Weak Laser Field Research Articles

Simulation of nonlinear optical signals via approximate solutions of the quantum–classical Liouville equation: Application to the pump–probe spectroscopy of a condensed phase electron transfer reaction

The equation-of-motion phase-matching approach provides an efficient way for calculating a system’s time-dependent polarization in any phase-matching direction subject to weak laser fields of arbitrary shape. Within this approach, we introduce the Poisson Bracket Mapping Equation and Forward–Backward methods, two approximate solutions of the quantum–classical Liouville equation, for simulating the laser-induced response of a quantum subsystem in a classical environment. We illustrate this approach by calculating the transient absorption signal in a model photo-induced condensed phase electron transfer reaction. The results are found to be in reasonable agreement with the exact results, which is promising for applications to realistic systems.

Resolution enhancement of photoelectron spectra by coherent phase control

In this paper, we study theoretically, the coherent phase control of (2+1) resonantly enhanced multiphoton ionization photoelectron spectra in cesium atom system by shaping the femtosecond pulse with π phase step modulation under weak laser field. Our results show that the photoelectron spectra can be greatly narrowed and the photoelectron intensity can be enhanced after π phase step modulation by precisely setting the phase step position. Also, we show that the high-resolution photoelectron spectra and the fine energy-level diagram of the two closed excited states can be obtained.

Non-Hermitian wave packet approximation of Bloch optical equations

We introduce a non-Hermitian approximation of Bloch optical equations. This approximation provides a complete description of the excitation, relaxation, and decoherence dynamics of ensembles of coupled quantum systems in weak laser fields, taking into account collective effects and dephasing. In the proposed method, one propagates the wave function of the system instead of a complete density matrix. Relaxation and dephasing are taken into account via automatically adjusted time-dependent gain and decay rates. As an application, we compute the numerical wave packet solution of a time-dependent non-Hermitian Schrödinger equation describing the interaction of electromagnetic radiation with a quantum nano-structure, and compare the calculated transmission, reflection, and absorption spectra with those obtained from the numerical solution of the Liouville-von Neumann equation. It is shown that the proposed wave packet scheme is significantly faster than the propagation of the full density matrix while maintaining small error. We provide the key ingredients for easy-to-use implementation of the proposed scheme and identify the limits and error scaling of this approximation.

Phase-controlled absorption-gain properties and optical switching in nanodiamond nitrogen-vacancy center

We study phase-controlled absorption-gain and dynamic switching behaviors in a nanodiamond nitrogen-vacancy (NV) center. The NV center is driven coherently by a weak probe laser field, a control laser field and a microwave field. To describe the transient behavior of the system, we go beyond the steady-state approximation and simultaneously solve the coupled Bloch–Maxwell equations for the NV center and the probe field on numerical grids as functions of space and time. The results show that the continuous-wave input weak probe field can be switched on and off when the relative phase of the applied field is externally varied periodically in time. The proposed scheme may have applications in the design of optical switching and optical gain devices.

Control of resonance enhanced multi-photon ionization photoelectron spectroscopy by phase-shaped femtosecond laser pulse

In this paper, we theoretically demonstrate that the (2+1+1) resonance enhanced multi-photon ionization photoelectron spectroscopy in sodium atom can be effectively controlled by shaping femtosecond laser pulse with a π phase step modulation in weak laser field, involving its total photoelectron energy, maximal photoelectron intensity, and spectroscopic bandwidth. Our results show that the total photoelectron energy can be suppressed but not enhanced, the maximal photoelectron intensity can be enhanced and also suppressed, and the photoelectron spectroscopy can be tremendously narrowed. These theoretical results can provide a feasible scheme to achieve the high-resolution photoelectron spectroscopy and study the excited state structure in atomic and molecular systems.

Intermediate state absorption enhancement in resonance-mediated (2+1) three-photon excitation process

In this paper, we theoretically study the control of intermediate state absorption in resonance-mediated (2+1) three-photon excitation process by shaping the femtosecond pulse with a π phase step modulation under weak laser field. Our results show that the intermediate state absorption can be enhanced, and the coherent enhancement increases with the increase of the pulse intensity and pulse duration. Our analysis indicates that the absorption enhancement results from the absorption reduction of the final state from the intermediate state in the shaped laser field. Furthermore, the effects of the population difference of the final and intermediate states in the unshaped laser field and the transition dipole moment from the intermediate state to the final state on the absorption enhancement are discussed and analyzed.

