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We apply the Small Tip-Angle Approximation in the Toggling Frame in order to analytically design robust pulses against resonance offsets for state to state transfer in two-level quantum systems. We show that a broadband or a local robustness up to an arbitrary order can be achieved. We provide different control parameterizations to satisfy experimental constraints and limitations on the amplitude or energy of the pulse. A comparison with numerical optimal solutions is made., Comment: 32 pages, 7 figures

Using strong-field ionization as a probe, we observe highly nonperiodic evolution of the spin-rotation wave packet launched by a nonionizing femtosecond pulse in oxygen. The nonperiodicity is readily apparent only in rotationally cold molecules that are pumped with a weak alignment pulse. We show that this behavior is a consequence of the spin-rotation and the spin-spin couplings in the triplet ground state of the neutral molecule. A model that includes these couplings in the field-free Hamiltonian but in neither the alignment nor the ionization step explains most of the observed dynamics, suggesting that neither process depends explicitly on the electronic spin. We also show that the angle dependence of strong-field ionization can be retrieved from the delay-dependent signal even when coupling to spin complicates the rotational dynamics.

We study phase-imprinted solitons of ultracold bosons in an optical lattice with a harmonic trap, which shows the superfluid (SF) and Mott-insulator (MI) shell structures. The earlier study [Konstantin V. Krutitsky, J. Larson, and M. Lewenstein, Phys. Rev. A 82, 033618 (2010).] reported three types of phase-imprinted solitons in the Bose-Hubbard model: in-phase soliton, out-of-phase soliton, and wavelet. In this paper, we uncover the dynamical phase diagram of these phase-imprinted solitons, and find another type of the phase-imprinted soliton namely, the hybrid soliton. In the harmonically trapped system, the solitonic excitations created at the SF core cannot penetrate into the outer SF shell. This repulsion at the surface of the outer SF shell can be cured by inposing a repulsive potential at the center of the trap. These results can be interpreted as a kind of the impedance matching of excitations in BECs in terms of the effective chemical potentials or the local particle numbers in the shell, and the analogous results can be observed also in the sound wave created by the local single-shot pulse potential.

We study the photoionization of molecule ${\mathrm{H}}_{2}^{+}$ in an XUV pulse by numerically solving the time-dependent Schr\"odinger equation simulation and focus on a zeptosecond birth time delay of a photoelectron from the different cores. We propose a simple and robust method to extract accurately the zeptosecond birth time delay with double-slit interference minima. Based on this extraction method, our results show that the birth time delay is strongly affected by the initial bound-electron wave function due to the deviation of the electron emission position from the central core. Furthermore, an experimental scheme is also proposed to testify this wave-function-dependent zeptosecond birth time delay. Our study sheds more light on the ultrafast molecular photoionization dynamics on the zeptosecond timescale.

A semiclassical theory that describes the generation of a coherent anti-Stokes Raman scattering (CARS) signal is presented that maximizes vibrational coherence in a mode predetermined by the pump, the Stokes, and the probe chirped pulse trains and takes into account the field propagation effects in a cloud of molecules. The buildup of the anti-Stokes signal, which may be used as a molecular signature in the backward CARS signal, is demonstrated numerically. The theory is based on the solution of the coupled Maxwell's and Liouville--von Neumann equations and focuses on the quantum effects induced in the target molecules by the control pulse trains. A deep convolutional neural network technique is implemented to evaluate time-dependent phase characteristics of the control fields. The effect of decoherence induced by spontaneous decay and collisional dephasing is examined.

We study cross correlation of a single-cycle circularly polarized laser pulse with its delayed and/or attenuated replica in the attoclock field configuration. In this configuration, tunneling ionization of the target atom is observed in the polarization plane of the driving laser pulse. The two-pulse attoclock displays a robust interference pattern in the photoelectron energy spectrum and the real time correlation between the photon absorption rates from the two pulses. This interference and correlation can be used for characterization of single-cycle laser pulses and monitoring the target population dynamics during the ionization process.

The generation of Raman solitons in the mid-IR range in a multicore fiber with two zero-dispersion wavelengths is studied analytically and numerically. The estimate for the maximum shift of the Raman soliton wavelength depending on the parameters of the media dispersion, the frequency-dependent losses, and the nonlinearity decreasing is obtained, which is in good agreement with the results of numerical simulation. A realistic design of a 10-core fiber made of a pair of compatible glasses is proposed for the Raman shift of the wavelength of soliton pulses propagating in an out-of-phase mode. The nonlinear dynamics of a laser pulse, specified at the wavelength of $2.3\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$, energy of 1.5 nJ, and duration of 100 fs, during propagation in a fiber with this design, is studied numerically. The generation of Raman solitons in the mid-IR range at wavelengths exceeding $4\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$, as well as dispersion waves in the $5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ range, emitted by a soliton when approaching the second zero-dispersion wavelength, is demonstrated.

