Quantum Path Interference Research Articles

Light-field-driven currents in graphene.

The ability to steer electrons using the strong electromagnetic field of light has opened up the possibility of controlling electron dynamics on the sub-femtosecond (less than 10-15 seconds) timescale. In dielectrics and semiconductors, various light-field-driven effects have been explored, including high-harmonic generation, sub-optical-cycle interband population transfer and the non-perturbative change of the transient polarizability. In contrast, much less is known about light-field-driven electron dynamics in narrow-bandgap systems or in conductors, in which screening due to free carriers or light absorption hinders the application of strong optical fields. Graphene is a promising platform with which to achieve light-field-driven control of electrons in a conducting material, because of its broadband and ultrafast optical response, weak screening and high damage threshold. Here we show that a current induced in monolayer graphene by two-cycle laser pulses is sensitive to the electric-field waveform, that is, to the exact shape of the optical carrier field of the pulse, which is controlled by the carrier-envelope phase, with a precision on the attosecond (10-18 seconds) timescale. Such a current, dependent on the carrier-envelope phase, shows a striking reversal of the direction of the current as a function of the driving field amplitude at about two volts per nanometre. This reversal indicates a transition of light-matter interaction from the weak-field (photon-driven) regime to the strong-field (light-field-driven) regime, where the intraband dynamics influence interband transitions. We show that in this strong-field regime the electron dynamics are governed by sub-optical-cycle Landau-Zener-Stückelberg interference, composed of coherent repeated Landau-Zener transitions on the femtosecond timescale. Furthermore, the influence of this sub-optical-cycle interference can be controlled with the laser polarization state. These coherent electron dynamics in graphene take place on a hitherto unexplored timescale, faster than electron-electron scattering (tens of femtoseconds) and electron-phonon scattering (hundreds of femtoseconds). We expect these results to have direct ramifications for band-structure tomography and light-field-driven petahertz electronics.

Manipulating quantum interferences in laser dressed-helium by the transferred momentum between the electron projectile and helium target

SynopsisWe present theoretical study of energetic electron-impact excitation of “six-level helium atom” embedded in a laser field. During the scattering process, the combined interactions lead to a change in the kinetic energy and the angular distribution of the scattered electron. The latter contains all information about the combined interactions. The analysis of the angular distribution reveals the emergence of a peak profile. This is will be discussed in terms of quantum-path interferences in bound-bound electronic transitions. Furthermore, the sensitivity of the phenomenon to the collision dynamics will also be discussed.

Below-threshold harmonic generation from strong non-uniform fields

Strong-field photoemission below the ionization threshold is a rich/complex region where atomic emission and harmonic generation may coexist. We studied the mechanism of below-threshold harmonics (BTH) from spatially non-uniform local fields near the metallic nanostructures. Discrete harmonics are generated due to the broken inversion symmetry, suggesting enriched coherent emission in the vuv frequency range. Through the numerical solution of the time-dependent Schrödinger equation, we investigate wavelength and intensity dependence of BTH. Wavelength dependence identifies counter-regular resonances; individual contributions from the multi-photon emission and channel-closing effects due to quantum path interferences. In order to understand the underlying mechanism of BTH, we devised a generalized semi-classical model, including the influence of Coulomb and non-uniform field interactions. As in uniform fields, Coulomb potential in non-uniform fields is the determinant of BTH; we observed that the generation of BTH are due to returning trajectories with negative energies. Due to large distance effectiveness of the non-uniformity, only long trajectories are noticeably affected.

Isolated-attosecond-pulse generation by suppressing multiple rescatterings with plasmon-enhanced laser fields

ABSTRACTAn efficient scheme is proposed to generate broadband supercontinuum spectra and isolated attosecond laser pulses by suppressing multiple rescatterings with plasmon-enhanced laser fields. High-order harmonic generation from helium atoms in long wavelength is theoretically investigated. It is found that a quantum path interference and a multiple rescatterings interference are two fundamental limitations against the smooth degree of harmonic spectra. Numerical results show that the coherent superposition state in combination with plasmon-enhanced laser fields is robust for broadband supercontinuum generation. Then an isolated 78-as pulse can be directly generated.

