High-precision molecular wave-packet interferometry with HgAr dimers

Rydberg-State Double-Well Potentials of Van der Waals Molecules

Recent progress in studies of Rydberg double-well electronic energy states of MeNg (Me = 12-group atom, Ng = noble gas atom) van der Waals (vdW) molecules is presented and analysed. The presentation covers approaches in experimental studies as well as ab initio-calculations of potential energy curves (PECs). The analysis is shown in a broader context of Rydberg states of hetero- and homo-diatomic molecules with PECs possessing complex 'exotic' structure. Laser induced fluorescence (LIF) excitation spectra and dispersed emission spectra employed in the spectroscopical characterization of Rydberg states are presented on the background of the diverse spectroscopic methods for their investigations such as laser vaporization-optical resonance (LV-OR), pump-and-probe methods, and polarization labelling spectroscopy. Important and current state-of-the-art applications of Rydberg states with irregular potentials in photoassociation (PA), vibrational and rotational cooling, molecular clocks, frequency standards, and molecular wave-packet interferometry are highlighted.

Picosecond-Scale Ultrafast Many-Body Dynamics in an Ultracold Rydberg-Excited Atomic Mott Insulator

We report the observation and control of ultrafast many-body dynamics of electrons in ultracold Rydberg-excited atoms, spatially ordered in a three-dimensional Mott insulator (MI) with unity filling in an optical lattice. By mapping out the time-domain Ramsey interferometry in the picosecond timescale, we can deduce entanglement growth indicating the emergence of many-body correlations via dipolar forces. We analyze our observations with different theoretical approaches and find that the semiclassical model breaks down, thus indicating that quantum fluctuations play a decisive role in the observed dynamics. Combining picosecond Rydberg excitation with MI lattice thus provides a platform for simulating nonequilibrium dynamics of strongly correlated systems in synthetic ultracold atomic crystals, such as in a metal-like quantum gas regime.

Nonlocality-Enabled Pulse Management in Epsilon-Near-Zero Metamaterials

Ultrashort optical pulses are integral to probing various physical, chemical, and biological phenomena and feature in a whole host of applications, not least in data communications. Super- and subluminal pulse propagation and dispersion management (DM) are two of the greatest challenges in producing or counteracting modifications of ultrashort optical pulses when precise control over pulse characteristics is required. Progress in modern photonics toward integrated solutions and applications has intensified this need for greater control of ultrafast pulses in nanoscale dimensions. Metamaterials, with their unique ability to provide designed optical properties, offer a new avenue for temporal pulse engineering. Here an epsilon-near-zero metamaterial is employed, exhibiting strong nonlocal (spatial dispersion) effects, to temporally shape optical pulses. The authors experimentally demonstrate, over a wide bandwidth of tens of THz, the ability to switch from sub to superluminal and further to "backward" pulse propagation (±c/20) in the same metamaterial device by simply controlling the angle of illumination. Both the amplitude and phase of a 10 ps pulse can be controlled through DM in this subwavelength device. Shaping ultrashort optical pulses with metamaterials promises to be advantageous in laser physics, optical communications, imaging, and spectroscopy applications using both integrated and free-standing devices.

Electron Wave Packet Interference in Atomic Inner-Shell Excitation

We report the observation of quantum interference between electron wave packets launched from the inner-shell 4d orbital of the Xe atom. Using pairs of femtosecond radiation wave packets from a synchrotron light source, we obtain time-domain interferograms for the inner-shell excitations. This approach enables the experimental verification and control of the quantum interference between the electron wave packets. Furthermore, the femtosecond Auger decay of the inner-shell excited state is tracked. To the best of our knowledge, this is the first observation of wave packet interference in an atomic inner-shell process, and also the first time-resolved experiment on few-femtosecond Auger decay using a synchrotron light source.