A tunable optical response of a hybrid semiconductor quantum dot-metal nanoparticle complex in the presence of optical excitations

We theoretically investigate the optical response of a hybrid nanocrystal complex composed of a semiconductor quantum dot (SQD) and a metal nanoparticle (MNP) in the presence of laser fields within a full quantum description. The analytic results demonstrate that the modified decay rate of the exciton is related to the exciton energy and the distance between SQD and MNP in terms of a quantum transformation method. The responses of the coupled system to a weak laser field and a strong laser field are demonstrated. When the two laser fields are presented simultaneously, the energy absorption rate of the coupled system to the weak laser field can be controlled by the strong laser field and the distance between SQD and MNP. This tunable optical response in such a hybrid system can be exploited for the development of the optical processing devices such as ultrafast optical switch in the future.

Mass shift effect on relativistic high-order harmonic generation

By solving the time-dependent Dirac and Schrödinger equations, we investigate the super high-order harmonic generation (HHG) from a one-dimensional model atom in a relativistic intense laser pulse. Our numerical simulations show that the relativistic results can be degraded to non-relativistic ones in the weak laser field, and the clear effect of the relativistic mass-shift can be gradually observed as the increase of the laser field intensity. Furthermore, the cutoff frequency and the emission efficiency of the HHG spectrum are analyzed by the wavelet time-frequency analysis and the relativistic "three-step" model.

Optical vortex filtering for the detection of electromagnetically induced transparency

We report on the realization of an optical filter based on an optical vortex mask designed to exclusively detect a weak coherent laser field in the presence of a much stronger, nearly spatially overlapping field. We demonstrate the performance of such an optical vortex filter to eliminate the strong control field and detect only a weak optical field's transmission under the conditions of electromagnetically induced transparency. The attractive feature of such a filter is its insensitivity to optical field frequencies and polarizations, which makes it applicable for a wide range of coherent processes.

The effect of light-induced conical intersections on the alignment of diatomic molecules

It has already been shown that dressing of diatomic molecules by standing or by running linearly polarized laser waves gives rise to conical intersections (CIs). Due to the presence of such light-induced CIs (LICI), the rovibronic molecular motions are strongly coupled. Here we investigate an impact of LICI on molecular alignment. We show that the degree of alignment of a diatomic molecule as a function of time as obtained from the rigid rotor calculations (where the LICI is ignored) is very different from the exact calculations (where the LICI is taken into consideration). This claim is valid under an assumption that the initially prepared wavepacket has a significant amplitude at the nuclear geometry where the LICI is located. Moreover, our results clearly show that the LICI increases the electronic excitation of the diatom. In particular for weak laser fields this effect is very significant. Our prediction of the LICI’s effect on the alignment of diatomic molecules can be confirmed by a two-laser experiment. Here, the first laser should have weak intensity and its duration should be sufficiently long as to align the molecules. The wavelength should be tuned in such a way as to ensure that the initial nuclear wavepacket has a significant amplitude at the internuclear distance corresponding to the LICI. The second laser pulse should be strong to produce measurable high-order harmonics. The high-order harmonic generation spectra should be measured as a function of the time delay between the two laser pulses, and are predicted to give an experimental evidence for the LICI effect on the alignment.

Laser-driven nonlinear cluster dynamics

Laser excitation of nanometer-sized atomic and molecular clusters offers various opportunities to explore and control ultrafast many-particle dynamics. Whereas weak laser fields allow the analysis of photoionization, excited-state relaxation, and structural modifications on these finite quantum systems, large-amplitude collective electron motion and Coulomb explosion can be induced with intense laser pulses. This review provides an overview of key phenomena arising from laser-cluster interactions with focus on nonlinear optical excitations and discusses the underlying processes according to the current understanding. A brief general survey covers basic cluster properties and excitation mechanisms relevant for laser-driven cluster dynamics. Then, after an excursion in theoretical and experimental methods, results for single- and multiphoton excitations are reviewed with emphasis on signatures from time- and angular resolved photoemission. A key issue of this review is the broad spectrum of phenomena arising from clusters exposed to strong fields, where the interaction with the laser pulse creates short-lived and dense nanoplasmas. The implications for technical developments include the controlled generation of ion, electron, and radiation pulses, as will be addressed along with corresponding examples. Finally, future prospects of laser-cluster research as well as experimental and theoretical challenges are discussed.

