Chapter 1 Introduction
1.3 Organization of Thesis
This thesis is based on the works that have been reported in the published papers. After the introduction, Chapter 2 will introduce the basic background, including Standard Model, atomic parity non-conservation, properties of the volume Bragg grating and Nd:GdVO4 solid state laser, for understanding the experiments and results. The experimental results achieved are presented in Chapter 3 to Chapter5. Chapter 3 covers the background and experiment of the developed solid state laser, where a 1070 nm Nd:GdVO4 laser have been constructed with a volume Bragg grating as an output coupler. The experimental results of the absolute frequency measurements of the molecular iodine hyperfine transitions at 535 nm are presented in Chapter 4, where the 535 nm light source is the second harmonic generation of the amplified 1070 nm laser which goes through a PPLN. Chapter 5 presents the precise frequency measurements of the hyperfine transitions of thallium with the developed 535 nm light source, where a hollow cathode lamp provides as the thallium vapor cell. Each chapter has its own brief introduction and a summary of its contents. Finally a summary of this thesis and future works are given in Chapter 6.
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Chapter 2
Basic Background
2.1 Parity Nonconservation and Thallium 2.1.1 Standard Model
The Standard Model (SM) of particle physics summarizes the present state knowledge of particles and their interactions. It is a quantum based theory using quantum chromodynamics to describe strong interactions and the electroweak theory to unify weak and electromagnetic interactions. The gravity is not included in the SM. The SM theory proposes that these interactions result from exchange of force carrier particles called gauge bosons. The strong interactions of quarks are thought to be mediated by massless gluons. And the electroweak theory claims that the interactions between leptons (electron, muon, tau, neutrinos) and spin 1/2 quarks (up, down, top, bottom, charm, strange) are all mediated by four spin 1 bosons: the photon (), the neutral boson (Z0), and the charged bosons (W+ and W-). The photons mediate electromagnetic interaction, and the W and Z bosons mediate the weak interactions. There are two types of weak interaction. If a charged boson (W+ or W-) is mediated, the interaction is called charged-current interaction, and is responsible for the beta decay phenomenon. If a neutral boson (Z0) is mediated, the interaction is called neutral current interaction. The Z0 boson mass has been determined from the experiment at LEP to be 91.1876 ± 0.0021 GeV [19]. And, in the same way that an electric charge of a particle responses to an electromagnetic force, each particle and atomic nuclei have a weak charge Qw which characterizes the weak force’s effect. SM is the most successful theory of particle physics to date. It provides a precise description of the observed phenomena and has been consistent with nearly all experimental results. Despite this great success, even more precise experiments are needed to continue testing the predictions of the SM as any deviation would imply a sign on new physics.
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2.1.2 Atomic Parity Non-conversation
Atomic PNC experiments have been important tests of the SM of electroweak interactions because they are sensitive to the electroweak interaction at low energy, determining the bound state of the electron in an atom. Atomic PNC experiments provide an important complement to the accelerator based high energy experiments and search for the new physics beyond the SM. In an atomic system, the interactions between electron and nucleus are ongoing and the electromagnetic interactions dominate through mediated photons. Meanwhile the weak interactions through mediated Z0 boson exist in the presence of the relative huge electromagnetic interactions, perturbing the wavefunction of the electron by as much as one part in 1010. The amplitude of the weak interaction must be measured under the interference of the electromagnetic interaction. The Z0 boson, however, has a parity non-conserving trait.
That is, the weak interaction violates parity symmetry, while the electromagnetic interaction does not. An observable parity violating effect in an atomic system can only be interpreted by the weak interaction. Precise atomic PNC experiments can be used to measure the weak charge Qw of the nucleus, which determines the strength of electroweak interaction, and test the electroweak theory.
The coupling between electron and nucleon may be determined experimentally by observing the PNC in the electron-nucleon interaction. The electroweak theory describes the electroweak transition amplitude as the sum of two different electron-nucleon contributions (Fig. 2-1): an electromagnetic one of amplitude Aem and a weak one of amplitude Aw,
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The first term is of negligible magnitude and can be ignored. The second term is the dominant term. The third term is the interference term. The interference term can be experimentally distinguished as it changes sign under a parity transformation. If a difference in rates between two coordinate system of opposite handedness is observed, a parity violating asymmetry (Apv) is proportional to the ratio of weak and
where GF is Fermi coupling constant, is fine structure constant, and Q is momentum transfer. An asymmetry as large as 10-4 has been observed in the SLAC polarized electron experiment operating at Q2~(1GeV)2[21]. In an atomic system, Q2~(me)2, the asymmetry is expected to be of the order of 10-14. In 1959, Zeldovich who predicted the optical activity of atomic media due to possible weak neutral currents [23]
demonstrated the first proposals concerning effects of a weak electron-nucleon interaction in atoms with stable nuclei. Zeldovich realized the effect would be
Fig. 2-1 Electrons in an atom interact with the nucleus through the electromagnetic force and weak force. The electromagnetic force is mediated by massless photons (γ). The weak force is mediated by Z0 bosons.