Coherence in laser-driven electrons at the surface and in the volume of solid matter

The femtosecond frequency comb allows controlling the carrier field of ultrashort laser pulses. We show two examples on how this control over fields oscillating with a few hundred terahertz can be utilized to control electrons at the surface and in the volume of solids. After a brief discussion of strong-field physics at metal needle tips, we show how ultrafast two-color laser pulses allow quantum path interference to dramatically alter the emission current from sharp tips, with an interference visibility of 94%. With carrier-envelope phase-controlled laser pulses, we show furthermore how light-field sensitive currents can be excited in monolayer graphene via an interplay of interband and intraband electron dynamics including multiple Landau–Zener transitions.

Spatially and spectrally resolved quantum path interference with chirped driving pulses

We measure spectrally and spatially resolved high-order harmonics generated in argon using chirped multi-cycle laser pulses. Using a stable, high-repetition rate laser we observe detailed interference structures in the far-field. The structures are of two kinds; off-axis interference from the long trajectory only and on-axis interference including the short and long trajectories. The former is readily visible in the far-field spectrum, modulating both the spectral and spatial profile. To access the latter, we vary the chirp of the fundamental, imparting different phases on the different trajectories, thereby changing their relative phase. Using this method together with an analytical model, we are able to explain the on-axis behaviour and access the dipole phase parameters for the short () and long () trajectories. The extracted results compare very well with phase parameters calculated by solving the time-dependent Schrödinger equation. Going beyond the analytical model, we are also able to successfully reproduce the off-axis interference structure.

Frequency dependence of quantum path interference in non-collinear high-order harmonic generation**Project supported by the National Key Basic Research Program of China (Grant Nos. 2013CB922401 and 2013CB922402), the National Key Scientific Instrument and Equipment Development Projects, China (Grant No. 2012YQ12004704), the National Natural Science Foundation of China (Grant No. 11374356), and the International Joint Research Program of National Natural Science Foundation

High-order harmonic generation (HHG) driven by two non-collinear beams including a fundamental and its weak second harmonic is numerically studied. The interference of harmonics from adjacent electron quantum paths is found to be dependent on the relative delay of the driving pulse, and the dependences are different for different harmonic orders. This frequency dependence of the interference is attributed to the spatial frequency chirp in the HHG beam resulting from the harmonic dipole phase, which in turn provides a potential way to gain an insight into the generation of high-order harmonics. As an example, the intensity dependent dipole phase coefficient α is retrieved from the interference fringe.

The influences of multiphoton excitation on near-threshold Harmonic emission in atoms

