Coherent Control Scheme Research Articles

Quantum Control for Broadband Attosecond Pulse Generation

In our work, we propose a scheme for coherent control the HHG with an ultrashort laser pulse in combination with a controlling pulse. It is shown that this method can significantly modulate the electron dynamics and a broadband supercontinuous high harmonics can be generated. Then an isolated sub-100 attosecond pulse can be obtained, which allows one to measure a wide range of ultrafast dynamics not normally accessible before.

Effect of the Gouy phase on the coherent phase control of chemical reactions

We show how the spatial phase of a focused laser beam may be used as a tool for controlling the branching ratio of a chemical reaction. Guoy discovered [Acad. Sci., Paris, C. R. 110, 1250 (1890)] that when an electromagnetic wave passes through a focus its phase increases by pi. In a coherent control scheme involving the absorption of n photons of frequency omega(m) and m photons of frequency omega(n), the overall phase shift produced by the Gouy phase is (n-m)pi. At any given point in space, this phase shift is identical for all reaction products. Nevertheless, if the yields for different reaction channels have different intensity dependencies, the Gouy phase produces a net phase lag between the products that varies with the axial coordinate of the laser focus. We obtain here analytical and numerical values of this phase as the laser focus is scanned across the diameter of the molecular beam, taking into account the Rayleigh range and astigmatism of the laser beam and saturation of the transition. We also show that the modulation depth of the interference pattern may be increased by optimizing the relative intensities of the two fields.

Time-Resolved Investigation of Coherently Controlled Electric Currents at a Metal Surface

Studies of current dynamics in solids have been hindered by insufficiently brief trigger signals and electronic detection speeds. By combining a coherent control scheme with photoelectron spectroscopy, we generated and detected lateral electron currents at a metal surface on a femtosecond time scale with a contact-free experimental setup. We used coherent optical excitation at the light frequencies omega(a) and omega(a)/2 to induce the current, whose direction was controlled by the relative phase between the phase-locked laser excitation pulses. Time- and angle-resolved photoelectron spectroscopy afforded a direct image of the momentum distribution of the excited electrons as a function of time. For the first (n = 1) image-potential state of Cu(100), we found a decay time of 10 femtoseconds, attributable to electron scattering with steps and surface defects.

Transient population and polarization gratings induced by(1+1)-dimensional ultrashort dipole soliton

An ultrafast transient population grating induced by a (1+1)-dimensional, ultrashort dipole soliton is demonstrated by solving the full-wave Maxwell-Bloch equations. The number of lines and the period of the grating can be controlled by the beam waist and the area of the pulse. Of interest is that a polarization grating is produced. A coherent control scheme based on these phenomena can be contemplated as ultrafast transient grating techniques.

Coherent Control of Vacuum Squeezing in the Gravitational-Wave Detection Band

We propose and demonstrate a coherent control scheme for stable phase locking of squeezed vacuum fields. We focus on sideband fields at frequencies from 10 Hz to 10 kHz, which is a frequency regime of particular interest in gravitational-wave detection and for which conventional control schemes have failed so far. A vacuum field with broadband squeezing covering this entire band was produced using optical parametric oscillation and characterized with balanced homodyne detection. The system was stably controlled over long periods utilizing two coherent but frequency shifted control fields. In order to demonstrate the performance of our setup the squeezed field was used for a nonclassical sensitivity improvement of a Michelson interferometer at audio frequencies.

Ac Stark-mediated quantum control with femtosecond two-color laser pulses

A critical dependence of the quantum interference on the optical Stark spectral shift produced when two-color laser pulses interact with a two-level medium is observed. The four-wave mixing of two ultrashort phase-locked $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ laser pulses propagating coherently in a two-level system depends on the pulses' relative phase. The phase dominating the efficiency of the coupling to the anti-Stokes Raman component is found to be determined by the sign of the total ac Stark shift induced in the system, in such a way that the phase sensitivity disappears precisely where the ac Stark effect due to both pulses is compensated. A coherent control scheme based on this phenomenon can be contemplated as the basis for nonlinear optical spectroscopy techniques.

