This Letter brings together two topics that, until now, have been the focus of intense but nonoverlapping research efforts. The first concerns high harmonic generation in solids, which occurs when intense light field excites highly non-equilibrium electronic response in a semiconductor or a dielectric. The second concerns many-body dynamics in strongly correlated systems such as the Mott insulator. Here we show that high harmonic generation can be used to time-resolve ultrafast many-body dynamics associated with optically driven phase transition, with accuracy far exceeding one cycle of the driving light field. Our work paves the way for time-resolving highly non-equilibrium many body dynamics in strongly correlated systems, with few femtosecond accuracy. * Electronic address: silva@mbi-berlin.de †

We present a theoretical study of H þ 2 ionization under strong IR femtosecond pulses by using a method designed to extract correlated (2D) photoelectron and proton kinetic energy spectra. The results show two distinct ionization mechanisms-tunnel and multiphoton ionization-in which electrons and nuclei do not share the energy from the field in the same way. Electrons produced in multiphoton ionization share part of their energy with the nuclei, an effect that shows up in the 2D spectra in the form of energy-conservation fringes similar to those observed in weak-field ionization of diatomic molecules. In contrast, tunneling electrons lead to fringes whose position does not depend on the proton kinetic energy. At high intensity, the two processes coexist and the 2D plots show a very rich behavior, suggesting that the correlation between electron and nuclear dynamics in strong field ionization is more complex than one would have anticipated. DOI: 10.1103/PhysRevLett.110.113001 PACS numbers: 33.20.Xx, 33.60.+q, 33.80.Rv The interaction of atoms and molecules with intense infrared laser pulses has been the object of continuous research for more than two decades [1][2][3][4][5][6][7][8][9]. Since the potential induced by such lasers on the electrons is comparable to or even stronger than that generated by the nuclei, the resulting electron dynamics is significantly different from that of the isolated system, which makes these lasers ideal tools to achieve electronic control [10][11][12][13]. Strong fields can efficiently excite and ionize atoms and molecules. The electrons, which can be ejected following either multiphoton absorption or tunneling, can either directly reach the detector after having been repeatedly accelerated and decelerated by the field [direct electrons (DE)] or recollide with the ionic core within an optical cycle [rescattered electrons (RE)] [14,15]. Only a small fraction of the ejected electrons rescatter, but this fraction is responsible for important nonlinear phenomena such as high-harmonic generation (HHG). In this process, high-energy photons are emitted as a result of electron recombination with the ionic core. HHG is currently used to produce ultrashort extreme ultraviolet laser pulses and trains of these pulses [16][17][18][19], and also to uncover multielectron dynamics in atoms and molecules [13,20] or the structure of atomic and molecular orbitals in the so-called orbital tomography [10,21,22].Rescattered electrons that do not recombine with the ion also leave their signature in the photoelectron spectra at relatively high energies, typically between 2U p and 10U p [23,24], where U p ¼ I=4! 2 is the electron ponderomotive energy (in a.u.), I is the laser intensity, and ! its frequency. Because of their high energy, in contrast with that of direct electrons which is 2U p , RE can be used as signal and DE as reference to image atomic and molecular structure by photoelectron holography [20,25].Compared to atoms, the study of strong-field electron dynamics in molecules, in particular ...

Conventional approaches to probing ultrafast molecular dynamics rely on the use of synchronized laser pulses with a well-defined time delay. Typically, a pump pulse excites a wavepacket in the molecule. A subsequent probe pulse can then dissociates or ionizes the molecule, and measurement of the molecular fragments provides information about where the wavepacket was for each time delay. In this work, we propose to exploit the ultrafast nuclear-position-dependent emission obtained due to large light-matter coupling in plasmonic nanocavities to image wavepacket dynamics using only a single pump pulse. We show that the time-resolved emission from the cavity provides information about when the wavepacket passes a given region in nuclear configuration space. This approach can image both cavity-modified dynamics on polaritonic (hybrid light-matter) potentials in the strong light-matter coupling regime as well as bare-molecule dynamics in the intermediate coupling regime of large Purcell enhancements, and provides a new route towards ultrafast molecular spectroscopy with plasmonic nanocavities. :1907.12607v1 [cond-mat.mes-hall] arXiv

In this work, the nonlinear optical response, and in particular, the high harmonic generation of semiconductors is addressed by using the Wannier gauge. One of the main problems in the time evolution of the Semiconductor Bloch equations resides in the fact that the dipole couplings between different bands can diverge and have a random phase along the reciprocal space and this leads to numerical instability. To address this problem, we propose the use of the Maximally Localized Wannier functions that provide a framework to map ab-initio calculations to an effective tight-binding Hamiltonian with great accuracy. We show that working in the Wannier gauge, the basis set in which the Bloch functions are constructed directly from the Wannier functions, the dipole couplings become smooth along the reciprocal space thus avoiding the problem of random phases. High harmonic generation spectrum is computed for a 2D monolayer of hBN as a numerical demonstration.

