The distinction between vacuum-field and source-radiation effects in phenomena such as the Lamb shift, Casimir forces, and spontaneous emission relies on additional assumptions at the theoretical level, and an experimental approach was never considered feasible. Fermi’s two-atom problem, a Gedankenexperiment on how atoms interact with the electromagnetic field via vacuum and source radiation, provides key theoretical insight. Advances in ultrafast optics now enable experimental analogues using two laser pulses in a nonlinear crystal. Here we demonstrate the detection of vacuum- and source-radiation-induced correlations between two pulses, separated by their causal properties. Specifically, vacuum fluctuations and source radiation are shown to correlate distinct quadratures of near-infrared pulses, enabling individual probing via phase-sensitive detection. Our results experimentally verify the time-domain fluctuation-dissipation theorem at the quantum level and open avenues for studying quantum radiation effects in time-dependent media, including entanglement harvesting from the vacuum and quantum field detection in curved-space analogues. Two nearby atoms build up correlations due to two fundamentally different effects: individual interactions with the same vacuum fluctuations, and photon exchange. It is normally assumed that only the total effect is experimentally observable, and not the two individual contributions. Here, the authors challenge this in an experiment using an electro-optic analogue of Fermi’s two atoms setup.
The distinction between vacuum-field and source-radiation effects in phenomena such as the Lamb shift, Casimir forces, and spontaneous emission relies on additional assumptions at the theoretical level, and an experimental approach was never considered feasible. Fermi’s two-atom problem, a Gedankenexperiment on how atoms interact with the electromagnetic field via vacuum and source radiation, provides key theoretical insight. Advances in ultrafast optics now enable experimental analogues using two laser pulses in a nonlinear crystal. Here we demonstrate the detection of vacuum- and source-radiation-induced correlations between two pulses, separated by their causal properties. Specifically, vacuum fluctuations and source radiation are shown to correlate distinct quadratures of near-infrared pulses, enabling individual probing via phase-sensitive detection. Our results experimentally verify the time-domain fluctuation-dissipation theorem at the quantum level and open avenues for studying quantum radiation effects in time-dependent media, including entanglement harvesting from the vacuum and quantum field detection in curved-space analogues. Two nearby atoms build up correlations due to two fundamentally different effects: individual interactions with the same vacuum fluctuations, and photon exchange. It is normally assumed that only the total effect is experimentally observable, and not the two individual contributions. Here, the authors challenge this in an experiment using an electro-optic analogue of Fermi’s two atoms setup.
The distinction between vacuum-field and source-radiation effects in phenomena such as the Lamb shift, Casimir forces, and spontaneous emission relies on additional assumptions at the theoretical level, and an experimental approach was never considered feasible. Fermi's two-atom problem, a Gedankenexperiment on how atoms interact with the electromagnetic field via vacuum and source radiation, provides key theoretical insight. Advances in ultrafast optics now enable experimental analogues using two laser pulses in a nonlinear crystal. Here we demonstrate the detection of vacuum- and source-radiation-induced correlations between two pulses, separated by their causal properties. Specifically, vacuum fluctuations and source radiation are shown to correlate distinct quadratures of near-infrared pulses, enabling individual probing via phase-sensitive detection. Our results experimentally verify the time-domain fluctuation-dissipation theorem at the quantum level and open avenues for studying quantum radiation effects in time-dependent media, including entanglement harvesting from the vacuum and quantum field detection in curved-space analogues.
Although the Fermi two-atom problem has so far been limited to theoretical discussion, we will present an experimental analogy by replacing the atoms with femtosecond laser pulses that interact with the ground state of light. Two different effects, namely vacuum fluctuations and source radiation, can introduce a correlation between the two laser pulses. A difference in the phase relation between the contributing electric fields allows for the individual probing of the two effects that were previously thought to be inseparable.