Coherent control in the extreme ultraviolet and attosecond regime by synchrotron radiation

Quantum manipulation of populations and pathways in matter by light pulses, so-called coherent control, is currently one of the hottest research areas in optical physics and photochemistry. The forefront of coherent control research is moving rapidly into the regime of extreme ultraviolet wavelength and attosecond temporal resolution. This advance has been enabled by the development of high harmonic generation light sources driven by intense femtosecond laser pulses and by the advent of seeded free electron laser sources. Synchrotron radiation, which is usually illustrated as being of poor temporal coherence, hitherto has not been considered as a tool for coherent control. Here we show an approach based on synchrotron radiation to study coherent control in the extreme ultraviolet and attosecond regime. We demonstrate this capability by achieving wave-packet interferometry on Rydberg wave packets generated in helium atoms.

Synchrotron light sources have wide range of tunable parameters like frequency, intensity. Here the authors demonstrate quantum control of Rydberg states of helium using delay controlled XUV wavepackets generated from synchrotron radiation.

Weak-field coherent control of photodissociation in polyatomic molecules

A coherent control scheme is suggested to modify the output of photodissociation in a polyatomic system. The performance of the scheme is illustrated by applying it to the ultrafast photodissociation of CH₃I in the A-band. The control scheme uses a pump laser weak field that combines two pulses of a few femtoseconds delayed in time. By varying the time delay between the pulses, the shape of the laser field spectral profile is modulated, which causes a change in the initial relative populations excited by the pump laser to the different electronic states involved in the photodissociation. Such a change in the relative populations produces different photodissociation outputs, which is the basis of the control achieved. The degree of control obtained over different photodissociation observables, like the branching ratio between the two dissociation channels of CH₃I yielding I(²P_3/2) and I*(²P_1/2) and the fragment angular distributions associated with each channel, is investigated. These magnitudes are found to oscillate strongly with the time delay, with the branching ratio changing by factors between two and three. Substantial variations of the angular distributions also indicate that the scheme provides a high degree of control. Experimental application of the scheme to general polyatomic photodissociation processes should be straightforward.

Ultrafast Coherent Control of Condensed Matter with Attosecond Precision

Coherent control is a technique to manipulate wave functions of matter with light. Coherent control of isolated atoms and molecules in the gas phase is well-understood and developed since the 1990s, whereas its application to condensed matter is more difficult because its coherence lifetime is shorter. We have recently applied this technique to condensed matter samples, one of which is solid para-hydrogen ( p-H₂). Intramolecular vibrational excitation of solid p-H₂ gives an excited vibrational wave function called a "vibron", which is delocalized over many hydrogen molecules in a manner similar to a Frenkel exciton. It has a long coherence lifetime, so we have chosen solid p-H₂ as our first target in the condensed phase. We shine a time-delayed pair of femtosecond laser pulses on p-H₂ to generate vibrons. Their interference results in modulation of the amplitude of their superposition. Scanning the interpulse delay on the attosecond time scale gives a high interferometric contrast, which demonstrates the possibility of using solid p-H₂ as a carrier of information encoded in the vibrons. In the second example, we have controlled the terahertz collective phonon motion, called a "coherent phonon", of a single crystal of bismuth. We employ an intensity-modulated laser pulse, whose temporal envelope is modulated with terahertz frequency by overlap of two positively chirped laser pulses with their adjustable time delay. This modulated laser pulse is shined on the bismuth crystal to excite its two orthogonal phonon modes. Their relative amplitudes are controlled by tuning the delay between the two chirped pulses on the attosecond time scale. Two-dimensional atomic motion in the crystal is thus controlled arbitrarily. The method is based on the simple, robust, and universal concept that in any physical system, two-dimensional particle motion is decomposed into two orthogonal one-dimensional motions, and thus, it is applicable to a variety of condensed matter systems. In the third example, the double-pulse interferometry used for solid p-H₂ has been applied to many-body electronic wave functions of an ensemble of ultracold rubidium Rydberg atoms, hereafter called a "strongly correlated ultracold Rydberg gas". This has allowed the observation and control of many-body electron dynamics of more than 40 Rydberg atoms interacting with each other. This new combination of ultrafast coherent control and ultracold atoms offers a versatile platform to precisely observe and manipulate nonequilibrium dynamics of quantum many-body systems on the ultrashort time scale. These three examples are digested in this Account.