The formation of quantum vortices in photodetachment by a sequence of left- and right-handed circularly polarized laser pulses in various configurations is analyzed using either the strong-field approximation or numerical solution of the time-dependent Schr\"odinger equation. Two types of pulse sequences are considered: reducible and irreducible. While the former can be decomposed into series of consecutive and identical (irreducible) subtrains of pulses, the latter cannot be decomposed in that way. As we show, the vortex pattern in the probability amplitude of photodetachment is fully determined by the irreducible pulse configuration. Additional repetitions of an irreducible train create, in the three-dimensional momentum space, nonvortex nodal surfaces, the position of which is estimated. The conditions for the experimental observation of quantum vortices are also determined.

The wave function of an electron interacting with a finite-range potential and an intense low-frequency laser pulse is analyzed within the adiabatic approximation. The closed analytic form for the wave function, which includes the rescattering corrections, is obtained with quasiclassical accuracy for an electron in both the initial bound and continuum states. We discuss the parametrizations of amplitudes of fundamental strong-field processes in terms of laser and binding-potential parameters. Based on the analytic results for the adiabatic wave functions, we develop the perturbation theory in an additional weak field. The modification of high-order harmonic generation amplitude caused by a weak extreme ultraviolet pulse is discussed in the first order of the perturbation theory.

We present a study of photon statistics associated with high-order harmonic generation (HHG) involving one-mode and intermodal correlations of the high harmonic photons. The aim of the paper is to give insight into the nonclassical properties of high-order harmonic modes. To this end, we use a simplified model describing an elementary quantum emitter: the model of a two-level atom. While the material system is extremely simplified in this description, the conclusions and the methods may be generalized for more complex cases. Our primary interest is an effective model of HHG in which the exciting pulse is classical, and the harmonics are quantized, although we touch upon the more generalized, fully quantized model as well. Evolution of the Mandel-parameter, photon antibunching, squeezing and cross-correlations are calculated. Results imply that with respect to a single quantized emitter, nonclassicality of the harmonics is present: sub-Poissonian photon statistic and squeezing can characterize certain optical modes, while strong anticorrelation can also be present., Comment: 21 pages, 13 figures

We theoretically investigate the modulated high-harmonic generation (HHG) driven by an intense few-cycle infrared (IR) laser field and a weak extreme-ultraviolet (XUV) pulse at a delayed time. We establish an extended quantitative rescattering (EQRS) model to simulate the HHG streaking spectra, with the ideas of correcting the IR ionization and the transition from the ground to continuum states in the strong-field approximation. The EQRS model has an accuracy comparable to that from ``exactly'' solving the time-dependent Schr\"odinger equation (TDSE). We reveal that the fringes in the streaking spectra are caused by the interference between the attosecond XUV pulse and harmonics resulting from different recombination pathways under the intense IR laser. We then demonstrate that the XUV pulse can be accurately retrieved by treating the single-atom TDSE results or macroscopic propagation results as the ``input'' data. This work provides with a tool for efficiently simulating and thoroughly analyzing the XUV-assisted HHG, which could also enhance its capability for tracing the electron dynamics involved in the strong-field phenomena.

High-energy photons can decay to electron-positron pairs via the nonlinear Breit-Wheeler process when colliding with an intense laser pulse. The energy spectrum of the produced particles is broadened because of the variation of their effective mass in the course of the laser pulse. Applying a suitable chirp to the laser pulse can narrow the energy distribution of the generated electrons and positrons. We present a scenario where a high-energy electron beam is collided with a chirped laser pulse to generate a beam of quasimonoenergetic $\ensuremath{\gamma}$ photons, which then decay in a second chirped, UV pulse to produce a quasimonoenergetic source of high-energy electrons and positrons.

Quantum memories are building blocks for a variety of quantum technologies. However, the collective transfer between optical excitations and spin-wave excitations determines the performance of the quantum memory. Here we propose a method for collective excitations transfer with high efficiency and fidelity in a multimode quantum memory. The pulse uses modulations of the control parameters to cancel the nonadiabatic transitions during the evolution. We demonstrate the universality of the control pulse by simulations for an atomic frequency comb spin-wave quantum memory. The protocol is robust to various experimental imperfections in the pulse amplitude and duration. The protocol also allows one to achieve high multiplexed storage at small cost on efficiency reduction. The protocol is particularly useful in retaining the phase coherence since the environment dissipation would decohere the system. These results pave a way for efficient and robust coherent manipulations in a multiplexed quantum memory.