The quantum description of the electromagnetic (EM) field, even in the absence of sources, reveals that the vacuum exhibits fluctuations in the energy and of the components of the field, known as quantum vacuum fluctuations. The coupling of these quantum fluctuations of the vacuum to electric charges leads to experimentally observable phenomena, such as the spontaneous emission of an excited atom, the Lamb effect, the Casimir effect, and the van der Waals interactions, which have been historically fundamental for the confirmation of the existence of these fluctuations. The optical response of simple atoms and the EM interaction between two atoms constitute the simplest realistic phenomena for studying these effects. This thesis focuses on the fundamental study of the properties of interatomic interactions, addressing aspects such as their dependence on the interatomic distance, their time dependence, and the emergence of nonreciprocal interatomic forces due to parity breaking. In particular, the detailed analysis of the electric dipole forces in a system of two atoms, one of which is initially excited, is carried out, along with the study of the implication of the resonant interactions in the appearance of collective effects in absorption and emission processes of many-atom systems. Due to the inherently time-dependent nature of the resonant forces between excited atoms, a time-dependent Hamiltonian approach is employed. The atomic interaction processes are represented with time-ordered diagrams. It is obtained that the atoms are subjected to resonant conservative forces, directed along the interatomic axis, which exert a net force on the system. This result implies an apparent violation of the action-reaction principle due to the lack of conservation of the kinetic momentum of the atoms. However, this net force on the atomic system is compensated by the time derivative of the transversal momentum of the EM field, associated with the resonant photons that mediate the interaction, ensuring the conservation of the total momentum of the system. In addition to these conservative forces, there are nonconservative forces which are a consequence of the time derivative of the so-called longitudinal momentum of the electromagnetic field and contain components perpendicular to the interatomic axis. We analyze the particular case of the interaction between identical atoms. In this scenario, the net force on the system becomes time-dependent. Furthermore, states with degenerate energy arise and evolve coherently through the periodic transfer of resonant photons between the atoms. This implies that in these degenerate states, there are contributions from interatomic interactions that cannot be expressed as an energy shift in the atomic wave functions. Consequently, these interactions give rise to collective phenomena observable in photon absorption and emission processes. At the same time, the strength of these forces is markedly superior to that calculated for different atoms, which makes this scenario a more favorable set-up for the experimental observation of the nonreciprocal forces and the associated coherent phenomena. Concerning collective effects and their application in the design of multi-atomic qubits, these phenomena have significant implications for the scalability and connectivity of such systems. To describe these collective properties, we have formulated a Hamiltonian that incorporates both the interaction processes, i.e., those that give rise to dynamic coherence and incoherence effects, and the stationary interaction processes that renormalize the energy of the atomic states. It is found that the photon absorption probability is determined by the ratio between the interatomic interaction and the intensity of the laser that excites the system. On the other hand, the spontaneous emission of photons is proportional to the number of decay channels, which decrease when the interatomic interaction between excited states breaks the degeneracy in the subspaces associated with the same number of excitations.
The solution to the wave equation as a Cauchy problem with prescribed fields at an initial time t=0 is purely retarded. Similarly, in the quantum theory of radiation the specification of Heisenberg picture photon annihilation and creation operators at time t>0 in terms of operators at t=0 automatically yields purely retarded source-fields. However, we show that two-time quantum correlations between the retarded source-fields of a stationary dipole and the quantum vacuum-field possess advanced wave-like contributions. Despite their advanced nature, these correlations are perfectly consistent with Einstein causality. It is shown that while they do not significantly contribute to photo-detection amplitudes in the vacuum state, they do effect the statistics of measurements involving the radiative force experienced by a point charge in the field of the dipole. Specifically, the dispersion in the charge's momentum is found to increase with time. This entails the possibility of obtaining direct experimental evidence for the existence of advanced waves in physical reality, and provides yet another signature of the quantum nature of the vacuum.
Abstract In recent years, electro-optic sampling, which is based on Pockel’s effect between an electromagnetic mode and a copropagating, phase-matched ultrashort probe, has been largely used for the investigation of broadband quantum states of light, especially in the mid-infrared and terahertz frequency range. The use of two mutually delayed femtosecond pulses at near-infrared frequencies allows the measurement of quantum electromagnetic radiation in different space-time points. Their correlation allows therefore direct access to the spectral content of a broadband quantum state at terahertz frequencies after Fourier transformation. In this work, we will prove experimentally and theoretically that when using strongly focused coherent ultrashort probes, the electro-optic sampling technique can be affected by the presence of a third-order nonlinear mixing of the probes’ electric field at near-infrared frequencies. Moreover, we will show that these third-order nonlinear phenomena can also influence correlation measurements of the quantum electromagnetic radiation. We will prove that the four-wave mixing of the coherent probes’ electric field with their own electromagnetic vacuum at near-infrared frequencies results in the generation of a higher-order nonlinear correlation term. The latter will be characterized experimentally, proving its local nature requiring the physical overlap of the two probes. The parameters regime where higher order nonlinear correlation results predominant with respect to electro-optic correlation of terahertz radiation is provided.
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)