We demonstrate time-domain sampling of mid-infrared electric field transients and their conjugate counterparts exploiting the dynamical Pockels effect. To this end, the complete polarization change of few-femtosecond probe pulses is studied. An intuitive picture based on a phasor representation is established before gaining quantitative understanding in experiment and theory. In the standard version of electro-optic sampling, the electric field is determined by analyzing the change of ellipticity of the probe polarization. Beyond this, we find that a temporal gradient of the input electric field manifests itself in a rotation of the polarization ellipsoid of the probe. The relative contribution of sum-and difference-frequency mixing processes and their spectral distribution over the near-infrared probe bandwidth are identified as key aspects. If one of these processes dominates, detecting ellipticity changes and polarization rotation as a function of time delay results in two wave forms which are Hilbert transforms of each other. Such conditions may be achieved by angle phase matching in birefringent materials or spectral filtering of the probe after the nonlinear interaction. In this case, a static phase introduced by birefringence or reflection at metallic mirrors results in a specific phase shift of both time traces with respect to the input electric field. Contributions from sum-and difference-frequency generation are found to be equivalent when using electro-optic sensors with isotropic refractive index. Polarization rotations in the lowand high-frequency parts of the probe then tend to cancel out. In this limit, spurious additional phase shifts do not change the phase of the detected transients. This fact leads to a robust recovery of the carrier-envelope phase of the input wave form. Clarifying the role of imperfections of superachromatic phase retarders completes our survey on proper determination of the electric field and its conjugate variable.

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We study spectral properties of quantum radiation of ultimately short duration. In particular, we introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by a coherent-field driving in a thin nonlinear crystal with second order susceptibility. We find the ultrabroadband spectra of the emitted quantum radiation perturbatively in the strength of the driving field. These spectra can be related to the spectra expected in an Unruh-Davies experiment with a finite time of acceleration. In the time domain, we describe the corresponding behavior of the normally ordered electric field variance. PACS numbers: 42.50.Dv, 42.50.Lc, 42.65.Re, 04.62.+v Introduction.-In quantum optics, parametric downconversion (PDC) in nonlinear crystals (NXs) has been routinely used to generate pairs of monochromatic entangled photons [1,2]. The so obtained squeezed states of light have found applications in a broad range of areas like gravitational wave detection [3,4], quantum communication systems [5][6][7] and precision measurements [8,9]. The active interest in squeezed states can be mainly related to the fact that the variance of a given phase space quadrature (a quantum-optical analogue of a canonical variable) is lower for a squeezed state than for a coherent state, including the vacuum state itself. In order to fulfill Heisenberg's uncertainty principle the variance of the conjugate quadrature exhibits the opposite behavior.In recent years, theoretical and experimental efforts have been made to describe and generate multimode squeezed states [10][11][12][13][14][15]. Although they have already been experimentally realized by a number of groups [12,15], most of the achievements so far are limited to squeezed states with relatively narrow spectra, where the central frequency approximation is still valid. New developments in ultra-stable few-cycle laser sources and advanced detection techniques have paved the way for the generation of few-cycle pulses of mid-infrared (MIR) squeezed light and the electro-optic detection of their electric field statistics with subcycle temporal resolution [16][17][18]. The subcycle features in the noise patterns of the generated quantum fields are due to the spatio-temporal modulation of the refractive index of the NX induced by the driving field [18]. This is analogous to a time-dependent metric for the space-time occupied by the electric field, which leads to photon creation in the perspective of a moving observer [19].The spectral properties of ultrabroadband squeezed states are also of particular interest because they can elucidate connections between quantum gravitational effects and their table-top optical analogues. A characteristic example is the Unruh-Davies effect [20,21], according to which an observer in a non-inertial reference frame,

A new theoretical framework to describe the experimental advances in electro-optic detection of broadband quantum states, specifically the quantum vacuum, is devised. Electro-optic sampling is a technique in ultrafast photonics which, when transferred into the quantum domain, can be utilized to resolve properties of a sampled quantum state via its interaction with a strong coherent probe pulse at ultrafast timescales. By making use of fundamental concepts from quantum field theory on spacetime metrics, the nonlinear interaction behind the electro-optic effect is shown to be equivalent to a stationary Unruh-DeWitt detector coupled to a conjugate field during a very short time interval. When the coupling lasts for a time interval comparable to the oscillation periods of the detected field mode (i.e., the subcycle regime), virtual particles inhabiting the field vacuum are transferred to the detector in the form of real excitation. We demonstrate that this behavior can be rigorously translated to the scenario of electro-optic sampling of the quantum vacuum, in which the (spectrally filtered) probe works as an Unruh-DeWitt detector, with its interaction-generated photons arising from virtual particles inhabiting the electromagnetic vacuum. Our analysis accurately encapsulates the quantum nature of the vacuum, and we propose the specific working regime in which we can experimentally verify the existence of virtual photons with quantum correlations in the electromagnetic ground state.

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