A proposed new scheme for vibronically resolved time-dependent photoelectron spectroscopy: pump-repump-continuous wave-photoelectron spectroscopy (prp-cw-pes)

We propose a new scheme for time-resolved photoelectron spectroscopy denoted as pump-repump-continuous wave-photoelectron spectroscopy (prp-cw-pes). This scheme is comprised of two femtosecond laser (pump) pulses under cw illumination (probe). By changing the time-delay between pump and repump lasers one can manipulate the populations of vibronic levels in electronic excited states. The cw laser acts on for a long time and establishes resonance between excited states and the continuum photo-ionized states. Sharp spectra can be obtained from the resonance condition [formula: see text]. The intensities in the spectra are sensitive to the time-delay between the pump-repump pulses, but only depend on the populations of excited states, not the phase relations (coherence). As a result, each time-delayed snapshot spectrum is a weighted sum of so-called fingerprints, where a fingerprint is the vibrationally resolved photoelectron spectrum for a single vibronic excited state. The latter information can potentially be simulated reliably using vibronic models and wave packet propagation methods. In the easiest application of the experiment, different time-delays produce different spectra, for a single molecular system. This wealth of experimental data can be fitted to an, ideally small, set of theoretical fingerprints by adjusting the populations as fitting parameters. This technique might be able to distinguish between closely related molecular species. Adopting a different viewpoint, the proposed scheme can also be employed to monitor the time-dependent dynamics by changing the phase relationship between the pump and repump laser that can be viewed as a "control mechanism" employed in wave packet interferometry. Simplifications arise as the change in the spectra is due to the changing populations, not because of the coherence. In this paper, we outline the ideas behind the scheme and illustrate the ideas theoretically using simple model systems.

Weak-field laser phase modulation coherent control of asymptotic photofragment distributions

Coherent control of the asymptotic photofragment state-resolved distributions by means of laser phase modulation in the weak-field limit is demonstrated computationally for a polyatomic molecule. The control scheme proposed applies a pump laser field consisting of two pulses delayed in time. Phase modulation of the spectral bandwidth profile of the laser field is achieved by varying the time delay between the pulses. The underlying equations show that such a phase modulation is effective in order to produce control effects on the asymptotic, long-time limit photofragment distributions only when the bandwidths of the two pulses overlap in a frequency range. The frequency overlap of the pulses gives rise to an interference term which is responsible for the modulation of the spectral profile shape. The magnitude of the range of spectral overlap between the pulses becomes an additional control parameter. The control scheme is illustrated computationally for the asymptotic photofragment state distributions produced from different scenarios of the Ne-Br2 predissociation. An experimental application of the control scheme is found to be straightforward.

Communication: Control of the fragment state distributions produced upon decay of an isolated resonance state

Control of the fragment state distributions produced upon decay of a resonance state is achieved by using a weak laser field consisting of two pulses with a varying time delay between them. It is shown that specific product fragment states can be significantly favored or quenched. The efficiency and flexibility of the control method are found to increase with increasing resonance width. The control scheme is completely independent of the specific system to which it is applied, which makes its applicability universal.

Pulse-train control of photofragmentation at constant field energy

We consider a phaselocked two-pulse sequence applied to photofragmentation in the weak-field limit. The two pulses are not overlapping in time, i.e., the energy of the pulse-train is constant for all time delays. It is shown that the relative yield of excited Br (*) in the nonadiabatic process: I + Br* ← IBr → I + Br, changes as a function of time delay when the two excited wave packets interfere. The underlying mechanisms are analyzed and the change in the branching ratio as a function of time delay is only a reflection of a changing frequency distribution of the pulse train; the branching ratio does not depend on the detailed pulse shape.

Measuring quantum coherence in bulk solids using dual phase-locked optical pulses

Electronic and phonon coherence are usually measured in different ways because their time-scales are very different. In this paper we simultaneously measure the electronic and phonon coherence using the interference of the electron-phonon correlated states induced by two phase-locked optical pulses. Interferometric visibility showed that electronic coherence remained in a semiconducting GaAs crystal until ~40 fs; in contrast, electronic coherence disappeared within 10 fs in a semimetallic Bi crystal at room temperature, differing substantially from the long damping time of its phonon coherence, in the picosecond range.