We simulate the photoemission from an electronically excited system by computing the escape of electron density in real space using time-dependent density functional theory in real time. We show that for a one-electron system, the angular resolved photoemission after an initial excitation can be interpreted as the mapping of a previously unoccupied orbital. For the molecule perylene-3,4,9,10-tetracarboxylic dianhydride, the angular resolved photoemission (ARPES) calculated after a preceding pump pulse reveals signatures of the many-particle character of the first electronic excitation: The photoemission results from more than one time-dependent orbital, and comparing the ARPES pattern to a particle-hole analysis of the first electronic excitation confirms that the excitation does not just correspond to one electron having been moved into a previously empty orbital, but is a superposition of several single-particle excitations.

The forerunners of the step-modulated sine pulse propagating in Drude dispersive media are calculated in the time domain. Two such problems are solved analytically. In the first problem, the plane source of the electric field is inside the medium. And the second problem considers the normal incidence of a linearly polarized wave from a vacuum upon a half-space medium. The obtained forerunners are identified as Sommerfeld precursors but the frequency of the oscillations and their amplitudes are closer to the exact solutions than the predictions of canonical Sommerfeld precursor. Moreover, the obtained periodicity of the forerunners is in perfect agreement with the exact solution. The developed analytics is an important contribution to the time-domain theory of the forerunners. The obtained data will be helpful for an experimental study of the forerunners and for the comparison with the forerunners in other dispersive media or with other waveforms of the incident pulse.

An ultrashort laser pulse focused in air creates a plasma that radiates broadband electromagnetic waves. We experimentally compare the generation of microwaves from plasmas produced with two different laser systems that operate in the near- and mid-infrared regimes. Changing the laser wavelength increases the microwave power by 100 times and changing the input pulse energy allows for tuning of the microwave frequency spectrum, which we absolutely calibrate over a range of 2--70 GHz. The variation of the spectrum with laser pulse energy confirms the existence of a distinct mechanism that generates microwave radiation from laser-produced plasmas in gases. We propose that a radial diffusive expansion wave of the plasma electrons drives a longitudinal current along the plasma surface whose amplitude varies with the total residual electron energy imparted by the laser field and this longitudinal current produces the detected radiation.

We show that the generalised nonlinear Schr\"{o}dinger equation (GNLSE) with quartic dispersion supports infinitely many multipulse solitons for a wide parameter range of the dispersion terms. These solitons exist through the balance between the quartic and quadratic dispersions with the Kerr nonlinearity, and they come in infinite families with different signatures. A travelling wave ansatz, where the optical pulse does not undergo a change in shape while propagating, allows us to transform the GNLSE into a fourth-order nonlinear Hamiltonian ordinary differential equation with two reversibilities. Studying families of connecting orbits with different symmetry properties of this reduced system, connecting equilibria to themselves or to periodic solutions, provides the key to understanding the overall structure of solitons of the GNLSE. Integrating a perturbation of them as solutions of the GNLSE suggests that some of these solitons may be observable experimentally in photonic crystal wave-guides over several dispersion lengths., Comment: 22 pages, 10 figure

Laser streaking of photoelectrons has been a well-established technique to extract ultrafast information. In analogy to the streaking of photoelectrons, in this paper, we study the laser streaking of nuclei by numerically simulating the time-dependent Schr\"odinger equations of ${\mathrm{D}}_{2}^{+}$ in strong laser fields. We first demonstrate the nuclear streaking, where the dissociating wave packet excited by an isolated attosecond pulse and propagating on molecular potential surfaces is streaked by a strong midinfrared laser pulse. Subsequently, we use an attosecond pulse train composing two successive attosecond pulses to initiate the dissociation of ${\mathrm{D}}_{2}^{+}$. Depending on the time delay between the attosecond pulse train and the midinfrared laser pulse, the streaked nuclear wave packets show a novel delay-dependent interference pattern. By tracing the wave-packet evolution in the adiabatic presentation, the complicated dissociation pathways are revealed. Based on the streaked nuclear pattern, one may conceive a strategy to probe the real-time nuclear streaking process and extract instantaneous dynamics information experimentally.

Although the time-dependent buildup processes of Autler-Townes splitting in attosecond transient absorption spectra have been observed in plenty of experiments, there still exists an open question of when the splitting is maximized, which tells us how fast the system responds to the pump field and how well the adiabatic following is in a slowly varying few-cycle laser pulse. In this Letter we work out a compact formula to quantify the buildup time of the Autler-Townes splitting, which is related to multiple timescales of the laser-atom system, e.g., the Rabi period, the laser cycle, and the pulse duration, according to a universal power law. This scaling law applies not only to singly excited states, but also to doubly excited states in which complex electron-electron interaction gets involved. Our findings have potential applications in calibrating the zero delay in a transient absorption spectroscopy.

Rogue wave in ultrafast fiber lasers is a hot research topic of nonlinear optics, which is generally monitored at the fixed cavity positions, despite its dramatic intra-cavity evolution. The shot-to-shot statistical properties change significantly if the chaotic pulse experiences strong changes along the cavity, which is rarely considered in the past. Here, we simulate the dynamic evolution of the rogue wave in the dispersion-managed fiber laser. Attributing to the temporal structure change induced by the dispersion, the rogue wave within the noise-like pulse appears in a limited cavity region while disappears in the rest parts. It is also demonstrated that the dispersion is capable of manipulating rogue waves in the pulse trains outside the cavity. Our results offer insightful views on the properties of chaotic waves in ultrafast lasers.

