Observation of coherent transients in ultrashort chirped excitation of an undamped two-level system

Sub-optical-cycle light-matter energy transfer in molecular vibrational spectroscopy

The evolution of ultrafast-laser technology has steadily advanced the level of detail in studies of light-matter interactions. Here, we employ electric-field-resolved spectroscopy and quantum-chemical modelling to precisely measure and describe the complete coherent energy transfer between octave-spanning mid-infrared waveforms and vibrating molecules in aqueous solution. The sub-optical-cycle temporal resolution of our technique reveals alternating absorption and (stimulated) emission on a few-femtosecond time scale. This behaviour can only be captured when effects beyond the rotating wave approximation are considered. At a femtosecond-to-picosecond timescale, optical-phase-dependent coherent transients and the dephasing of the vibrations of resonantly excited methylsulfonylmethane (DMSO₂) are observed. Ab initio modelling using density functional theory traces these dynamics back to molecular-scale sample properties, in particular vibrational frequencies and transition dipoles, as well as their fluctuation due to the motion of DMSO₂ through varying solvent environments. Future extension of our study to nonlinear interrogation of higher-order susceptibilities is fathomable with state-of-the-art lasers.

Energy transfer between the electromagnetic field and atoms or molecules is fundamentally interesting. Here the authors demonstrate stepwise energy transfer between broadband mid-infrared optical pulses and vibrating methylsulfonylmethane molecules in aqueous solution.

Observation and quantification of the quantum dynamics of a strong-field excited multi-level system

The quantum dynamics of a V-type three-level system, whose two resonances are first excited by a weak probe pulse and subsequently modified by another strong one, is studied. The quantum dynamics of the multi-level system is closely related to the absorption spectrum of the transmitted probe pulse and its modification manifests itself as a modulation of the absorption line shape. Applying the dipole-control model, the modulation induced by the second strong pulse to the system’s dynamics is quantified by eight intensity-dependent parameters, describing the self and inter-state contributions. The present study opens the route to control the quantum dynamics of multi-level systems and to quantify the quantum-control process.

Rabi oscillations produced by adiabatic pulse due to initial atomic coherence

If an electromagnetic pulse is detuned from atomic transition frequency by amount Δ>1/τ, where τ is the turn-on time of the pulse, then atomic population adiabatically follows the pulse intensity without causing Rabi oscillations. Here we show that, if initially, the atom has nonzero coherence, then the adiabatic pulse yields Rabi oscillations of atomic population ρ_aa(t), and we obtain analytical solutions for ρ_aa(t). Our findings can be useful for achieving generation of coherent light in the backward direction in the QASER scheme in which modulation of the coupling between light and atoms is produced by Rabi oscillations. Initial coherence can be created by sending a short resonant pulse into the medium followed by a long adiabatic pulse, which leads to the light amplification in the backward direction.

Enhanced nonlinear interaction in a microcavity under coherent excitation

The large field enhancement that can be achieved in high quality factor and small mode volume photonic crystal microcavities leads to strengthened nonlinear interactions. However, the frequency shift dynamics of the cavity resonance under a pulsed excitation, which is driven by nonlinear refractive index change, tends to limit the coupling efficiency between the pulse and the cavity. As a consequence, the cavity enhancement effect cannot last for the entire pulse duration, limiting the interaction between the pulse and the intra-cavity material. In order to preserve the benefit of light localization throughout the pulsed excitation, we report the first experimental demonstration of coherent excitation of a nonlinear microcavity, leading to an enhanced intra-cavity nonlinear interaction. We investigate the nonlinear behavior of a Silicon-based microcavity subject to tailored positively chirped pulses, enabling to increase the free carrier density generated by two-photon absorption by up to a factor of 2.5 compared with a Fourier-transform limited pulse excitation of equal energy. It is accompanied by an extended frequency blue-shift of the cavity resonance reaching 19 times the linear cavity bandwidth. This experimental result highlights the interest in using coherent excitation to control intra-cavity light-matter interactions and nonlinear dynamics of microcavity-based optical devices.

Cooperative Emission of a Coherent Superflash of Light

We investigate the transient coherent transmission of light through an optically thick cold strontium gas. We observe a coherent superflash just after an abrupt probe extinction, with peak intensity more than three times the incident one. We show that this coherent superflash is a direct signature of the cooperative forward emission of the atoms. By engineering fast transient phenomena on the incident field, we give a clear and simple picture of the physical mechanisms at play.

Ultrafast Ramsey interferometry to implement cold atomic qubit gates

Quantum computing is based on unitary operations in a two-level quantum system, a qubit, as the fundamental building block, and the ability to perform qubit operations in an amount of time that is considerably shorter than the coherence time is an essential requirement for quantum computation. Here, we present an experimental demonstration of arbitrary single-qubit SU(2) quantum gate operations achieved at a terahertz clock speed. Implemented by coherent control methods of tailored ultrafast laser interaction with cold rubidium atomic qubits, Bloch vector manipulation about all three rotational axes was successfully demonstrated. The dynamic evolution of the qubits was successfully measured by devised femtosecond Ramsey interferometry. We anticipate this demonstration to be a starting point to process quantum algorithm in a simplified manner by a programmed sequence of femtosecond laser pulses.

