A stable frequency comb directly referenced to rubidium electromagnetically induced transparency and two-photon transitions

Theories unifying gravity with other interactions suggest spatial and temporal variation of fundamental “constants” in the Universe. A change in the fine structure constant, $$\alpha = {e}^{2}/\hslash c$$ , could be detected via shifts in the frequencies of atomic transitions in quasar absorption systems. Recent studies using 140 absorption systems from the Keck telescope and 153 from the Very Large Telescope, suggest that α varies spatially (61). That is, in one direction on the sky α seems to have been smaller at the time of absorption, while in the opposite direction it seems to have been larger. To continue this study we need accurate laboratory measurements of atomic transition frequencies. The aim of this paper is to provide a compilation of transitions of importance to the search for α variation. They are E1 transitions to the ground state in several different atoms and ions, with wavelengths ranging from around 900–6000 Å, and require an accuracy of better than 10 − 4 Å. We discuss isotope shift measurements that are needed in order to resolve systematic effects in the study. The coefficients of sensitivity to α-variation (q) are also presented.

When a pump field and probe field simultaneously drive an electronic-state atomic transition, the probe field absorption spectrum can consist of an absorption peak centered near \ensuremath{\Delta}'=0 and amplification peak centered near \ensuremath{\Delta}'=2\ensuremath{\Delta} (\ensuremath{\Delta} and \ensuremath{\Delta}' are the pump and probe field detunings from the atomic transition frequency, respectively). This type of spectrum is seen in the limit \ensuremath{\Vert}\ensuremath{\Delta}\ensuremath{\Vert}\ensuremath{\gg}\ensuremath{\chi}\ensuremath{\gg}\ensuremath{\Gamma}, where \ensuremath{\chi} is the Rabi frequency associated with the pump field and 2\ensuremath{\Gamma} is the homogeneous width associated with the atomic transition. For atoms cooled below the recoil limit of laser cooling, the qualitative nature of the probe absorption spectrum can undergo a dramatic change. Provided that the recoil splitting ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$ is larger than the homogeneous decay rate (as might occur in the case of a forbidden transition), the absorption and amplification features each split into an absorption-amplification doublet. In addition, structure is found in the probe absorption spectrum near \ensuremath{\Delta}'=\ensuremath{\Delta}; this structure consists of two absorption-amplification doublets. Both doublets can be resolved if ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>\ensuremath{\Gamma}. If ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$, one of the doublets can be resolved provided that ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$, where ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$ is some effective atomic ground state width in the problem. The positions, widths, and relative weights of all the components are readily predicted using a dressed-atom theory in which quantization of the center-of-mass momentum is included. An analytical expression for the probe field spectrum is obtained for a simple case in which spontaneous decay to the lower level is neglected. Validity criteria for the results are discussed.

Simultaneous strong coherent pumping of the two transitions of a V-level atom with very different decay rates has been predicted to create almost perfect inversion on the narrower transition. Using the example of the blue and red transitions in Strontium we show that for suitable operating conditions the corresponding resonant gain can be used to continuously operate a laser on the narrow transition. In particular, for a strong detuning of the pump field with respect to the narrow transition, coherent laser emission occurs close to the bare atomic transition frequency exhibiting only a negligible contribution from coherent pump light scattered into the lasing mode. Calculations of the cavity output spectrum show that the resulting laser linewidth can get much smaller than the bandwidth of the pump light and even the natural linewidth of the narrow atomic transition. Its frequency is closely tied to the atomic transition frequency for properly chosen atom numbers. Simulations including atomic motion show Doppler cooling on the strong transition with minor motion heating on the lasing transition, so that continuous laser operation in the presence of a magneto-optical trap should be possible with current experimental technology.

We theoretically show that a self-induced transparency (SIT) soliton and a Bragg soliton can coexist in a nonlinear photonic band gap (PBG) medium doped uniformly with inhomogeneous-broadening two-level atoms. The Maxwell-Bloch equations for the pulse propagating through such a uniformly doped PBG structure are derived first and further reduced to an effective nonlinear Schrödinger equation. This model describes an equivalent physical mechanism for a Bragg-soliton propagation resulting from the effective quadratic dispersion balancing with the effective third-order nonlinearity. Because the resonant atoms are taken into account, the original band gap can be shifted both by the dopants and the instantaneous nonlinearity response originating from an intense optical pulse. As a result, even if a SIT soliton with its central frequency deep inside the original forbidden band, it still can propagate through the resonant PBG medium as long as this SIT soliton satisfies the effective Bragg-soliton propagation. An approximate soliton solution describing such coexistence is found. We also show that the pulse width and group velocity of this soliton solution can be uniquely determined for given material parameters, atomic transition frequency, and input central frequency of the soliton. The numerical examples of the SIT soliton in a one-dimensional As2S3-based PBG structure doped uniformly with Lorentzian line-shape resonant atoms are shown. It is found that a SIT soliton with approximately 100-ps width in such a resonant PBG structure can travel with the velocity being two orders of magnitude slower than the light speed in an unprocessed host medium.