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immeasurably small at that time. However, the atomic PNC can be enhanced by several mechanisms. In 1974, M.A. Bouchiat and C. Bouchiat demonstrated that the strength of the atomic PNC scales with the cube of atomic number, the so-called Z3 law [24]. Since then, it thus possible to test the atomic PNC effects in heavy atoms.
The parity-violating parts of the weak force between electrons and nucleons in an atom can be separated into two groups according to the dependence on the nuclear spin:
nuclear spin dependent effects (NSD-PV) and nuclear spin independent effects (NSI-PV). The spin independent effects are much easier to measure since they are proportional to the number of nucleons, while NSD-PV effects, which include Z boson exchange between electrons and nucleons, and the nuclear anapole moment, have a net contribution only from the unpaired nucleons—of which there is typically only one.
Consequently, the NSI-PVs dominate atomic PNC, whereas NSD-PVs contribute small corrections.
In the non-relativistic limit, the NSI-PV can be written as [25],
( ) matrix and (r) is the nucleon density function. In the SM, the nuclear charge
(1 4sin2 )
w w
Q N Z N, (2.5) where N is the neutron number, Z is the proton number, and w, the weak mixing angle, is given to lowest order accuracy by sin2(w)=0.23. The relation between Qw and the PNC amplitude, EPNC, can be represented as [26]
PNC w
E kQ , (2.6)
where k is an atomic-structure factor that can be computed from the atomic wavefunctions. The size of EPNC is determined not only by the weak nuclear charge, but
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also the electron probability density inside the nucleus. To interpret a PNC measurement as a measurement of Qw requires an accurate atomic calculation. Precise measurements of the parameters such as the hyperfine structure and lifetime are helpful in improving the wavefunction calculation. With the atomic-structure calculations of k, an atomic PNC measurement can determine an experimental value of the weak charge.
Any deviation of the SM predicted weak charge from the experimental weak charge will indicate a new physics.
2.1.3 Observations of Atomic Parity Nonconservation
Optical rotation and Stark interference are so far the only two different types of experimental measurements of atomic PNC. Optical rotations have been measured in atomic bismuth [27], lead [28], thallium [3, 4] and samarium [29]. In Stark inference experiments the atomic PNC can be measured by observing its interference with a Stark-induced electric dipole (E1) transition amplitude. The E1 transitions between atomic states of the same parity are strictly forbidden by QED. The Stark interference atomic PNC measurements have been performed on atomic cesium [1], thallium [30], and ytterbium [31]. In the case of Cs, a PNC measurement of 0.35% accuracy combined with a calculation of 0.5% accuracy leads to the most accurate result for the weak charge of cesium nucleus, which can be compared with the prediction of the SM [1, 2].
On the contrary, the 1.7% uncertainty of the PNC experiment in the Tl system using the 6P1/2 → 6P3/2 transition [3, 4], combining with the 2.5% accuracy of Tl atomic theory, leads to a total uncertainty of 3.0% for the weak charge of thallium nucleus. The Tl atom, which has only one unpaired electron, is one of the best candidates to measure the weak charge of nucleus. However, its atomic structure is more complicated than the alkali metals and the accuracy of theoretical calculation is limited. Precision
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measurements of thallium atomic structure, such as the absolute transition energy, HFS and IS can serve as the experimental constraints and benchmarks for the improvements of theory calculation. Our motivation for measuring the hyperfine structure and IS in thallium atom is to guide the refinement and to test the accuracy of the atomic theory calculation for the short-range electron wavefunction.
2.1.3 Thallium Structure
The thallium atom of atomic number 81 is a lead-like metal with a bright, freshly cut surface. It is soft and can be cut with a knife. After exposure to air an oxide layer forms quickly on surface. The water soluble thallium is highly toxic.
High atomic number makes Tl one of the best candidates to measure the weak charge of nucleus because of the Z3 law [24]. The Tl electron configuration is [Xe]4f14 5d10 6s2 6p1, which has only one unpaired electron outside the S-state. Thallium has two stable isotopes, 205Tl ~70.5% and 203Tl~29.5%. Each Tl isotope has nuclear spin 1/2.
This tells us that each fine structure state splits into two hyperfine states. A ground stat 6P1/2 electron has a greater probability of being found near the nucleus. A partial energy level diagram is shown in Fig. 2-2.
