Spontaneous radiation and lamb shift in three-dimensional photonic crystals

Giant Quantum Electrodynamic Effects on Single SiV Color Centers in Nanosized Diamonds

Understanding and mastering quantum electrodynamics phenomena is essential to the development of quantum nanophotonics applications. While tailoring of the local vacuum field has been widely used to tune the luminescence rate and directionality of a quantum emitter, its impact on their transition energies is barely investigated and exploited. Fluorescent defects in nanosized diamonds constitute an attractive nanophotonic platform to investigate the Lamb shift of an emitter embedded in a dielectric nanostructure with high refractive index. Using spectral and time-resolved optical spectroscopy of single SiV defects, we unveil blue shifts (up to 80 meV) of their emission lines, which are interpreted from model calculations as giant Lamb shifts. Moreover, evidence for a positive correlation between their fluorescence decay rates and emission line widths is observed, as a signature of modifications not only of the photonic local density of states but also of the phononic one, as the nanodiamond size is decreased. Correlative light-electron microscopy of single SiVs and their host nanodiamonds further supports these findings. These results make nanodiamond-SiVs promising as optically driven spin qubits and quantum light sources tunable through nanoscale tailoring of vacuum-field fluctuations.

Photon density of states effect on Lamb shift in plasmas

A possible effect of the low photon density of states in plasma on the Lamb shift is analysed. It is found that because of a significant contribution of high-energy virtual photons to the Lamb shift, its modification in plasma does not exceed 1 % with respect to vacuum even at electron concentrations as high as 1022 cm–3. This behavior results from an asymptotic tendency of plasma properties to vacuum ones at an unlimited frequency growth.

Bound state and non-Markovian dynamics of a quantum emitter around a surface plasmonic nanostructure

A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the excited QE will not relax completely to its ground state and is partially stabilized in its excited state after a long time. We develop some theoretical methods for investigating this problem and show how to form such a bound state and its effect on the non-Markovian decay dynamics. We put forward an efficient numerical approach for calculating the analytical part of the self-energy for frequency below the lower energy threshold. We also propose an efficient formalism for obtaining the long-time value of the excited-state population without calculating the eigenfrequency of the bound state or performing a time evolution of the system, in which the probability amplitude for the excited state in the steady limit is equal to one minus the integral of the evolution spectrum over the positive frequency range. With the above two quantities obtained, we show that the non-Markovian decay dynamics of an initially excited QE can be efficiently obtained by the method based on the Green's function expression for the evolution operator when a bound state exists. A general criterion for identifying the existence of a bound state is presented. The performances of the above methods are numerically demonstrated for a QE located around a metal nanosphere and in a gap plasmonic nanocavity. Numerical results show that these methods work well and the QE becomes partially stabilized in its excited state at a long time for the transition dipole moment beyond its critical value. In addition, it is also found that this critical value is heavily dependent on the distance between the QE and the metal surface, but nearly independent on the size of the nanosphere or the rod. Our methods can be utilized to understand the suppressed decay dynamics for a QE in an open quantum system and provide a general picture on how to form such a bound state.

Quantum speedup, non-Markovianity and formation of bound state

In this paper, we investigate the relationship between the quantum speedup, non-Markovianity and formation of a system-environment bound state. Previous results show a monotonic relation between these three such that providing bound states with more negative energy can lead to a higher degree of non-Markovianity, and hence to a greater speed of quantum evolution. By studying dynamics of a dissipative two-level system or a V-type three-level system, when similar and additional systems are present, we reveal that the quantum speedup is exclusively related to the formation of the system-environment bound state, while the non-Markovian effect of the system dynamics is neither necessary nor sufficient to speed up the quantum evolution. On the other hand, it is shown that only the formation of the system-environment bound state plays a decisive role in the acceleration of the quantum evolution.

Spontaneous Emission and Resonant Scattering in Transition from Type I to Type II Photonic Weyl Systems

Spontaneous emission and scattering behavior of an emitter or a resonant scatterer strongly depend on the density of states of the surrounding medium. It has been shown that the resonant scattering cross section (RSC) may diverge at the Weyl frequency of a type I Weyl system due to the diminishing density of states. Here we study the spontaneous emission (SE) and RSC in a photonic metacrystal across the critical transition between type I and type II Weyl systems. Theoretical results show that the SE rate of an emitter in a type I Weyl system diminishes to zero at the Weyl frequency. When the system is tuned towards the transition point between type I and type II Weyl point, the dip in the SE spectrum at the Weyl frequency becomes infinitely sharp. The dip vanishes at the critical transition, and transforms into a peak when the system changes into a type II Weyl system. We further show that the resonant scattering cross section also exhibits dramatically different spectral features across the transition. Our study demonstrates the ability to tune SE and RSC through altering the dispersion of the Weyl medium between type I and type II, which provides a fundamentally new route in manipulating light-matter interactions.

