It is shown that the photon, the quantum of electromagnetic field, allows the consideration in the framework of the scheme which in some aspects is typical for the phonon, an excitation of the crystal lattice of a solid. The conclusion is drawn that the photon may be interpreted as an elementary excitation in a fine-grained space. The corollary is in excellent agreement with the space structure and submicroscopic quantum mechanics, which have recently been constructed by the author in a series of works.
A wavefunction for single- and many-photon states is defined by associating photons with different momenta to different spectral and polarization components of the classical, generally complex, electromagnetic field that propagates in a definite direction. By scaling each spectral component of the classical field to the square root of the photon energy, the appropriately normalized photon wavefunction acquires the desired interpretation of probability density amplitude, in contradistinction to the Riemann-Silbertsein wavefunction that can be considered as the amplitude of the photon probabilit…
We study the effects of the four-wave mixing (4WM) in a quantum memory scheme based on electromagnetically induced transparency (EIT). We treat the problem of field propagation on the quantum mechanical level, which allows us to calculate the fidelity for propagation for a quantum light pulse such as a single photon. While 4WM can be beneficial for classical, all-optical information storage, the quantum noise associated with the signal amplification and idler generation is in general detrimental for a quantum memory. We identify a range of parameters where 4WM makes a single photon quantum mem…
We have measured the photon statistics of pump and probe beams after interaction with Rb atoms in a situation of Electromagnetically Induced Transparency. Both fields present super-poissonian statistics and their intensities become correlated, in good qualitative agreement with theoretical predictions in which both fields are treated quantum-mechanically. The intensity correlations measured are a first step towards the observation of entanglement between the fields.
We study properties of collective radiations of coherently driven two three-level ladder-type atoms trapped in a single-mode cavity. Using the electromagnetically induced transparency technique, we show that the three-photon blockade effect can be observed and the properties of collective radiations are strongly dependent on the phase between two atoms. In the case of in-phase radiations, the frequency range to realize the three-photon blockade can be broadened as the control field increases. However, in the regime of the three-photon blockade, the property of collective radiations changes fro…
The ignition of two-quantum collective emission of inverted sub-ensemble of radiators due to mutual interaction of this sub-ensemble with other two dipole active atomic subsystems in process of two-photon exchanges between the atoms through the vacuum field is proposed. The three particle resonances between two-photon and single quantum transitions of inverted radiators from the ensemble are proposed for acceleration of collective decay rate of bi-photons, obtained relatively dipole-forbidden transitions of excited atomic sub-ensemble. This mutual interaction between three super-fluorescent pr…
It has very recently been suggested that asymmetric coupling of electromagnetic fields to thermal reservoirs under nonequilibrium conditions can produce unexpected oscillatory behavior in the local photon statistics in layered structures. Better understanding of the predicted phenomena could enable useful applications related to thermometry, noise filtering, and enhancing optical interactions. In this work we briefly review the field quantization and study the local steady state temperature distributions in optical cavities formed of lossless and lossy media to show that also local field tempe…
The interaction of a quantized field with three-level atoms in $Λ$ configuration inside a two-mode cavity is analyzed in the small noise approximation. The atoms are in a two-photon detuning with respect to the carriers of the field. We calculate the stationary quadrature noise spectrum of the field outside the cavity in the case where the input probe field is a squeezed state and the input pump field is a coherent state. The mean value of the field is unaltered in all the analysis: the atoms shows electromagnetically induced transparency (EIT). The effect of the atoms' base level decoherence …
An antisymmetric tensor, the photon tensor, is defined for the description of the photon as a massless relativistic particle. The photon can be visualized as an essentially two dimensional rotating object. The quantum mechanical description of a single photon is presented and it is shown that it is wrong to associate the quantum states of a photon with the macroscopic electromagnetic fields. This work is part of a series devoted to the attempt to understand the quantum of electromagnetic radiation, based on the assumption that the photons are the primary ontology and that the electromagnetic f…
The phenomenon of the electromagnetic absorption by arbitrarily distributed discrete absorbers is analyzed from the photon point of view. It is shown that apart from the decrease in the intensity of the signal the net effect of absorption includes a relative increase in the photon bunching.
