes in two-color polarization spectroscopy for cesium.

We present a theoretical study of lineshape in polarization spectroscopy for the 6S1/2-6P3/2-7S1/2 transition line in cesium atoms. A circularly polarized pump beam is tuned either to the lower or the upper transition line, while a linearly polarized probe beam is tuned to the other transition line. The polarization rotation of the probe beam is accurately calculated using a semi-classical density-matrix formalism taking into account all relaxation processes.

Relaxation of an unstable state in parametrically excited cold atoms.

We investigate the scaling behavior of the relaxation process for an unstable state near a subcritical Hopf bifurcation point. When the parametric modulation is applied to a magneto-optical trap, the atomic cloud becomes unstable and decays to the dynamic bistable states. Near the subcritical Hopf bifurcation point, we experimentally show that the relaxation process exhibits the scaling behavior; the relaxation time shows a scaling exponent of -1.002 (±0.024). We also present the passage time distribution for the statistical interpretation of the escape process associated with the relaxation of the unstable state. We compare the experimental results to the numerical and analytic results, demonstrating the good agreement between them.

Modulation transfer spectroscopy for 87Rb atoms: theory and experiment.

We conducted a theoretical and experimental study of lineshape in modulation transfer spectroscopy for 87Rb atoms. When a linearly polarized pump beam, modulated at an angular frequency of Ω, overlaps in parallel with an unmodulated linearly polarized probe beam, combined modulated probe beams are generated via nonlinear interaction with atoms. The detected modulation transfer signals are calculated by numerically solving the complete optical Bloch equations for the 87Rb atoms without the use of any phenomenological parameters. We find that the calculated results are in good agreement with experimental results.

Discrimination of one-photon and two-photon coherence parts in electromagnetically induced transparency for a ladder-type three-level atomic system.

We present discrimination of the effect of one-photon and two-photon coherences in electromagnetically induced transparency for a three-level ladder-type atomic system. After the optical Bloch equations for a three-level atom, with either cycling or non-cycling transitions, were solved numerically, the solutions were averaged over the velocity distribution and finite transit time. Through this we were able to discriminate one-photon and two-photon coherence parts of the calculated spectra. We also found that the spectra showed peaks as the branching ratio of the intermediate (excited) state increased (decreased). The experimental results of previous reports [H. S. Moon, et al., Opt. Express 16, 12163 (2008); H. S. Moon and H. R. Noh, J. Phys. B 44, 055004 (2011)] could well be accounted for by this discrimination of one-photon and two-photon coherences in the transmittance signals for the simplified three-level atomic system.

Ideal mean-field transition in a modulated cold atom system.

We show that an atomic system in a periodically modulated optical trap displays an ideal mean-field symmetry-breaking transition. The symmetry is broken with respect to time translation by the modulation period. We describe experimental observations and develop a full microscopic theory of the observed critical phenomena. The transition is explained as resulting from the interplay of the long-range interatomic interaction and nonequilibrium fluctuations in the strongly modulated system. The observations, including anomalous fluctuations in the symmetry broken phase, are fully described by the theory.