Funding Information: This work was supported by the National Key R&D Program of China (Grant No. 2017YFA0303800), the National Natural Science Foundation of China (Grants No. 11634010 and No. 11874300), and the Fundamental Research Funds for the Central Universities (Grants No. 3102019JC008 and No. 3102019PY002). Publisher Copyright: © 2021 American Physical Society. The transitions from the incoherent noise to the coherent soliton have been fully revealed in ultrafast lasers. However, the soliton transformation between different coherent states, termed as soliton metamorphosis, remains an attractive yet uncharted territory. Here, we reveal the ultrafast dynamics of the soliton metamorphosis via single-shot spectroscopy in a specially designed fiber laser capable of emitting fast-switchable dissipative solitons and stretched pulses. It is demonstrated that the soliton metamorphosis is a consecutive evolution process including the self-phase modulation stage, pulse split stage, and transient stretched pulse stage. Particularly, the long-period pulse breathing and the spectral period doubling appear in the forepart and middle part of the last stage. The metamorphosis dynamics and soliton properties are substantiated by numerical simulation based on a three-step model. This work not only unveils the transient evolution physics of the pulse in soliton metamorphosis, but also provides a simple and effective way to control operations of ultrafast lasers.

A nonlinear integrodifferential equation of the ``reaction-diffusion'' type is derived for an optical pulse propagating in a gain resonant two-level medium with the inhomogeneous broadening of the quantum transitions. The stable exact analytical solution of this equation in the form of a dissipative optical soliton with an asymmetric temporal profile is found and analyzed. The temporal duration of this soliton is much longer than the characteristic phase relaxation time but much shorter than the energy relaxation time. It is shown that the formation of such a soliton requires the presence of linear losses, created by the equilibrium part of the medium. It is noted that the found soliton solution qualitatively coincides with the dissipative soliton recently discovered experimentally in a laser microcavity.

The adiabatic quantum information processing task requires that the evolution of a system must be kept in its instantaneous eigenstate. However, normally the adiabaticity will be ruined due to the interaction between the system and the noisy environment in its long evolution time. Here, in this paper, we show that zero-area pulse control can be used to realize the adiabatic process in a nonadiabatic regime. A concrete example is provided where one spin chain is cut into two chains. The pulse function is applied in the laboratory frame and suitable pulse conditions are obtained numerically. We find that compared with the pulse conditions obtained in the adiabatic frame, the results are similar for low-energy-level systems but tend to deviate when the system's energy level increases. We then obtain the pulse conditions theoretically by writing the control Hamiltonian in the adiabatic frame. It is found that a sequence of pulses with intensities tuned by a time-dependent energy difference is required to guarantee an effective adiabatic speedup.

The properties of the forced oscillations of electron-positron plasma (EPP) generated from vacuum under the action of a short laser pulse are considered. Calculating the density of the conduction and polarization currents within the quantum kinetic approach, we demonstrate the presence of plasma oscillations at the frequency of the external field and its odd harmonics. It is expected that radiation generated by these plasma oscillations can be observed outside the interaction region, for example, outside the focal spot of two counterpropagating laser beams, and can serve as an indicator of the Schwinger mechanism of the EPP creation from vacuum., Comment: 7 pages, 4 figures

A theory of pulse transmission is presented in which the medium through which the pulse propagates is characterized by an inhomogeneous distribution that is either an atomic frequency comb (AFC) or a medium of randomly spaced frequency spikes (RSM). For an AFC, we obtain analytic expressions for the transmitted field amplitude, which is composed of the (partially) transmitted incident pulse, plus a train of equally spaced echoes. For RSM, we derive expressions for the average transmitted field amplitude and field intensity. In the limit that the spike width is much less than the spike separation, normally encountered with AFC, the overall atom-field dynamics is dominated by dispersion---absorption plays a negligible role. The importance of the average group time delay of the pulse is discussed.