Observation and symmetry-based coherent control of transient two-photon absorption: the bright side of dark pulses

We present and experimentally demonstrate for the first time the observation and femtosecond coherent control over the temporal evolution of a transient population that is excited via nonresonant two-photon absorption. Based on symmetry properties of the two-photon absorption process, the exciting femtosecond pulses are phase-shaped to photoinduce different evolutions of the transient excited population for a given final excited population. As a study case, we focus here on the attractive case of two-photon dark pulses that, although inducing zero final population (hence, the terminology of "dark pulses"), they induce a transient excited population during the pulse irradiation that can significantly deviate from zero. This nonzero transient population can be viewed as the bright side of such dark pulses. The symmetry-based coherent control is demonstrated first with dark pulses that we shape to induce transient excited population that at all times is kept below different target levels. Then, it is further demonstrated with pairs of dark pulses where one is rationally shaped to induce temporal evolution of the transient excited population that is the inverse of the evolution induced by the other. The work is conducted in the weak-field regime with the sodium atom as the model system. The approach developed here is general, conceptually simple, and very effective.

Observation of infrared free-induction decay and optical nutation signals from nitrous oxide using a current modulated quantum cascade laser

Free induction decay (FID), optical nutation, and rapid passage induced signals in nitrous oxide, under both optically thin and optically thick conditions, have been observed using a rapid current pulse modulation, or chirp, applied to the slow current ramp of a quantum cascade (QC) laser. The variation in optical depth was achieved by increasing the pressure of nitrous oxide in a long path length multipass absorption cell. This allows the variation of optical depth to be achieved over a range of low gas pressures. Since, even at the highest gas pressure used in the cell, the chirp rate of the QC laser is faster than the collisional reorientation time of the molecules, there is minimal collisional damping, allowing a large macroscopic polarization of the molecular dipoles to develop. This is referred to as rapid passage induced polarization. The resultant FID signals are enhanced due to the constructive interference between the field within the gas generated by the slow ramp of the laser (pump), and that of the fast chirp of the laser (probe) signal generated by pulse modulation of the continuously operating QC laser. The FID signals obtained at large optical depth have not been observed previously in the mid-infrared regions, and unusual oscillatory signals have been observed at the highest gas pressures used.

Control of the attosecond synchronization of XUV radiation with phase-optimized mirrors

We report on the advanced amplitude and phase control of attosecond radiation allowed by specifically-designed multilayer XUV mirrors. We first demonstrate that such mirrors can compensate for the intrinsic chirp of the attosecond emission over a large bandwidth of more than 20 eV. We then show that their combination with metallic foils introduces a third-order dispersion that is adjustable through the mirror's incidence angle. This results in a controllable beating allowing the radiation to be shaped from a single to a series of sub-100 as pulses.

Control of coherent excitation of neon in the extreme ultraviolet regime

Coherent excitation of a superposition of Rydberg states in neon by the 13th harmonic of an intense 804 nm pulse and the formation of a wave packet is reported. Pump-probe experiments are performed, where the 3d-manifold of the 2p6-->2p5 (2P3/2) 3d [1/2]1- and 2p6-->2p5 (2P3/2) 3d [3/2]1-transitions are excited by an extreme ultraviolet (XUV) radiation pulse, which is centered at 20.05 eV photon energy. The temporal evolution of the excited state population is probed by ionization with a time-delayed 804 nm pulse. Control of coherent transient excitation and wave packet dynamics in the XUV-regime is demonstrated, where the spectral phase of the 13th harmonic is used as a control parameter. Modulation of the phase is achieved by propagation of the XUV-pulse through neon of variable gas density. The experimental results indicate that phase-shaped high-order harmonics can be used to control fundamental coherent excitation processes in the XUV-regime.

Characterization of attosecond XUV pulses utilizing a broadband UV approximately VUV pumping

We propose a simple scheme to characterize attosecond extreme ultraviolet (XUV) pulses. A broadband ultraviolet (UV) approximately vacuum ultraviolet (VUV) pump pulse creates a coherent superposition of atomic bound states, from which photoionization takes place by the time-delayed attosecond XUV probe pulse. Information on the spectral phase of the XUV pulse can be extracted from the phase offset of the interference beating in the photoelectron spectra using a standard SPIDER (spectral phase interferometry for direct electric-field reconstruction) algorithm. We further discuss the influence of the chirp and polychromaticity of the pump pulse, and show that they do not spoil the reconstruction process. Since our scheme is applicable for various simple atoms such as H, He, and Cs, etc., and capable of characterizing attosecond XUV pulses with a pulse duration of a few hundred attoseconds or even less, it can be an alternative technique to characterize attosecond XUV pulses. Specific numerical examples are presented for the H atom utilizing the 2p and 3p states.