Strong coupling of quantum emitters with confined electromagnetic modes of nanophotonic structures may be used to change optical, chemical and transport properties of materials, with significant theoretical effort invested towards a better understanding of this phenomenon. However, a full theoretical description of both matter and light is an extremely challenging task. Typical theoretical approaches simplify the description of the photonic environment by describing it as a single or few modes. While this approximation is accurate in some cases, it breaks down strongly in complex environments, such as within plasmonic nanocavities, and the electromagnetic environment must be fully taken into account. This requires the quantum description of a continuum of bosonic modes, a problem that is computationally hard. We here investigate a compromise where the quantum character of light is taken into account at modest computational cost. To do so, we focus on a quantum emitter that interacts with an arbitrary photonic spectral density and employ the cumulant or cluster expansion method to the Heisenberg equations of motion up to first, second and third order. We benchmark the method by comparing with exact solutions for specific situations and show that it can accurately represent dynamics for many parameter ranges.Light-matter interaction is of paramount importance for unraveling the laws of nature and its deep understanding allows us to control and manipulate physical and chemical systems. In particular, one can modify the properties of a quantum emitter simply by changing its electromagnetic environment, for example by enclosing it within an optical cavity. This may give rise to a change of the decay rate for spontaneous emission in the weak coupling regime, the so-called Purcell effect 1 , or to the appearance of hybrid light-matter states, socalled polaritons, in the strong-coupling regime 2-5 . Over the last decades, it has been shown that strong light-matter coupling can be achieved using a large variety of physical implementations as the "cavity" that provides the electromagnetic field confinement. These include Fabry-Perot cavities consisting of two mirrors 5 , propagating surface plasmon polaritons 6 , plasmonic hole 7 and nanoparticle arrays 8 , isolated plasmonic nanoparticles 9 and nanoparticle-on-mirror geometries 10,11 , as well as hybrid cavities combining plasmonic and dielectric materials [12][13][14] . In many of these systems, the electromagnetic field modes are not well-described by isolated lossy cavity modes, and a correct treatment demands theoretical approaches that are able to deal with the complexity of the electromagnetic field modes and their spectrum.In principle, to treat the problem of light-matter interaction, one can rely on the most general theory that describes light and matter on equal footing, i.e., quantum electrodynamics (QED) 15 . However, treating all light and matter degrees of freedom in the systems described above in a quantum mechanical way is an intractable problem and approx...

Isotropic gases irradiated by long pulses of intense IR light can generate very high harmonics of the incident field. It is generally accepted that, due to the symmetry of the generating medium, be it an atomic or an isotropic molecular gas, only odd harmonics of the driving field can be produced. Here we show how the interplay of electronic and nuclear dynamics can lead to a marked breakdown of this standard picture: a substantial part of the harmonic spectrum can consist of even rather than odd harmonics. We demonstrate the effect using ab-initio solutions of the time-dependent Schrödinger equation for H 2 + and its isotopes in full dimensionality. By means of a simple analytical model, we identify its physical origin, which is the appearance of a permanent dipole moment in dissociating homonuclear molecules, caused by light-induced localization of the electric charge during dissociation. The effect arises for sufficiently long laser pulses and the region of the spectrum where even harmonics are produced is controlled by pulse duration. Our results (i) show how the interplay of femtosecond nuclear and attosecond electronic dynamics, which affects the charge flow inside the dissociating molecule, is reflected in the nonlinear response, and (ii) force one to augment standard selection rules found in nonlinear optics textbooks by considering light-induced modifications of the medium during the generation process.Attosecond technology originated in nonlinear optics, with high harmonic generation (HHG) being the fundamental physical process underlying the generation of attosecond pulses 1,2 . In the two decades since its inception, attosecond science has grown rapidly 3-5 with applications in physics, chemistry [6][7][8] , materials science 9-11 and even biology 12,13 . High harmonic emission results from nonlinear response of a medium to an intense laser field. Its basic mechanism was first described in refs 14-16 (see also ref. 17). After the intense laser field frees an electron from the ionic core, the electron gains energy from the field and revisits the parent ion. Radiative recombination converts the gained energy into high-frequency radiation.In isotropic atomic gases irradiated by long IR pulses, the electron round-trips between ionization and recombination are launched during successive laser half-cycles. Mirror symmetry of the driving electric field implies that these round trips are mirror images of each other. Electrons revisiting the parent ion from opposite directions yield emission bursts with the same amplitude but opposite signs. As a consequence, even-order harmonics interfere destructively and vanish, while the odd-order harmonics interfere constructively 18 , leading to the spectral peaks at odd multiples of the fundamental frequency, Ω n = (2n + 1)ħω IR .A similar behavior is commonly expected for any isotropic medium, such as an isotropic distribution of homonuclear diatomic molecules. However, the physical picture underlying high harmonic generation suggests that the expectation of odd-only ...

We present a theoretical study of H 2 ionization by a pump-probe scheme consisting on an attosecond pulse train (APT) and a near-infrared (IR) pulse. We focus on the autoionization dynamics of the first series of resonant states of the molecule, the Q 1 doubly excited states. The APT central frequency is tuned to populate the 1 + u resonant states. The trace of autoionization is clearly visible in the two-dimensional (2D) proton-electron coincidence spectra and in the proton kinetic energy spectra. The dynamics of the autoionization process is clearly visible in the movie obtained by plotting the 2D spectrum as a function of the time delay between the APT and IR pulses. An analysis of the final symmetries g and u allows us to track the origin of the different structures.

A pump-probe scheme is proposed to investigate the autoionization dynamics of the optically forbidden Q(1)(1)Σ(g)(+) doubly excited states of the H(2) molecule. The scheme consists of a pump that contains an attosecond pulse train (APT) and an infrared (IR) pulse, which is phase-locked with the APT, and an IR probe identical to the former IR pulse. The dynamical information is obtained by analyzing the electron kinetic energy spectra (EKE) and proton kinetic energy spectra (PKE) as a function of the time delay between the pump and the probe. The essential requirement for an efficient population of the Q(1)(1)Σ(g)(+) states is that they are resonantly coupled to both the dipole-allowed Q(1)(1)Σ(u)(+) doubly excited states and the ground state of H(2) by the combined effect of the APT + IR fields.