Polyatomic molecules in strong laser fields can undergo substantial nuclear motion within tens of femtoseconds. Ion imaging methods based on dissociation or Coulomb explosion therefore have difficulty faithfully recording the geometry dependence of the field ionization that initiates the dissociation process. Here we compare the strong-field double ionization and subsequent dissociation of water (both H$_2$O and D$_2$O) in 10-fs and 40-fs 800-nm laser pulses. We find that 10-fs pulses turn off before substantial internuclear motion occurs, whereas rapid internuclear motion can take place during the double ionization process for 40-fs pulses. The short-pulse measurements are consistent with a simple tunnel ionization picture, whose predictions help interpret the motion observed in the long-pulse measurements., 9 pages, 5 figures

Physical review / A 103(4), 043102 (1-11) (2021). doi:10.1103/PhysRevA.103.043102, We investigate the capability of attosecond transient absorption spectroscopy to characterize the dynamics of inner-shell-excited systems. In the transient absorption spectroscopy setup considered, wave packets are prepared by an attosecond XUV pulse and probed by a femtosecond NIR pulse. By using this, we study coherent electron dynamics in core-excited xenon atoms. In particular, we clarify which aspects of the dynamics can be revealed when the wave packets are probed using an NIR pulse and analyze why the inner-shell hole dynamics is more difficult to probe than the dynamics of the excited electron. We perform a theoretical analysis of the transient absorption signal as a function of the time delay between the XUV pump and NIR probe pulses, treating the excitation pulse perturbatively and the probe pulse nonperturbatively. We also demonstrate that an additional NIR dressing field can dramatically influence the transient absorption spectrum. Our theoretical predictions are compared with experimental results, suggesting that a precise characterization of the NIR pulse is necessary for a qualitative and quantitative comparison., Published by Inst., Woodbury, NY

We analyze the relationship between qubit-environment entanglement that can be created during the pure dephasing of the qubit and the effectiveness of the spin echo protocol. We focus here on mixed states of the environment. We show that while the echo protocol can obviously counteract classical environmental noise, it can also undo dephasing associated with qubit-environment entanglement, and there is no obvious difference in its efficiency in these two cases. Additionally, we show that qubit-environment entanglement can be generated at the end of the echo protocol even when it is absent at the time of application of the local operation on the qubit (the {\pi} pulse). We prove that this can occur only at isolated points in time, after fine-tuning of the echo protocol duration. Finally, we discuss the conditions under which the observation of specific features of the echo signal can serve as a witness of the entangling nature of the joint qubit-environment evolution., Comment: 10 pages, 1 figure

Enantio-conversion with the help of electromagnetic fields is an essential issue due to the chirality-dependence of many chemical, biological, and pharmaceutical processes. Here, we propose a method for this issue based on a five-level double-$\Delta$ model of chiral molecules. By utilizing the breaking of left-right symmetry in the two $\Delta$-type sub-structures, we can establish the chiral-state-selective excitation with one chiral ground state being excited to an achiral excited state and the other one being undisturbed. In the meanwhile, the achiral excited state will relax to the two chiral ground states. The two effects simultaneously acting on the chiral mixtures can convert molecules of different chiralities to the ones of the same chirality, i.e., the enantio-conversion via optical pumping. With typical parameters in gas-phase experiments, we numerically show that highly efficient enantio-conversion can be achieved. Our method works in the appearance of decoherences and without the precise control of pulse-durations (pulse-areas) and/or pulse-shapes. These advantages offer it promising features in promoting the future exploring of enantio-conversion., Comment: 7 pages, 3 figures

The authors show theoretically and experimentally how the time-varying phase or frequency of a chirped strong-field ultrafast laser pulse can be used to control the ionization yield to different ionic states in a polyatomic molecule. The results are interpreted in terms of a competition between two types of nonadiabatic dynamics: multiphoton resonance and internal conversion.

Formation of geometrically regular interference patterns in the photoelectron momentum distributions (PMDs) corresponding to the photoionization of atoms by two single-color, crossing ultrashort pulses is investigated both analytically and numerically. It is shown that, in contrast to the photoionization by monochromatic pulses, PMDs for the ionization by crossing and co-propagating broadband pulses are essentially different (unless both pulses are linearly polarized), namely, when one pulse is linearly polarized along the propagation direction, $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}$, of the circularly polarized (CP) pulse, then interference maxima (minima) of the ionization probability have the form of three-dimensional single-arm regular spirals which are wound along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}$. Next, the interference maxima (minima) of the ionization probability by a pair of crossing elliptically polarized pulses have the form of either Newton's rings or two-arm Fermat's spirals, depending on the position of a detection plane. Remarkably, these regular patterns occur only for certain values of the pulse ellipticities, and they become distorted for CP pulses. For both above-mentioned pulse configurations, the features of interference patterns depend on the time delay between pulses, their relative electric field amplitude, and relative carrier-envelope phase. Our predictions, illustrated by the numerical results for the ionization of H and He atoms by two orthogonal pulses, are quite general and we expect them to be valid for the ionization of any randomly oriented atomic or molecular target.

The computational quantum field theory (CQFT) is applied to study the dependence of the total EPP number on the time interval under the spatially localized double cosine-Gaussian pulse and the alternating-sign double-Gaussian pulse. The total EPP number damply oscillates with the time interval, and the oscillation frequency is about the energy gap ($2m{c}^{2}$) for all of the scenarios. This characteristic oscillation of the total EPP number is consistent with a formula, which is related to the amplitude mode in the BCS superconductors. Besides, we find that the Ramsey interference effect is not responsible for the characteristic oscillation by studying the double-Gaussian pulse with the same sign. Finally, when the favorable time interval is applied, the EPP number is much larger than the sum of the EPP number obtained in two single pulses. The favorable time interval mainly depends on the pulse duration and the carrier envelope phase (the quantity in cosine-Gaussian pulse).

