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<jats:p>Effective Hamiltonian method is widely used in quantum information. We introduce a method to calculate effective Hamiltonians and give two examples in quantum information to demonstrate the method. We also give a relation between the effective Hamiltonian in the Shrödinger picture and the corresponding effective Hamiltonian in the interaction picture. Finally, we present a relation between our effective Hamiltonian method and the James–Jerke method which is currently used by many authors to calculate effective Hamiltonians in quantum information science.</jats:p>

<jats:p>The pre-Bötzinger complex (pre-BötC) in mammalian brainstem is essential for the generation of respiratory rhythms. Most dynamic studies on the pre-BötC neuron have been focused on its firing activities modulated by the ion conductances rather than that by the electromagnetic radiation or the external forcing current. In this paper, by adding the electromagnetic radiation and external forcing current to Park and Rubin’s model, we mainly investigate the influences of those two factors on the mixed bursting (MB) of single pre-BötC neuron. First, we explore how the variation of external forcing current affects the MB patterns of the system with non-vanishing magnetic flux. We classify the MB patterns and show their dynamic mechanism through fast-slow decomposition and bifurcation analysis. Then, by modifying the feedback coefficient, we further analyze the sole effect of electromagnetic radiation on the firing activities of the system. Our results may be instructive in understanding the dynamical behavior of pre-BötC neuron.</jats:p>

<jats:p>A nuclear spin gyroscope based on an alkali-metal–noble-gas co-magnetometer operated in spin-exchange relaxation-free (SERF) regime is a promising atomic rotation sensor for its ultra-high fundamental sensitivity. However, the fluctuation of probe light intensity is one of the main technical error sources that limits the bias stability of the gyroscope. Here we propose a novel method to suppress the bias error induced by probe light intensity fluctuations. This method is based on the inherent magnetic field response characteristics of the gyroscope. By the application of a bias magnetic field, the gyroscope can be tuned to a working point where the output signal is insensitive to probe light intensity variation, referred to herein as ‘zero point’, thus the bias error induced by intensity fluctuations can be completely suppressed. The superiority of the method was verified on a K–Rb–<jats:sup>21</jats:sup>Ne co-magnetometer, and a bias stability of approximately 0.01 °/<jats:italic>h</jats:italic> was obtained. In addition, the method proposed here can remove the requirement of the closed-loop control of probe light intensity, thereby facilitating miniaturization of the gyroscope volume and improvement of reliability.</jats:p>

<jats:p>Magnetic coils for specific requirements are widely used in modern quantum physics. In this study, a general analytical method of designing the shielded coils for generating an arbitrary axial magnetic field is proposed. The theoretical formula for an axial magnetic field generated by a single shielded coil is obtained and used to construct specific coils. The structural parameters of these coils are determined by fitting the theoretical formula with their specific requirements. The feasibility of this method is proved by realizing four concrete kinds of coils: uniform magnetic field generating coils, gradient magnetic field generating coils, asymmetrical uniform magnetic field generating coils, and parabolic magnetic field generating coils. The correctness of these theoretical results is demonstrated by both the finite element simulations and the relevant experimental results. Furthermore, the application of this method is of great significance for developing the quantum physics and quantum devices in future.</jats:p>

<jats:p>It is important for environmental protection to search for catalysts with excellent performance and cost-effective to reduce SO<jats:sub>2</jats:sub> by CO. In this work, using first-principles calculation, we have studied the catalytic performance of Au<jats:sub>5</jats:sub> <jats:italic>M<jats:sup>n</jats:sup> </jats:italic> (<jats:italic>M</jats:italic> = Ni, Pd, Pt, Cu, Ag, Au; <jats:italic>n</jats:italic> = 1, 0, −1) clusters, and showed that, by giving a negative charge to the Au<jats:sub>5</jats:sub> <jats:italic>M</jats:italic> (<jats:italic>M</jats:italic> = Cu, Ag, Au, Pd) clusters, we could improve the selectivity of SO<jats:sub>2</jats:sub> and avoid effectively catalyst CO poisoning simultaneously. At the same time, the catalytic reaction rate for the reduction of SO<jats:sub>2</jats:sub> by CO with Au<jats:sub>5</jats:sub> <jats:italic>M</jats:italic> <jats:sup>−</jats:sup> (<jats:italic>M</jats:italic> = Cu, Ag, Au, Pd) clusters is greatly improved when the Au<jats:sub>5</jats:sub> <jats:italic>M</jats:italic> clusters are charged. These advantages can be well explained by the charge transfer between the clusters and adsorbed molecules, which means that we can effectively control the performance of the catalyst. The equilibrium structures of Au<jats:sub>5</jats:sub> <jats:italic>M<jats:sup>n</jats:sup> </jats:italic> (<jats:italic>M</jats:italic> = Ni, Pd, Pt, Cu, Ag, Au; <jats:italic>n</jats:italic> = 1, 0, −1) clusters without or with adsorbed SO<jats:sub>2</jats:sub> or CO molecule are also discussed, and the most stable geometrical structures of Au<jats:sub>5</jats:sub> <jats:italic>M<jats:sup>n</jats:sup> </jats:italic>-ML (ML = SO<jats:sub>2</jats:sub>, CO, SO, and COS) can be explained very well by the match of orbitals symmetry and density of electron cloud through their frontier molecular orbitals. Considering the catalyst cost (Cu is much cheaper than Ag and Au), selectivity of SO<jats:sub>2</jats:sub>, and effectively avoiding the catalyst CO poisoning, we propose that Au<jats:sub>5</jats:sub>Cu<jats:sup>−</jats:sup> is an ideal catalyst for getting rid of SO<jats:sub>2</jats:sub> and CO simultaneously.</jats:p>

