In quantum mechanics, photonic de Broglie waves have been understood as a unique property of quantum mechanics satisfying the complementarity between particle and wave natures of light, where the photonic de Broglie wavelength is inversely proportional to the number of entangled photons acting on a beam splitter. Very recently, the heart of nonclassical feature of photon bunching on a beam splitter was newly interpreted using pure wave nature of coherence optics [arXiv:1911.07174v2], paving a road to unconditionally secured classical key distribution [arXiv:1807.04233v3]. Here, Mach-Zehnder interferometer-based deterministic photonic de Broglie waves are studied in a coherence regime for both fundamental physics and potential applications of coherence-quantum metrology.
Using a basic Mach-Zehnder interferometer, we demonstrate experimentally the measurement of the photonic de Broglie wavelength of an entangled photon pair (a biphoton) generated by spontaneous parametric down-conversion. The observed interference manifests the concept of the photonic de Broglie wavelength. The result also provides a proof-of-principle of the quantum lithography that utilizes the reduced interferometric wavelength.
The photonic de Broglie wave, in which an ensemble of $N$ identical photons with wavelength $λ$ reveals $λ/N$ interference fringes, has been known to be a unique feature exhibited by the photon number-path entangled state or the NOON state. Here, we report the observation of the photonic de Broglie wave for a pair of photons, generated by spontaneous parametric down-conversion, that are not photon number-path entangled. We also show that the photonic de Broglie wave can even be observed for a pair of photons that are completely separable (i.e., no entanglement in all degrees of freedom) and di…
Quantum measurements have been intensively researched over decades due to quantum advantage of Heisenberg limit beating the standard quantum limit toward potential applications of quantum metrology. The kernel of quantum measurements is in the quantum correlation between bipartite photon pairs or squeezed light quenched by one parameter over corresponding noncommuting variable satisfying Heisenberg uncertainty principle. As a result, quantum measurements bring a quantum gain of the square root law in measurement sensitivity. Photonic de Broglie waves (PBW) have been the key feature of such a g…
Photonic de Broglie waves (PBWs) via two-mode entangled photon pair interactions on a beam splitter show a pure quantum feature which cannot be obtained by classical means1-4. Although PBWs have been intensively studied for quantum metrology5-13 and quantum sensing14-25 over the last several decades, their implementation has been limited due to difficulties of high-order NOON state generation4. Recently a coherence version of PBWs, the so-called coherence de Broglie waves (CBWs), has been proposed in a pure classical regime of an asymmetrically coupled Mach-Zehnder interferometer (MZI)26. Unli…
Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour oscillations. The classical wave theory of light is derived from these laws for the case in which temporal variation of path amplitudes may be neglected, whereas specific experiments, sensitive to the temporal properties of path amplitudes, are suggested. The reflection coefficient of light from the surface of a transparent medium is found to be markedly different…
We prove that, under the condition of validity of the Fresnel approximation, diffraction and interference for a wave traveling in the z-direction may be described in terms of the spreading in time of the transverse (x,y)-wave packet. The time required for the evolved wave packet to yield identical patterns as given by standard optics corresponds to the time for the quantum to cross the optical apparatus. This point of view may provide interesting cues in wave mechanics and quantum physics education.