Role of flow of information in the speedup of quantum evolution

Quantum evolution can be accelerated in a non-Markovian environment. Previous results show that the formation of a system-environment bound state governs the quantum speedup. Although a stronger bound state in the system-environment spectrum may seem like it should cause greater speed of evolution, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a classical-driven qubit interacting with a photonic crystal waveguide in the presence of a mirror, resulting in non-Markovian dynamics for the system. Within the considered model, we show the influence of the mirror and the classical field on the evolution speed of the system. In particular, we find that the formation of a bound state is not the essential reason for the acceleration of evolution. The quantum speedup is attributed to the flow of information, regardless of the direction in which the information flows. Our conclusion can also be used in other non-Markovian environments.

Electromagnetic scattering laws in Weyl systems

Wavelength determines the length scale of the cross section when electromagnetic waves are scattered by an electrically small object. The cross section diverges for resonant scattering, and diminishes for non-resonant scattering, when wavelength approaches infinity. This scattering law explains the colour of the sky as well as the strength of a mobile phone signal. We show that such wavelength scaling comes from the conical dispersion of free space at zero frequency. Emerging Weyl systems, offering similar dispersion at non-zero frequencies, lead to new laws of electromagnetic scattering that allow cross sections to be decoupled from the wavelength limit. Diverging and diminishing cross sections can be realized at any target wavelength in a Weyl system, providing the ability to tailor the strength of wave–matter interactions for radiofrequency and optical applications.

Scattering characteristics are important optical properties but they depend strongly on the relative electromagnetic size and environment of a particle. Here, the authors study the frequency-dependence of the scattering cross section for a scatterer located inside a photonic Weyl system.

Mechanism for Hall conductance of two-band systems against decoherence

The Kubo formula expresses a linear response of the quantum system to weak classical fields. Previous studies showed that the environment degrades the quantum Hall conductance. By studying the dynamics of dissipative two-band systems, in this paper we find that the formation of system-environment bound states is responsible for the Hall conductance immune to the effect of the environment. The bound states can form only when the system-environment couplings are below a threshold. Our results may be of both theoretical and experimental interest in exploring dissipative topological insulators in realistic situations, and may open new perspectives for designing active quantum Hall devices working in realistic environments.

Quantum phase transition in a coupled two-level system embedded in anisotropic three-dimensional photonic crystals

The quantum phase transition (QPT) describes a sudden qualitative change of the macroscopic properties mapped from the eigenspectrum of a quantum many-body system. It has been studied intensively in quantum systems with the spin-boson model, but it has barely been explored for systems in coupled spin-boson models. In this paper, we study the QPT with coupled spin-boson models consisting of coupled two-level atoms embedded in three-dimensional anisotropic photonic crystals. The dynamics of the system is derived exactly by means of the Laplace transform method, which has been proven to be equivalent to the dissipationless non-Markovian dynamics. Drawing on methods for analyzing the ground state, we obtain the phase diagrams through two exact critical equations and two QPTs are found: one QPT is that from the phase without one bound state to the phase with one bound state and another is that from one phase with the bound state having one eigenvalue to another phase where the bound state has two eigenvalues. Our analytical results also suggest a way of control to overcome the effect of decoherence by engineering the spectrum of the reservoirs to approach the non-Markovian regime and to form the bound state of the whole system for quantum devices and quantum statistics.

Breakdown of Bose-Einstein distribution in photonic crystals

In the last two decades, considerable advances have been made in the investigation of nano-photonics in photonic crystals. Previous theoretical investigations of photon dynamics were carried out at zero temperature. Here, we investigate micro/nano cavity photonics in photonic crystals at finite temperature. Due to photonic-band-gap-induced localized long-lived photon dynamics, we discover that cavity photons in photonic crystals do not obey Bose-Einstein statistical distribution. Within the photonic band gap and in the vicinity of the band edge, cavity photons combine the long-lived non-Markovain dynamics with thermal fluctuations together to form photon states that memorize the initial cavity state information. As a result, Bose-Einstein distribution is completely broken down in these regimes, even if the thermal energy is larger or much larger than the cavity detuning energy. In this investigation, a crossover phenomenon from equilibrium to nonequilibrium steady states is also revealed.

