Quantum mechanics ascribes to the ground state of the electromagnetic radiation 1 zero-point electric field fluctuations that permeate empty space at all frequencies. No energy can be extracted from the ground state of a system and, therefore, these fluctuations cannot be measured directly with an intensity detector. The experimental proof of their existence came thus from more indirect evidence, such as the Lamb shift, 2-4 the Casimir force between close conductors 5-7 or spontaneous emission. 1,8 A direct method to determine the spectral characteristics of vacuum field fluctuations has been missing so far. In this work, we perform a direct measurement of the field correlation on these fluctuations in the terahertz frequency range using electro-optic detection 9 in a non-linear crystal placed in a cryogenic environment. We investigate their temporal and spatial coherence, which, at zero time delay and spatial distance, has a peak value of 6.2 · 10 −2 V 2 /m 2 , corresponding to a fluctuating vacuum field 10,11 of 0.25 V /m. With this measurement, we determine the spectral composition of the ground state of electromagnetic radiation which lies within the bandwidth of electro-optic detection.The spectral properties of the ground state of a quantum system intimately determine its behavior. An optical cavity, for example, shapes the spectral density of states of vacuum fluctuations and spontaneous emission is enhanced at its resonance frequency. 12 Moreover, systems in which polaritons are created by the ultra-strong coupling of matter excitations to light 13-15 are predicted to have a ground state which contains virtual photons. 16,17 A method to measure the spectral properties of the electromagnetic ground state in-situ would provide a direct experimental test of these properties predicted theoretically.The electric field correlator G (1) (τ ) = E * (t)E(t + τ ) defines the coherence properties of light and yields its power spectrum after a Fourier transformation. Typically, G (1) (τ ) is retrieved by measuring the intensity of the electric field interfering with a delayed version of itself. The real part of the field correlation function (G (1) (τ )) is readily retrieved by

Electro-optic quantum coherent interfaces map the amplitude and phase of a quantum signal directly to the phase or intensity of a probe beam. At terahertz frequencies, a fundamental challenge is not only to sense such weak signals (due to a weak coupling with a probe in the near-infrared) but also to resolve them in the time domain. Cavity confinement of both light fields can increase the interaction and achieve strong coupling. Using this approach, current realizations are limited to low microwave frequencies. Alternatively, in bulk crystals, electro-optic sampling was shown to reach quantum-level sensitivity of terahertz waves. Yet, the coupling strength was extremely weak. Here, we propose an on-chip architecture that concomitantly provides subcycle temporal resolution and an extreme sensitivity to sense terahertz intracavity fields below 20 V/m. We use guided femtosecond pulses in the near-infrared and a confinement of the terahertz wave to a volume of V T H z ∼ 10 − 9 ( λ T H z / 2 ) 3 in combination with ultraperformant organic molecules ( r 33 = 170 p m / V ) and accomplish a record-high single-photon electro-optic coupling rate of g e o = 2 π × 0.043 G H z , 10,000 times higher than in recent reports of sensing vacuum field fluctuations in bulk media. Via homodyne detection implemented directly on chip, the interaction results into an intensity modulation of the femtosecond pulses. The single-photon cooperativity is C 0 = 1.6 × 10 − 8 , and the multiphoton cooperativity is C = 0.002 at room temperature. We show > 70 d B dynamic range in intensity at 500 ms integration under irradiation with a weak coherent terahertz field. Similar devices could be employed in future measurements of quantum states in the terahertz at the standard quantum limit, or for entanglement of subsystems on subcycle temporal scales, such as terahertz and near-infrared quantum bits.

We report a thin film phase modulator employing organic nonlinear optical molecules, with an electro-optic bandwidth of 1.25 THz. The device acts as a polarization sensitive broadband Pockels medium for coherent electric field detection in a dual wavelength terahertz time-domain spectroscopy setup in the telecom band at 1550 nm. To increase the sensitivity, we combine a three-dimensional bow-tie antenna structure with strongly electro-optically active molecules JRD1 in poly­(methyl methacrylate) supporting polymer. The antenna provides subwavelength field confinement of the terahertz wave with its waveguide gap with lateral dimensions of 2.2 μm × 5 μm × 4 μm. In the gap, the electric field is up to 150× stronger than in a diffraction limited space-time volume, such that an interaction length of only 4 μm suffices for the detection of fields below 10 V/m. This device is promising in the growing field of quantum optics in the terahertz, single photon terahertz detection, nonlinear imaging, and on-chip telecommunication.