Freezing phase scheme for fast adaptive control and its application to characterization of femtosecond coherent optical pulses reflected from semiconductor saturable absorber mirrors

We report on the development of a freezing phase scheme for complete-field characterization and adaptive coherent control with a femtosecond pulse shaper. The operational principle is based on a concept that the highest peak intensity will correspond to a frozen phase state of all spectral components involved in a coherent optical pulse. Our experimental and theoretical results reveal this new scheme to be fast and immune to the noise and laser power fluctuation. The freezing phase method has been used to investigate three types of semiconductor saturable absorber Bragg reflector (SBR). The optical pulses reflected from the SBR can be distorted in the spectral phase by a minor structural change of the SBR devices and can be clearly resolved with our method. The technique is useful for a variety of applications that require complete-field characterization and adaptive coherent control on the same setup.

Strong coupling in a single quantum dot–semiconductor microcavity system

Cavity quantum electrodynamics, a central research field in optics and solid-state physics, addresses properties of atom-like emitters in cavities and can be divided into a weak and a strong coupling regime. For weak coupling, the spontaneous emission can be enhanced or reduced compared with its vacuum level by tuning discrete cavity modes in and out of resonance with the emitter. However, the most striking change of emission properties occurs when the conditions for strong coupling are fulfilled. In this case there is a change from the usual irreversible spontaneous emission to a reversible exchange of energy between the emitter and the cavity mode. This coherent coupling may provide a basis for future applications in quantum information processing or schemes for coherent control. Until now, strong coupling of individual two-level systems has been observed only for atoms in large cavities. Here we report the observation of strong coupling of a single two-level solid-state system with a photon, as realized by a single quantum dot in a semiconductor microcavity. The strong coupling is manifest in photoluminescence data that display anti-crossings between the quantum dot exciton and cavity-mode dispersion relations, characterized by a vacuum Rabi splitting of about 140 microeV.

Controlling continuum harmonic generation with attosecond pulses

Photo-ionization and high-order harmonic generation (HOHG) in molecular systems under the combined action of infrared femtosecond (fs) and UV attosecond (as) intense laser pulses are investigated numerically for a one-dimensional non-Born–Oppenheimer H+2 ion. It is shown that such a coherent control scheme of fs–as ionization leads to significant enhancement of HOHG, with efficiencies exceeding the one obtained from a single fs pulse by several orders of magnitude. The basic mechanism for this enhancement is established as enhanced ionization and control of the recollision of a high-energy non-zero-velocity ionized electron, as compared to tunneling ionization models where the ionized electron has initial zero velocity. The combined superposition of fs–as pulses results in broad HOHG spectra with a large continuum near the cutoff, thus providing a new source for synthesizing new X-ray (vacuum ultraviolet) as pulses.

Manipulating electron wave packets

Technological advances over the last decade have led to a significant amount of research being aimed at investigating the time-dependent behaviour of electron wave packets. The ultimate goal is to generate customized wave packets that can control electronic processes in atoms and molecules. Coherent control schemes involving electron wave packets have proved to be of fundamental importance in our quest to understand quantum phenomena. Exotic quantum states such as the Schro¨dinger cat states have been excited and studied. The wavefunction of a wave packet may now be characterized completely and manipulated into a new form. Autoionization of electron dynamics in complex two-electron systems can be suppressed. Electron wave packets have been excited in molecules. This review provides an overview of the relatively new and rapidly expanding field of electron wave-packet manipulation with particular focus on the experimental achievements and their implications.

