Floquet theory for short laser pulses

We develop adiabatic perturbation theory for quantum systems responding to short laser pulses, with or without a frequency chirp. Our approach rests on lifting the time-dependent Schr?dinger equation to an extended Hilbert space, then applying standard perturbational techniques to Floquet states in this extended space, and finally projecting back to the physical Hilbert space. The same strategy also allows us to construct superadiabatic bases for monitoring the quantum evolution in the course of a pulse. These bases provide a diagnostic tool for improving the efficiency of pulse-induced population transfer. The formalism is applied to the selective excitation of molecular vibrational states by chirped laser pulses, which exploit either successive single-photon resonances or a multiphoton resonance, and by a STIRAP-like process. Received: 23 June 1998 / Revised: 18 August 1998 / Accepted: 25 August 1998     

Resonance fluorescence spectrum of a three-level atom driven by coherent and stochastic fields

The dressed-state populations and the resonance fluorescence spectrum of a V-type three-level atom driven by a strong coherent field and a weak stochastic one simultaneously are investigated. There can be significant population inversion due to the effect of the stochastic field. The atomic resonance fluorescence spectrum can be controlled by adjusting the frequency difference between the coherent field and the stochastic one and the coherent Rabi frequency. Peak suppression and line narrowing occur under appropriate conditions. Received 23 June 2000 and Received in final form 18 January 2001     

Wavelength control in Er <Emphasis Type="Bold">3+</Emphasis>-doped fluoride glasses laser by a coherent field

A five-level system to control the wavelength of the in-line amplifier by the quantum interference is proposed. It is found that the gains of the first and the second probe can be adjusted by changing the coherent field and the incoherent pumping. The new scheme may find its application in optical switch and optical communications. Received 9 October 2002 Published online 24 April 2003 RID="a" ID="a"e-mail: qol@mail.jlu.edu.cn     

High-order harmonic generation from organic molecules in ultra-short pulses

We have studied high-order harmonic generation (HHG) from organic molecules irradiated with near-infrared high intensity laser pulses of 70 fs and 240 fs duration. The molecular systems studied were the aromatics benzene and naphthalene and the alkanes cyclopropane and cyclohexane (cyclic) and n-hexane (linear). Harmonic intensities were measured both as a function of laser intensity (in the range 5×10¹³-5×10¹⁵ W cm^-2) and as a function of ellipticity of the laser field polarisation. The results were compared with those from the xenon atom. For 70 fs pulses, harmonic generation from the organic systems was similar to that of xenon, revealing an atom-like behaviour for molecules when the laser pulse duration is shorter than the fragmentation timescale of the molecule. We note significant differences between molecules with respect to HHG efficiencies and the suppression of HHG in larger species. We discuss these differences in the context of the molecular properties, electronic structure and behaviour of ionisation and fragmentation that result in enhancement of field ionisation in larger systems. Study of the polarisation ellipticity dependence of HHG shows that the harmonic yield in molecules is less sensitive to the polarisation than for atoms (xenon). This is consistent with the expected behaviour given the larger recollision cross-section presented by the core in the molecular system compared to the atom. Our results suggest that study of HHG from molecules exposed to ultra-short pulses is potentially a powerful tool for understanding the electron dynamics of molecules exposed to an intense field. Received 14 September 2000 and Received in final form 6 December 2000     

An electromagnetic wave propagation in a non-uniform plasma controlled by EIT

We investigate the conditions in which the propagation of an electromagnetic wave is changed from transparency to cutoff in a non-uniform plasma. The allowed frequency range of the driving wave is obtained for the case that the probe frequency is above the plasma frequency. The effect of the power of the driving field on the range is analyzed. Received 23 May 2001     

Distribution of local entropy in the Hilbert space of bi-partite quantum systems: origin of Jaynes' principle

For a closed bi-partite quantum system partitioned into system proper and environment we interpret the microcanonical and the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible pure-state trajectories are confined to certain regions in Hilbert space. We show that in a properly defined thermodynamical limit almost all states within those accessible regions represent states of some maximum local entropy. For the microcanonical condition this dominant state still depends on the initial state; for the canonical condition it coincides with that defined by Jaynes' principle. It is these states which thermodynamical systems should generically evolve into. Received 13 June 2002 / Received in final form 14 November 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: jochen@theol.physik.uni-stuttgart.de     

Effects of relative phase in an open ladder system without incoherent pumping

We studied effects of the relative phase between the probe and driving fields on the absorption and dispersion properties in an open three-level ladder system with spontaneously generated coherence but without incoherent pumping. It is shown that by the phase controlling, switching from absorption to lasing without inversion (LWI) and enhancing remarkablely LWI gain can be realized; large index of refraction with zero absorption and the electromagnetically induced transparency can be obtained. We also find that varying the atomic injection and exit rates has a considerable influence on the phase dependent-absorption property of the probe field, existent of the atomic injection and exit rates gives the necessary condition of the realization of LWI, getting LWI is impossible in the corresponding closed system without incoherent pumping.     