According to quantum field theory, empty space—the ground state with all real excitations removed—is not empty, but filled with quantum-vacuum fluctuations. Their presence can manifest itself through phenomena such as the Casimir force, spontaneous emission, or dispersion forces. These fluctuating fields possess correlations between space-time points outside the light cone, i.e. points causally disconnected according to special relativity. As a consequence, two initially uncorrelated quantum objects in empty space which are located in causally disconnected space-time regions, and therefore unable to exchange information, can become correlated. Here, we have experimentally demonstrated the existence of correlations of the vacuum fields for non-causally connected space-time points by using electro-optic sampling. This result is obtained by detecting vacuum-induced correlations between two 195 fs laser pulses separated by a time of flight of 470 fs. This work marks a first step in analyzing the space-time structure of vacuum correlations in quantum field theory.

We use micro-Raman spectroscopy to study strain profiles in graphene monolayers suspended over SiN membranes micropatterned with holes of non-circular geometry. We show that a uniform differential pressure load ∆P over elliptical regions of free-standing graphene yields measurable deviations from hydrostatic strain conventionally observed in radially-symmetric microbubbles. The top hydrostatic strain ε we observe is estimated to be ≈ 0.7% for ∆P = 1 bar in graphene clamped to elliptical SiN holes with axis 40 and 20 µm. In the same configuration, we report a G± splitting of 10 cm −1 which is in good agreement with the calculated anisotropy ∆ε ≈ 0.6% for our device geometry. Our results are consistent with the most recent reports on the Grüneisen parameters. Perspectives for the achievement of arbitrary strain configurations by designing suitable SiN holes and boundary clamping conditions are discussed.

Bridging the “terahertz gap“ relies upon synthesizing arbitrary waveforms in the terahertz domain enabling applications that require both narrow band sources for sensing and few-cycle drives for classical and quantum objects. However, realization of custom-tailored waveforms needed for these applications is currently hindered due to limited flexibility for optical rectification of femtosecond pulses in bulk crystals. Here, we experimentally demonstrate that thin-film lithium niobate circuits provide a versatile solution for such waveform synthesis by combining the merits of complex integrated architectures, low-loss distribution of pump pulses on-chip, and an efficient optical rectification. Our distributed pulse phase-matching scheme grants shaping the temporal, spectral, phase, amplitude, and farfield characteristics of the emitted terahertz field through designer on-chip components. This strictly circumvents prior limitations caused by the phase-delay mismatch in conventional systems and relaxes the requirement for cumbersome spectral pre-engineering of the pumping light. We propose a toolbox of basic blocks that produce broadband emission up to 680 GHz and far-field amplitudes of a few V m−1 with adaptable phase and coherence properties by using near-infrared pump pulse energies below 100 pJ.

The effect of cavities or plates upon the electromagnetic quantum vacuum are considered in the context of electro-optic sampling, revealing how they can be directly studied. These modifications are at the heart of e.g. the Casimir force or the Purcell effect such that a link between electro-optic sampling of the quantum vacuum and environment-induced vacuum effects is forged. Furthermore, we discuss the microscopic processes underlying electro-optic sampling of quantum-vacuum fluctuations, leading to an interpretation of these experiments in terms of exchange of virtual photons. With this in mind it is shown how one can reveal the dynamics of vacuum fluctuations by resolving them in the frequency and time domains using electro-optic sampling experiments.

Bridging the "terahertz (THz) gap" relies upon synthesizing arbitrary waveforms in the THz domain enabling applications that require both narrow band sources for sensing and few-cycle drives for classical and quantum objects. However, realization of custom-tailored waveforms needed for these applications is currently hindered due to limited flexibility for optical rectification of femtosecond pulses in bulk crystals. Here, we experimentally demonstrate that thin-film lithium niobate (TFLN) circuits provide a versatile solution for such waveform synthesis through combining the merits of complex integrated architectures, low-loss distribution of pump pulses on-chip, and an efficient optical rectification. Our distributed pulse phase-matching scheme grants shaping the temporal, spectral, phase, amplitude, and farfield characteristics of the emitted THz field through designer on-chip components. This strictly circumvents prior limitations caused by the phase-delay mismatch in conventional systems and relaxes the requirement for cumbersome spectral pre-engineering of the pumping light. We provide a toolbox of basic blocks that produce broadband emission up to 680 GHz with adaptable phase and coherence properties by using near-infrared pump pulse energies below 100 pJ.