Atomic transitions of Rb, D2 line in strong magnetic fields: Hyperfine Paschen–Back regime

We discuss the results of high-resolution, sub-Doppler two-photon-absorption laser-induced fluorescence (TPALIF) spectroscopy of nitric oxide at low pressure and room temperature. The measurements were performed using the single-longitudinal mode output of a diode-laser-seeded optical parametric generator (OPG) system with a measured frequency bandwidth of 220 MHz. The measurements were performed using a counter-propagating pump beam geometry, resulting in sub-Doppler TPALIF spectra of NO for various rotational transitions in the (0,0) vibrational band of the A2Σ+ - X2Π electronic transition. The experimental results are compared with the results of a perturbative treatment of the rotational line strengths for the 20 different rotational branches of the X2Π(v″ = 0) → A2Σ+(v' = 0) two-photon absorption band. In the derivation of the expressions for the two-photon transition absorption strength, the closure relation is used for rotational states in the intermediate levels of the two-photon transition in analogy with the Placzek treatment of Raman transitions. The theoretical treatment of the effect of angular momentum coupling on the two-photon rotational line strengths features the use of irreducible spherical tensors and 3j symbols. The final results are expressed in terms of the Hund's case (a) coupling coefficients aJ and bJ for the X2Π(v″ = 0) rotational level wavefunctions, which are intermediate between Hund's case (a) and case (b). Considerable physical insight is provided by this final form of the equations for the rotational line strengths. Corrections to the two-photon absorption rotational line strength for higher order effects such as centrifugal stretching can be included in a straightforward fashion in the analysis by incorporating higher order terms in these coupling coefficients aJ and bJ, although these corrections are essentially negligible for J < 50. The theoretical calculations of relative line intensities are in good agreement both with our experiment and with published experimental results. In addition, the calculated line shapes and relative intensities for closely spaced main branch and satellite transitions are in excellent agreement with our experimental measurements.

The production of Te atoms by the multiphoton dissociation of diethyltelluride

The research work carried out within the framework of this PhD has focused on the generation of Optical Frequency Combs (OFC) in semiconductor lasers using the gain-switching (GS) technique. The work has been mainly experimental, although simulations have been used to contribute to a better understanding of the internal physics of the OFCs generation process. Various types of lasers have been used, specially distributed feedback (DFB) lasers and discrete mode lasers (DML). An exhaustive experimental characterisation of the properties of the OFCs generated by GS in a full range of operating conditions has been performed. Two ranges of repetition frequencies have been explored: the GHz range with applications in optical communications, and the range of hundreds of MHz for application in spectroscopy. The effect of the optical injection (OI) on the properties of the OFCs has been investigated, and interesting results have been obtained, such as the improvement or deterioration of the quality of the spectra depending on the GS and OI conditions. The optimal operating conditions to generate high quality OFCs at the different frequencies considered have been found. In order to improve the understanding of the different physical processes involved in the generation of the OFCs generated by GS, a simulation tool based on the rate equation model for semiconductor lasers has been developed, with detailed treatment of the noise sources. For a correct simulation of the OFCs the values of a set of internal laser parameters is are required. They were obtained through an original procedure based on the measurement of the relative intensity noise (RIN) spectra. Using this procedure, the uncertainty in the simulated results has been reduced, since it allows to extract more parameters than other procedures due to an adequate analytical treatment of the RIN equations. The simulations have completely reproduced the temporal and spectral response of different lasers in a wide range of electrical and optical injection conditions. From the simulations, the predominant physical processes that contribute to the generation of OFCs, dynamic chirp at high repetition frequencies, and adiabatic chirp at low frequencies, have been identified. It has been shown that it is possible to improve the characteristics of low frequency OFCs by driving the laser with electric pulses, instead of using sinusoidal driving. High quality 100 MHz OFCs (up to 866 tones in 10 dB) with good carrier-to-noise (CNR) ratio have been generated. It has also been shown that step-recovery diodes (SRDs) can be used as a source of electrical pulses to generate OFCs, thus reducing the cost and size of the equipment involved, while maintaining the quality of the OFCs. The role of the “jitter” of the electrical source in the quality of the OFCs has been studied theoretically and experimentally. Finally, the OFCs generated by gain-switching and optical injection have been used to measure the absorption spectra of different elements, using three different architectures: heterodyne detection, and dual-comb spectroscopy and a new implementation of this technique. In this implementation the dual-comb is generated from a single GS laser by alternating the repetition frequency. Promising results for the application of these OFCs in gas spectroscopy have been obtained.

