The ground state of quantum systems is characterized by zero-point motion. This motion, in the form of vacuum fluctuations, is generally considered to be an elusive phenomenon that manifests itself only indirectly. Here, we report direct detection of the vacuum fl uctuations of electromagnetic radiation in free space. The ground·state electric-field variance is inversely proportional to the four-dimensional space·time volume, which we sampled electro-optically with tightly focused laser pulses lasting a few femtoseconds. Subcycle temporal readout and nonlinear coupling far from resonance provide signals from purely virtual photons without amplification. Our findings enable an extreme time-domain approach to quantum physics, with nondestructive access to the quantum state of light. Operating at multiterahertz frequencies, such techniques might also allow time-resolved studies of intrinsic fluctuations of elementarY excitations in condensed matter. The quantum properties of light (10) are typi calJy analyzed either by phcton oorrelation (11 14), bomodyning (15 18), or hybrid measurements (19). In those approaches, information is averaged over multiple cycles, and aocessing the vacuum state requires amplification. Femtnsecond studies still rely on pulse envelopes that vary slowly relative tn the carrier frequency (20 23). In our work, we directly probed the varuum noise of the electric field on a subcycle time scale using laser pulses lasting a few femtnseoonds. In ultrabroad band electro optic sampling (24 27), a horizon tally polarized electric field waveform (red in Fig. lA) propagates through an electro optic crystal (EOX), inducing a change Lln of the linear re fractive index 11.o that is proportional to its local amplitude Em:. (Fig. lA and fig. SI). The geometty is adjusted so that a new index ellipsoid emerges under46°tothe polarization of Ern., with nv and nr = 11.o :1:: !!:.n. An ultrashort optical probe pulse at a much higher carrier frequency vp (green in Fig. 1A; intensity, I p, electric field, E.J coprop~ with Em~ at a variable delay time td. The envelope ·of!Pbastn be on theorderofhalfacycle oflightat the highest frequencies il/2rt of En~ that are detected. We used probe pulses as short as tp = 5.8 fs, oorresponding tn Jess than L5 optical cycles at vp = 255 1Hz ( fig. 82). Upon passage through the EOX, the a! andy' components of Ep acquire a relative phase delay proportional to Lln and Eml.,td). The final polarizatim state of the probe is analyzed with ellipsometry. The differential photn rurrent 111/I is proportional tn the electric field Eml.,t,V. We used a radio frequency lock in ampli tier (R.FLA) for readout.We a

No abstract

We report on non-sequential double ionization of Ar by a laser pulse consisting of two counter rotating circularly polarized fields (390 nm and 780 nm). The double ionization probability depends strongly on the relative intensity of the two fields and shows a "knee"-like structure as function of intensity. We conclude that double ionization is driven by a beam of nearly monoenergetic recolliding electrons, which can be controlled in intensity and energy by the field parameters. The electron momentum distributions show the recolliding electron as well as a second electron which escapes from an intermediate excited state of Ar + .Strong laser fields efficiently lead to the ejection of electrons from atoms and molecules. In the continuum the electron wave packet is driven by the laser field and its trajectory can be controlled by tailoring the time evolution of the electric field vector of the laser pulse on a sub cycle basis. A laser pulse composed of two harmonic colors offers already a significant amount of control parameters, such as polarization, relative intensity and phase between the two fields. This allows shaping the light field and thus to steer the electron motion in the continuum or in a bond [1][2][3][4][5][6][7][8][9]. Particularly versatile and in addition well controllable waveforms are generated by counter rotating circular two-color fields (CRTC) shown in Fig. 1 panels (c), (f), (i). These waveforms have spawned recent activities because, unlike circularly polarized light consisting of only a single color, CRTC fields can initially drive electrons away from the atom they have escaped from but later drive them back -often on triangularly shaped trajectories to re-encounter their parent ion. The recapture of these electrons gives rise to the emission of circularly polarized higher harmonic light as predicted in pioneering work by Becker and coworkers [10] and confirmed by recent experimental studies [11]. The recollision in such fields has also been identified by high energetic electrons [12] as well as by characteristic structures in the electron momentum distribution at very low energies where the electrons are Coulomb focused [13].In the present work we experimentally show that CRTC fields also lead to efficient double ionization mediated by the re-colliding electron as predicted by recent classical ensemble calculations [14]. Studying the probability of double ionization and in particular the three dimensional momentum distribution of the emitted electrons gives unprecedented insight into the recollision dy- * Electronic address: doerner@atom.uni-frankfurt.de namics occurring in these two-color laser fields. In particular they support that CRTC fields can be used to create a nearly monoenergetic electron beam for attosecond time-resolved studies. Additionally, very recent theoretical work [15] building on [16] predicts that these recolliding electrons can be generated such that they are spin polarized [17].In order to generate two-color fields, we use a 200 µm BBO to double the frequency of a 7...