A local-ether wave equation and speed-dependent mass and quantum energy

The east-west directional anisotropy in clock rate observed in the Hafele-Keating experiment with circumnavigation atomic clocks is commonly ascribed to the special relativity. In this investigation, based on the local-ether wave equation, an entirely different interpretation of this anisotropy is presented by showing that the clock-rate variation can originate from an intrinsic quantum property of the atom. For a harmonic-like wavefunction, the local-ether wave equation leads to a first-order time evolution equation similar to Schr?dinger's equation. However, the time derivative incorporates a speed-dependent factor similar to that in the Lorentz mass-variation law. Consequently, the quantum energy, the transition frequency, and hence the atomic clock rate decrease with the atom speed by this speed-dependent mass-variation factor. According to the local-ether model, the speed is referred specifically to a geocentric or heliocentric inertial frame for an earthbound or interplanetary clock, respectively. It is shown that this restriction on reference frame is actually in accord with the various experimental results of the anisotropy and the clock-rate difference in the Hafele-Keating experiment, the synchronism and the clock-rate adjustment in GPS (global positioning system), and of the spatial isotropy in the Hughes-Drever experiment. Moreover, the switching of the unique reference frame is in accord with the frequency-shift formulas adopted in earthbound and interplanetary spacecraft microwave links. Meanwhile, the local-ether model predicts a constant deviation in frequency shift from the calculated result reported in an interplanetary spacecraft link. This discrepancy then provides a means to test the local-ether wave equation. Received 11 December 2000 and Received in final form 20 August 2001     

Atomic coherent states studied by virtue of the EPR entangled state and their Wigner functions

Based on the newly constructed Einstein, Podolsky and Rosen (EPR) entangled state representation we introduce macroscopic classical functions associated with atomic coherent state τ with angular momentum value j. These functions are proportional to the ordinary one-variable Hermite polynomials of order 2j. The corresponding Wigner quasiprobability function for τ in phase space is also derived which turns out to be a two-variable Hermite polynomial H _{2j, 2j}. In so doing, a new classical-quantum correspondence scheme for angular momentum system is established. Received 7 August 2002 / Received in final form 14 December 2002 Published online 24 April 2003 RID="a" ID="a"Work supported by the National Natural Science Foundation of China under grant 10175057. RID="b" ID="b"e-mail: fhym@sjtu.edu.en     

Phase and amplitude control of the inversionless gain in a microwave-driven <Emphasis Type="Bold">Λ</Emphasis>-type atomic system

In order to achieve the phase-sensitive probe gain without population inversion, we investigate a three-level Λ-type atomic system driven by a coherent field and a microwave field. It is shown that, by modulating the relative phase of applied fields, we can obtain quite high inversionless gain at different probe detunings and change the gain behavior of the probe correspondingly. We find that amplitudes of the coherent field and the microwave field are also important factors that can result in different gain behavior of the probe. Here, we use the microwave field to induce the quantum coherence between the two ground levels, which is necessary for phase-sensitive effects, since it can result in the interference between two different transition channels. Received 20 June 2002 / Received in final form 5 December 2002 Published online 4 March 2003     

Non-adiabatic quantum molecular dynamics: General formalism and case study H<Subscript>2</Subscript><Superscript>+</Superscript> in strong laser fields

In Rydberg atoms subject to static and harmonic collinear electric fields, intrashell transition can be induced by the first order perturbation from a small perpendicular electric or magnetic field, or by effects of the second order in the major fields. Both mechanisms lead to resonances that are suppressed under certain conditions, and high-frequency interference oscillations in case of non-adiabatic field switching. Recent measurements of microwave ionization signals show very rich and fascinating structures similar to the ones predicted for intrashell mixing. We show that the observed ionization structures may be explained by diabatic electric-field ionization and the consistent use of perturbation theory for intrashell mixing. In particular, the dominant oscillation frequency is successfully interpreted in terms of interference between first and second order transition amplitudes. New predictions are provided. The present approach gives a comprehensive picture of intrashell transitions, which may be tested in future experiments designed to observe such transitions directly. Received 2 May 2002 / Received in final form 23 September 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: Valentin.Ostrovsky@pobox.spbu.ru RID="b" ID="b"e-mail: horsdal@ifa.au.dk     

Comprehensive experimental test of quantum erasure

In an interferometer, path information and interference visibility are incompatible quantities. Complete determination of the path will exclude any possibility of interference, rendering zero visibility. However, it is, under certain conditions, possible to trade the path information for improved (conditioned) visibility. This procedure is called quantum erasure. We have performed such experiments with polarization-entangled photon pairs. Using a partial polarizer, we could vary the degree of entanglement between the object and the probe. We could also vary the interferometer splitting ratio and thereby vary the a priori path predictability. This allowed us to test quantum erasure under a number of different experimental conditions. All experiments were in good agreement with theory. Received 15 July 2001 and Received in final form 30 November 2001     

Floquet study of ionization and high-order harmonic generation for a hydrogen atom in high-frequency laser fields