When an atom or a molecule interacts with an intense laser field, a coherent high-order harmonic emission is observed at a frequency that is an integer multiple magnitude of the initial frequency of the incident laser field. The harmonic emission has the characteristic of high emission efficiency at relatively high orders, and it also has a wide expansion in the frequency domain. Thus, the high-order harmonic generation can be utilized to generate coherent EUV or soft X-ray light sources as well as ultrashort at to second laser pulses. It is promising that the attosecond laser pulse will be an important tool for detecting and controlling the electron dynamics in atom and molecule systems. The mechanisms of high-order harmonics especially the high energy part of the harmonic spectrum can be explained by the well-known three-step model. The three-step model assumes that the electron in the bound state firstly are ionized by the potential barrier formed by the laser electric field and the atomic potential, then the ionized electrons oscillate in the laser field, and finally the electron with high kinetic energy gained in the laser field has the possibility to return back to the parent ion and recombines with the ground state of the system with a high energy photon emitted. As for harmonics with low orders, especially those with single photon energy near the ionization threshold, the Coulomb potential of the atom has significant influences on them. However,the effect of the Coulomb potential of the atom are not included in the three-step model, so the mechanism of near-threshold harmonics (NTH) cannot be clearly interpreted with the three-step model alone. In this circumstance, the study of the mechanism of near-threshold harmonic emission attracted people's attention in general. One important application of NTH is that it can be utilized to generate optical comb with EUV frequencies. Theoretically, Xiong et al. studied the mechanism of below-threshold harmonic (BTH) emission and found that the mechanism of this part of harmonics include the effect of the quantum-path interference and the Coulomb potential. He et al. analyzed the emission of BTH in various laser intensity regions and found that the harmonic spectrum exhibits a periodic structure as a function of the harmonic frequency when the incident laser intensity is about 1013 W/cm2. Utilizing the quantum-path and time-frequency analyses of the harmonic emission, He et al. indicated that this periodic structure can be attributed to the interference effect between two specific quantum paths. Li et al. adopted the synchrosqueezing scheme to study the near-and below-threshold harmonic emission of Cs atoms in an intense mid-infrared laser field and they showed that the multiphoton and the multiple rescattering trajectories have an effect on the NTH and BTH generation processes. Shafir et al. found that the ionic potential plays an critical role in NTH emission. Under the interaction between the atom and the intense laser field, electron in the ground state not only can be ionized but also be pumped into excited state, and these excitation processes also affect the harmonic emission. We studied the harmonic emission process near the ionization threshold by solving the time-dependent Schrdinger equation of an atom interacting with a strong laser field. Utilizing the obtained wavefunction, we systematically studied the high-order harmonic emission with the variation of the incident laser intensity. Meanwhile, through solving the TDSE with the momentum-space method, the excited-state population is precisely calculated and achieved. We show that the ninth harmonic exhibits a periodic oscillation structure with the intensity of the incident laser field increasing, and we reveals that there is a synchronous variation between the harmonic intensity and the relatively high bound state population.Within a certain range of laser intensity, the increase of the total population of the excited states corresponds to the low efficiency of harmonic emission, and this competition relationship is quite clear. Therefore, when the wavelength of the driving laser pulse is fixed, we can optimize the driving laser intensity to achieve the near-threshold harmonic emission with high efficiency.

Spectrally resolved spatiotemporal features of quantum paths in high-order-harmonic generation

We experimentally disentangle the contributions of different quantum paths in high-order harmonic generation (HHG) from the spectrally and spatially resolved harmonic spectra. By adjusting the laser intensity and focusing position, we simultaneously observe the spectrum splitting, frequency shift and intensity-dependent modulation of harmonic yields both for the short and long paths. Based on the simulations, we discriminate the physical mechanisms of the intensity-dependent modulation of HHG due to the quantum path interference and macroscopic interference effects. Moreover, it is shown that the atomic dipole phases of different quantum paths are encoded in the frequency shift. In turn, it enables us to retrieve the atomic dipole phases and the temporal chirps of different quantum paths from the measured harmonic spectra. This result gives an informative mapping of spatiotemporal and spectral features of quantum paths in HHG.

Quantum-path signatures in attosecond helical beams driven by optical vortices

High-order harmonic generation (HHG) driven by beams carrying orbital angular momentum has been recently demonstrated as a unique process to generate spatio-temporal coherent extreme ultraviolet (XUV)/x-ray radiation with attosecond helical structure. We explore the details of the mapping of the driving vortex to its harmonic spectrum. In particular we show that the geometry of the harmonic vortices is complex, arising from the superposition of the contribution from the short and long quantum paths responsible of HHG. Transversal phase-matching and quantum path interferences provide an explanation of the dramatic changes in the XUV vortex structure generated at different relative positions of the target respect to the laser beam focus. Finally, we show how to take advantage of transversal phase-matching to select helical attosecond beams generated from short or long quantum paths, exhibiting positive or negative temporal chirp respectively.