Manipulating electron wave packets

Technological advances over the last decade have led to a significant amount of research being aimed at investigating the time-dependent behaviour of electron wave packets. The ultimate goal is to generate customized wave packets that can control electronic processes in atoms and molecules. Coherent control schemes involving electron wave packets have proved to be of fundamental importance in our quest to understand quantum phenomena. Exotic quantum states such as the Schro¨dinger cat states have been excited and studied. The wavefunction of a wave packet may now be characterized completely and manipulated into a new form. Autoionization of electron dynamics in complex two-electron systems can be suppressed. Electron wave packets have been excited in molecules. This review provides an overview of the relatively new and rapidly expanding field of electron wave-packet manipulation with particular focus on the experimental achievements and their implications.

Coherent control of second harmonic generation using spectrally phase coded femtosecond waveforms

We report the demonstration of coherent control of second harmonic generation (SHG) with over three orders of magnitude contrast in the SHG yield. Under conditions of large group-velocity mismatch and narrow phase matching bandwidth, we show that SHG can serve (in the perturbative limit) as a nonlinear optical but classical analogue for quantum mechanical two-photon transitions in atomic media, with advantages in efficiency and ease of implementation. Our coherent control scheme results in a spectral phase correlator for ultrashort pulse waveforms, which may have applications in novel high-bandwidth optical communication schemes. We demonstrate a set of different waveforms with similar strong control yields by introducing families of binary phase codes taken from communication theory into the coherent control process. The response to these waveforms under certain nonideal situations is also studied.

Quantum coherent control of Coulomb enhancement by two‐color pulseshaping

AbstractPulse shaping based on two‐color optical excitation is shown to provide a versatile coherent control scheme for electron inter(sub)band transitions in semiconductors. In semiconductor heterostructures, this control scheme provides both phase‐sensitive absorption and exciton formation, as well as interwell tunneling of photoexcited charge carriers. Our microscopic analysis shows that this control mechanism is due to a combination of many‐body effects arising from the coherent part of the electron–electron Coulomb interaction and pulse‐shaping arising from the spectral overlap between the two pulses. This control mechanism is applicable to a wide range of semiconductors, both bulk and low‐dimensional structures, and may have a practical application for phase sensitive absorbers and the generation of THz radiation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Femtosecond pump–probe photoelectron spectroscopy on Na2: a tool to study basic coherent control schemes

Femtosecond pump–probe photoelectron spectroscopy has become a common tool in ultrafast gas-phase science because of its sensitivity both to structural and electronic changes in a molecule upon excitation. Here a summary and extended discussion of our experiments is presented. We focus on the potential of this method to study basic femtosecond coherent control schemes. Multi-photon excitation of the Na2 molecule with femtosecond laser pulses leads to preparation of vibrational wave packets. Mapping of the vibrational wave-packet dynamics by time-resolved photoelectron spectroscopy offers the high spatial and temporal resolution required to investigate a variety of laser-control parameters in great detail. Besides an illustration of the Tannor–Kosloff–Rice scheme we demonstrate electronic transitions at Franck–Condon forbidden internuclear distances due to the intensity of the applied laser pulses. Further we discuss the influence of simple phase-modulated (linearly chirped) laser pulses on a molecular multi-photon process. An enhanced population transfer is derived due to synchronization of the wave-packet motion on an electronic potential to an appropriate chirp of the laser pulses. In addition, the influence of the temporal profile on the population transfer and the role of the pulse duration are studied.

Spectral phase correlation of coded femtosecond pulses by second-harmonic generation in thick nonlinear crystals

We demonstrate a novel all-optical scheme for measuring the correlation of spectrally phase-coded ultrashort optical waveforms that uses second-harmonic generation (SHG) in long, periodically poled lithium niobate crystals. The SHG yield can be controlled over a range of ~30 dB, depending on the correlation of the applied phase codes. Such a spectral phase correlator has applications for ultrashort-pulse optical code-division multiple-access networking and could serve as a nonlinear optical but classical analog for certain schemes for coherent quantum control of multiphoton processes.

