Field Programmable Gate Array‐Based Control Systems for Highly Stable Laser Applications

10. Electric Arcs

Two kinds of optical heterodyne saturation spectroscopies, namely, frequency modulation spectroscopy (FMS) and modulation transfer spectroscopy (MTS), are demonstrated for locking a fiber laser to the transition lines of metastable (4)He atoms around 1083 nm. The servo-loop error signals of FMS and MTS for stabilizing laser frequency are optimized by studying the dependence of the peak-to-peak amplitude and slope on the optical power of pump and probe beams. A comparison of the stabilization performances of FMS/MTS and polarization spectroscopy (PS) is presented, which shows that MTS exhibits relatively superior performance with the least laser frequency fluctuation due to its flat-background dispersive signal, originated from the four-wave mixing process. The Allan deviation of the stabilized laser frequency is 5.4 × 10(-12)@100 s with MTS for data acquired in 1000 s, which is sufficiently applicable for fields like laser cooling, optical pumping, and optical magnetometry.

We report laser frequency stabilization with modulation transfer spectroscopy (MTS) on 85Rb atoms. With both PZT (piezo-electric transducer) slow-loop feedback and current fastloop feedback to the laser head, we get a linewidth narrowing less than 5 kHz simultaneously. Laser injection to a laser diode and frequency beating with another polarization spectroscopy based stabilization setup are also employed to check the narrow linewidth property. With the help of the technique, a linewidth around kHz-level laser is obtained and pave the way for the locking of the lattice laser of ytterbium clock with transfer cavity technique. The setup can be used as a frequency reference for precise frequency control of atomic clock system.

One of the key parts of laser system of atomic gravimeter based on cold atoms is investigated. In order to construct optical system of atomic gravimeter the laser offset frequency stabilization is needed. Method for frequencydoubled fiber laser’s offset frequency stabilization is suggested and developed. This method is based on modulation transfer spectroscopy and the usage of fiber electro-optical modulator. The experimental scheme of this method is described. The error signals for offset frequency stabilization of frequency-doubled fiber laser are obtained. In order to maximize error signal’s amplitude, experimental parameters such as cell’s temperature, pump and probe beam intensities and electrooptical modulators signal amplitudes are optimized. The influence of polarization on error signal’s amplitude is investigated. It is shown that circular polarization allows to achieve error signal with higher amplitude. The achieved results can be applied to the construction of quantum gravimeter, quantum frequency standards and to the laser cooling experiments.

We demonstrate frequency stabilization of DFB laser via modulation transfer spectroscopy, which avoids the interference of Doppler absorption spectrum. By modulating the frequency of laser beam(pump laser beam), the other laser beam(probe laser beam) overlap pump laser beam is modulated as the same frequency by nonlinear interaction. By demodulating the signal from detection beam, an error signal is generated through the low pass filter. The frequency is stabilized at the 0 point position of the MTS frequency discrimination curve by PID loop which shows frequency fluctuation is less than 149 kHz, and the relative frequency stability is improved by nearly two orders of magnitude.

Quantum computing promises an exponential speed-up of computation compared to what is nowadays achievable with classical computers. In this way, it enables the evaluation of more complex models and the breaching of current security algorithms. For the operation of a quantum system, many questions remain to be answered. Currently, there are several quantum technologies that promise to be both reliable and scalable, two features required for large scale quantum operations. Common to all technologies is the operating temperature that needs to be close to absolute zero, i.e. below 100 mK, to suppress environment noise and allow the quantum properties to become 'visible'.<br/><br/>In order for any quantum processor to be operated, a so-called quantum-classical interface is required for the quantum bit (qubit) read-out and control. This interface consists of various electronic blocks, such as analog-to-digital converters, digital-to-analog converters, mixers, amplifiers and a digital controller. Especially the analog blocks require effort to meet the noise and stability constraints as not to disturb the very sensitive qubits and allow reading of the tiny signals. As the qubits live in extremely deep-cryogenic temperatures, long wires interface the cryogenic with the room temperature environment, where most of the electronics is situated. However, for a scalable system, heat injection becomes a serious problem, with many wires between 300 K and sub-Kelvin. Furthermore, such amount of interconnects is challenging to mechanically place in a dilution refrigerator. <br/><br/>Therefore, in this work, we propose to implement the electronics not at room temperature, but at a temperature much closer to the qubits, for example at 4 K. This not only reduces significantly the wiring between room temperature and the qubits, but we can also benefit from lower electronic noise at such a temperature. The operation of conventional electronics almost 200°C below its normal temperature range is not trivial as device properties alter significantly and most circuits no longer operate as intended.<br/><br/>In CMOS processes, the main technology in the integrated electronics world, the behaviour of the transistors, required for the implementation of any circuit, deviates considerably at low temperatures. The transistor's threshold voltage goes up, the mobility increases and the subthreshold slope becomes steeper, to name just a few of these deviations. Although there are improvements in performance, there are also some counter effects, and characterization of the transistors is needed to observe the changes. Once devices are characterized at such low temperatures, new models can be built and circuits can be simulated and adapted to operate properly at cryogenic temperatures. Luckily, there are various commercially available devices that can already withstand the chills of cold. We demonstrated various commercially available devices, such as a field-programmable gate array (FPGA) implemented in a 28 nm CMOS process, to be operating without major concerns at 4~K. Its properties alter only slightly, within 5 to 10%, and all tested circuit implementations, working at 300~K, also worked at 4 K. <br/><br/>We combined both commercially available devices, that operate 200 K below their specified temperature range, with custom designed CMOS circuits to implement a cryogenic read-out platform for spin qubits. This system comprises amplifiers, an ADC, an FPGA, voltage regulators and a clock generator. It allows to amplify the tiny signal from the qubits and digitize it directly in the FPGA in order to process the data locally at 4~K. This system is one of the first systematic attempts at operating a part of the quantum-classical interface at cryogenic temperatures and forms the basis for future systems comprising the complete electronic interface for qubits to operate at such low temperatures. <br/><br/>One of the main problems to tackle for cryogenic electronic systems is their power consumption. Power budgets are simply limited to roughly 1 or 2 Watts at 4 K and exponentially lower at deeper cryogenic temperatures, thus limiting the size of large-scale electronic systems. Our approach of combined commercial and custom circuits will have to be steadily replaced by a single (custom) technology that meets both power and scalability constraints. One of the best candidates is CMOS, a technology that the industry has relied upon for several decades and benefits from many optimizations thanks to Moore's law.

