Nuclear charge radii of light isotopes based on frequency comb measurements

Optical frequency comb technology has been used in this work for the first time to investigate the nuclear structure of light radioactive isotopes. Therefore, three laser systems were stabilized with different techniques to accurately known optical frequencies and used in two specialized experiments. Absolute transition frequency measurements of lithium and beryllium isotopes were performed with accuracy on the order of 10^(−10). Such a high accuracy is required for the light elements since the nuclear volume effect has only a 10^(−9) contribution to the total transition frequency. For beryllium, the isotope shift was determined with an accuracy that is sufficient to extract information about the proton distribution inside the nucleus. A Doppler-free two-photon spectroscopy on the stable lithium isotopes (6,7)^Li was performed in order to determine the absolute frequency of the 2S → 3S transition. The achieved relative accuracy of 2×10^(−10) is improved by one order of magnitude compared to previous measurements. The results provide an opportunity to determine the nuclear charge radius of the stable and short-lived isotopes in a pure optical way but this requires an improvement of the theoretical calculations by two orders of magnitude. The second experiment presented here was performed at ISOLDE/CERN, where the absolute transition frequencies of the D1 and D2 lines in beryllium ions for the isotopes (7,9,10,11)^Be were measured with an accuracy of about 1 MHz. Therefore, an advanced collinear laser spectroscopy technique involving two counter-propagating frequency-stabilized laser beams with a known absolute frequency was developed. The extracted isotope shifts were combined with recent accurate mass shift calculations and the root-mean square nuclear charge radii of (7,10)^Be and the one-neutron halo nucleus 11^Be were determined. Obtained charge radii are decreasing from 7^Be to 10^Be and increasing again for 11^Be. While the monotone decrease can be explained by a nucleon clustering inside the nucleus, the pronounced increase between 10^Be and 11^Be can be interpreted as a combination of two contributions: the center-of-mass motion of the 10^Be core and a change of intrinsic structure of the core. To disentangle these two contributions, the results from nuclear reaction measurements were used and indicate that the center-of-mass motion is the dominant effect. Additionally, the splitting isotope shift, i.e. the difference in the isotope shifts between the D1 and D2 fine structure transitions, was determined. This shows a good consistency with the theoretical calculations and provides a valuable check of the beryllium experiment.

Generation of a frequency comb of squeezing in an optical parametric oscillator

The multimode operation of an optical parametric oscillator (OPO) operating below threshold is calculated. We predict that squeezing can be generated in a comb that is limited only by the phase matching bandwidth of the OPO. Effects of technical noise on the squeezing spectrum are investigated. It is shown that maximal squeezing can be obtained at high frequency even in the presence of seed laser noise and cavity length fluctuations. Furthermore the spectrum obtained by detuning the laser frequency off OPO cavity resonance is calculated.

Design and Applications of a Decade-Spanning Terahertz Frequency Comb Spectrometer: Doppler-limited Rotational Spectroscopy of Methanol and Methanol-OD

This thesis details the design and applications of a terahertz (THz) frequency comb spectrometer. The spectrometer employs two offset locked Ti:Sapphire femtosecond oscillators with repetition rates of approximately 80 MHz, offset locked at 100 Hz to continuously sample a time delay of 12.5 ns at a maximum time delay resolution of 15.6 fs. These oscillators emit continuous pulse trains, allowing the generation of a THz pulse train by the master, or pump, oscillator and the sampling of this THz pulse train by the slave, or probe, oscillator via the electro-optic effect. Collecting a train of 16 consecutive THz pulses and taking the Fourier transform of this pulse train produces a decade-spanning frequency comb, from 0.25 to 2.5 THz, with a comb tooth width of 5 MHz and a comb tooth spacing of ~80 MHz. This frequency comb is suitable for Doppler-limited rotational spectroscopy of small molecules. Here, the data from 68 individual scans at slightly different pump oscillator repetition rates were combined, producing an interleaved THz frequency comb spectrum, with a maximum interval between comb teeth of 1.4 MHz, enabling THz frequency comb spectroscopy.