A single-photon switch is an important element for the building of scalable quantum networks. In this paper, we propose a feasible scheme for efficient single-photon switching. The proposed switch is controlled by a state of a qubit formed by the pair of the lowest levels of a three-level system (qutrit) coupled to a resonator. This resonator-qutrit system comprises a switching unit of the considered setup. For suppression of the Purcell relaxation of the control qubit, the switching unit is embedded into a coupled-resonator array serving as an engineered electromagnetic environment with a ban…
In both the equations for matter and light wave propagation, the momentum of the electromagnetic fields Pe reflects the relevant em interaction. As a review of some applications of wave propagation properties, an optical experiment which tests the speed of light in moving rarefied gases is described. Moreover, Pe is also the link to the unitary vision of the quantum effects of the Aharonov-Bohm (AB) type, which provide a useful quantum approach for the limit of the photon mass mph. A bench-top experiment based on effects of the AB type that exploit new interferometric techniques, is foreseen t…
The purpose of this article is to show that the standard method of introducing the quantum description of the electromagnetic field -- by canonical field quantization -- is not the only one. We have chosen instead as the starting point the relativistic quantum mechanics of photons. Our present understanding of the nature of photons significantly differs from what has been known years ago when the concept of a photon has only been emerging. We show how the description of photons treated as elementary particles merges smoothly with the classical description of the electromagnetic field and leads…
Creation of charged massless fermion pair by a photon in external constant crossed electromagnetic field is considered. For this we use the expression of elastic scattering amplitude (EAS) of photon in the one-loop approximation of massive quantum electrodynamics obtained earlier and calculate its massless limit. We assume that the imaginary part of EAS of photon describes the total probability of charged massless fermion pair creation in external electromagnetic field. Photon emission by a charged massless fermion is also studied in constant crossed electromagnetic field. We obtain the total …
Violations of Bell inequalities have been an incontestable indicator of non-classicality since the seminal paper by John Bell. However, recent claims of Bell inequalities violations with classical light have cast some doubts on their significance as hallmarks of non-classicality. Here, we challenge those claims. The crux of the problem is that such classical experiments simulate quantum probabilities with intensities of classical fields. However, fields intensities measurements are radically different from single-photon detections, which are primitives of any genuine Bell experiment. We show t…
We propose, as another pedagogical approach, a quantification of the e.m. field better adapted in isolated systems, a quantification of e.m. fields in finite-spacetime which does not rely explicitly on the notion of photon, nor on the general application of gauge. Being based on the development of e.m. field in TE-TM modes and states, it obeys the limit conditions of a finite-spacetime which follows from the solution of an eigenvalue equation and allows to interpret more profoundly some phenomenons, notably: the equivalence of a Pauli principle in stationary TE-TM states, the notion of non-loc…
The free electromagnetic field, solution of Maxwell's equations and carrier of energy, momentum and spin, is construed as an emergent collective property of an ensemble of photons, and with this, the consistency of an interpretation that considers that the photons, and not the electromagnetic fields, are the primary ontology is established.
All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann-Silberstein vector -- a complex combination of the electric and magnetic field vectors -- that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. B…
The notion of ``radiating'' and ``non-radiating'' current sources in classical electrodynamics plays an important role in calculations of direct and inverse electromagnetic scattering problems. Such a decomposition of the current is central for the notion of localized non-radiating electromagnetic modes. A completely quantum electrodynamic view is explored in this work. Photon emission and absorption current sources are classified as being either radiating or non-radiating. This quantum classification corresponds, respectively and exactly, to the notion of ``real'' and ``virtual'' photon proce…
The questions of whether a photon can be localized in an arbitrarily small volume and what is the allowable strength of that localization (the decrease with distance of the functional form) are questions of current interest. We propose a measure of localization for the single photon that is the expectation values of the electromagnetic field strength components in a coherent wavepacket state of mean photon number unity. As such, we deal with real quantities that have a physical meaning rather than complex amplitudes. It is seen that the real parts of complex amplitudes proposed previously as m…
In a recent paper Mahler {\em et al.} have argued that the experiments of Kocsis {\em et al.} provide experimental evidence for Bohmian mechanics. Unfortunately these experiments used relativistic, zero rest mass photons whereas Bohmian mechanics is based on non-relativistic Schrödinger particles having non-zero rest mass. The experimental results can be accounted for in terms of a different approach based on the electromagnetic field that was already outlined by Bohm in an appendix of the second of his 1952 papers. A subsequent development of this approach by Bohm, Hiley, Holland, Kaloyerou, …
It is commonly agreed that the electromagnetic vacuum is not empty but filled with virtual photons. This leads to effects like Lamb shift and spontaneous emission. Here we argue that if the vacuum has virtual photons it might mean that it is very weakly squeezed and therefore the electromagnetic field is not in its ground state (vacuum) but in an excited dark state. We suggest a stringent test relying on measuring various properties of the electromagnetic field to exclude this yet-untested squeezing hypothesis. This could be done by measuring the number of photons as a function of frequency an…