No abstract

Photoionization is one of the fundamental light-matter interaction processes in which the absorption of a photon launches the escape of an electron. The time scale of this process poses many open questions. Experiments have found time delays in the attosecond (10−18 seconds) domain between electron ejection from different orbitals, from different electronic bands, or in different directions. Here, we demonstrate that, across a molecular orbital, the electron is not launched at the same time. Rather, the birth time depends on the travel time of the photon across the molecule, which is 247 zeptoseconds (1 zeptosecond = 10−21 seconds) for the average bond length of molecular hydrogen. Using an electron interferometric technique, we resolve this birth time delay between electron emission from the two centers of the hydrogen molecule.

We demonstrate a clear similarity between attoclock offset angles and Rutherford scattering angles taking the Keldysh tunnelling width as the impact parameter and the vector potential of the driving pulse as the asymptotic velocity. This simple model is tested against the solution of the timedependent Schrödinger equation using hydrogenic and screened (Yukawa) potentials of equal binding energy. We observe a smooth transition from a hydrogenic to 'hard-zero' intensity dependence of the offset angle with variation of the Yukawa screening parameter. Additionally we make comparison with the attoclock offset angles for various noble gases obtained with the classical-trajectory Monte Carlo method. In all cases we find a close correspondence between the model predictions and numerical calculations. This suggests a largely Coulombic origin of the attoclock offset angle and casts further doubt on its interpretation in terms of a finite tunnelling time.

We report on the non-adiabatic offset of the initial electron momentum distribution in the plane of polarization upon single ionization of argon by strong field tunneling and show how to experimentally control the degree of non-adiabaticity. Two-color counter-and co-rotating fields (390 and 780 nm) are compared to show that the non-adiabatic offset strongly depends on the temporal evolution of the laser electric field. We introduce a simple method for the direct access to the non-adiabatic offset using two-color counter-and co-rotating fields. Further, for a single-color circularly polarized field at 780 nm we show that the radius of the experimentally observed donut-like distribution increases for increasing momentum in the light propagation direction. Our observed initial momentum offsets are well reproduced by the strong-field approximation (SFA). A mechanistic picture is introduced that links the measured non-adiabatic offset to the magnetic quantum number of virtually populated intermediate states.

For a circularly polarized single-color field at a central frequency of 2ω, the final electron momentum distribution upon strong field ionization does not carry any information about the phase of the initial momentum distribution. Adding a weak, corotating, circularly polarized field at a central frequency of ω gives rise to a subcycle interference pattern [holographic angular streaking of electrons (HASE)]. This interference pattern allows for the retrieval of the derivative of the phase of the initial momentum distribution after tunneling φ off (p i). A trajectory-based semiclassical model (HASE model) is introduced which links the experimentally accessible quantities to φ off (p i). It is shown that a change in φ off is equivalent to a displacement in position space x of the initial wave packet after tunneling. This offset in position space allows for an intuitive interpretation of the Wigner time delay τ W in strong-field ionization for circularly polarized single-color fields. The influence of Coulomb interaction after tunneling is investigated quantitatively.