The accuracy of the THz frequency comb spectrometer was tested, achieving a root mean square error of 92 kHz measuring selected absorption center frequencies of water vapor at 10 mTorr, and a root mean square error of 150 kHz in measurements of a K-stack of acetonitrile. This accuracy is sufficient for fitting of measured transitions to a model Hamiltonian to generate a predicted spectrum for molecules of interest in the fields of astronomy and physical chemistry. As such, the rotational spectra of methanol and methanol-OD were acquired by the spectrometer. Absorptions from 1.3 THz to 2.0 THz were compared to JPL catalog data for methanol and the spectrometer achieved an RMS error of 402 kHz, improving to 303 kHz when excluding low signal-to-noise absorptions. This level of accuracy compares favorably with the ~100 kHz accuracy achieved by JPL frequency multiplier submillimeter spectrometers. Additionally, the relative intensity performance of the THz frequency comb spectrometer is linear across the entire decade-spanning bandwidth, making it the preferred instrument for recovering lineshapes and taking absolute intensity measurements in the THz region. The data acquired by the Terahertz Frequency Comb Spectrometer for methanol-OD is of comparable accuracy to the methanol data and may be used to refine the fit parameters for the predicted spectrum of methanol-OD.

Phase discrimination and simultaneous frequency conversion of the orthogonal components of an optical signal by four-wave mixing in an SOA

Simultaneous conversion of the two orthogonal phase components of an optical input to different output frequencies has been demonstrated by simulation and experiment. A single stage of four-wave mixing between the input signal and four pumps derived from a frequency comb was employed. The nonlinear device was a semiconductor optical amplifier, which provided overall signal gain and sufficient contrast for phase sensitive signal processing. The decomposition of a quadrature phase-shift keyed signal into a pair of binary phase-shift keyed outputs at different frequencies was also demonstrated by simulation.

Mapping and controlling molecular processes: The application of control theory and system identification algorithms to ASOPS and other fast pulse spectroscopies

Asynchronous Optical Sampling (ASOPS) [1,2] and frequency comb spectrometry [3] based on dual Ti:saphire resonators operated in a master/slave mode have the potential to improve signal to noise ratio in THz transient and IR sperctrometry. The multimode Brownian oscillator time-domain response function described by state-space models is a mathematically robust framework that can be used to describe the dispersive phenomena governed by Lorentzian, Debye and Drude responses. In addition, the optical properties of an arbitrary medium can be expressed as a linear combination of simple multimode Brownian oscillator functions. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing the recorded THz transients in the time or frequency domain will be outlined [4,5]. Since a femtosecond duration pulse is capable of persistent excitation of the medium within which it propagates, such approach is perfectly justifiable. Several de-noising routines based on system identification will be shown. Furthermore, specifically developed apodization structures will be discussed. These are necessary because due to dispersion issues, the time-domain background and sample interferograms are non-symmetrical [6-8]. These procedures can lead to a more precise estimation of the complex insertion loss function. The algorithms are applicable to femtosecond spectroscopies across the EM spectrum. Finally, a methodology for femtosecond pulse shaping using genetic algorithms aiming to map and control molecular relaxation processes will be mentioned.

High signal to noise ratio THz spectroscopy with ASOPS and signal processing schemes for mapping and controlling molecular and bulk relaxation processes

Asynchronous Optical Sampling has the potential to improve signal to noise ratio in THz transient sperctrometry. The design of an inexpensive control scheme for synchronising two femtosecond pulse frequency comb generators at an offset frequency of 20 kHz is discussed. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing recorded THz transients in the time and frequency domain are outlined. Finally, possibilities for femtosecond pulse shaping using genetic algorithms are mentioned.

Towards a new test of time dilation: Laser spectroscopy on lithium ions stored at a velocity of 33.8 % of the speed of light

The subject of the presented thesis is the accurate measurement of time dilation, aiming at a quantitative test of special relativity. By means of laser spectroscopy, the relativistic Doppler shifts of a clock transition in the metastable triplet spectrum of ^7Li^+ are simultaneously measured with and against the direction of motion of the ions. By employing saturation or optical double resonance spectroscopy, the Doppler broadening as caused by the ions' velocity distribution is eliminated. From these shifts both time dilation as well as the ion velocity can be extracted with high accuracy allowing for a test of the predictions of special relativity. A diode laser and a frequency-doubled titanium sapphire laser were set up for antiparallel and parallel excitation of the ions, respectively. To achieve a robust control of the laser frequencies required for the beam times, a redundant system of frequency standards consisting of a rubidium spectrometer, an iodine spectrometer, and a frequency comb was developed. At the experimental section of the ESR, an automated laser beam guiding system for exact control of polarisation, beam profile, and overlap with the ion beam, as well as a fluorescence detection system were built up. During the first experiments, the production, acceleration and lifetime of the metastable ions at the GSI heavy ion facility were investigated for the first time. The characterisation of the ion beam allowed for the first time to measure its velocity directly via the Doppler effect, which resulted in a new improved calibration of the electron cooler. In the following step the first sub-Doppler spectroscopy signals from an ion beam at 33.8 %c could be recorded. The unprecedented accuracy in such experiments allowed to derive a new upper bound for possible higher-order deviations from special relativity. Moreover future measurements with the experimental setup developed in this thesis have the potential to improve the sensitivity to low-order deviations by at least one order of magnitude compared to previous experiments; and will thus lead to a further contribution to the test of the standard model.