<jats:p>We macroscopically investigate the effect of the laser intensity and gas density on quantum trajectories in the high-order harmonic generation of Ne atoms irradiated by few-cycle, 800-nm laser pulses. The time–frequency profile of the harmonics shows that the long quantum trajectory is dominant at both lower and higher gas densities for a low laser intensity. At high laser intensities, the long quantum trajectory plays an important role for lower gas densities, while the short quantum trajectory is dominant at higher gas densities. An analysis of the phase mismatch for high-order harmonic generation shows that the primary emission of the quantum trajectories is determined by dynamic changes in the laser electric field during the propagation process.</jats:p>

<jats:p>The molecular orientation created by laser fields is important for steering chemical reactions. In this paper, we propose a theoretical scheme to manipulate field-free molecular orientation by using an intense super-Gaussian laser pulse and a time-delayed terahertz half-cycle pulse (THz HCP). It is shown that the degree of field-free orientation can be doubled by the combined pulse with respect to the super-Gaussian pulse or THz HCP alone. Moreover, different laser intensities, carrier envelop phases, shape parameters, and time delays have great influence on the positive and negative orientations, with other conditions unchanged. Furthermore, it is indicated that the maximum degree and direction of molecular orientation can be precisely controlled by half of the duration of the super-Gaussian pulse. Finally, by adjusting the laser parameters of the super-Gaussian laser pulse and THz HCP, the optimal results of negative orientation and corresponding rotational populations are obtained at different temperatures of the molecular system.</jats:p>

<jats:p>A highly sensitive optical fiber temperature sensor based on a section of liquid-filled silica capillary tube (SCT) between single mode fibers is proposed. Two micro-holes are drilled on two sides of SCT directly by using femtosecond laser micromachining, and liquid polymer is filled into the SCT through the micro-holes without any air bubbles and then sealed by using ultra-violet (UV) cure adhesive. The sidewall of the SCT forms a Fabry–Perot resonator, and loss peaks are achieved in the transmission spectrum of the SCT at the resonant wavelength. The resonance condition can be influenced by the refractive index variation of the liquid polymer filled in SCT, which is sensitive to temperature due to its high thermo-optical coefficient (−2.98 × 10<jats:sup>−4</jats:sup> °C<jats:sup>−1</jats:sup>). The experimental result shows that the temperature sensitivity of the proposed fiber structure reaches 5.09 nm/°C with a perfect linearity of 99.8%. In addition, it exhibits good repeatability and reliability in temperature sensing application.</jats:p>

<jats:p>Air lasing is a concept that refers to remote no-cavity (mirrorless) optical amplification in ambient air with the air constituents as the gain media. Due to the high potential of air lasing in view of applications in atmospheric sensing, a variety of pumping schemes have been proposed so far for building up population-inverted gain media in air and producing forward and/or backward directional lasing emissions. This review paper presents an overview of recent advances in the experimental observations and physical understanding of air lasing in various pumping schemes of air molecules by intense laser fields. Special emphasis is given to the strong-field-induced <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{N}}}_{2}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi mathvariant="normal">N</mml:mi> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_11_114204_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> air lasing, the mechanism of which is currently still in a hot debate.</jats:p>

<jats:p>The high-order harmonic generation from a model solid structure driven by an intense laser pulse is investigated using the semiconductor Bloch equations (SBEs). The main features of harmonic spectrum from SBEs agree well with the result of the time-dependent Schrödinger equation (TDSE), and the cut-off energy can be precisely estimated by the recollision model. With increasing the field strength, the harmonic spectrum shows an extra plateau. Based on the temporal population of electron and the time–frequency analysis, the harmonics in the extra plateau are generated by the Bloch oscillation. Due to the ultrafast time response of the Bloch electron, the generated harmonics provide a potential source of shorter isolated attosecond pulse.</jats:p>