We theoretically investigate the implementation of a quantum phase gate in a system constituted by a single atom inside an optical cavity, based on the electromagnetically induced transparency effect. Firstly we show that a probe pulse can experience a $π$ phase shift due to the presence or absence of a classical control field. Considering the interplay of the cavity-EIT effect and the quantum memory process, we demonstrated a controlled phase gate between two single photons. To this end, firstly one needs to store a (control) photon in the ground atomic states. In the following, a second (tar…
We propose a technique for quantum nondemolition (QND) measurement and heralded preparation of Fock states by dynamics of electromagnetically induced transparency (EIT). An atomic ensemble trapped in an optical cavity is driven by two external continuous-wave classical fields to form EIT in steady state. As soon as a weak coherent field is injected into the cavity, the EIT system departs from steady state, falls into transient state dynamics by the dispersive coupling between cavity injected photons and atoms. Because the imaginary part of time-dependent linear susceptibility Im[X(t)] of the a…
We present an experimental proposal to achieve a strong photon blockade by employing electromagnetically induced transparency (EIT) with single alkaline-earth-metal atom trapped in an optical cavity. In the presence of optical Stark shift, both second-order correlation function and cavity transmission exhibit asymmetric structures between the red and blue sidebands of the cavity. For a weak control field, the photon quantum statistics for the coherent transparency window (i.e. atomic quasi-dark state resonance) are insensitive to the Stark shift, which should also be immune to the spontaneous …
We study the effect of laser photon merging, or equivalently high harmonic generation, in the quantum vacuum subject to inhomogeneous electromagnetic fields. Such a process is facilitated by the effective nonlinear couplings arising from charged particle-antiparticle fluctuations in the quantum vacuum subject to strong electromagnetic fields. We derive explicit results for general kinematic and polarization configurations involving optical photons. Concentrating on merged photons in reflected channels which are preferable in experiments for reasons of noise suppression, we demonstrate that pho…
Motivated by recent experiments where interference patterns behind a grating are obtained by accumulating single photon events, here we provide an electromagnetic energy flow-line description to explain the emergence of such patterns. We find and discuss an analogy between the equation describing these energy flow lines and the equation of Bohmian trajectories used to describe the motion of massive particles.
At present, the sources of entangled photons have a low rate of photon generation. This limitation is a key component of quantum informatics for the realization of such functions as linear quantum computation and quantum teleportation. In this paper, we propose a method for high intensity generation of entangled photons in a two-mode electromagnetic field. On the basis of exact solutions of the Schr{ö}dinger equation, in the conditions of interaction of the electrons in an atom with a strong two-mode electromagnetic field, it is shown that there may be large quantum entanglement between photon…
A broadband quantum echo effect in a three level $\varLambda$-type system interacting with two laser fields is investigated theoretically. Inspired by the emerging field of nuclear quantum optics which typically deals with very narrow resonances, we consider broadband probe pulses that couple to the system in the presence of an inhomogeneous control field. We show that such a setup provides an all-electromagnetic-field solution to implement high bandwidth photon echoes, which are easy to control, store and shape on a short time scale and therefore may speed up future photonic information proce…
Starting from the Heisenberg-Euler effective Lagrangian, we determine the photon current and photon polarization tensor in inhomogeneous, slowly varying electromagnetic fields. To this end, we consider background field configurations varying in both space and time, paying special attention to the tensor structure. As a main result, we obtain compact analytical expressions for the photon polarization tensor in realistic Gaussian laser pulses, as generated in the focal spots of high-intensity lasers. These expressions are of utmost importance for the investigation of quantum vacuum nonlinearitie…
We introduce a simple model for electromagnetically induced transparency in which all fields are treated quantum mechanically. We study a system of three separated atoms at fixed positions in a one-dimensional multimode optical cavity. The first atom serves as the source for a single spontaneously emitted photon; the photon scatters from a three-level Lambda-configuration atom which interacts with a single-mode field coupling two of the atomic levels; the third atom serves as a detector of the total transmitted field. We find an analytical solution for the quantum dynamics. From the quantum am…
We study the photon creation inside a perfectly conducting, spherical oscillating cavity. The electromagnetic field inside the cavity is described by means of two scalar fields which satisfy Dirichlet and (generalized) Neumann boundary conditions. As a preliminary step, we analyze the dynamical Casimir effect for both scalar fields. We then consider the full electromagnetic case. The conservation of angular momentum of the electromagnetic field is also discussed, showing that photons inside the cavity are created in singlet states.
We investigate photon merging and splitting processes in inhomogeneous, slowly varying electromagnetic fields. Our study is based on the three-photon polarization tensor following from the Heisenberg-Euler effective action. We put special emphasis on deviations from the well-known constant field results, also revisiting the selection rules for these processes. In the context of high-intensity laser facilities, we analytically determine compact expressions for the number of merged/split photons as obtained in the focal spots of intense laser beams. For the parameter range of a typical petawatt …
This paper aims to present an elaborate view on the motivation and realization of the idea to extend Maxwell's electrodynamics to Extended Electrodynamics in a reasonable and appropriate way in order to make it possible to describe electromagnetic (3+1)-soliton-like objects in vacuum and in the presence of continuous media (external fields), exchanging energy-momentum with the electromagnetic field.