Unitary operator coherent states, as defined by Klauder (1963), Perelomov (1972) and Gilmore (1974), are considered for the harmonic series irreducible representations of U(p,q). Various properties of these states are reviewed, including their reproducing kernel and measure explicit forms, as well as the representation they lead to for the U(p,q) generators. Starting from a contraction of the su(p,q) Lie algebra, both Dyson and Holstein-Primakoff boson realisations of u(p,q) are obtained in terms of pq pairs of boson creation, annihilation operators and of the generators of a U(p)*U(q) intrinsic group. Such boson realisations are applied to determine the matrix elements of the U(p,q) generators between discrete bases classified according to the chain U(p,q) contains/implies U(p)*U(q). Finally, the isomorphism between so(4,2) and su(2,2) is employed to derive the corresponding properties of the SO(4,2) unitary operator coherent states for application in atomic physics.

A compact extended cavity laser using a micromachined silicon flexure for atomic spectroscopy

We overview the second solution of the Dirac equation for hydrogen atoms that became legitimate with the allowance for the actual charge density distribution inside the protons. It led to the possible existence of hydrogen atoms having only the S-states and therefore not interacting with the electromagnetic radiation – remaining dark . The actual existence of such Second Flavor of Hydrogen Atoms (SFHA) is evidenced by three different types of atomic experiments. In addition to their application for explaining the atomic experiments, they were the basis for resolving the long-standing puzzle of the neutron lifetime. Also, the SFHA was the basis for explaining the baffling astrophysical observation of the anomalous absorption in the 21 cm line from the early Universe, what made the SFHA the leading candidate for baryonic dark matter. Further, by comparing astrophysical observations with atomic experiments, it was demonstrated that the SFHA constitutes the majority of baryonic dark matter. Lastly, it was shown that neutron stars slowly but continuously generate new baryonic dark matter in the form of the SFHA and that there is astrophysical evidence of this process.

Considering Stark-effect applications in atomic physics and especially in plasma spectroscopy, we established several formulas for spectral line intensity, energy level, and ionization rate. In particular, by means of the systematic numerical check on an intermediate formula [Eq. (36d) in the text], we show that the ionization rate may be expressed completely in terms of the energy level according to $\ensuremath{\Gamma}({n}_{1},{n}_{2},m,\ensuremath{\lambda})=\frac{1}{2\ensuremath{\pi}}\frac{\ensuremath{\partial}E({n}_{1},{n}_{2},m,\ensuremath{\lambda})}{\ensuremath{\partial}{n}_{2}}\mathrm{exp}[\ensuremath{-}K({n}_{1},{n}_{2},m,\ensuremath{\lambda})],$ where $\ensuremath{\lambda}={({n}_{1}+{n}_{2}+m+1)}^{3}\frac{F}{4{Z}^{3}}$, and $K({n}_{1},{n}_{2},m,\ensuremath{\lambda})=\frac{1}{6\ensuremath{\lambda}}+\mathrm{ln}\frac{{\ensuremath{\lambda}}^{2{n}_{2}+m+1}{n}_{2}!({n}_{2}+m)!}{2\ensuremath{\pi}}+3({n}_{2}\ensuremath{-}{n}_{1})\ensuremath{-}\frac{1}{6}\ensuremath{\int}{0}^{\ensuremath{\lambda}}\left[{n}^{3}\frac{\ensuremath{\partial}E({n}_{1},{n}_{2},m,{\ensuremath{\lambda}}^{\ensuremath{'}})}{\ensuremath{\partial}{n}_{2}}\ensuremath{-}1+6(2{n}_{2}+m+1){\ensuremath{\lambda}}^{\ensuremath{'}}\right]\frac{d{\ensuremath{\lambda}}^{\ensuremath{'}}}{{\ensuremath{\lambda}}^{\ensuremath{'}2}}.$ The two factors on the right-hand side of (i) are interpreted, respectively, as the atomic-electron-collision frequency and transmission coefficient through the potential barrier created by the electric field $F$. By using the ninth-order perturbation series for resonance energy $E({n}_{1},{n}_{2},m,\ensuremath{\lambda})$ it is found that (i) is in fairly good agreement with the most recent numerical solutions of the Schr\"odinger equation. A discussion follows in connection with other analytical and empirical formulas.

