The wavefunction is the complex distribution used to completely describe a quantum system, and is central to quantum theory. But despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of the wavefunction through its use to calculate measurement outcome probabilities by way of the Born rule. At present, the wavefunction is determined through tomographic methods, which estimate the wavefunction most consistent with a diverse collection of measurements. The indirectness of these methods compounds the problem of defining the wavefunction. Here we show that the wavefunction can be measured directly by the sequential measurement of two complementary variables of the system. The crux of our method is that the first measurement is performed in a gentle way through weak measurement, so as not to invalidate the second. The result is that the real and imaginary components of the wavefunction appear directly on our measurement apparatus. We give an experimental example by directly measuring the transverse spatial wavefunction of a single photon, a task not previously realized by any method. We show that the concept is universal, being applicable to other degrees of freedom of the photon, such as polarization or frequency, and to other quantum systems--for example, electron spins, SQUIDs (superconducting quantum interference devices) and trapped ions. Consequently, this method gives the wavefunction a straightforward and general definition in terms of a specific set of experimental operations. We expect it to expand the range of quantum systems that can be characterized and to initiate new avenues in fundamental quantum theory.

An analysis of the influence of the magnetic field of an intense, high-frequency laser pulse on the stabilization of an atomic system is presented. We demonstrate that at relatively modest intensities the magnetic field can significantly alter the dynamics of the system. In particular, a breakdown of stabilization occurs, thereby restricting the intensity regime in which the atom is relatively stable against ionization. Counterpropagating pulses do not negate the detrimental effects of the magnetic field. We compare our quantum mechanical results with classical Monte Carlo simulations. PACS numbers: 32.80.Fb, 32.80.Rm, 42.50.Hz Theoretical studies of atoms interacting with highfrequency intense laser pulses have predicted a significant decrease in the ionization probability with increasing laser intensity. This phenomenon is referred to as atomic stabilization, and has been extensively studied over the past decade [1]. Many aspects of this phenomenon can be understood by performing a Kramers-Henneberger (KH) transformation to the rest frame of a classical electron in the laser field. In particular, by developing a highfrequency Floquet theory in the KH frame [2], stabilization can be seen to have its origin in the rapid quiver motion of the atomic electron in the laser field. This allows the electron dynamics to be described by an effective potential that, on average, localizes the electron away from the vicinity of the nucleus. Subsequent ab initio Floquet calculations confirmed that ionization rates decrease with increasing intensity in a high-frequency field [3]. By directly integrating the time-dependent Schrödinger equation numerically, simulations in one [4] and three dimensions [5] demonstrated reductions in the ionization probability with increasing laser intensity when an atom interacts with realistic laser pulses having a finite duration. Further work has been carried out in order to elucidate the effects of the pulse shape and duration [6,7]. We also note that evidence of atomic stabilization of Rydberg states has been observed experimentally [8].In the above-mentioned theoretical studies, the magnetic component of the laser pulse was neglected. However, as the laser intensity increases, relativistic effects that alter the stabilization dynamics become important. Classical Monte Carlo simulations have indicated that the magnetic field pushes the electron in the laser pulse propagation direction, reducing the degree of stabilization [9]. Relativistic wave equations have also been considered within the context of reduced dimensional models [10,11]. However, it is also of interest to study the effects that are neglected in the dipole approximation by using the fully space-and time-dependent vector potential in the nonrelativistic Schrödinger equation [12]. For atomic hydrogen, this results in the cylindrical symmetry of the system being broken, thereby requiring a fully three-dimensional calculation to be carried out for extremely high laser intensities. This is a computationally demanding task. Howev...

At sufficiently high laser intensities, the magnetic-field component of the laser field can strongly influence the stabilization of atoms in the high-frequency regime by inducing motion along the laser pulse propagation direction. Using a two-dimensional model atom, we investigate how the duration of the laser pulse affects stabilization in this nondipole regime. Results obtained using a fully spatially dependent vector potential are compared to a long-wavelength approximation. We also discuss nondipole effects when the atom interacts with two counterpropagating pulses.

We present a numerical method for investigating the non-perturbative quantum mechanical interaction of light with atoms in two dimensions, without a basis expansion. This enables us to investigate intense laser-atom interactions with light of arbitrary polarization without approximation. Results are presented for the dependence of ionization and high harmonic generation on ellipticity seen in recent experiments. Strong evidence of stabilization in circular polarization is found.

The structural evolution from void modification to self-assembled nanogratings in fused silica is observed for moderate (NA > 0.4) focusing conditions. Void formation, appears before the geometrical focus after the initial few pulses and after subsequent irradiation, nanogratings gradually occur at the top of the induced structures. Nonlinear Schrödinger equation based simulations are conducted to simulate the laser fluence, intensity and electron density in the regions of modification. Comparing the experiment with simulations, the voids form due to cavitation in the regions where electron density exceeds 10²⁰ cm^-3 but is below critical. In this scenario, the energy absorption is insufficient to reach the critical electron density that was once assumed to occur in the regime of void formation and nanogratings, shedding light on the potential formation mechanism of nanogratings.