Quantum path interference in the wavelength-dependent below-threshold harmonic generation

We have theoretically investigated the wavelength-dependent below-threshold harmonic (BTH) generation in different laser intensity regimes. Based on the simulations of the time-dependent Schr\"odinger equation, we find a periodic fluctuation in the wavelength-dependent BTH yields with laser intensities in the magnitude of ${10}^{13}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$. This result shows significant differences from the resonance peak structures in the recent study with intensities about ${10}^{12}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$ [Xiong et al., Phys. Rev. Lett. 112, 233001 (2014)]. By performing both the quantum path analysis and time-frequency transform of the harmonic spectra, we demonstrate that the difference in the wavelength-dependent BTH yields is due to the complicated quantum path distributions of BTHs with the intensities in the magnitude of ${10}^{13}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$. And the periodic fluctuation is further demonstrated to originate from the interference between the two quantum paths that dominate the harmonic generation.

Mechanisms of Below-Threshold Harmonic Generation in Atoms

Most previous studies have focused on high-order harmonic generation beyond the ionization threshold; mechanisms of below-threshold harmonics are less understood. We schematically study the harmonic emission process in this region by numerically solving the time-dependent Schrödinger equation of an atom in laser fields. We show that, besides the quantum path interference mechanism recently identified, the effects induced by the Coulomb potential also have a critical impact on these harmonics. These mechanisms can be distinguished in the structure of harmonic spectra by changing the laser wavelength and peak intensity. We find that the long quantum orbits can influence lower-order harmonics at a higher laser intensity. In addition, we show that the intensity-dependent steps of harmonic yield can disappear for certain harmonic orders, due to the trapping in the Rydberg states before recombination, which can explain recent experimental observations.

High-harmonic generation and parametric amplification in the soft X-rays from extended electron trajectories

We report, for the first time, the generation of high-order harmonics in a spectral range between 200 eV and 1 keV with an unusual spectral property: only every 4th (4i + 1, i∈ℵ) harmonic line appears, whereas the usual high-harmonic spectra consist of every odd (2i + 1) harmonic. We attribute this unique property to the quantum path interference of two extended electron trajectories that experience multiple re-scattering. In the well-established theory, electrons emitted via tunnel ionisation are accelerated by a laser field, return to the ion and recombine. The acceleration typically lasts for less than one optical cycle, and the electrons radiate in the extreme ultraviolet range at recombination. In contrast, for extended trajectories, electrons are accelerated over two or more optical cycles. Here, we demonstrate that two sets of trajectories dominate and provide substantial contributions to the generated soft X-ray radiation because they fulfil the resonance condition for X-ray parametric amplification.

Tailoring isolated attosecond pulses using quantum path interferences

By performing calculations on the generation of isolated attosecond pulses by intense and few-cycle laser fields, we demonstrate that the pulse temporal width is sensitive to the angle of emission. We show that this effect results from the interference of the short and long electronic trajectory contributions, responsible for high-order harmonic generation. In particular, we find that the shortest pulses are emitted off-axis, which are substantially shorter than those emitted on-axis, where single trajectory contributions dominate.

Ultra-broadband water window supercontinuum generation with high efficiency in a three-color laser field

We propose an efficient method to generate an ultra-broadband supercontinuum by using a three-color field synthesized by a 1600 nm driving pulse and two weak (3200 nm and 400 nm) control pulses. The results show that the acceleration and ionization steps in the HHG process are simultaneously controlled in our scheme, which can not only broaden the bandwidth but also enhance the harmonic yields of the generated spectrum. Thus a high-efficiency supercontinuum with the photon energies ranging from 205 eV to 480 eV is observed. Based on our 3D propagation simulations, we show that the short quantum path of the supercontinuum is well phase-matched and can be selected under suitable propagation conditions. Thereby, the modulation due to quantum path interference is largely reduced and intense isolated sub-100 as pulses with tunable central wavelengths are directly obtained within water window spectral region.