Emergence of electromagnetically induced absorption in a perturbation solution of optical Bloch equations

We study phenomenon of electromagnetically induced absorption (EIA) in the Hanle configuration by applying a perturbative method to solve linear system of optical Bloch equations (OBEs) for the case of closed Fg = 1 → Fe = 2 transition. The method is applied assuming stationary case and a weak laser fields (Ω ≪ Γ, i.e., Rabi frequency small compared to spontaneous emission rate). This way, we calculate (both numerically and analytically) higher order corrections to density matrix. Odd corrections give contributions to optical coherences, while even corrections contribute to populations and Zeeman coherences. The method gives insight into mechanism of transfer of coherences and transfer of populations between Zeeman sublevels. We have found that the ground-state coherences (2nd correction to coherences) are crucial for the 4th correction to the change of populations which brings EIA type behavior of the Hanle spectrum. Using exact analytical expressions we further discuss further the role of decoherence of the ground-state sublevels when forming EIA.

Perturbative Solution of Optical Bloch Equations for Analysis of Electromagnetically Induced Absorption

We study phenomenon of electromagnetically induced absorption in the Hanle configuration by solving time-dependent optical Bloch equations for the case of the closed multilevel Fg = 1 → Fe = 2 transition. Our model gives optical Bloch equations as a non-homogeneous system of ordinary linear differential equations. For weak laser fields (Ω ? Γ i.e. Rabi frequency small compared to spontaneous emission rate), a perturbative method to solve linear differential equations can be applied. Perturbative method is realized by solving (in the time-domain) higher-order corrections to the density matrix which in the sum converge to the exact solution of optical Bloch equations. By its form, each successive correction is also system of ordinary linear differential equations which depends on the solution of previous ones. Corrections are partitioned such that odd give corrections to optical coherences, while even give corrections to populations and Zeeman coherences. We present numerical results for the behavior of density matrix elements with successive corrections, and compare them with exact solution of optical Bloch equations. Electromagnetically induced absorption is observed as a 4th and higher (even) correction to populations, when behavior in respect to both time and magnetic field is viewed. Since in our method each correction depends on the solution of previous ones, we can analyze how (through mechanism of transfer of coherences and transfer of populations between Zeeman sublevels) electromagnetically induced absorption is formed. We also discuss qualitative differences in the behavior (with respect to time) of certain density matrix elements for magnetic fields “inside” and “outside” electromagnetically induced absorption resonance.

Resonant interaction of femtosecond radiation with a cloud of cold 87Rb atoms

The resonant interaction of 87Rb atoms in a magneto-optical trap with femtosecond laser radiation in the spectral range 760–820 nm has been investigated experimentally. It has been demonstrated that femtosecond laser radiation with a spectral width of 10 nm interacts with an atomic ensemble as a set of spectrally narrow modes and as an ionizing laser field simultaneously. The dynamics of trap loading in the presence of ionization by femtosecond radiation has been studied, and the 5D5/2 level population produced by an additional weak laser field has been measured.

Forces-induced pinpoint denaturation of short DNA

A method that can pinpoint control DNA denaturation is reported. In the single molecule experiment using spFRET, DNA adhered on a quartz surface is acted upon by both a weak laser field force and a fast temporal mechanical force. The experiment showed that increasing strengths of laser power result in increasing percentage of denatured DNA; different mechanical forces produce different numbers of DNA opening. Besides the method’s simplicity and convenience for DNA melting, its crucial advantage and potential application is the ability to denature DNA at specified locations, i.e., a weak laser and a fast temporal mechanical force can be used in pinpoint denaturation of short DNA.

Dynamic Chirp Control and Pulse Compression for Attosecond High-Order Harmonic Emission

We propose a scheme to compensate dynamically the intrinsic chirp of the attosecond harmonic pulses. By adding a weak second harmonic laser field to the driving laser field, the chirp compensation can be varied from the negative to the positive continuously by simply adjusting the relative time delay between the two-color pulses. Using this technique, the compensation of the negative chirp in harmonic emission is demonstrated experimentally for the first time and the nearly transform-limited attosecond pulse trains are obtained.

