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

We calculate the ground and excited electron and hole levels in spherical Si quantum dots inside SiO 2 in a multiband effective mass approximation. The Luttinger Hamiltonian is used for holes, and the strong anisotropy of the conduction electron effective mass in Si is taken into account. As the boundary conditions for the electron and hole wave functions, we use the continuity of the wave functions and the flux at the boundaries of the quantum dots.

Direct detection of vacuum fluctuations and analysis of sub-cycle quantum properties of the electric field are explored by a paraxial quantum theory of ultrafast electro-optic sampling. The feasibility of such experiments is demonstrated by realistic calculations adopting a thin ZnTe electrooptic crystal and stable few-femtosecond laser pulses. We show that nonlinear mixing of a short near-infrared probe pulse with multi-terahertz vacuum field modes leads to an increase of the signal variance with respect to the shot noise level. The vacuum contribution increases significantly for appropriate length of the nonlinear crystal, short probe pulse durations, tight focusing, and sufficiently large number of photons per probe pulse. If the vacuum input is squeezed, the signal variance depends on the probe delay. Temporal positions with noise level below the pure vacuum may be traced with a sub-cycle accuracy.PACS numbers: 42.50. Ct, 42.50.Lc, 42.65.Re, 78.20.Jq Finite fluctuation amplitudes in the ground state of empty space represent the ultimate hallmark of the quantum nature of the electromagnetic radiation field. These vacuum fluctuations manifest themselves indirectly in a number of phenomena that are accessible to spectroscopy such as the spontaneous decay of excited atomic states as well as the Lamb shift [1] in atoms [2] and in quantummechanical electric circuits [3]. Access to the quantum aspects of electromagnetic radiation is provided by the analysis of photon correlation [4,5] or homodyning [6][7][8][9][10][11] measurements. However, these approaches require amplification of the quantum field under study to finite intensity and averaging of the information over multiple optical cycles.On the other side, precise determination of voltage or electric field amplitude as a function of time represents a fundamental task in science and engineering. Optical techniques have to be applied when detecting electric fields oscillating in the terahertz (THz) range and above. Those approaches involve probing with ultrashort laser pulses of a temporal duration on the order of half an oscillation period at the highest frequencies under study. Far-infrared electric transients [12,13] can be characterized by photoconductive switching [14]. Electro-optic sampling in free space [15][16][17] allows field-resolved detection at high sensitivity in the entire far-and mid-infrared spectral range [18,19]. Direct studies of the complexvalued susceptibilities of materials and the elementary dynamics in condensed matter may be performed with these methods [20,21]. The time integral of near-infrared to visible electric-field wave packets is accessible with attosecond streaking [22]. So far, all those techniques were restricted to the classical field amplitude.In this Letter, we demonstrate theoretically that the quantum properties of light may be accessed directly in the time domain, i.e. with sub-cycle temporal resolution. Our considerations are based on the realistic example of electro-optic detection with zincblende-type materials T...