Lifetime distribution of spontaneous emission from emitter(s) in three-dimensional woodpile photonic crystals

Spontaneous emission lifetime distribution in the basic unit cell or on a plane of the excited emitters embedded in woodpile photonics crystals with low refractive index contrast are investigated. It is found that the spontaneous emission lifetime distribution strongly depends on the position and transition frequency of the emitters, and has the same symmetry as that of the unit cell. The lifetimes of emitters near the upper gap edge are longer than that in the center of the pseudo-gap, which is quite a contrast to the conventional concept. Furthermore, it is revealed that the polarization orientation of the emitters has significant influence on the lifetime distribution, and may result in a high anisotropy factor (defined as the difference between the maximum and minimum values of the lifetime) up to 4.2. These results may be supplied in probing the lifetime distribution or orientation-dependent local density of states in future experiments.

Observation of Lamb shift and modified spontaneous emission dynamics in the YBO3:Eu3+ inverse opal

The study of Lamb shift plays a unique role in quantum electrodynamics because it provides an excellent test of the theory on photonic crystals (PCs). In this Letter, we present the first observation of large Lamb shift in the YBO(3):Eu(3+) inverse opals fabricated by the polystyrene templating method. In addition, it is very interesting to observe that the luminescent dynamics of Eu(3+) decayed with a faster power law (t(-3)), followed by a slower exponential process due to the coexistence of the diffusion field and the propagating field in the PCs.

Rabi splitting with excitons in effective (near) zero-index media

We study theoretically the properties of a thin film of a semiconductor embedded in the interface of two kinds of single-negative materials. At some frequencies the structure with suitable size is equivalent to an effective (near) zero-index medium. The coupling of exciton resonance in the semiconductor and the interface mode in a zero-index medium leads to Rabi splitting. Compared with Rabi splitting observed in cavities, the splitting modes in zero-index media are robust against the scaling change of the length and direction of incident wave.

Spontaneous emission field of a two-level atom embedded in one-dimensional left-handed- and right-handed-material photonic crystals

We investigate the spontaneous emission (SpE) of a two-level atom embedded in one-dimensional photonic crystals composed of left-hand material (LHM) and right-hand material. A complete set of mode functions is constructed for quantizing the radiation field. The radiated field distribution under the condition of impedance matching is calculated. The radiated field is focused in each layer and propagates along the direction normal to each layer due to the LHM. With such a structure we can control the propagation of the SpE field without changing the SpE rate.

Photonic band gap effects on spontaneous emission lifetimes of an assembly of atoms in two-dimensional photonic crystals

The lifetime distribution functions of the spontaneous emission (SE) of the excited atoms embedded in two-dimensional (2D) photonic crystals (PCs) with square lattice, consisting of square air rods in dielectric medium with different filling factors, are calculated by using the plane wave expansion method. The numerical results show that the SE in the 2D PCs cannot be prohibited completely but it can be inhibited intensively by the pseudo-PBG of the PCs. In the pseudoband edges, the SE is accelerated obviously. The reduced average lifetime of the excited atoms and the extension of the reduced lifetime distribution in the 2D PCs both are the same as those in the 3D PCs in the order of magnitude. Our results provide an available way to control the behavior of the SE by changing the structures of the 2D PCs.

Radiation pattern of a classical dipole in a photonic crystal: photon focusing

An asymptotic analysis of the radiation pattern of a classical dipole in a photonic crystal possessing an incomplete photonic bandgap is presented. The far-field radiation pattern demonstrates a strong modification with respect to the dipole radiation pattern in vacuum. Radiated power is suppressed in the direction of the spatial stop band and strongly enhanced in the direction of the group velocity, which is stationary with respect to a small variation of the wave vector. An effect of radiated power enhancement is explained in terms of photon focusing. A numerical example is given for a square-lattice two-dimensional photonic crystal. Predictions of asymptotic analysis are substantiated with finite-difference time-domain calculations, revealing a reasonable agreement.