Manipulation of quantum paths for space–time characterization of attosecond pulses

An all-optical method to measure the space–time characteristics of an isolated attosecond pulse, without temporal and spatial averaging, is now demonstrated. The approach will provide further insight into the generation of ultrafast light, and may possibly be used to finely control the pulse characteristics. Attosecond extreme-ultraviolet pulses1 have a complex space–time structure2. However, at present, there is no method to observe this intricate detail; all measurements of the duration of attosecond pulses are, to some extent, spatially averaged1,3,4,5. A technique for determining the full space–time structure would enable a detailed study of the highly nonlinear processes that generate these pulses as a function of intensity without averaging6,7. Here, we introduce and demonstrate an all-optical method to measure the space–time characteristics of an isolated attosecond pulse. Our measurements show that intensity-dependent phase and quantum-path interference both play a key role in determining the pulse structure. In the generating medium, the attosecond pulse is strongly modulated in space and time. Propagation modifies but does not erase this modulation. Quantum-path interference of the single-atom response, previously obscured by spatial and temporal averaging, may enable measuring the laser-field-driven ion dynamics with sub-cycle resolution.

Molecular internal dynamics studied by quantum path interferences in high order harmonic generation

We investigate how short and long electron trajectory contributions to high harmonic emission and their interferences give access to information about intra-molecular dynamics. In the case of unaligned molecules, we show experimental evidence that the long trajectory contribution is more dependent upon the molecular species than the short one, providing a high sensitivity to cation nuclear dynamics from 100’s of as to a few fs after ionisation. Using theoretical approaches based on the strong field approximation and numerical integration of the time dependent Schrödinger equation, we examine how quantum path interferences encode electronic motion when the molecules are aligned. We show that the interferences are dependent upon which ionisation channels are involved and any superposition between them. In particular, quantum path interferences can encode signatures of electron dynamics if the laser field drives a coupling between the channels. Hence, molecular quantum path interferences are a promising method for attosecond spectroscopy, allowing the resolution of ultra-fast charge migration in molecules after ionisation in a self-referenced manner.

Quantum path interferences of high-order harmonic generation in two-color Gaussian beams

The phase matching of the quantum paths in high-order harmonic generation is investigated in two-color laser fields. The results show that the spatial distribution of the laser field is optimized by adjusting the laser beam waist, the phase-matching properties of the long trajectories can be modulated effectively, and then good phase matching for both the two paths can be achieved from on-axis region to off-axis region. A radial clear interference fringe induced by the well phase-matching of two paths can be observed by placing a near-field filter, which has great potential for distinguishing clearly different interference effects and observing higher order trajectories with improved detection sensitivity.

Driving-frequency scaling of high-harmonic quantum paths

We have developed an analytical theory explaining how the single-atom efficiency of high-harmonic generation scales with laser frequency, and verified this by numerically solving the time-dependent Schrödinger equation in three spatial dimensions. According to our saddle-point analysis of quantum paths, the imaginary part of the action has a significant impact on the scaling law. Furthermore, we found that the scaling law depends on the analytical properties of the ground–continuum transition matrix element. Our analysis elucidates how the relative contributions of different quantum orbits and their relative phases vary with the driving laser frequency and how the resulting quantum-path interferences in high-harmonic spectra can be controlled with an attosecond accuracy.

Spatial fingerprint of quantum path interferences in high order harmonic generation

We have spatially and spectrally resolved the high order harmonic emission from an argon gas target. Under proper phase matching conditions we were able to observe for the first time the spatial fine structure originating from the interference of the two shortest quantum paths in the harmonic beam. The structure can be explained by the intensity-dependent harmonic phase of the contributions from the two paths. The spatially and spectrally resolved measurements are consistent with previous spatially integrated results. Our measurement method represents a new tool to clearly distinguish between different interference effects and to potentially observe higher order trajectories in the future with improved detection sensitivity. Here, we demonstrate additional experimental evidence that the observed interference pattern is only due to quantum-path interferences and cannot be explained by a phase modulation effect. Our experimental results are fully supported by simulations using the strong field approximation and including propagation.