2Coherent states represent the closest counterpart to a classical electromagnetic wave that exists in quantum electrodynamics. The quantum noise amplitudes of their electric and magnetic fields coincide precisely with those of the vacuum state 19 . Recently, we have succeeded to directly detect the bare vacuum fluctuations of the mid-infrared electric field with highly sensitive electro-optic sampling based on ultrashort laser pulses 15,16 . One key aspect of this technique is that it operates out of a time-domain perspective. Therefore, it should provide a resolution substantially below the duration of an oscillation period of any quantum field under study. Naturally, it is tempting to think about an experiment that synchronously couples a nonclassical state of light into the space-time volume which is probed, thus providing a quantum noise amplitude that deviates from pure vacuum fluctuations. Especially, it would be an attractive manifestation of quantum physics if less noise as compared to the quantum vacuum could be localized in time and space. In conventional homodyning studies, the carrier wave of a local oscillator needs to be phaselocked to a quantum state 11,16 . Instead, we have to prepare a squeezed electromagnetic transient with a noise pattern that is synchronized with the intensity envelope of an ultrashort probe pulse. This tightly focussed few-femtosecond optical wave packet then defines a subcycle space-time segment in which the quantum statistics of a mid-infrared nonclassical signal is sampled. Our scheme to implement such an experiment is sketched in Fig. 1(a). We send an intense near-infrared pump pulse (red-yellow envelope) with duration of 12 fs and centre frequency of 200 THz into a thin generation crystal (GX). In a first step, a carrier-envelope phase-locked electric field transient 20 is generated by optical rectification (red line). Once built up, it starts to locally phase shift the co-propagating multi-terahertz vacuum fluctuations (green shaded band) by means of the electro-optic effect in the GX which establishes a change in refractive index n(t) proportional to the mid-infrared electric field amplitude E THz (t). In a simplified picture, the resulting local anomalies in the speed of light might induce depletion of vacuum amplitude at certain space-time regions (blue shaded sections), piling it up in others (stained in red). A high efficiency for this two-step mechanism to squeeze the mid-infrared vacuum is 3 ensured by the large second-order nonlinearity of the 16-m-thick exfoliated piece of GaSe we employ as GX 20 . Tight focussing of the pump to a paraxial spot radius w pump of 3.6 m also defines the transverse spatial mode for the nonclassical electric field pattern. After the GX, the squeezed vacuum is collimated and residual pump is removed by a 70-m-thick GaSb filter inserted under Brewster's angle. A mode-matched 5.8 fs probe pulse (blue envelope) is then superimposed onto the multi-terahertz field and focussed to w probe = 3.6 m in a AgGaS 2 detector crystal (DX) of...

We report on the first experimental observation of a concentric-ring pattern in a short planar dielectric barrier gas-discharge system and study its spatiotemporal behavior. While increasing the gas pressure the destabilization of the rings into a filamentary structure is observed. The charge carriers deposited on the dielectric electrodes determine the spatiotemporal behavior of the pattern.

We report on an observation of a fast 1.5 microm photoluminescence band from Er3+ ions embedded in an SiO2 matrix doped with Si nanocrystals, which appears and decays within the first microsecond after the laser excitation pulse. We argue that the fast excitation and quenching are facilitated by Auger processes related to transitions of confined electrons or holes between the space-quantized levels of Si nanocrystals dispersed in SiO2. We show that a great part--about 50%--of all Er dopants is involved in these fast processes and contributes to the submicrosecond emission.

We present a high-resolution photoluminescence study of Er-doped SiO 2 sensitized with Si nanocrystals ͑Si NCs͒. Emission bands originating from recombination of excitons confined in Si NCs, internal transitions within the 4f-electron core of Er 3+ ions, and a band centered at Ϸ 1200 nm have been identified. Their kinetics were investigated in detail. Based on these measurements, we present a comprehensive model for energy-transfer mechanisms responsible for light generation in this system. A unique picture of energy flow between the two subsystems was developed, yielding truly microscopic information on the sensitization effect and its limitations. In particular, we show that most of the Er 3+ ions available in the system are participating in the energy exchange. The long-standing problem of apparent loss of optical activity in the majority of Er dopants upon sensitization with Si NCs is clarified and assigned to the appearance of a very efficient energy exchange mechanism between Si NCs and Er 3+ ions. Application potential of SiO 2 : Er, sensitized by Si NCs, was discussed in view of the newly acquired microscopic insight.

We investigate theoretically the relative time delay of photoelectrons originating from different atomic subshells of noble gases. This quantity was measured via attosecond streaking and studied theoretically by Schultze et al (2010 Science 328 1658) for neon. A substantial discrepancy was found between the measured and the calculated values of the relative time delay. Several theoretical studies were put forward to resolve this issue, e.g., by including correlation effects. In the present paper we explore a further aspect, namely the directional dependence of time delay. In contrast to neon, for argon target a strong angular dependence of the time delay is found near the Cooper minimum.