The present work is devoted to the study of the dynamics of multi-photon processes in semiconductor heterostructures. A time-dependent description is important for understanding in detail the transient response of semiconductors excited by ultrashort optical pulses. In the first part of this thesis, we set up a phenomenological model based on rate equations, in order to investigate the possibility of measuring degenerate two-photon gain in a semiconductor microcavity. The amplification predicted by the model is fairly low ( 2%) and mainly limited by the intra-band relaxation of the carriers, which leads to rapid saturation. In the second part, we develop a general theory for the dynamics of multi-photon processes in semiconductors. It will give insight into complex effects related to the coherence between the bands, which are not included in usual absorption coefficients or susceptibilities. For this purpose, we derive effective multi-band Bloch equations that include resonant multi-photon processes induced by two linearly polarized electromagnetic pulses of frequency close to the band gap and close to the half of the band gap respectively. The benefit of the proposed approach is two-fold. First, the description of the dynamics is restricted to a reduced number of bands. However, the discarded bands are not neglected, but consistently taken into account in the higher order processes. Second, all quantities appearing in the effective multi-band Bloch equations vary on the same time scale, which makes the numerical integration much more efficient. The time-dependent polarization current, as well as some susceptibilities, are derived on a consistent level of approximation, and are discussed in detail. The propagation of the electromagnetic fields is neglected. Such a model is appropriate for the description of low-dimensional quantum confined systems (e.g. quantum wells or quantum wires) excited by two colinearly propagating pulses. It accounts for various linear and nonlinear optical processes, such as one- and two-photon absorption, second-harmonic generation, difference-frequency mixing, or coherent control of photocurrent. In this thesis, the general theory is applied to the study of three specific physical situations. First, we investigate the charge and spin current in a symmetric AlGaAs/GaAs quantum well, injected by interference between one- and two-photon inter-band transitions. We identify new coherent terms in the expression of the current, which contribute significantly to the terahertz emission. The effects of the Stark shifts and the inter-valence band two-photon transitions are also calculated and discussed. Second, we calculate the anisotropic two-photon absorption spectra of an AlGaAs/GaAs V-shaped quantum wire with realistic band structure. The Coulomb interaction is taken into account within the Hartree-Fock approximation. The various excitonic peaks are identified with respect to the involved subbands and to the symmetry properties. We also show that excitons that are dark for one-photon excitation may become bright for two-photon spectroscopy, when the light is polarized perpendicularly to the growth direction, but not along a symmetry axis of the wire. Finally, the last application focuses on the optical injection of current in the presence of excitonic effects. Concentrating on the same AlGaAs/GaAs V-shaped quantum wire, we show that the Coulomb interaction within the Hartree-Fock approximation induces terahertz oscillations in the injected charge current. The oscillation frequency corresponds to the energy spacing between the two lowest excitonic resonances, slightly below the band gap, excited respectively by the laser pulse with frequency close to the band gap, and the one with frequency close to the half of the band gap.

It is shown that an infinite gravitational flux tube solution in 5D Kaluza-Klein gravity with the cross section in the Planck region after 5D ⇒ 4D reduction and isometrical embedding in a Minkowski spacetime can be considered as a moving infinite string-like object. Such an object carries an electric and a magnetic flux. The 4D gravitational waves on the tube are considered.