Nuclear charge radius determination of 7,10 Be and the one-neutron halo nucleus 11 Be

The only nuclear model independent method for the determination of nuclear charge radii of short-lived radioactive isotopes is the measurement of the isotope shift. For light elements (Z < 10) extremely high accuracy in experiment and theory is required and was only reached for He and Li so far. The nuclear charge radii of the lightest elements are of great interest because they have isotopes which exhibit so-called halo nuclei. Those nuclei are characterized by a a very exotic nuclear structure: They have a compact core and an area of less dense nuclear matter that extends far from this core. Examples for halo nuclei are 6^He, 8^He, 11^Li and 11^Be that is investigated in this thesis. Furthermore these isotopes are of interest because up to now only for such systems with a few nucleons the nuclear structure can be calculated ab-initio. In the Institut für Kernchemie at the Johannes Gutenberg-Universität Mainz two approaches with different accuracy were developed. The goal of these approaches was the measurement of the isotope shifts between (7,10,11)^Be^+ and 9^Be^+ in the D1 line. The …first approach is laser spectroscopy on laser cooled Be^+ ions that are trapped in a linear Paul trap. The accessible accuracy should be in the order of some 100 kHz. In this thesis two types of linear Paul traps were developed for this purpose. Moreover, the peripheral experimental setup was simulated and constructed. It allows the efficient deceleration of fast ions with an initial energy of 60 keV down to some eV and an effcient transport into the ion trap. For one of the Paul traps the ion trapping could already be demonstrated, while the optical detection of captured 9^Be^+ ions could not be completed, because the development work was delayed by the second approach. The second approach uses the technique of collinear laser spectroscopy that was already applied in the last 30 years for measuring isotope shifts of plenty of heavier isotopes. For light elements (Z < 10), it was so far not possible to reach the accuracy that is required to extract information about nuclear charge radii. The combination of collinear laser spectroscopy with the most modern methods of frequency metrology …finally permitted the …first-time determination of the nuclear charge radii of (7,10)^Be and the one neutron halo nucleus 11^Be at the COLLAPS experiment at ISOLDE/ CERN. In the course of the work reported in this thesis it was possible to measure the absolute transition frequencies and the isotope shifts in the D1 line for the Be isotopes mentioned above with an accuracy of better than 2 MHz. Combination with the most recent calculations of the mass effect allowed the extraction of the nuclear charge radii of (7,10,11)^Be with an relative accuracy better than 1%. The nuclear charge radius decreases from 7^Be continuously to 10^Be and increases again for 11^Be. This result is compared with predictions of ab-initio nuclear models which reproduce the observed trend. Particularly the "Greens Function Monte Carlo" and the "Fermionic Molecular Dynamic" model show very good agreement.