Coherent control of electron intersubband transitions by frequency-detuned light fields

We present a brief overview over some of our recent theoretical results regarding coherent control in semiconductor heterostrutures. Three potential schemes for optical coherent control of electron intersubband transitions in semiconductor heterostructures are reviewed. They use the relative phase between two external light fields to manipulate fundamental physical properties, such as absorption, optical gain, final-state population, phonon emission rates, and emission of THz radiation. In this paper we focus on the coherent control of absorption (exciton formation) using two frequency-detuned light fields in asymmetric GaAs/AlGaAs double wells. We show that in the short-pulse regime the change of relative phase amounts to pulse shaping which, in conjunction with excitonic effects, allows substantial control of inter(sub)band transitions. In the long-pulse regime this phase sensitivity is lost, however, charge oscillations between wells can be induced.

A Simple Theory of Optimal Coherent Control

By combining the theories of optimal control and coherent control, we derive an analytical formulation to evaluate the optimal 1-photon and n-photon fields together with their relative phase and intensity in the optimal “1 + n”-coherent control scheme. The optimal coherent control exploits tailored light pulses to produce the best overlap with a predefined nuclear target in an electronically degenerate region. It also exploits explicitly the quantum interference between two optimal excitation pathways to achieve the product electronic selectivity. Numerical demonstrations are carried out to selectively control a minimum-uncertainty outgoing wave packet target in a molecular system. The electronically degenerate byproduct is shown to be completely discriminated against via the destructive interference between two optimal excitation pathways. The target considered in this paper would neither be achievable via the conventional continuous-wave coherent control nor via a single optimal control pathway in the w...

Phase lag near the resonances in (ω1,ω3) coherent control

Molecular phases are computed near the resonances in the (ω1,ω3) coherent control scheme for excitations to predissociating final states. We show that the phase factors for the one- and three-photon transition amplitudes are identical, giving a vanishing molecular phase, when the intermediate manifolds consist only of discrete states and when the final continuum states do not interact. The phase lag between the dissociation products identically vanishes across the resonance in this case. On the other hand, when there is contribution of the intermediate continuum states, the imaginary part of the three-photon transition operator can give different phase factors for the one- and three-photon transition amplitudes, yielding very important effects of the molecular phase in (ω1,ω3) coherent control. It is also shown that couplings between the final continuum states can give different molecular phase for different product channels in the absence of the effects of the intermediate continuum states, exhibiting the phase lag of the products near resonances. We demonstrate that the phase lag may show minimum near the top of the resonance, as was observed in Gordon and co-workers’ recent observations [Zhu et al., Science 270, 77 (1995)] on the phase lag in HI coherent control experiments, indicating that the observed phase lag is due to the effects of the molecular phase.

On the molecular phase in coherent control

Systematic analysis is carried out for molecular phase in (ω1,ω3) coherent control scheme. Two mechanisms for nonzero molecular phase are proposed. It is shown that the imaginary part of the three-photon transition operator, which is due to the contribution of the intermediate continuua, can give different phase factors for the one- and three-photon transition amplitudes, yielding very important effects of molecular phase in (ω1,ω3) coherent control. We also show that the interactions between the final continuum states can result in nonzero molecular phase, when the intermediate states are discrete. These findings are discussed in relation to Gordon and co-workers’ recent observations [Zhu et al., Science 270, 77 (1995)] on phase lag.

Coherent control of molecular orientation

A coherent control scheme is proposed for the orientation of heteronuclear molecules by two-color phase-locked laser excitation. In the case of hexapole state-selected NO, a superposition of both negative and positive ground-state parity levels is formed, where the internuclear axis of the molecule is oriented along the laser polarization axis. The proposed scheme allows rotationally cold distributions of ground-state heteronuclear molecules to be macroscopically oriented, as in the “brute force” dc electric field orientation technique. Computer simulations show that for a typical 1 Σ ground-state diatomic molecule ( B rot = 0.32 cm −1) picosecond two-color phase-locked laser excitation can provide orientation during or after the laser pulse.