Alkali atoms, such as rubidium and cesium, have been well studied because their atomic structures are relatively easy to calculate. The main purpose of this research was to observe the hyperfine structure of the 5D state of ⁸⁵ Rb and ⁸⁷ Rb via direct frequency comb spectroscopy (DFCS). Rubidium's well-understood atomic structure was a great tool in exploring the working mechanism of the frequency comb and its application to spectroscopy. Once the DFCS technique is validated, it will hold the potential to enable a wide variety of ultra-precise spectroscopy of atoms such as potassium or samarium in order to look for new and exotic physics, such as the permanent electric dipole moment of electrons, the asymmetry between matter and anti-matter in the universe, and variation of the fine structure constant. \indent The frequency comb is a series of evenly spaced frequency modes which is generated by a erbium-doped fiber laser. The comb, mode spacing at ≈ 250 MHz, was used to probe two atomic transitions in rubidium, 5S½→ 5P and 5P → 5D. The atomic population of the final 5D state was monitored via fluorescence from the second stage of a cascade decay. The spectrum of the fluorescence intensity reflected the hyperfine structure of the 5D state. The spectrum was compared to a theoretical model and to another spectrum which was generated by a different frequency comb whose mode spacing was ≈ 925 MHz. From this comparison, we discovered how the fluorescence spectra depended on the mode spacing and the energy differences among various atomic levels.

The two-photon decay of the 2S state to the ground state in dressed atoms and one- or two-electron ions has been studied for several decades. Relativistic calculations have shown an Z-dependence of the spectral shape of this two-photon transition in one- or two-electron ions. We have measured the spectral distribution of the 1s2s \(^1\!S_0\) → 1s 2 \(^1\!S_0\) two-photon transition in He-like tin at the ESR storage ring using a new approach for such experiments. In this method, relativistic collisions of initially Li-like projectiles with a gaseous target were used to populate exclusively the first excited state, 1s2s, of He-like tin, which provided a clean two-photon spectrum. The measured two-photon spectral distribution was compared with fully relativistic calculations. The obtained results show very good agreement with the calculations for He-like tin.

As a bridge connecting microwave frequency and optical frequency, femtosecond laser has important significance in optical frequency measurement. Compared with the traditional Ti-sapphire femtosecond optical frequency comb, with the advantages of compact structure, strong anti-interference ability and low cost, the fiber femtosecond optical frequency comb has a wider application prospect. An experiment of spectrum broadening in a highly nonlinear photonic crystal fiber pumped by an Er-fiber mode-locked femtosecond laser is studied in this paper. Based on optical amplification and frequency doubling, the central wavelength of the output spectrum is 780nm and the average power is 232mW. With the femtosecond pulses coupled into two different photonic crystal fibers, the coverage of visible spectrum is up to 500nm-960nm. The spectral shape and width can be optimized by changing the polarization state for satisfying the requirments of different optical frequencies measurement.

Precise phase control of ultra-wide-bandwidth optical frequency combs has produced remarkable and unexpected progress in precision metrology and ultrafast science. The combination of the ability to do completely arbitrary, optical, waveform synthesis with recently developed optical pulse measurement techniques is analogous to the development of oscilloscopes and waveform generators in the early 20th century. The development of ultra-stable optical frequency standards into optical atomic clocks and optical frequency synthesizers again complement and rival the similar technologies developed in the radio frequency domain. I will cover a range of key advances that have been enabled by this revolutionary merge between the ultrafast and ultra-precision fields, including direct optical frequency measurement, carrier-envelope phase control, alloptical atomic clocks, optical frequency synthesizers, coherent pulse synthesis and distribution, and nonlinear spectroscopy.

Porphycenes are structural isomers of porphyrins that have many unique properties and features. In the present work, the resonant two-photon absorption of 2,7,12,17-tetraphenylporphycene (TPPo) and its palladium(II) complex (PdTPPo) has been investigated. The data obtained are compared to those from the isomeric compound, meso-tetraphenylporphyrin (TPP). Detection of phosphorescence from singlet molecular oxygen, O2(a(1)Delta(g)), produced upon irradiation of these compounds, was used to obtain two-photon excitation spectra and to quantify two-photon absorption cross sections, delta. In the spectral region of 750-850 nm, the two-photon absorption cross sections at the band maxima for both TPPo and PdTPPo, delta = 2280 and 1750 GM, respectively, are significantly larger than that for TPP. This difference is attributed to the phenomenon of so-called resonance enhancement; for the porphycenes, the two-photon transition is nearly resonant with a comparatively intense one-photon Q-band transition. The results of quantum mechanical calculations using density functional quadratic response theory are in excellent agreement with the experimental data and, as such, demonstrate that comparatively high-level quantum chemical methods can be used to interpret and predict nonlinear optical properties from such large molecular systems. One important point realized through these experiments and calculations is that one must exercise caution when using qualitative molecular-symmetry-derived arguments to predict the expected spectral relationship between allowed one- and two-photon transitions. From a practical perspective, this study establishes that, in comparison to porphyrins and other tetrapyrrolic macrocyclic systems, porphycenes exhibit many desirable attributes for use as sensitizers in two-photon initiated photodynamic therapy.