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 fluctuations 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 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 fluctuations 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.
A time-domain approach to quantum electrodynamics is presented, covering the entire mid-infrared and terahertz frequency ranges. Ultrabroadband electro-optic sampling with few-femtosecond laser pulses allows direct detection of the vacuum fluctuations of the electric field in free space [1,2]. Besides the Planck and electric field fundamental constants, the variance of the ground state is determined solely by the inverse of the four-dimensional space-time volume over which a measurement or physical process integrates. Therefore, we can vary the contribution of multi-terahertz vacuum fluctuations and discriminate against the trivial shot noise due to the constant flux of near-infrared probe photons. Subcycle temporal resolution based on a nonlinear phase shift provides signals from purely virtual photons for accessing the ground-state wave function without amplification to finite intensity. Recently, we have succeeded in generation and analysis of mid-infrared squeezed transients with quantum noise patterns that are time-locked to the intensity envelope of the probe pulses. We find subcycle temporal positions with a noise level distinctly below the bare vacuum which serves as a direct reference. Delay times with increased differential noise indicate generation of highly correlated quantum fields by spontaneous parametric fluorescence. Our time-domain approach offers a generalized understanding of spontaneous emission processes as a consequence of local anomalies in the co-propagating reference frame modulating the quantum vacuum, in combination with the boundary conditions set by Heisenberg’s uncertainty principle. [1] C. Riek et al., Science 350, 420 (2015) [2] A. S. Moskalenko et al., Phys. Rev. Lett. 115, 263601 (2015)
Direct detection of vacuum fluctuations and analysis of subcycle 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 electro-optic crystal and stable few-femtosecond laser pulses. We show that nonlinear mixing of a short near-infrared probe pulse with the multiterahertz vacuum field 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 pulse duration, tight focusing, and a 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 a noise level below the pure vacuum may be traced with subcycle resolution.
Quantum fluctuations associated with the ground state of a system exist as a consequence of Heisenberg's uncertainty principle. These fluctuating fields manifest themselves indirectly through their influence on matter which has been extensively studied by considering e.g. the Casimir and Casimir-Polder force. More recently, these ground state fluctuations have been measured directly using nonlinear crystals by means of electro-optical sampling. Despite their common origin, these direct versus indirect evidence of ground-state fluctuations remain disjoint phenomena to date. Here we develop a theoretical framework for describing propagation of a quantized electric field through a nonlinear crystal, allowing for arbitrarily-shaped dispersive and absorptive environments. It can be used in different contexts, one of which is to forge the missing link between the different approaches to observing the quantum vacuum mentioned above. To demonstrate this we show that the change of the vacuum fluctuations induced by a macroscopic object can be directly observed using electro-optical sampling.
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.
Studies on the nature of light have often played pivotal roles in the development of physics. The particle nature of light served as benchmark for the foundation of quantum physics and its derived branches, while its referential-independent speed in the vacuum, as seen through wave equations, led to the merge of space and time and culminated in the foundation of general relativity and cosmology. In spite of that, many light-based measurement techniques still rely heavily on a classical description of light, as has been for many years the case for electrooptic sampling. Luckily, this scenario has been changed in the course of the last few years, with both experimental and theoretical works highlighting the advantages and hidden properties that a quantum and/or relativistic description of light can unveil. Speci fically, the electrooptic sampling of a broadband section of the electric- field vacuum opened an entirely new window of possibilities, and the works presented here aim at filling a small portion of the gap opened by this simple, yet remarkable, technological leap. As a starting point, I study the spectral properties of quantum radiation of ultrashort duration. In particular, I introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by a coherent-pulse driving in a thin nonlinear crystal with second-order susceptibility. The spectra of these ultrabroadband squeezed states can be found perturbatively in the strength of the driving electric-fi eld pulse. These can be related, for suitable choices of the driving pulses, to the spectra that one should