We demonstrate the formation of periodic waves and envelope solitons in dispersive optical media having a Kerr nonlinear response under the influence of third-order dispersion and self-steepening effect. The stability properties of the bright- and dark-soliton solutions are proved using the stability criterion based on the theory of nonlinear dispersive waves. Regimes for the modulation instability of a continuous wave signal propagating inside the dispersive optical medium are also investigated. The results show that the gain spectrum depends crucially on the self-steepening parameter, while the third-order dispersion has no effect on the modulation instability condition. A similarity transformation is presented to reduce the generalized extended nonlinear Schr\"odinger equation with distributed coefficients which models the pulse evolution in the presence of the inhomogeneities of media to the related constant-coefficient one. The propagation behaviors of self-similar bright and dark solitons are discussed in a periodic distributed fiber system and an exponential dispersion decreasing fiber.

A method for measuring small energy level shifts in a qubit by coherent amplification of their effect is proposed. It is based on the repeated application of the same interaction pulse in two manners: with the same phase of each subsequent pulse, and with an alternating phase shift of $\pi$ (i.e. a minus sign) from pulse to pulse. Two specific types of pulses are considered: a resonant $\pi$ pulse and an adiabatic chirped pulse, both of which produce complete population inversion with high fidelity. In the presence of a weak ambient external electric or magnetic field, the ensuing Stark or Zeeman shift leads to an energy level shift and hence a static detuning. In both the resonant and adiabatic approaches, a small level shift does not alter the transition probability very much; however, it can significantly change the dynamical phases in the propagator. The repeated application of the same pulse greatly amplifies the changes in the dynamical phases and maps them onto the populations. Hence the effect of the level shift can be measured with good accuracy. It is found that sequences of pulses with alternating phases deliver much greater error amplification and much steeper excitation profiles around resonance, thereby providing much higher sensitivity to small energy level shifts. Explicit analytic estimates of the sensitivity are derived using the well-known non-crossing Rosen-Zener and Rabi models and the level-crossing Demkov-Kunike model. This recipe provides a simple tool for rapid and accurate sensing of weak electric and magnetic fields by using the same pulse generating an inversion quantum gate, without sophisticated tomography or entangling operations., Comment: 10 pages, 6 figures

We introduce an alternative definition of the main frequency of an ultrashort laser pulse, the principal frequency $\omega_P$. This parameter is complementary to the most accepted and widely used carrier frequency $\omega_0$. Given the fact that these ultrashort pulses, also known as transients, have a temporal width comprising only few cycles of the carrier wave, corresponding to a spectral bandwidth $\Delta\omega$ covering several octaves, $\omega_P$ describes, in a more precise way, the dynamics driven by these sources. We present examples where, for instance, $\omega_P$ is able to correctly predict the high-order harmonic cutoff independently of the carrier envelope phase. This is confirmed by solving the time-dependent Schr\"odinger equation in reduced dimensions, supplemented with the time-analysis of the quantum spectra, where it is possible to observe how the sub-cycle electron dynamics is better described using $\omega_P$. The concept of $\omega_P$, however, can be applied to a large variety of scenarios, not only within the strong field physics domain., Comment: 11 pages, 6 figures, accepted in PRA

We theoretically investigate the emission of high-harmonic (HH) radiation in model crystals by bichromatic few-cycle driving pulses that are composed as the phase-coherent superposition of a mid-infrared fundamental pulse and its second harmonic. Adjusting the model-crystal parameters to reproduce the lowest band gap of MgO, we examine the extent to which distinct domains of the HH spectrum can be controlled and enhanced by tuning the temporal profile of the bichromatic driving laser electric field. We change the driving-pulse shape by varying its fundamental-versus-second-harmonic pulse amplitude ratio and delay, while keeping the energy of the driving laser pulse fixed. For suitable amplitude ratios and delays, we find an up to fivefold enhancement of the spectral HH yield and significant shifts of the HH cutoff frequency.

We investigate the influence of the environment on the rapid adiabatic passage scheme for optimal population transfer in a two-level system. To cope with strong coupling to an external phonon bath with super-Ohmic spectral density, we are solving the time-dependent Schr\"odinger equation of the extended system, including a finite number of bath modes using the multi-Davydov D2 ansatz. This allows for the treatment of the non-Markovian reduced dynamics of the two-level subsystem. Surprisingly, it is found that strong system-bath coupling stabilizes the transition probability from the lower to the upper level as a function of the area under the laser pulse. This dissipative engineering effect could only be uncovered by a non-Markovian treatment. For strong coupling, the transition probability then becomes a monotonically increasing function of the pulse area at zero temperature of the heat bath. Finite temperatures break the monotonicity in the range of pulse areas that we studied, but not the stability of the observed effect.