Quantum interference and phase-dependent fluorescence spectrum of a four-level atom with antiparallel dipole moments

We investigate the effects of spontaneously generated interference on the spectrum of quantum fluctuations in phase quadratures of resonant fluorescence emitted from the transition of j = 1/2 to j = 1/2 of a monochromatically driven four-level atom with antiparallel dipole moments. It is found that the spectrum exhibits obvious characteristics of quantum interference in both cases of weak and strong laser fields. For the Zeeman-degenerate system, strong radiation squeezing in weak atomic excitation can occur at the central frequency of the spectrum, which is quite different from the case without consideration of the interference. Moreover, when we apply an external magnetic field to the atom, we find that the quantum interference can lead to a narrowing spectrum with much stronger squeezing by adjusting the magnetic field strength. These results suggest that the phase-dependent fluorescence spectrum can serve as a probe of the quantum interference effects in a realistic system such as a trapped 198Hg+ ion or charged quantum dots.

Efficient Calculation of Time- and Frequency-Resolved Four-Wave-Mixing Signals

"Four-wave-mixing" is the generic name for a family of nonlinear electronic and vibrational spectroscopies. These techniques are widely used to explore dissipation, dephasing, solvation, and interstate coupling mechanisms in various material systems. Four-wave-mixing spectroscopy needs a firm theoretical support, because it delivers information on material systems indirectly, through certain transients, which are measured as functions of carrier frequencies, durations, and relative time delays of the laser pulses. The observed transients are uniquely determined by the three-pulse-induced third-order polarization. There exist two conceptually different approaches to the calculation of the nonlinear polarization. In the standard perturbative approach to nonlinear spectroscopy, the third-order polarization is expressed in terms of the nonlinear response functions. As the material systems become more complex, the evaluation of the response functions becomes cumbersome and the calculation of the signals necessitates a number of approximations. Herein, we review alternative methods for the calculation of four-wave-mixing signals, in which the relevant laser pulses are incorporated into the system Hamiltonian and the driven system dynamics is simulated numerically exactly. The emphasis is on the recently developed equation-of-motion phase-matching approach (EOM-PMA), which allows us to calculate the three-pulse-induced third-order polarization in any phase-matching direction by performing three (with the rotating wave approximation) or seven (without the rotating wave approximation) independent propagations of the density matrix. The EOM-PMA is limited to weak laser fields (its domain of validity is equivalent to the approach based on the third-order response functions) but allows for arbitrary pulse durations and automatically accounts for pulse-overlap effects. As an illustration, we apply the EOM-PMA to the calculation of optical three-pulse photon-echo two-dimensional (2D) signals for a generic model system, which represents a characteristic photophysical dynamics of large molecules or chromophores in condensed phases. The EOM-PMA is easy to implement and can straightforwardly be incorporated into any computational scheme, which provides the time-dependent density matrix or wave function of the material system of interest. In particular, EOM-PMA-based computer codes can efficiently be implemented on parallel computers. The EOM-PMA facilitates considerably the computation of four-wave-mixing signals and 2D spectra, in both vibrational and electronic spectroscopy. The EOM-PMA can be extended to higher order optical responses, e.g., heterodyned 3D IR, transient 2D IR, and other six-wave-mixing techniques.

Time-evolution operator method for non-Markovian density matrix propagation in time and space representation: Application to laser association of OH in an environment

An efficient method for the numerical solution of a non-Markovian, open-system density matrix equation of motion in coordinate representation is developed. We apply the scheme to model simulations of the laser-assisted $\mathrm{O}+\mathrm{H}\ensuremath{\rightarrow}\mathrm{O}\mathrm{H}$ association reaction in an environment. The suggested approach is based on the application of the time-evolution operator to the ``closed-system'' part of the overall Hamiltonian and transformation of the open-system equation of motion to the Heisenberg picture suitable for numerical propagation. A dual role of the system-environment coupling with respect to the infrared (ir) laser-driven association of OH is demonstrated: the association probability is increased due to the coupling at relatively weak laser fields, but decreased at strong laser fields. Moreover, at a certain strength of the ir laser field, the association probability does not depend on the strength of the system-bath coupling at all.

Propagation property of ultra-short laser pulses in multi-level quantum system

The propagation property of an ultrashort pulse in multi-level quantum system has been investigated with numerical method. A strong absorption is observed and its degree depends on the characteristic time of quantum system. For rather weak laser field, the self-induced transparency can still be observed with proper pulse area of the input ultrashort laser. When the ultrashort laser pulse becomes stronger, it will be split, and its basic split unit （i.e. the minimum area of a stably propagating laser pulse） A0 is not the same as that of two-level quantum system, which depends on the number of the excited states and their dipoles. Furthermore, after a rather long propagating distance, there only remains a shorter but more intense sub-pulse with an area of A0.