The interaction of mesoscopic interference devices with nonclassical electromagnetic fields is studied. The external quantum fields induce a phase factor on the electric charges. This phase factor, which is a generalization of the standard Aharonov-Bohm phase factor, is in the case of nonclassical electromagnetic fields a quantum mechanical operator. Its expectation value depends on the density matrix describing the nonclassical photons and determines the interference. Several examples are discussed, which show that the quantum noise of the nonclassical photons destroys slightly the electron i…
We study the coherent scattering process of a single photon confined in an one-dimensional (1D) coupled cavity-array, where a $Λ$-type three-level atom is placed inside one of the cavities in the array and behaves as a functional quantum node (FQN). We show that, through the electromagnetic induced transparency (EIT) mechanism, the $Λ$-type FQN bears complete control over the reflection and transmission of the incident photon along the cavity-array. We also demonstrate the emergence of a quasibound state of the single photon inside a secondary cavity constructed by two distant FQN's as two end…
We report the observation of photon generation in a microwave cavity with a time-dependent boundary condition. Our system is a microfabricated quarter-wave coplanar waveguide cavity. The electrical length of the cavity is varied using the tunable inductance of a superconducting quantum interference device. It is measured in the quantum regime, where the temperature is significantly less than the resonance frequency (~ 5 GHz). When the length is modulated at approximately twice the static resonance frequency, spontaneous oscillations of the cavity field are observed. Time-resolved measurements …
The realization of equilibrium superradiant quantum phases (photon condensates) in a spatially-uniform quantum cavity field is forbidden by a "no-go" theorem stemming from gauge invariance. We here show that the no-go theorem does not apply to spatially-varying quantum cavity fields. We find a criterion for its occurrence that depends solely on the static, non-local orbital magnetic susceptibility $χ_{\rm orb}(q)$, of the electronic system (ES) evaluated at a cavity photon momentum $\hbar q$. Only 3DESs satisfying the Condon inequality $χ_{\rm orb}(q)>1/(4π)$ can harbor photon condensation. Fo…
We study the influence of a lossless material medium on the coherent storage and quantum state transfer of a quantized probe light in an ensemble of $Λ$-type atoms. The medium is modeled as uniformly distributed two-level atoms with same energy level spacing, coupling to a probe light. This coupled system can be simplified to a collection of two-mode polaritons which couple to one transition of the $Λ$-type atoms. We show that, when the other transition of $Λ$-type atoms is controlled by a classical light, the electromagnetically induced transparency can also occur for the polaritons. In this …
Long range quantum communication and quantum information processing require the development of light-matter interfaces for distributed quantum networks. Even though photons are ideal candidates for network links to transfer quantum information, the system of choice for the realization of quantum nodes has not been identified yet. Ideally, one strives for a hybrid network architecture, which will consist of different quantum systems, combining the strengths of each system. However, interfacing different quantum systems via photonic channels remains a major challenge because a detailed understan…
Electromagnetic modes are instrumental in building quantum machines. In this experiment, we introduce a method to manipulate these modes by effectively controlling their phase space. Preventing access to a single energy level, corresponding to a number of photons N, confined the dynamics of the field to levels 0 to N-1. Under a resonant drive, the level occupation was found to oscillate in time, similarly to an N-level system. Performing a direct Wigner tomography of the field revealed its nonclassical features, including a Schrödinger cat-like state at half period in the evolution. This fine …
We reconsider the recently proposed nonlinear QED effect of quantum reflection of photons off an inhomogeneous strong-field region. We present new results for strong fields varying both in space and time. While such configurations can give rise to new effects such as frequency mixing, estimated reflection rates based on previous one-dimensional studies are corroborated. On a conceptual level, we critically re-examine the validity regime of the conventional locally-constant-field approximation and identify kinematic configurations which can be treated reliably. Our results further underline the…
We study the effect of stimulated photon emission from the vacuum in strong space-time-dependent electromagnetic fields. We emphasize the viewpoint that the vacuum subjected to macroscopic electromagnetic fields with at least one nonzero electromagnetic field invariant, as, e.g., attainable by superimposing two laser beams, can represent a source term for outgoing photons. We believe that this view is particularly intuitive and allows for a straightforward and intuitive study of optical signatures of quantum vacuum nonlinearity in realistic experiments involving the collision of high-intensity…
We consider the Heisenberg-Euler action for an electromagnetic field in vacuum, which includes quantum corrections to the Maxwell equations induced by photon-photon scattering. We show that, in some configurations, the plane monochromatic waves become unstable, due to the appearance of secularities in the dynamical equations. These secularities can be treated using a multiscale approach, introducing a slow time variable. The amplitudes of the plane electromagnetic waves satisfy a system of ordinary differential nonlinear equations in the slow time. The analysis of this system shows that, due t…