Correlations between photons are interesting for a number of applications and concepts in metrology in particular for resolution improvements in different methods of quantum imaging. Since Fock-states of N-photons of wavelength lambda in interference schemes acquire N-times the phase shift of single photons these states can appear as if they had a de Broglie wavelength of lambda/N. A biphoton beam diffracted at a blazed grating shows this reduced de Broglie wavelength. This experiment can be seen as a purification of biphotons of a certain correlation strength on the one hand. On the other han…
We investigate the atom-optical analog of degenerate four-wave mixing of photons by colliding two Bose-Einstein condensates (BECs) of metastable helium and measuring the resulting momentum distribution of the scattered atoms with a time and space resolved detector. For the case of photons, phase matching conditions completely define the final state of the system, and in the case of two colliding BECs, simple analogy implies a spherical momentum distribution of scattered atoms. We find, however, that the final momenta of the scattered atoms instead lie on an ellipsoid whose radii are smaller th…
Superposition is one of the most distinct features of quantum theory and has been demonstrated in numerous realizations of Young's classical double-slit interference experiment and its analogues. However, quantum entanglement - a significant coherent superposition in multiparticle systems - yields phenomena that are much richer and more interesting than anything that can be seen in a one-particle system. Among them, one important type of multi-particle experiments uses path-entangled number-states, which exhibit pure higher-order interference and allow novel applications in metrology and imagi…
We construct a projection measurement process for the maximally entangled N-photon state (the NOON-state) with only linear optical elements and photodetectors. This measurement process will give null result for any N-photon state that is orthogonal to the NOON state. We examine the projection process in more detail for N=4 by applying it to a four-photon state from type-II parametric down-conversion. This demonstrates an orthogonal projection measurement with a null result. This null result corresponds to a dip in a generalized Hong-Ou-Mandel interferometer for four photons. We find that the d…
The paper proposes an envelope soliton model of the electron that propagates as a protuberance on a fictitious waveguide, which acts as trajectory. The model is based on de Broglie's original electron wave-particle relativistic theory, and on the observation that the Klein-Gordon equation governs the propagation mode of a common microwave waveguide - with the Schroedinger equation as a low group velocity approximation. This analogy opened for practical physical models, including solitons. In the linear case a conceived corpuscle zigzags within the fictitious waveguide - a zigzagging that resem…
All-optical photonic devices are crucial for many important photonic technology and applications, ranging from optical communication to quantum information processing. Conventional design of all-optical devices is based on photon propagation and interference in real space, which may reply on large numbers of optical elements and are challenging for precise control. Here we propose a new route for engineering all-optical devices using photon internal degrees of freedom, which form photonic crystals in such synthetic dimensions for photon propagation and interference. We demonstrate this new des…
Atomic diffraction through double slits and transmission gratings is well described in terms of the associated de Broglie waves and classical wave optics. However, for weakly bound and relatively large systems, such as the He_2 dimer, this might no longer hold true due to the possibility of break-up processes and finite-size effects. We therefore study the diffraction of weakly bound two-particle systems. If the bar and slit widths of the grating are much larger than the diameter of the two-particle system we recover the usual optics results. For smaller widths, however, deviations therefrom o…
Over the last several decades, entangled photon pairs generated from \c{hi}^((2)) nonlinear optical materials via spontaneous parametric down conversion processes have been intensively studied for various quantum correlations such as Bell inequality violation and anticorrelation. In a Mach-Zehnder interferometer, the photonic de Broglie wavelength has also been studied for quantum sensing with an enhanced phase resolution overcoming the standard quantum limit. Here, the fundamental principles of quantumness are investigated in an interferometric scheme for controllable quantum correlation not …
We propose a new scheme for solid-state photonic quantum computation in which trapped photons in optical cavities are taken as a quantum bit. Quantum gates can be realized by coupling the cavities with quantum dots through waveguides. The proposed scheme allows programmable and deterministic gate operations and the system can be scaled up to many quantum bits.
We use single self-assembled InGaAs quantum dots as internal probes to map the local density of optical states of photonic crystal membranes. The employed technique separates contributions from non-radiative recombination and spin-flip processes by properly accounting for the role of the exciton fine structure. We observe inhibition factors as high as 55 and compare our results to local density of optical states calculations available from the literature, thereby establishing a quantitative understanding of photon emission in photonic crystal membranes.
In this paper, we have explained transverse electro-optic effect by quantum-photonic model (QPM). This model interpret this effect by photon-electron interaction in attosecond regime. We simulate applied electric field on molecule and crystal by Monte-Carlo method in time domain when a light beam is propagated through the waveguide. We show how the waveguide response to an optical signal with different wavelengths when a transverse electric field applied to the waveguide.
We investigate the possibility to achieve scalable photonic quantum computing by the giant optical circular birefringence induced by a quantum-dot spin in a double-sided optical microcavity as a result of cavity quantum electrodynamics. We construct a deterministic controlled-not gate on two photonic qubits by two single-photon input-output processes and the readout on an electron-medium spin confined in an optical resonant microcavity. This idea could be applied to multi-qubit gates on photonic qubits and we give the quantum circuit for a three-photon Toffoli gate. High fidelities and high ef…
The effects of an intracavity photonic crystal in a multimode optical parametric oscillator are studied, with a special focus on quantum fluctuations. The capability to either stimulate or inhibit the spatial instability, lowering or increasing the parametric threshold, allows to control the intensity fluctuations and correlations. A significative quantum noise reduction and an increase of the range of squeezed quadratures are found above threshold where spatial Einstein-Podolsky-Rosen entanglement and inseparability are found.