Electromagnetically induced transparency with quantum interferometry

We have shown that electromagnetically induced transparency can be achieved by control-probe interferometry using two delayed phase-locked ultrashort pulses. Two vibrational wavepackets on the excited state, excited by two delayed phase-locked ultrashort pulses, interfere constructively or destructively leading to enhancement or suppression of absorption to a selective set of vibrational levels. Depending on the phase difference and the delay between the pulses with same carrier frequency, one can design different transparency windows between absorption peaks at consecutive even(odd) vibrational levels by eliminating absorption at odd(even) vibrational levels. We have shown that by switching the phase difference of two delayed femtosecond pulses, one can switch to complete elimination of absorption from enhanced absorption to a particular set of vibrational levels in the excited state. Thus, switching of transparency through window between odd vibrational levels to that between even vibrational levels is possible. By properly choosing the temporal width and the carrier frequency of the pulses, lossless transmission of complete or bands of frequencies of the pulses can be achieved through these transparency windows. Hence, designing of single- or multi-mode transparency windows in NaH molecule is feasible by control-probe quantum interferometry.

Rotational coherence imaging and control for CN molecules through time-frequency resolved coherent anti-Stokes Raman scattering

Numerical wave packet simulations are performed for studying coherent anti-Stokes Raman scattering (CARS) for CN radicals. Electronic coherence is created by femtosecond laser pulses between the X(2)Σ and B(2)Σ states. Due to the large energy separation of vibrational states, the wave packets are superpositions of rotational states only. This allows for a specially detailed inspection of the second- and third-order coherences by a two-dimensional imaging approach. We present the time-frequency domain images to illustrate the intra- and intermolecular interferences, and discuss the procedure to rationally control and experimentally detect the interferograms in solid Xe environment.

CONTROLLING WAVE PACKET INTERFERENCE OF DISSOCIATING MOLECULES BY SHAPING LASER PULSES IN FREQUENCY DOMAIN

The interference of dissociating wave packets for the Br 2 molecule in femtosecond laser field is studied theoretically using time-dependent quantum wave packet method. The interference of dissociating wave packets can be determined by the spectrum of laser field. By shaping laser pulses in frequency domain, the corresponding R- and v-dependent density functions can be effectively controlled. Compared with the 2-pulse excitation scheme, the resolution of the interference patterns can be improved by using 3- and 4-pulse excitation schemes. The dissociating velocity can be steered by varying laser parameters.

Using wave-packet interferometry to monitor the external vibrational control of electronic excitation transfer

We investigate the control of electronic energy transfer in molecular dimers through the preparation of specific vibrational coherences prior to electronic excitation, and its observation by nonlinear wave-packet interferometry (nl-WPI). Laser-driven coherent nuclear motion can affect the instantaneous resonance between site-excited electronic states and thereby influence short-time electronic excitation transfer (EET). We first illustrate this control mechanism with calculations on a dimer whose constituent monomers undergo harmonic vibrations. We then consider the use of nl-WPI experiments to monitor the nuclear dynamics accompanying EET in general dimer complexes following impulsive vibrational excitation by a subresonant control pulse (or control pulse sequence). In measurements of this kind, two pairs of polarized phase-related femtosecond pulses following the control pulse generate superpositions of coherent nuclear wave packets in optically accessible electronic states. Interference contributions to the time- and frequency-integrated fluorescence signals due to overlaps among the superposed wave packets provide amplitude-level information on the nuclear and electronic dynamics. We derive the basic expression for a control-pulse-dependent nl-WPI signal. The electronic transition moments of the constituent monomers are assumed to have a fixed relative orientation, while the overall orientation of the complex is distributed isotropically. We include the limiting case of coincident arrival by pulses within each phase-related pair in which control-influenced nl-WPI reduces to a fluorescence-detected pump-probe difference experiment. Numerical calculations of pump-probe signals based on these theoretical expressions are presented in the following paper [J. D. Biggs and J. A. Cina, J. Chem. Phys. 131, 224302 (2009)].