hypothetically observe in an Unruh-Davies experiment, in which an observer (more precisely a particle detector) moving with constant proper acceleration in the Minkowski vacuum during a finite (life)time detects a thermal distribution of (virtual) particles. On the other hand, when describing the corresponding behavior of the normally ordered electric- field variance in the time domain, a connection to experiments in which such states have been generated and detected can be traced. This variance builds up as the electric fi eld (or correspondingly its state) evolves via propagation through the nonlinear crystal, and it can be shown that the world lines followed by the fi eld modes when propagating are indeed curved, as is usually the case for the Unruh-DeWitt detectors used to study the Unruh-Davies effect. Alongside the study of the states generated in a nonlinear crystal, I also investigate what influence these states have on the electrooptic measurements that rely on the same effective nonlinear interaction. When electrooptically sampling the electric- field vacuum, the evolution of the electric fi eld leads to a change in the initially sampled vacuum state. This change piles up backaction contributions that remain in superposition with the vacuum state after the measurement. When the superposition coefficients of the back-action contributions are small, the electrooptic-signal variance is dominated by the shot noise, with a small vacuum-related contribution on top. As the sampling regime shifts towards stronger probe-pulse intensities, the state superposition undergoes a change, which can be traced back to the signal variance and the clear change in its behavior, with a steep departure from the shot noise. This approach is then further extended to model another setup in which two probes, time-shifted relative to each other, are impinged on the nonlinear crystal to probe the vacuum. This approach allows for the evasion of shot noise and produces a way richer variety of back-action contributions that are then investigated.
This article develops an expanded critical–propositional analysis of Claudius Riek et al.’s 2015 experiment, “Direct Sampling of Electric-Field Vacuum Fluctuations,” published in Science, in systematic dialogue with the Theory of Objectivity (TO) developed by Vidamor Cabannas and Denivaldo Silva. The experiment is scientifically significant because it provided time-domain electro-optic access to the variance of the electromagnetic ground state in free space, using few-femtosecond optical pulses and nonlinear electro-optic coupling. Riek et al. showed that the measurable contribution attributed to quantum-vacuum fluctuations depends on the four-dimensional space-time volume sampled by the probe and can be distinguished from probe shot noise by changing the temporal and transverse dimensions of the sampling region. The present study does not interpret this experiment as a direct proof of the modal axioms of the Theory of Objectivity. Instead, it investigates whether specific empirical structures identified by Riek et al.—field persistence in the ground state, dependence on physical boundaries and sampling domains, relational measurement, transformation of field configurations into physically recoverable information, and the absence of any necessary role for human consciousness—can function as operational bridges to selected propositions of the TO. Special attention is given to the First Absolute Truth, according to which primordial Nothing is not absolute nonbeing but an eternal logical and mathematical essence; the Second Absolute Truth, according to which every element possesses its own exclusive magnetic field that individualizes it; and the Fifth Absolute Truth, according to which logical existence requires observation by, or frequency inclusion within, at least two other elements, where observation is an objective physical relation rather than human perception. The analysis also considers the Third, Fourth, Sixth, and Seventh Absolute Truths, the TO concept of the transcendent element as knowledge or information produced in atomic relations and equivalent to atomic radiation, the phenomenic elements, Inductive Effects, the Cosmogonic Theorem, and the cosmological Eras. The article argues that Riek et al. offer particularly strong operational dialogue with TO propositions concerning boundary, relational observation, physical mediation, and information-producing interactions. However, the experiment does not establish the TO’s primordial logical Nothing, does not demonstrate a unique individualizing magnetic field for every existing element, and does not prove that relational observation is a necessary ontological condition of existence rather than a necessary condition of measurement. The strongest scientific use of the experiment within the TO is therefore as an empirical bridge for the development of falsifiable operational consequences, rather than as an independent demonstration of modal necessity. Keywords: Theory of Objectivity; quantum vacuum; vacuum fluctuations; electro- optic sampling; zero-point field; modal ontology; relational observation; information; radiation; quantum electrodynamics; cosmology; Riek.