Laser systems for collinear spectroscopy and the charge radius of 12 Be

Die kollineare Laserspektroskopie hat sich in den vergangenen drei Jahrzehnten zur Bestimmung der Kernladungsradien mittelschwerer und schwerer kurzlebiger Atomkerne in ausgezeichneter Weise bewährt. Auf die Isotope sehr leichter Elemente konnte sie allerdings erst kürzlich erweitert werden. Dieser Bereich der Nuklidkarte ist von besonderem Interesse, denn die ersten ab-initio Modelle der Kernphysik, die den Aufbau eines Atomkerns basierend auf individuellen Nukleonen und realistischenWechselwirkungspotentialen beschreiben, sind gegenwärtig nur für die leichtesten Elemente anwendbar. Außerdem existiertrnin dieser Region eine besonders exotische Form von Atomkernen, die sogenanntenrnHalokerne. Die Isotopenkette der Berylliumisotope zeichnet sich durch das Auftreten des Ein-Neutronen Halokerns 11Be und des Zwei- oder Vier-Neutronen-Halos 14Be aus. Dem Isotop 12Be kommt durch seine Position zwischen diesen beiden Exoten und den im Schalenmodell erwarteten magischen Schalenabschluss N = 8 eine besondere Bedeutung zu.rnIm Rahmen dieser Arbeit wurden mehrere frequenzstabilisierte Lasersysteme für die kollineare Laserspektroskopie aufgebaut. An TRIGA-SPEC stehen nun unter anderem ein frequenzverdoppeltes Diodenlasersystem mit Trapezverstärker und frequenzkammstabilisierter Titan-Saphirlaser mit Frequenzverdopplungsstufe für die Spektroskopie an refraktären Elementen oberhalb von Molybdän zur Verfügung, die für erste Testexperimente eingesetzt wurden. Außerdem wurde die effiziente Frequenzvervierfachung eines Titan-Saphirlasers demonstriert. An ISOLDE/CERN wurde ein frequenzkammstabilisierter und ein jodstabilisierter Farbstofflaser installiert und für die Laserspektroskopie an 9,10,11,12Be eingesetzt. Durch das verbesserte Lasersystem und den Einsatz eines verzögerten Koinzidenznachweises für Photonen und Ionen gelang es die Empfindlichkeitrnder Berylliumspektroskopie um mehr als zwei Größenordnungen zu steigern und damit die früheren Messungen an 7−11Be erstmals auf das Isotop 12Be auszuweiten. Außerdem wurde die Genauigkeit der absoluten Übergangsfrequenzen und der Isotopieverschiebungen der Isotope 9,10,11Be signifikant verbessert.rnDurch den Vergleich mit Ergebnissen des Fermionic Molecular Dynamics Modells kann der Trend der Ladungsradien der leichteren Isotope durch die ausgeprägte Clusterstruktur der Berylliumkerne erklärt werden. Für 12Be wird ersichtlich, dass der Grundzustand durch eine (sd)2 Konfiguration statt der vom Schalenmodell erwarteten p2 Konfiguration dominiert wird. Dies ist ein klares Indiz für das bereits zuvor beobachtete Verschwinden des N = 8 Schalenabschlusses bei 12Be.

Test der Speziellen Relativitätstheorie mittels Laserspektroskopie an relativistischen 7 Li +-Ionen am ESR

Die Invarianz physikalischer Gesetze unter Lorentztransformationen ist eines der fundamentalen Postulate der modernen Physik und alle Theorien der grundlegenden Wechselwirkungen sind in kovarianter Form formuliert. Obwohl die Spezielle Relativitätstheorie (SRT) in einer Vielzahl von Experimenten mit hoher Genauigkeit überprüft und bestätigt wurde, sind aufgrund der weitreichenden Bedeutung dieses Postulats weitere verbesserte Tests von grundsätzlichem Interesse. Darüber hinaus weisen moderne Ansätze zur Vereinheitlichung der Gravitation mit den anderen Wechselwirkungen auf eine mögliche Verletzung der Lorentzinvarianz hin. In diesem Zusammenhang spielen Ives-Stilwell Experimente zum Test der Zeitdilatation in der SRT eine bedeutende Rolle. Dabei wird die hochauflösende Laserspektroskopie eingesetzt, um die Gültigkeit der relativistischen Dopplerformel – und damit des Zeitdilatationsfaktors γ – an relativistischen Teilchenstrahlen zu untersuchen. Im Rahmen dieser Arbeit wurde ein Ives-Stilwell Experiment an 7Li+-Ionen, die bei einer Geschwindigkeit von 34 % der Lichtgeschwindigkeit im Experimentierspeicherring (ESR) des GSI Helmholtzzentrums für Schwerionenforschung gespeichert waren, durchgeführt. Unter Verwendung des 1s2s3S1→ 1s2p3P2-Übergangs wurde sowohl Λ-Spektroskopie als auch Sättigungsspektroskopie betrieben. Durch die computergestützte Analyse des Fluoreszenznachweises und unter Verwendung optimierter Kantenfilter für den Nachweis konnte das Signal zu Rauschverhältnis entscheidend verbessert und unter Einsatz eines zusätzlichen Pumplasers erstmals ein Sättigungssignal beobachtet werden. Die Frequenzstabilität der beiden verwendeten Lasersysteme wurde mit Hilfe eines Frequenzkamms spezifiziert, um eine möglichst hohe Genauigkeit zu erreichen. Die aus den Strahlzeiten gewonnen Daten wurden im Rahmen der Robertson-Mansouri-Sexl-Testtheorie (RMS) und der Standard Model Extension (SME) interpretiert und entsprechende Obergrenzen für die relevanten Testparameter der jeweiligen Theorie bestimmt. Die Obergrenze für den Testparameter α der RMS-Theorie konnte gegenüber den früheren Messungen bei 6,4 % der Lichtgeschwindigkeit am Testspeicherring (TSR) des Max-Planck-Instituts für Kernphysik in Heidelberg um einen Faktor 4 verbessert werden.