Giant lamb shift in photonic crystals

We obtain a general result for the Lamb shift of excited states of multilevel atoms in inhomogeneous electromagnetic structures and apply it to study atomic hydrogen in inverse-opal photonic crystals. We find that the photonic-crystal environment can lead to very large values of the Lamb shift, as compared to the case of vacuum. We also suggest that the position-dependent Lamb shift should extend from a single level to a miniband for an assembly of atoms with random distribution in space, similar to the velocity-dependent Doppler effect in atomic/molecular gases.

Lamb shift of laser-dressed atomic states

We discuss radiative corrections to an atomic two-level system subject to an intense driving laser field. It is shown that the Lamb shift of the laser-dressed states, which are the natural state basis of the combined atom-laser system, cannot be explained in terms of the Lamb shift received by the atomic bare states which is usually observed in spectroscopic experiments. In the final part, we propose an experimental scheme to measure these corrections based on the incoherent resonance fluorescence spectrum of the driven atom.

Decay kinetic properties of atoms in photonic crystals with absolute gaps

Decay kinetic properties of a two-level atom near the band edges of photonic crystals (PCs) with absolute gaps are studied based on the Green's function expression for the evolution operator. The local coupling strength between the photons and an atom is evaluated by an exact numerical method. It is found that the decay behavior of an excited atom can be fundamentally changed by the variation of the atomic position: Weisskopf-Wigner and non-Weisskopf-Wigner decay phenomena occur at different atomic positions in the PCs as a result of a significant difference in the local coupling strength. Our finding implies that it is possible to engineer the luminescence spectrum by controlling the atomic position.

Conservative form of the density of states of a photonic crystal with a pseudogap

We show that the total number of states in a photonic crystal in the entire allowed frequency regime will be conserved, and it is equal to that of its corresponding effective medium, i.e., if the density of states (DOS) has a valley(s) in some range(s) of frequencies, it must be compensated for by increases over some other range(s). This rule is of importance in developing a model pseudogap in order to describe the mean emission characteristics of the system when there is a collection of dependently emitting atoms or molecules with essentially random dipole orientations in a large volume and the spectrum of the active atoms is wide enough. This is because, with this rule, the states-conservative model always results in DOS-induced suppression, absolute enhancement, narrowing, spectrum splits, and redshift or blueshift of spontaneous-emission spectra.

Spontaneous emission in a photonic crystal near the band edge: field versus population dynamics

We investigate the dynamical properties of the radiation field emitted from an excited two-level atom in a photonic crystal. If the transition frequency of the atom lies within a certain frequency range above the band edge, the emitted field consists of two components that show a different decay dynamics. In particular it is shown that one field component decreases faster than the atomic population with a decay constant depending on the distance from the atom. As a consequence, the decay rate of the electromagnetic field is spatially varying and, in general, can not be identified with the corresponding rate for the atomic population.

Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with pseudogaps

Spontaneous decay behaviors from an assembly of atoms (or molecules) in 3D photonic crystals (PC's) with pseudogaps are investigated. Theoretically, a lifetime distribution function for these atoms or molecules is defined to reveal decay kinetics. Our calculations show that quite wide or narrow lifetime distributions can occur for different spread configurations of the atoms (or molecules). The pure PC effect may lead to coexistence of both accelerated and inhibited decay processes. These results provide theoretical clarification for substantial discrepancies in the recent reported experiments.

Anisotropic vacuum-induced interference in decay channels

We demonstrate how the anisotropy of the vacuum of the electromagnetic field can lead to quantum interferences among the decay channels of close lying states. Our key result is that interferences are given by the scalar formed from the antinormally ordered electric field correlation tensor for the anisotropic vacuum and the dipole matrix elements for the two transitions. We present results for emission between two conducting plates as well as for a two photon process involving fluorescence produced under coherent cw excitation.

Spontaneous emission from photonic crystals: full vectorial calculations

Quantum electrodynamics of atom spontaneous emission from a three-dimensional photonic crystal is studied in a full vectorial framework. The electromagnetic fields are quantized via solving the eigenproblem of photonic crystals with use of a plane-wave expansion method. It is found that the photon density of states and local density of states (LDOS) with a full band gap vary slowly near the edge of band gap, in significant contrast to the singular character predicted by the previous isotropic model. Therefore, the spontaneous emission can be solved by conventional Weisskopf-Wigner approximate theory, which yields a pure exponentially decaying behavior with a rate proportional to the LDOS.