Photonic hyper-crystals combine the most interesting features of hyperbolic metamaterials and photonic crystals. Since the dispersion law of extraordinary photons in hyperbolic metamaterials does not exhibit the usual diffraction limit, photonic hyper-crystals exhibit light localization on deep subwavelength scales, leading to considerable enhancement of nonlinear photon-photon interaction. Therefore, similar to their conventional photonic crystal counterparts, nonlinear photonic hyper-crystals appear to be very promising in optical limiting and optical computing applications. Nonlinear optics…
We demonstrate the generation of quantum-correlated photon pairs from a Si photonic-crystal coupled-resonator optical waveguide. A slow-light supermode realized by the collective resonance of high-Q and small-mode-volume photonic-crystal cavities successfully enhanced the efficiency of the spontaneous four-wave mixing process. The generation rate of photon pairs was improved by two orders of magnitude compared with that of a photonic-crystal line defect waveguide without a slow-light effect.
Maxwell matter waves emerge from a perspective, complementary to de Broglie's, that matter is fundamentally a wave phenomenon whose particle aspects are revealed by quantum mechanics. Their quantum mechanical description is derived through the introduction of a matter vector potential, having frequency $ω_0$, to Schrodinger's equation for a massive particle. Maxwell matter waves are then seen to be coherent excitations of a single-mode of the matter-wave field. In the classical regime, their mechanics is captured by a matter analog of Maxwell's equations for the electromagnetic field. As such,…
Advanced electro-optic processing combines electrical control with optical modulation and detection. For quantum photonic applications these processes must be carried out at the single photon level with high efficiency and low noise. Integrated quantum photonics has made great strides achieving single photon manipulation by combining key components on integrated chips which are operated by external driving electronics. Nevertheless, electrical interconnects between driving electronics and the electro-optic components, some of which require cryogenic operating conditions, can introduce parasiti…
Future quantum networks in which superconducting quantum processors are connected via optical links, will require microwave-to-optical photon converters that preserve entanglement. A doubly-resonant electro-optic modulator (EOM) is a promising platform to realize this conversion. Here, we present our progress towards building such a modulator by demonstrating the optically-resonant half of the device. We demonstrate high quality factor ring, disk and photonic crystal resonators using a hybrid silicon-on-lithium-niobate material system. Optical quality factors up to 730,000 are achieved, corres…
In the past decade, the concept of parity-time ($\mathcal{PT}$) symmetry, originally introduced in non-Hermitian extensions of quantum mechanical theories, has come into thinking of photonics, providing a fertile ground for studying, observing, and utilizing some of the peculiar aspects of $\mathcal{PT}$ symmetry in optics. Together with related concepts of non-Hermitian physics of open quantum systems, such as non-Hermitian degeneracies (exceptional points) and spectral singularities, $\mathcal{PT}$ symmetry represents one among the most fruitful ideas introduced in optics in the past few yea…
Erbium dopants in crystals exhibit highly coherent optical transitions well suited for solid-state optical quantum memories operating in the telecom band. Here we demonstrate coupling of erbium dopant ions in yttrium orthosilicate to a photonic crystal cavity fabricated directly in the host crystal using focused ion beam milling. The coupling leads to reduction of the photoluminescence lifetime and enhancement of the optical depth in microns-long devices, which will enable on-chip quantum memories.
We present a practical method for active phase control on a photonic chip that has immediate applications in quantum photonics. Our approach uses strain-optic modification of the refractive index of individual waveguides, effected by a millimeter-scale mechanical actuator. The resulting phase change of propagating optical fields is rapid and polarization-dependent, enabling quantum applications that require active control and polarization encoding. We demonstrate strain-optic control of non-classical states of light in silica, showing the generation of 2-photon polarisation N00N states by mani…
The Lorentz transformation (LT) is explained by changes occurring in the wave characteristics of matter as it changes inertial frame. This explanation is akin to that favoured by Lorentz, but informed by later insights, due primarily to de Broglie, regarding the underlying unity of matter and radiation. To show the nature of these changes, a massive particle is modelled as a standing wave in three dimensions. As the particle moves, the standing wave becomes a travelling wave having two factors. One is a carrier wave displaying the dilated frequency and contracted ellipsoidal form described by …
This chapter will primarily focus on the studies of quantum optics with semiconductor, epitaxially grown quantum dots embedded in photonic crystal cavities. We will start by giving brief introductions into photonic crystals and quantum dots, then proceed with the introduction to cavity quantum electrodynamics (QED) effects, with a particular emphasis on the demonstration of these effects on the quantum dot-photonic crystal platform. Finally, we will focus on the applications of such cavity QED effects.