However, Tl with three valence electrons has a more complicated atomic structure compared with Cs, which has only one valance electron. The large correlations between three-valence electrons cannot be accurately calculated using many-body perturbation theory (MBPT) [35]. Several new theoretical approaches have been developed for such atoms, for example, MBPT combined with configuration interaction and MBPT combined with coupled-cluster [36]. Precision measurements of thallium atomic structure, such as the absolute transition energy, HFS and IS can provide cross-checks for the new theory.
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Early literatures have reported precise HFS measurements with uncertainties less than 1 kHz for both 6P1/2 and 6P3/2 states using microwave magnetic resonance techniques in the 1950s [32, 33]. Recently precise measurements of the absolute transition frequency and the HFS of the 6P1/2 → 7S1/2 transition have been reported [9].
However, no precise measurements have been carried out for the 6P3/2 → 7S1/2
transition at 535 nm up to now. This motivated us to measure the hyperfine structure of Tl transition 6P3/2 → 7S1/2 using our developed single frequency Nd:GdVO4 laser.
2.2 Volume Bragg Gratings
2.2.1 Properties of Volume Bragg Grating
VBG is a periodic phase grating recorded in a bulk material. Based on a linear Fig. 2-2 Partial energy-level diagram of 203Tl and 205Tl with the HFSs and
isotope level shifts in the unit of MHz. Energy levels are not to scale. [9] [32-34].
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photosensitivity photo-thermo-refractive (PTR) glasses are the most successful material used to manufacture a high efficiency VBG. The PTR is a silicate glass doped with cerium, silver, and fluorine. After UV-exposure with a holographic technique and thermal development the precipitation of a minor crystalline phase results in a holographic phase pattern throughout the whole glass volume.
The PTR VBGs provide extremely narrow spectral selectivity down to 20 pm, good narrow angular selectivity down to 100 μrad, high absolute diffractive efficiency (above 99.9%), and thermally stability of 400°C [37]. PTR VBG is mechanically, chemically and thermally stable. The damage threshold is close to that of the typical silicate glass. It has a laser damage threshold of 40 J/cm2 for 8 ns pulses, and tolerance to CW laser radiation in the near IR region up to several tens of kilowatts per square centimeter. By changing the temperature of VBG, the central reflection wavelength can be tuned by about 10 pm/K around 1μ m due to thermal expansion of PTR glass. The PTR properties [37]:
o Photosensitivity ranges from 280 to 350 nm o Transparency from 350 to 2700 nm
o Absorption in the near IR region below 0.0001 cm-1 o Refractive index 1.49
o Abbe number 60
o Photo-induced refractive index increment up to 1200 ppm o Spatial frequencies from 0 (zero) to 10,000 mm-1
o Phase pattern cannot be erased by any type of optical or ionizing radiation
2.2.2 Volume Bragg Grating Applications in Lasers
Both reflecting and transmitting Bragg grating can be developed in the PTR glass.
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These unique features make VBG ideal for working as intracavity wavelength selectors or resonator couplers in various types of lasers, depending on designed properties.
VBGs offer an alternative approach for the wavelength selection and line narrowing in solid state lasers [12]. Its excellent wavelength selectivity has been demonstrated with laser diodes [38, 39], solid state lasers [12-13,40-48], optical parametric oscillators [49-52] and fiber lasers [53-56]. Transversely chirped VBG has also been used for the wavelength tuning to obtain tunable solid-state laser [57] and OPO [58]. The VBG can also be used as a high power high-density beam combiner [59]. Thorough reviews of the prosperities and applications were given in refs. [60-64].
2.2.3 Diffraction Analysis for a Reflecting Volume Bragg grating
A theory which is based on a coupled-wave analysis for plane waves incident on a VBG was first presented by Kogelnik [65]. The PTR VBG consists of a sinusoidally varying refractive index modulation with period Λ according ton n0 n1sin(2x/ ) , where the modulation n1 is up to
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3in magnitude. Assume a plane wave incident on the grating with an angle θ and wavelength λ. The reflected wavelength by Bragg condition is expressed as reflecting VBG, there is the maximum wavelength
Bmax, which corresponds to normal incidence at0 0,16
shorter wavelengths incident at larger angles can be reflected by a Bragg mirror. The total power reflectivity at the plane x0 can be expressed as [63]
where m is an integer. m should be altered at the reflectivity zero points to give the phase continuity. The peak diffraction efficiency is at 0,
2 ' 2 1 2 1
The zero-to-zero bandwidth of the reflection is defined as the distance between the two zeros closest to the peak to get a simple expression for the VBG bandwidth. The zero-to-zero bandwidth for the wavelength at constant incidence angle is
2 2
where 0is the incident angle at Bragg condition. The bandwidth and the reflectivity can be varied independently by varying parameters n1 and d. At a constant wavelength, the zero-to-zero angular bandwidths for normal incidence are
n 2
The temperature dependence of the central wavelength for normal incidence is
17 dependences of wavelength change are 23.4 pm/℃at 2479 nm [66] and 10 pm/℃ at 1024 nm [67]. As the nonlinear refractive index of PTR [68] the wavelength change with temperature is not directly proportional to the Bragg wavelength. The temperature tuning capability can be used to thermally control laser wavelength. The VBG thermal tuning capability for a solid-state laser was demonstrated in a Ti:sapphire laser system.
