Establishing the structure of molecules and solids has always had an essential role in physics, chemistry and biology. The methods of choice are X-ray and electron diffraction, which are routinely used to determine atomic positions with sub-ångström spatial resolution. Although both methods are currently limited to probing dynamics on timescales longer than a picosecond, the recent development of femtosecond sources of X-ray pulses and electron beams suggests that they might soon be capable of taking ultrafast snapshots of biological molecules and condensed-phase systems undergoing structural changes. The past decade has also witnessed the emergence of an alternative imaging approach based on laser-ionized bursts of coherent electron wave packets that self-interrogate the parent molecular structure. Here we show that this phenomenon can indeed be exploited for laser-induced electron diffraction (LIED), to image molecular structures with sub-ångström precision and exposure times of a few femtoseconds. We apply the method to oxygen and nitrogen molecules, which on strong-field ionization at three mid-infrared wavelengths (1.7, 2.0 and 2.3 μm) emit photoelectrons with a momentum distribution from which we extract diffraction patterns. The long wavelength is essential for achieving atomic-scale spatial resolution, and the wavelength variation is equivalent to taking snapshots at different times. We show that the method has the sensitivity to measure a 0.1 Å displacement in the oxygen bond length occurring in a time interval of ∼5 fs, which establishes LIED as a promising approach for the imaging of gas-phase molecules with unprecedented spatio-temporal resolution.

Over the past thirty years, extensive studies of strong-field photoionization of atoms have revealed both quantum and classical aspects including above-threshold ionization 1 , electron wave-packet drift, quiver and rescattering motions. Increasingly sophisticated spectroscopic techniques 2 and sculpted laser pulses 3 coupled with theoretical advances have led to a seemingly complete picture of this fundamental laser-atom interaction. Here, we describe an effect that seems to have escaped observation: the photoelectron energy distribution manifests an unexpected characteristic spike-like structure at low energy, which becomes prominent using mid-infrared laser wavelengths (λ > 1.0 µm). The low-energy structure is observed in all atoms and molecules investigated and thus seems to be universal. The structure is qualitatively reproduced by numerical solutions of the time-dependent Schrödinger equation but its physical origin is not yet identified.Atomic photoionization under intense laser irradiation is considered a well-understood process. In the low-intensity/shortwavelength limit, it is described quantum mechanically as multiphoton absorption: above-threshold ionization (ATI) is the absorption of photons beyond the minimum required for ionization. In the high-intensity/long-wavelength limit, the photoelectron energy distribution can be understood classically according to the Simpleman theory 4 , as the drift kinetic energy of an electron as a function of the phase at which it was released in the laser cycle. Inclusion of the d.c.-tunnelling rate to describe the ionization probability completes a semi-classical theory. A corresponding quantum approach is provided by the Keldysh-Faisal-Reiss [5][6][7] (KFR) strong-field approximation. The KFR theory incorporates the effect of the external field on the continuum state but neglects the influence of the core potential and ignores the atom's excited states. Keldysh linked these two limits in terms of a single dimensionless parameter γ = √ (IP/2U p ), where IP is the ionization potential and U p is the cycle-averaged kinetic energy of an electron quivering in the field. In the limit defined by γ < 1, the electric field of the wave can be considered quasi-static and the total ionization rate approximated by d.c.-tunnelling in accordance with the semi-classical picture. The photoelectron distribution in this case has a classical cutoff energy at 2U p . A more elusive feature, discovered in the mid-nineties 8,9 , is the plateau in the photoelectron distribution extending to 10U p . Understanding the origin of this plateau requires a straightforward extension of the Simpleman theory that enables a returning electron to elastically scatter off the core. As illustrated in the inset of Fig. 1, the photoelectron spectrum exhibits both of these features, 'direct' and 'rescattered'. The amplitude of the plateau can be described by the scattering cross-section and the spread of the electron wave packet 10 . More detailed features associated with rescattering, such as the plateau'...

In 1964 Keldysh1 helped lay the foundations of strong-field physics by introducing a theoretical framework that characterized atomic ionization as a process that evolves with the intensity and wavelength of the fundamental field. Within this context, experiments 2 have examined the intensity-dependent ionization but, except for a few cases, technological limitations have confined the majority to wavelengths below 1 µm. The development of intense, ultrafast laser sources in the midinfrared (1 µm < l < 5 µm) region enables exploration of the wavelength scaling of the Keldysh picture while enabling new opportunities in strong-field physics, control of electronic motion and attosecond science. Here we report a systematic experimental investigation of the wavelength scaling in this region by concurrently analysing the production of energetic electrons and photons emitted by argon atoms interacting with few-cycle, mid-infrared fields. The results support the implicit predictions contained in Keldysh's work, and pave the way to the realization of brighter and shorter attosecond pulsed light sources using longer-wavelength driving fields. Keldysh 1 described the two main effects an intense lowfrequency laser field has on an atom as (1) a bending of the Coulomb potential by the field, forming a sufficiently narrow barrier for the electron to tunnel into the continuum, and (2) an oscillating motion of the free electron induced by the field of strength E and frequency ω. The cycle-averaged kinetic energy of the oscillating electron (ponderomotive energy) is given in atomic units as U p = E 2 /4ω 2 . The limit of validity of the Keldysh approach is defined by the condition that the adiabaticity parameter γ = √

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