Multicolour nonlinearly bound chirped dissipative solitons

The dissipative soliton regime is one of the most advanced ways to generate high-energy femtosecond pulses in mode-locked lasers. On the other hand, the stimulated Raman scattering in a fibre laser may convert the excess energy out of the coherent dissipative soliton to a noisy Raman pulse, thus limiting its energy. Here we demonstrate that intracavity feedback provided by re-injection of a Raman pulse into the laser cavity leads to formation of a coherent Raman dissipative soliton. Together, a dissipative soliton and a Raman dissipative soliton (of the first and second orders) form a two (three)-colour stable complex with higher total energy and broader spectrum than those of the dissipative soliton alone. Numerous applications can benefit from this approach, including frequency comb spectroscopy, transmission lines, seeding femtosecond parametric amplifiers, enhancement cavities and multiphoton fluorescence microscopy.

WDM orthogonal subcarrier multiplexing

Electro-optical transceivers can be implemented employing all-analog signal processing in order to achieve low values of power consumption and latency. This paper shows that the spectral efficiency of such solutions can be increased by combining orthogonal multicarrier techniques and off-the-shelf microwave components. A real-time 108-Gbit/s experiment was performed emulating a wavelength division multiplexing (WDM) system composed of five optical channels. The optical carriers were provided by an externally injected gain switched optical frequency comb. Each optical channel transmitted a 21.6-Gbit/s orthogonal subcarrier multiplexing (SCM) signal that was modulated and demodulated in the electrical domain without the requirement for digital signal processing. The net data rate remained higher than 100 Gbit/s after taking into account forward error correction overheads. The use of orthogonally overlapping subchannels achieves an unprecedented spectral efficiency in all-analog real-time broadband WDM/SCM links.

Polyphase Implementation of Non-recursive Comb Decimators for Sigma-Delta A/D Converters

In a sigma-delta analog to digital (A/D) As most of the sigma-delta ADC applications require converter, the most computationally intensive block is decimation filters with linear phase characteristics, the decimation filter and its hardware implementation symmetric Finite Impulse Response (FIR) filters are may require millions of transistors. Since these widely used for implementation. But the number of FIR converters are now targeted for a portable application, filter coefficients will be quite large for implementing a a hardware efficient design is an implicit requirement. narrow band decimation filter. Implementing decimation In this effect, this paper presents a computationally filter in several stages reduces the total number of filter efficient polyphase implementation of non-recursive coefficients, and hence reduces the hardware complexity cascaded integrator comb (CIC) decimators for and power consumption [2]. Sigma-Delta Converters (SDCs). The SDCs are The first stage of decimation filter can be operating at high oversampling frequencies and hence implemented very efficiently using a cascade of integrators require large sampling rate conversions. The filtering and comb filters which do not require multiplication or and rate reduction are performed in several stages to coefficient storage. The remaining filtering is performed reduce hardware complexity and power dissipation. either in single stage or in two stages with more complex The CIC filters are widely adopted as the first stage of FIR or infinite impulse response (IIR) filters according to decimation due to its multiplier free structure. In this the requirements. The amount of passband aliasing or research, the performance of polyphase structure is imaging error can be brought within prescribed bounds by compared with the CICs using recursive and increasing the number of stages in the CIC filter. The non-recursive algorithms in terms of power, speed and width of the passband and the frequency characteristics area. This polyphase implementation offers high speed outside the passband are severely limited. So, CIC filters operation and low power consumption. The polyphase are used to make the transition between high and low implementation of 4th order CIC filter with a sampling rates. Conventional filters operating at low decimation factor of '64' and input word length of sampling rate are used to attain the required transition '4-bits' offers about 70% and 37% of power saving bandwidth and stopband attenuation. compared to the corresponding recursive and Several papers are available in literature that deals non-recursive implementations respectively. The same with different implementations of decimation filter polyphase CIC filter can operate about 7 times faster architecture for sigma-delta ADCs. Hogenauer has than the recursive and about 3.7 times faster than the described the design procedures for decimation and non-recursive CIC filters.