Wave-Packet and Coherent Control Dynamics

This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.

Temporal and Spatial Interference between Four-Wave Mixing and Six-Wave Mixing Channels

Using phase control between four-wave mixing (FWM) and six-wave mixing (SWM) channels in a four-level atomic system, we demonstrate temporal and spatial interferences between these two nonlinear optical processes. Efficient and coexisting FWM and SWM signals are produced in the same electromagnetically induced transparency window via atomic coherence. The temporal interference has a femtosecond time scale corresponding to the optical transition frequency. Such studies of intermixing between different order nonlinear optical processes with a controllable phase delay can have important applications in high-precision measurements, coherence quantum control, and quantum information processing.

Development of high resolution Michelson interferometer for stable phase-locked ultrashort pulse pair generation

We developed a high resolution Michelson interferometer with a two-frequency He-Ne laser positioning system in order to stabilize the relative phase of a pulse pair. The control resolution corresponded to a 12 as time resolution or a phase of 1.5 degrees at 900 nm. This high resolution Michelson interferometer can generate a phase-locked pulse pair either with a specific relative phase such as 0 or pi radians or with an arbitrary phase. Coherent control of an InAs self-assembled quantum dot was demonstrated using the high resolution Michelson interferometer with a microspectroscopy system.

Factorization of numbers with the temporal Talbot effect: optical implementation by a sequence of shaped ultrashort pulses

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number.

Quantum interference spectroscopy of rubidium-helium exciplexes formed on helium nanodroplets

Femtosecond multiphoton pump-probe photoionization is applied to helium nanodroplets doped with rubidium (Rb). The yield of Rb+ ions features pronounced quantum interference (QI) fringes demonstrating the coherence of a superposition of electronic states on a time scale of tens of picoseconds. Furthermore, we observe QI in the yield of formed RbHe exciplex molecules. The quantum interferogram allows us to determine the vibrational structure of these unstable molecules. From a sliced Fourier analysis one cannot only extract the population dynamics of vibrational states but also follow their energetic evolution during the RbHe formation.

Development of ultrahigh-precision coherent control and its applications

Coherent control is based on optical manipulation of the amplitudes and phases of wave functions. It is expected to be a key technique to develop novel quantum technologies such as bond-selective chemistry and quantum computing, and to better understand the quantum worldview founded on wave-particle duality. We have developed high-precision coherent control by imprinting optical amplitudes and phases of ultrashort laser pulses on the quantum amplitudes and phases of molecular wave functions. The history and perspective of coherent control and our recent achievements are described.

Nonlinear wave-packet interferometry and molecular state reconstruction in a vibrating and rotating diatomic molecule

We formulate two-color nonlinear wave-packet interferometry (WPI) for application to a diatomic molecule in the gas phase and show that this form of heterodyne-detected multidimensional electronic spectroscopy will permit the reconstruction of photoinduced rovibrational wave packets from experimental data. Using two phase-locked pulse pairs, each resonant with a different electronic transition, nonlinear WPI detects the quadrilinear interference contributions to the population of an excited electronic state. Combining measurements taken with different phase-locking angles isolates various quadrilinear interference terms. One such term gives the complex overlap between a propagated one-pulse target wave packet and a variable three-pulse reference wave packet. The two-dimensional interferogram in the time domain specifies the complex-valued overlap of the given target state with a collection of variable reference states. An inversion procedure based on singular-value decomposition enables reconstruction of the target wave packet from the interferogram without prior detailed characterization of the nuclear Hamiltonian under which the target propagates. With numerically calculated nonlinear WPI signals subject to Gaussian noise, we demonstrate the reconstruction of a rovibrational wave packet launched from the A state and propagated in the E state of Li2.