In the present work we review the twisted field construction of quantum field\ntheory on noncommutative spacetimes based on twisted Poincar\\'e invariance. We\npresent the latest development in the field, in particular the notion of\nequivalence of such quantum field theories on a noncommutative spacetime, in\nthis regard we work out explicitly the inequivalence between twisted quantum\nfield theories on Moyal and Wick-Voros planes; the duality between deformations\nof the multiplication map on the algebra of functions on spacetime\n$\\mathscr{F}(\\mathbb{R}^4)$ and coproduct deformations of the Poincar\\'e-Hopf\nalgebra $H\\mathscr{P}$ acting on~$\\mathscr{F}(\\mathbb{R}^4)$; the appearance of\na nonassociative product on $\\mathscr{F}(\\mathbb{R}^4)$ when gauge fields are\nalso included in the picture. The last part of the manuscript is dedicated to\nthe phenomenology of noncommutative quantum field theories in the particular\napproach adopted in this review. CPT violating processes, modification of\ntwo-point temperature correlation function in CMB spectrum analysis and\nPauli-forbidden transition in ${\\rm Be}^4$ are all effects which show up in\nsuch a noncommutative setting. We review how they appear and in particular the\nconstraint we can infer from comparison between theoretical computations and\nexperimental bounds on such effects. The best bound we can get, coming from\nBorexino experiment, is $\\gtrsim 10^{24}$ TeV for the energy scale of\nnoncommutativity, which corresponds to a length scale $\\lesssim 10^{-43}$ m.\nThis bound comes from a different model of spacetime deformation more adapted\nto applications in atomic physics. It is thus model dependent even though\nsimilar bounds are expected for the Moyal spacetime as well as argued\nelsewhere.\n

Vibration modes in spherical geometry can be classified based on the number and position of nodal planes. However, the geometry of these planes is non-trivial and cannot be easily displayed in two dimensions. We present 3D-printed models of those vibration modes, enabling a haptic approach for understanding essential features of bound states in quantum physics and beyond. In particular, when applied to atomic physics, atomic orbitals are obtained in a natural manner. Applied to nuclear physics, the same patterns of vibration modes emerge as cornerstone for the nuclear shell model. These applications of the very same model in a range of more than 5 orders of magnitude in length scales leads to a general discussion of the applicability and limits of validity of physical models in general.

This paper addresses several issues involved for routing in Field‐Programmable Gate Arrays (FPGAs) that have both horizontal and vertical routing channels, with wire segments of various lengths. Routing is studied by using CAD routing tools to map a set of benchmark circuits into FPGAs, and measuring the effects that various parameters of the CAD tools have on the implementation of the circuits. A two‐stage routing strategy of global followed by detailed routing is used, and the effects of both of these CAD stages are discussed, with emphasis on detailed routing. We present a new detailed routing algorithm designed specifically for the types of routing structures found in the most recent generation of FPGAs, and show that the new algorithm achieves significantly better results than previously published FPGA routers with respect to the speed‐performance of implemented circuits.The experiments presented in this paper address both of the key metrics for FPGA routing tools, namely the effective utilization of available interconnect resources in an FPGA, and the speed‐performance of implemented circuits. The major contributions of this research include the following: 1) we illustrate the effect of a global router on both area‐utilization and speed‐performance of implemented circuits, 2) experiments quantify the impact of the detailed router cost functions on area‐utilization and speed‐performance, 3) we show the effect on circuit implementation of dividing multi‐point nets in a circuit being routed into point‐to‐point connections, and 4) the paper illustrates that CAD routing tools should account for both routability and speed‐performance at the same time, not just focus on one goal.

We developed a laser stabilization system composed of optical fibers. In this system all optical devices used for stabilization are connected with optical fibers. This system has advantages for space use and for low-frequency (< 10 Hz) stabilization. We suppressed the intensity noise to 6 × 10-7/√Hz at 1 Hz, and to 4 × 10-8/√Hz at 1 kHz. We also suppressed the frequency noise to 20 Hz/√Hz at 1 Hz, and to 2 Hz/√Hz at 80 Hz. This system is one of the candidates for the laser stabilization system of DECIGO.

Summary of United States Human Proteome Organisation (HUPO) Symposium Entitled “Standardized Clinical Proteomics Platforms”