In this paper, we investigate the dynamics of a hydrogen atom in high-frequency (several atomic units) super strong (up to several tens of atomic units) laser fields within the high frequency Floquet theory framework. The ionization rate, ionization spectrum, angular distribution and high-order harmonic generation are all investigated. Our studies reveal the universal behavior of the total ionization rate, excess-photon ionization spectrum and angular distribution of the ionization rate in the stabilization regime, and achieve a deep insight into the dynamics of high-order harmonic generation in the stabilization regime. Received 6 June 2001 and Received in final form 31 August 2001     

Coherent population trapping involving Rydberg states in xenon probed by ionization suppression

We report the observation of pronounced coherent population trapping and dark resonances in Rydberg states of xenon. A weak two-photon coupling with radiation of = 250 nm is induced between the 5p^{6 1} S ₀ ground state of xenon and state 5p ⁵6p[1/2]₀, leading to (2+1) resonantly enhanced three-photon ionization. The state 5p ⁵6p[1/2]₀ is strongly coupled by radiation with ≃ 600 nm to 5p ⁵ ns[J _C]₁ or 5p ⁵ nd[J _C]₁ Rydberg states with principal quantum numbers n in the range 18 ?n? 23 and with the rotational quantum number of the ionic core J _C = 1/2 or J _C = 3/2. The ionization is monitored through observation of the photoelectrons with an energy resolution ΔE = 150 meV which is sufficient to distinguish the ionization processes into the two ionization continua. Pronounced and robust dark resonances are observed in the ionization rate whenever is tuned to resonance with one of the ns- or nd-Rydberg states. The dark resonances are due to efficient population trapping in the atomic ground state 5p^{6 1} S ₀ through the suppression of excitation of the intermediate state 5p ⁵6p[1/2]₀. The resolution is sufficient to resolve the hyperfine structure of the ns-Rydberg levels for odd xenon isotopes. The hyperfine splitting does not vary significantly with n in the given range. Results from model calculations taking the natural isotope abundance into account are in good agreement with the observed spectral structures. Pronounced dark resonances are also observed when the dressing radiation field with is generated from a laser with poor coherence properties. The maximum reduction of the ionization signal clearly exceeds 50%, a value which is expected to be the maximum, when the dip is caused by saturation of the transition rate between the intermediate and the Rydberg state due to incoherent radiation. This work demonstrates the potential of dark resonance spectroscopy of high lying electronic states of rare gas atoms. Received 7 May 2000 and Received in final form 25 June 2001     

Algebraic methods in quantum mechanics: from molecules to polymers

We present a brief review of algebraic techniques developed and applied in molecular spectroscopy in the last five years. We also outline perspectives for new applications of the Lie algebraic method in the first decade of the new century. Received 21 November 2001     

Instability of the tunneling destruction effect in a quasi-periodically driven two-level system

Here we consider the dynamics of a two-level system under an external time-dependent field. We show that in the case of a bichromatic field the dynamical localization effect is strongly sensitive with respect to the commensurability of the driving frequencies. Received 8 May 2002 / Received in final form 4 July 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: Sacchetti@unimo.it     

Infinite chain of different deltas: A simple model for a quantum wire

We present the exact diagonalization of the Schr?dinger operator corresponding to a periodic potential with N deltas of different couplings, for arbitrary N. This basic structure can repeat itself an infinite number of times. Calculations of band structure can be performed with a high degree of accuracy for an infinite chain and of the correspondent eigenlevels in the case of a random chain. The main physical motivation is to modelate quantum wire band structure and the calculation of the associated density of states. These quantities show the fundamental properties we expect for periodic structures although for low energy the band gaps follow unpredictable patterns. In the case of random chains we find Anderson localization; we analize also the role of the eigenstates in the localization patterns and find clear signals of fractality in the conductance. In spite of the simplicity of the model many of the salient features expected in a quantum wire are well reproduced. Received 24 June 2002 Published online 29 November 2002     

Localization of a macroscopic object induced by the factorization of internal adiabatic motion

To account for the phenomenon of quantum decoherence of a macroscopic object, such as the localization and disappearance of interference, we invoke the adiabatic quantum entanglement between its collective states (such as that of the center-of-mass (CM)) and its inner states based on our recent investigation. Under the adiabatic limit where motion of the CM does not excite the transition of inner states, it is shown that the wave function of the macroscopic object can be written as an entangled state with correlation between adiabatic inner states and quasi-classical motion configurations of the CM. Since the adiabatic inner states are factorized with respect to each component of the macroscopic object, this adiabatic separation can induce the quantum decoherence. This observation thus provides us with a possible solution to the Schr?dinger cat paradox. Received 24 October 2000 and Received in final form 8 March 2001     

Spectral determinant on graphs with generalized boundary conditions

The spectral determinant of the Schr?dinger operator ( - Δ + V(x)) on a graph is computed for general boundary conditions. (Δ is the Laplacian and V(x) is some potential defined on the graph). Applications to restricted random walks on graphs are discussed. Received 9 July 2001