Toward Separation of Nuclear Spin Isomers with Coherent Light

We propose an approach for separating nuclear spin isomers with coherent light and illustrate it by numerical calculations using fulvene as a model system. The scheme employs the equivalence of torsion and interchange of equivalent H-atoms in a class of molecules of which fulvene is a simple example. The exchange symmetry couples with the rotational symmetry to produce a spatial distinction between the two photo-excited nuclear spin isomers, and wavepacket interferometry is applied to separate the species.

Control of nonadiabatic dissociation dynamics with the use of laser-induced wave packet interferences

Based on wave packet interferences induced by a stationary laser field, a simple way of controlling nonadiabatic dissociation dynamics is proposed. We treat a simple two-state model of diatomic molecules. In this model, there exist two dissociative potential energy curves which cross and are strongly coupled at an internuclear distance, and thus dissociations into one channel are predominant. We propose a control scheme to selectively dissociate a molecule into any favorite channel by choosing the laser frequency and intensity appropriately. The semiclassical estimation of desirable laser parameters can be performed easily by regarding the dissociation processes as nonadiabatic transitions between the Floquet states. The agreement between the semiclassical estimation and the quantum wave packet calculation is found to be satisfactory in the high frequency region (> or =1000 cm(-1)) where the Floquet state picture is valid. In the low frequency region (<1000 cm(-1)), on the other hand, there are discrepancies between them due to the invalidity of the Floquet picture and the dissociation probability is sensitive to the laser phase. This control scheme is applied to the predissociation dynamics of NaI, NaI-->Na+I.

Coherent spin control of matrix isolated molecules by IR+UV laser pulses: quantum simulations for ClF in Ar

Two coherent sequential IR+UV laser pulses may be used to generate two time-dependent nuclear wave functions in electronic excited triplet and singlet states via single (UV) and two photon (IR+UV) excitation pathways, exploiting spin-orbit coupling and vibrational pre-excitation, respectively. These wave functions evolve from different Franck-Condon domains until they overlap in a domain of bond stretching with efficient intersystem crossing. Here, the coherence of the laser pulses is turned into optimal interferences of the wave packets, yielding the total wave packet at the target place, time, and with dominant target spin. The time resolution of spin control is few femtoseconds. The mechanism is demonstrated by means of quantum model simulations for ClF in an Ar matrix.

Implementation of quantum gate operations in molecules with weak laser fields

We numerically propose a way to perform quantum computations by combining an ensemble of molecular states and weak laser pulses. A logical input state is expressed as a superposition state (a wave packet) of molecular states, which is initially prepared by a designed femtosecond laser pulse. The free propagation of the wave packet for a specified time interval leads to the specified change in the relative phases among the molecular basis states, which corresponds to a computational result. The computational results are retrieved by means of quantum interferometry. Numerical tests are implemented in the vibrational states of the B state of I2 employing controlled-NOT gate, and 2 and 3 qubits Fourier transforms. All the steps involved in the computational scheme, i.e., the initial preparation, gate operation, and detection steps, are achieved with extremely high precision.

Quantum state measurement using coherent transients

We present the principle and experimental demonstration of time resolved quantum state holography. The quantum state of an excited state interacting with an ultrashort chirped laser pulse is measured during this interaction. This has been obtained by manipulating coherent transients created by the interaction of femtosecond shaped pulses and rubidium atoms.

Real-time observation of phase-controlled molecular wave-packet interference

The quantum interference of two molecular wave packets has been precisely controlled in the B electronic state of the I2 molecule by using a pair of fs laser pulses whose relative phase is locked within the attosecond time scale and its real-time evolution has been observed by another fs laser pulse. It is clearly observed that the temporal evolution changes drastically as a function of the relative phase between the locked pulses, allowing us to read both amplitude and phase information stored in the wave functions of the molecular ensemble.

Simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling

We present a new dimensional scaling transformation of the Schrödinger equation for the two electron bond. This yields, for the first time, a good description of the bond via D scaling. There also emerges, in the large-D limit, an intuitively appealing semiclassical picture, akin to a molecular model proposed by Bohr in 1913. In this limit, the electrons are confined to specific orbits in the scaled space, yet the uncertainty principle is maintained. A first-order perturbation correction, proportional to 1/D, substantially improves the agreement with the exact ground state potential energy curve. The present treatment is very simple mathematically, yet provides a strikingly accurate description of the potential curves for the lowest singlet, triplet, and excited states of H2. We find the modified D-scaling method also gives good results for other molecules. It can be combined advantageously with Hartree-Fock and other conventional methods.

Molecular wave packet interferometry and quantum entanglement

We study wave packet interferometry (WPI) considering the laser pulse fields both classical and quantum mechanically. WPI occurs in a molecule after subjecting it to the interaction with a sequence of phase-locked ultrashort laser pulses. Typically, the measured quantity is the fluorescence of the molecule from an excited electronic state. This signal has imprinted the interference of the vibrational wave packets prepared by the different laser pulses of the sequence. The consideration of the pulses as quantum entities in the analysis allows us to study the entanglement of the laser pulse states with the molecular states. With a simple model for the molecular system, plus several justified approximations, we solve for the fully quantum mechanical molecule-electromagnetic field state. We then study the reduced density matrices of the molecule and the laser pulses separately. We calculate measurable corrections to the case where the fields are treated classically.

Pump–probe spectroscopy with phase-locked pulses in the condensed phase: decoherence and control of vibrational wavepackets

Electronic and vibrational coherences of Cl2 embedded in solid Ar are investigated by exciting to the B state with a phase-locked pulse pair from an unbalanced Michelson interferometer, where the chirp difference matches the B state anharmonicity. Recording the A' --> X fluorescence after relaxation is compared to probing to charge transfer states by a third pulse. The three-pulse experiment delivers more details on the decoherence processes. The signal modulation due to phase tuning up to the third vibrational round-trip time indicates that the electronic coherence in the B <-- X transition is preserved for more than 660 fs in the solid Ar environment where many body electronic interactions take place. Vibrational coherence lasts longer than 3 ps according to the observed half revival of the wavepacket. Control of the coupling between wavepacket motion and lattice oscillation is demonstrated by tuning the relative phase between the phase-locked pulses, preparing wavepackets predominantly composed of either zero-phonon lines or phonon side bands.

Molecular state reconstruction by nonlinear wave packet interferometry

We show that time- and phase-resolved two-color nonlinear wave packet interferometry can be used to reconstruct the probability amplitude of an optically prepared molecular wave packet without prior knowledge of the underlying potential surface. We analyze state reconstruction in pure- and mixed-state model systems excited by shaped laser pulses and propose nonlinear wave packet interferometry as a tool for identifying optimized wave packets in coherent control experiments.

Coarse-grained controllability of wavepackets by free evolution and phase shifts

We describe an approach to controlling wavepacket dynamics and a criterion of wavepacket controllability based on discretized properties of the wavepacket's localization on the orbit. The notion of "coarse-grained control" and the coarse-grained description of the controllability in infinite-dimensional Hilbert spaces are introduced and studied using the mathematical apparatus of loop groups. We prove that 2D rotational wavepackets are controllable by only free evolution and phase kicks by AC Stark shift implemented at fractional revivals. This scheme works even if the AC Stark shifts can have only a smooth coordinate dependence, correspondent to the action of a linearly polarized laser field.

Optimal control of ultrafast selection

Optimal laser control for ultrafast selection of closely lying excited states whose energy separation is smaller than the laser bandwidth is reported on the two-photon transition of atomic cesium; Cs(6S-->7D(J), J=5/2 and 3/2). Selective excitation was carried out by pulse shaping of ultrashort laser pulses which were adaptively modulated in a closed-loop learning system handling eight parameters representing the electric field. Two-color fluorescence from the respective excited states was monitored to measure the selectivity. The fitness used in the learning algorithm was evaluated from the ratio of the fluorescence yields. After fifty generations, a pair of nearly transform-limited pulses were obtained as an optimal pulse shape, proving the effectiveness of the "Ramsey fringes" mechanism. The contrast of the selection ratio was improved by approximately 30% from the simple "Ramsey fringes" experiment.