Atom In Photonic Crystals Research Articles

Lattice mapping for many-body open quantum systems and its application to atoms in photonic crystals

We present a derivation that maps the original problem of a many-body open quantum system (OQS) coupled to a harmonic oscillator reservoir into that of a many-body OQS coupled to a lattice of harmonic oscillators. The present method is particularly suitable to analyze the dynamics of atoms arranged in a periodic structure and coupled with the electromagnetic field within a photonic crystal. It allows to solve the dynamics of a many-body OQS with methods alternative to the commonly used master, stochastic Schr\"odinger, and Heisenberg equations, and thus to reach regimes well beyond the weak coupling and Born-Markov approximations.

Control of Spontaneous Emission from a Microwave Field Coupled Five-Level M-type Atom in Photonic Crystals

We investigate the spontaneous emission spectrum of a five-level M-type atom driven by a microwave field, in which one lower level is coupled by the same modified reservoir to two upper levels. The results show that a few interesting phenomena in spontaneous emission spectra, such as spectral-line shift, spectral-line enhancement and spectral-line suppression, which can be controlled by adjusting the proper parameters of the system. These phenomena can originate from quantum interference of the strong coupling system.

The coherent control of the spontaneous emission spectrum of a driven atom in photonic crystals with two atomic position-dependent bands

The coherent control of the spontaneous emission spectrum of a driven atom located within photonic crystals with two atomic position-dependent bands is investigated. The driving laser field splits the excited atomic level into a doublet that is further dressed by two bands bonded together with the atomic position in the crystal unit cell. The spontaneous emission spectrum of the atomic transition in free space is discussed. We find that frequency shift and the intensity of the spectrum can be perfectly manipulated by variation of the atomic position and detuning of the laser field. The result perhaps offers us an interesting route towards tunable photonic devices.

Controlled entanglement of two atoms in photonic crystals

The exact entanglement dynamics of two dipole–dipole interacting two-level atoms coupled to a common photonic band-gap (PBG) environment has been investigated. We show that the detuning conditions and the dipole–dipole interaction (DDI) are two essential ingredients and their interplay plays a crucial role in controlling the entanglement of the two-qubit system. For the negative detuning, corresponding to the case where the atomic transition frequency is inside the band gap, the entanglement of the two-qubit system can survive in the long-time limit. For the positive detuning, although the fast disentanglement presents, the DDI effects can be used to fight against the deterioration of the entanglement. The theoretical results could be applied to the implementation of quantum information processing in nanostructured materials.

Calculation of spontaneous emission from a V-type three-level atom in photonic crystals using fractional calculus

Fractional time derivative, an abstract mathematical operator of fractional calculus, is used to describe the real optical system of a V-type three-level atom embedded in a photonic crystal. A fractional kinetic equation governing the dynamics of the spontaneous emission from this optical system is obtained as a fractional Langevin equation. Solving this fractional kinetic equation by fractional calculus leads to the analytical solutions expressed in terms of fractional exponential functions. The accuracy of the obtained solutions is verified through reducing the system into the special cases whose results are consistent with the experimental observation. With accurate physical results and avoiding the complex integration for solving this optical system, we propose fractional calculus with fractional time derivative as a better mathematical method to study spontaneous emission dynamics from the optical system with non-Markovian dynamics.

Spontaneous emission spectra of a four-level atom in photonic crystals driven by two coherent fields

We investigate the spontaneous emission spectra of a four-level tripod-type atom embedded in a photonic crystal and driven by two coherent fields. It is found that due to the quantum interference caused by two driving fields, the spontaneous emission spectra have different features from the case of only one driving field. The spectra are sensitively dependent on the detuning of the driving fields. A dark line occurs for some particular initial states. By appropriately adjusting the external driving fields, the spectral-line can be narrowed, enhanced or suppressed.

Microwave control of spontaneous emission of a driven four-level atom in photonic crystals

We study the coherent control of spontaneous emission of a double-driven four-level atom embedded in photonic crystals. Combined effect of different relative locations between the upper band edge and the two upper levels and the phase of microwave coupling field is discussed. It is shown that quantum interference effect such as laser-induced dark line depends strongly on the phase of microwave field.

Spontaneous emission from a two-level atom in anisotropic one-band photonic crystals: A fractional calculus approach

Spontaneous emission (SE) from a two-level atom in a photonic crystal (PC) with anisotropic one-band model is investigated using the fractional calculus. Analytically solving the kinetic equation in terms of the fractional exponential function, the dynamical discrepancy of SE between the anisotropic and isotropic systems is discussed on the basis of different photon density of states (DOS) and the existence of incoherent diffusion field that becomes even more clearly as the atomic transition frequency lies close to the band edge. With the same atom-field coupling strength and detuning in the forbidden gap, the photon-atom bound states in the isotropic system turn into the unbound ones in the anisotropic system that is consistent with the experimental observation in $Phys.$ $Rev.$ $Lett.$ \textbf{96}, 243902 (2006). Dynamics along different wavevectors with various curvatures of dispersion is also addressed with the changes of the photon DOS and the appearance of the diffusion fields.

