Probing the quantum vacuum with nonlinear crystals

A. S. Moskalenko, Claudius Riek, Denis V. Seletskiy +2 more

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.

Chloe Watson

Frieder Lindel, Robert G. Bennett, Stefan Yoshi Buhmann

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.

Nikolay N. Rosanov

T.R. KOEHLER

Thiago Lucena Macedo Guedes

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.