For polar molecules, the degree of orientation is an essential variable with many interesting manifestations in strong-field phenomena. However, there is no direct way to measure the orientation degree in experiments. On the other hand, current indirect methods based on high-order harmonic generation (HHG) require specific laser conditions for characterization. In this study, we propose a general method to probe the whole range of orientation degrees by calibrating the time profile of harmonics. To develop the method, we first study the sensitivity of the harmonic time profile to the degree of orientation and then present a detailed procedure to extract this quantity from the harmonic time profile, which in turn is obtained from the HHG measurements. In our study, the ``experimental'' HHG data emitted from CO molecules are simulated by numerically solving the time-dependent Schr\"odinger equation. A strong point of the suggested method is its universal applicability with arbitrary laser pulse parameters. Moreover, not only the magnitude but also the sign of the degrees of orientation can be extracted accurately.

A comparative study on the chromatic dispersions and the interactions with ultrashort pulses in epsilon-near-zero (ENZ) transparent conducting oxides (TCOs) is theoretically presented. The ENZ TCOs exhibit rapidly varying and unprecedentedly large $N\mathrm{th}$-order dispersions in the ENZ region, which is exclusive to ENZ plasmonic materials. However, it is found that in both physical and mathematical senses, the concepts of high $N\mathrm{th}$-order chromatic dispersions are inapplicable for ENZ TCOs with Drude-like permittivity. Subsequently, the impacts of the complex permittivity dispersion profiles on ultrashort pulse interactions are discussed. Comparisons are made between propagation patterns in an ENZ AZO waveguide obtained from the nonlinear Schr\"odinger equation (NLSE) and Maxwell's equations, as well as between interactions of femtosecond pulses with different temporal widths in a subwavelength ENZ AZO slab. Results show that the well-received NLSE is not suitable for modeling ENZ TCOs in either case, and subwavelength interaction patterns with different pulse widths are quite different, where the shorter pulse can excite stronger localized resonance.

We investigate the photoionization of ${\mathrm{H}}_{2}$ by an attosecond pulse train using reduced density matrices and reveal that the phase of the photoelectron introduces a time delay in the coherent vibrational motion of ${\mathrm{H}}_{2}^{+}$. We show that, even when the ionization laser pulse is Fourier limited, the reduced density matrix of ${\mathrm{H}}_{2}^{+}$ contains an intrinsic phase ascribed to the phase of the photoelectron wave function and that the intrinsic phase can be extracted by pump-probe measurements as long as the pump-probe time delay is measured with precision of the order of tens of attoseconds.

Generation of electron vortices in photodetachment of ${\mathrm{H}}^{\ensuremath{-}}$ by circularly polarized laser pulses is analyzed by means of strong-field approximation and by numerically solving the time-dependent Schr\"odinger equation. A very good agreement is shown for the magnitude and the phase of the probability amplitude of photodetachment from both approaches. We demonstrate that spiral-like patterns in the probability amplitude of detachment, observed for a pair of counter-rotating circularly polarized laser pulses, cannot be associated with nonvanishing topological charge vortices. The latter can be generated, on the other hand, by a circularly polarized laser pulse or a sequence of such pulses with corotating polarizations. Such interpretation of our results follows from the hydrodynamical formulation of quantum mechanics and its generalization to arbitrary parametric spaces.

Impacts of quantum stochasticity on the dynamics of an ultra-relativistic electron beam head-on colliding with a linearly polarized ultra-intense laser pulse are theoretically investigated in a quasi-classical regime. Generally, the angular distribution of the electron beam keeps symmetrically in transverse directions in this regime, even under the ponderomotive force of the laser pulse. Here we show that when the initial angular divergence $\Delta \theta_i \lesssim 10^{-6} a_0^2$ with $a_0$ being the normalized laser field amplitude, an asymmetric angular distribution of the electron beam arises due to the quantum stochasticity effect, via simulations employing Landau-Lifshitz, quantum-modified Landau-Lifshitz equations, and quantum stochastic radiation reaction form to describe the radiative electron dynamics respectively. The asymmetry is robust against a variety of laser and electron parameters, providing an experimentally detectable signature for the nature of quantum stochasticity of photon emission with laser and electron beams currently available.

$Q$-switching instability restricts pulse shortening in Kerr-lens mode-locked lasers (KLMLs). However, $Q$-switching suppression in KLMLs has not been discussed to date because of the difficulty of treating the Kerr-lens effect theoretically. We investigated parameter ranges for stable Kerr-lens mode locking (KLM) against $Q$ switching theoretically and experimentally. We found the parameters and ranges required to suppress $Q$ switching in hard- and soft-aperture KLMLs. In soft-aperture KLMLs, both intracavity power and spatial mode matching between a pump beam and a cavity mode were found to be critical. These findings were verified experimentally using an Yb:${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ KLML. Our results provide cavity design criteria for stable KLMLs against $Q$ switching.