[12]
When a thick VBG is used as one of the mirrors of a short Fabry-Perot cavity, the grating’s physical length can be a substantial part of the total cavity length. The effective round trip distance can be calculated from the phase acquired from a reflection of a Bragg grating. The effective cavity length Lcav is deuced to be [13]
1/2 transverse beam profile of a finite incident beam on the grating will be altered in both transmission and reflection, for the different angular components of the incident beam experience different reflectivities. Theory and experiments of finite beams in reflective VBG have been presented in ref. [63] and [69]. In ref. [69], the diffraction efficiency for finite beam incidence was demonstrated and shown in Fig. 2-3. With the finite beam behavior, the VBG can be used as a spatial filter, since higher order transverse modes have a broader angular spectrum. And, adjustingthe beam incident waist can cause the Gaussian mode to be reflected completely, but the higher order
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ones only partially. Thus the VBG can be used as a mode filter to limit the number of transverse modes in a laser cavity.
The reflection spectrum of our PTR VBG made from OptiGrate is shown in Fig. 2-4 [from 70]. The peak reflectivity is centered at 1069.8 nm with full width at half maximum (FWHM) about 0.356 nm. The peak reflectivity is larger than 0.99 according to OptiGrate.
Fig. 2-3 Comparison of Modeling with experimental diffraction efficiency of finite beam in reflective volume Bragg grating (a) 1.24 mrad beam divergence; (b) 23 mrad beam divergence [from ref. 70]
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Fig. 2-4 Reflection spectrum of the VBG is centered at about 1069.8 nm with FWHM 0.356 nm and peak reflectivity larger than 99%.
[from ref. 70, 71 ]
2.3 Nd:GdVO4 Solid State Laser
A laser is a light source based on light amplification by stimulated emission of radiation.
Every laser system essentially is constructed from three basic components: a gain medium, a pump, and a cavity, shown schematically in Fig. 2-5. A gain medium placed between a pair of optically parallel and highly reflecting mirrors with one of them partially transmitting. An energy source pumps gain medium that has appropriate energy levels, where population inversion is obtained. The cavity provides a resonant amplification via the stimulated emission after the population inversion. The gain media may be solid, liquid, or gas. The basics of the laser theory can be found in photonics textbooks.
In this thesis, the gain medium is lanthanide ions doped in a crystal or glass host
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and the pump source is a laser diode, the so called diode pump solid-state lasers. The laser cavity feedback was constructed by a dielectric mirrors and a spectrally selective volume Bragg grating.
Fig. 2-5 Schematic diagram of a typical laser, showing the three major components: a gain medium, a pump and a resonant cavity by the mirrors.
2.3.1 Laser Gain Mediun Nd:GdVO4
The laser crystal is one of the most important components of a solid-state laser, and it can determine the efficiency of the laser. Nd:GdVO4, which is similar to Nd:YVO4
crystal and Nd:GdVO4 crystal, is an excellent laser crystal for diode pumped laser used as a four-level laser pumped at 808 nm. It is common lasing at 1064 nm.
Nd:GdVO4 have higher optical efficiency than Nd: YAG crystals and better thermal conductivity and higher power output than Nd: YVO4 crystals, so they are a good choice for high power output diode pumped solid state laser. Also, Nd:GdVO4 can be operated at linear polarization. These properties make Nd:GdVO4 a good laser material for many laser applications. Table 2-1 shows the comparison of Nd-doped solid state materials. Figure 2-6 shows a simplified energy level diagram of the
4F3/2→4I11/2 manifolds. The close view of 4F3/2→4I11/2 transitions manifold has been shown in Fig. 1-2. It was acquired by an Agilent 70950B optical spectrum analyzer when the crystal is pumped by an optical power of 2.3 W at 808 nm [70]. Nd:GdVO4
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has an emission line at about 1070 nm, which was used to generate 535 nm laser by second harmonic generation in this thesis work.
Table 2-1 Comparison of Nd-doped solid state material [96, 97]
Nd:GdVO4 Nd:YVO4 Nd:YAG Polarized Laser Emission parallel to optic
axis
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2.3.2 Wavelength Selection
The Nd-doped laser systems are well known for its 1064 nm lasing output wavelength, which belongs to the transition between 4F3/2 and one of the Stark levels of 4I11/2. The
The Nd-doped laser systems are well known for its 1064 nm lasing output wavelength, which belongs to the transition between 4F3/2 and one of the Stark levels of 4I11/2. The