Femtosecond spectroscopy from the perspective of a global multidimensional response function

At the microscopic level, multidimensional response functions, such as the nonlinear optical susceptibility or the time-ordered response function, are commonly used tools in nonlinear optical spectroscopy for determining the nonlinear polarization resulting from an arbitrary excitation. In this Account, we point out that the approach successfully developed for the nonlinear polarization can also be used in the case of a directly observable macroscopic quantity. This observable can be, for example, the electric field radiated in a nonlinear mixing experiment, the rate of fluorescence resulting from one- or two-photon absorption, or the rate of a photochemical reaction. For each of these physical processes, perturbation theory can be used to expand the measured quantity in a power series of the exciting field, and an appropriate global response function can be introduced for each order of perturbation. At order n, the multidimensional response function will depend on n variables (either time or frequency) and have the same general properties as the nonlinear susceptibility resulting, for example, from time invariance or causality. The global response function is introduced in this Account in close analogy with the nonlinear susceptibility or the time-ordered microscopic response. We discuss various applications of the global response function formalism. For example, it can be shown that in the weak field limit, a stationary signal induced in a time-invariant system is independent of the spectral phase of the exciting field. Although this result had been demonstrated previously, the global response function enables its derivation in a more general way because no specific microscopic model is needed. Multidimensional spectroscopy is obviously ideally suited to measure the global multidimensional response function. It is shown that the second (or third)-order response can be exactly measured with 2D (or 3D) spectroscopy by taking into account the exact shape of the exciting pulses. In the case of a 2D measurement of the third-order response, a particular projection of the complete 3D response function is actually measured. This projection can be related to a mixed time and frequency representation of the response function when the pulses are assumed to be infinitely short. We thus show that the global response function is a useful tool for deriving general results and that it should help in designing future experimental schemes for femtosecond spectroscopy.

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.

Simple route to strong-field coherent control

Coherent-control schemes to manipulate weak-field interactions are generally invalid at stronger fields, since strong-field interactions are accompanied by level power broadenings and level shifts that usually elude simple analytical treatments. Here we show that a broad subgroup of weak-field solutions (those with real fields, i.e., fields with only one quadrature in the complex plane) can be extended to the strong-field regime while retaining their properties. The salient feature of these fields is a symmetry that cancels out power broadening effects. Such fields can be generated from ultrashort coherent pulses or from incoherent broadband down-converted light. Weak-field coherent-control approaches based on these solutions can therefore be extended to the strong-field regime as we demonstrate in a two-photon absorption experiment in atomic cesium.

Observation of selectivity of coherent population transfer induced by optical interference

A fs time-resolved selective control of multilevel systems using superposition of two identical, frequency-chirped fields is proposed and demonstrated. By adjusting the delay between the pulses, a selected transition of the Rb doublet was brought into the "holes" of the interference pattern and remained nonexcited, thus allowing to manipulate another transition by the laser field as if it were an isolated two-level system. Based on light interference, this technique needs neither strong driving field intensities nor controlling the chirp direction to achieve the selectivity.

Quantum interference of virtual and real amplitudes in a semiconductor exciton system

By two-color pulse shaping, we simultaneously create virtual and real amplitudes for excitons in GaAs quantum wells, and monitor population and amplitude by pump-probe and four-wave mixing spectroscopies. Excited-state probability amplitude can be induced by the off-resonant, virtual excitations as well as by the resonant, real excitations. Population modulation in time-domain results from the interference between the virtual and real amplitudes, and the modulation depth reveals the relative contributions of these two amplitudes. The fact that virtual and real amplitudes have a phase difference of 90 degrees is demonstrated directly in time-domain.

Realization of a time-domain Fresnel lens with coherent control

Perturbative chirped pulse excitation leads to oscillations of the excited state amplitude. These coherent transients are governed by interferences between resonant and off-resonant contributions. Control mechanisms in both frequency and time domain are used to modify these dynamics. First, by applying a phase step in the spectrum, we manipulate the phase of the oscillations. By direct analogy with Fresnel zone lenses, we then conceive highly phase-amplitude modulated pulse shapes that slice destructive interferences out of the excitation time structure and enhance the final population.

Coherent transient enhancement of optically induced resonant transitions

By applying pulse shaping techniques to a broadband 100 fs pulse in resonance with a two-level atomic transition, we are able to enhance the peak transient excited level population relative to that achievable with transform limited pulses. We also demonstrate how the dispersion induced by the absorption line itself leads to similar rapidly oscillating transients in the excited population. These transient population effects are applicable in any multiphoton resonant transition.