Generation of electron vortices in photodetachment driven by linearly polarized laser pulses is demonstrated, both within the strong-field approximation and by numerically solving the time-dependent Schr\"odinger equation. The sensitivity of the resulting vortex patterns in the momentum distributions of photoelectrons to the laser pulse parameters (including the pulse duration, its intensity, and the carrier-envelope phase) is analyzed. It is shown that, for a nonzero carrier-envelope phase of the driving pulse, vortex structures in the probability amplitude of detachment occur, similar to von K\'arm\'an vortex streets in fluid mechanics. In addition, hexagonal regions of high probability (honeycomb patterns) are observed, with vortex-antivortex pairs located at their vertices.

In this paper we evaluate the performance of two superadiabatic stimulated Raman adiabatic passage (STIRAP) protocols derived from Gaussian and sin-cos pulses, under dissipation and Ornstein-Uhlenbeck noise in the energy levels. We find that, for small amplitudes of Stokes and pump pulses, the population transfer is mainly achieved directly through the counterdiabatic pulse, while for large amplitudes the conventional STIRAP path dominates. This kind of ``hedging'' leads to a remarkable robustness against dissipation in the lossy intermediate state. For small pulse amplitudes and increasing noise correlation time the performance is decreased, since the dominant counterdiabatic pulse is affected more, while for large pulse amplitudes, where the STIRAP path dominates, the efficiency is degraded more for intermediate correlation times (compared to the pulse duration). For the Gaussian superadiabatic STIRAP protocol we also investigate the effect of delay between pump and Stokes pulses and find that under the presence of noise the performance is improved for increasing delay. We conclude that the Gaussian protocol with suitably chosen delay and the sin-cos protocol perform quite well even under severe noise conditions. The present work is expected to have a broad spectrum of applications, since STIRAP has a crucial role in modern quantum technology.

Electrons have much shorter timescales of movement than nuclei, and thus electron dynamics is generally averaged out in the study of molecular rotation. However, our numerical study shows that the electron dynamical localization on different nuclei during the molecular dissociation may determine the molecular rotation directions. Taking $\mathrm{D}{{}_{2}}^{+}$ as the prototype, an isolated linearly polarized attosecond pulse initiates the molecular dissociation, and then a time-delayed linearly polarized middle-infrared pulse, with the polarization cross angle $\ensuremath{\pi}/4$ to the attosecond pulse, exerts opposite torques on the molecule when the electron localizes on different nuclei, resulting in the clockwise or counterclockwise rotation of the dissociating $\mathrm{D}{{}_{2}}^{+}$. The time-dependent analysis explores the complex behavior of molecular rotation determined by the ultrafast electron dynamics, and sheds light on quantum control of molecular rotation.

Over the past three decades numerous numerical methods for solving the time-dependent Schr\"odinger equation within the single-active electron approximation have been developed for studying ionization of atomic targets exposed to an intense laser field. In addition, various numerical techniques for extracting the photoelectron spectra from the time-dependent wave function have emerged. In this paper we compare photoelectron spectra obtained by either projecting the time-dependent wave function at the end of the laser pulse onto the continuum state having the proper incoming boundary condition or by using the window-operator method. Our results for three different atomic targets show that the boundary condition imposed onto the continuum states plays a crucial role for obtaining correct spectra accurate enough to resolve fine details of the interference structures of the photoelectron angular distribution.

In this work, we implement a scheme to combine six coherent, spatially separated Raman sidebands generated in single-crystal diamond into a collinear beam. With appropriate phase tuning, this results in a pulse much shorter than the generating pump. We elucidate the characteristics of the synthesized pulse by using an interferometric collinear cross-correlation frequency-resolved optical gating setup (ix-FROG). The beating of the synchronized sidebands results in an additional component in the signal, which we use to optimize the relative phases of our sidebands. In this way, we synthesize and measure visible-range, near-single cycle isolated pulses of approximately 5 fs total pulse duration., Comment: 7 pages, 3 figures, one conference paper, two conference abstracts, two workshops

The method of the laser pulse self-compression in the process of noise-seeded Raman scattering in a plasma created by a counterpropagating ionized pulse is considered. The sharpness of the ionization front ensures the formation of an output pulse close to the $\ensuremath{\pi}$-pulse solution with a sharp leading edge. The dependence of the gain increment on the transverse wave number leads to the formation of a smooth phase front of the output pulse. The energy efficiency in the output pulse reaches 28% of the total pump energy. A study of the influence of quasistatic inhomogeneities showed only a slight slowdown in the process, even in a plasma with 8% density modulation.