Transparency induced by the quantum interference of a six-level atom in photonic crystals with defect modes

The absorption–dispersion spectra of a six-level atom embedded in double-band photonic crystals are investigated. It is shown that if there is no defect mode in the photonic band gap, there are three types of transparency windows appear in the absorption–dispersion spectra. If a defect mode is introduced into the photonic band gap, we found some additional transparency windows in the absorption–dispersion spectra. One type of them appears as long as the defect mode exists, but the others appear only when the quantum interference occurs. The transparency windows can be changed by varying the parameters of the defect mode.

Widely tunable lifetimes for donor-acceptor pair states created by displacing an intrinsic atom in photonic crystals

This paper theoretically investigates the formation processes of intrinsic defect states in two-dimensional photonic crystals. We observe two types of defect states—what could be called the donor and acceptor states—created simultaneously by merely displacing a single rod atom from its regular site. The localization of light in the vicinity of these states is reasonably explained in terms of the stability of light around them. Finally, we demonstrate that the lifetimes of light trapped at these states can be tuned in a wide range by adjusting the position of the displaced rod appropriately.

Coherent Coupling Between a Three-Level Atom and a Structured Reservoir

-type atom in photonic crystals. The air-band, the dielectric-band and the free-space vacuum reservoirs coupled with the atom are considered. With the consideration of the phase dierence between the air-band and the dielectricband fields, two band reservoirs become coherent and can interfere with each other. This interference eect depends on the embedded position of the atom and the band-gap width and can aect the SE spectrum. The eect of this interference on the SE spectrum is shown.

Fractional Dynamics of the Spontaneous Emission of an Atom in Photonic Crystals

We suggest a better mathematical method, fractional calculus, for studying the behavior of the atom-field interaction in photonic crystals. By studying the spontaneous emission of an atom in a photonic crystal with one-band isotropic model, we found that the long-time inducing memory of the spontaneous emission is a fractional phenomenon. This behavior could be well described by the fractional calculus. And the results show no steady photon-atom bound state for the atomic resonant transition frequency lying in the proximity of allowed band edge which is encountered in the previous study [J. Opt. B: Quantum Semiclass. Opt. {\bf 5}, R43 (2003)]. The correctness of this result is validated by the ``cut-off smoothing'' density of photon states (DOS) with fractional calculus. By obtaining a rigorous solution without the multiple-valued problem for the system, we show the method of fractional calculus has logically concise property.

Modified spontaneous emission spectra of a three-level V-type atom in photonic crystals

We introduce a modified density of modes to investigate the spontaneous emission spectrum of a three-level V-type atom in photonic crystal using Laplace transform. The atom’s steady state behavior of spontaneous emission is treated for different locations of the upper band-edge frequency. Furthermore; the influence of quantum interference between the two decay channels on spontaneous emission is discussed.

Control of spontaneous emission from a laser-driven four-level atom in photonic crystals

We study the steady-state behaviour of spontaneous emission of a driven four-level atom embedded in photonic crystals. Considering different initial conditions, we discuss the influence of photonic band gap and detuning of external driving field on the atomic spontaneous emission spectrum. The photonic band gap and external driving field will impact strongly on the atomic spontaneous emission properties. Some interesting phenomena were found such as laser-induced dark line, laser-induced spectral-line narrowing and laser-induced pushing of a dressed state out of the band gap, which can be attributed to the quantum interference effect and control of the external driving field.

Design of highly efficient optical diodes based on the dynamics of nonlinear photonic crystal molecules

We investigate the unidirectional transmission behavior of photonic crystal (PC) molecules consisting of defect pairs with Kerr nonlinearity and focus on how to enhance the transmission contrast and maximum transmission of the resulting optical diodes. Theoretical analyses in combination with the numerical simulations based on the finite-difference time-domain technique are employed to evaluate the designed optical diodes. It is found that by intentionally and properly misaligning the resonant frequencies of the constitutional PC atoms, the transmission contrast as well as the maximum transmission of the nonlinear PC molecules can be significantly improved. The figure of merit that characterizes the performance of optical diodes can be enhanced by a factor of 5 as compared with the optical diodes constructed by single asymmetrically confined PC atoms. In addition, the optimum performance of the optical diodes can be achieved only when the operating frequency is properly chosen.

All-optical diodes based on photonic crystal molecules consisting of nonlinear defect pairs

We investigate the unidirectional transmission behavior of photonic crystal (PC) molecules consisting of nonlinear defect pairs by use of the coupled mode theory and the finite-difference time-domain technique. As compared with the all-optical diodes based on single asymmetrically confined PC defects (or PC atoms), a significant enhancement in the transmission contrast is achieved. A qualitative comparison of the dynamical response to external excitation is carried out for nonlinear PC atoms and molecules and the physical origins responsible for the enhancement of transmission contrast are clarified. In addition, the tolerance of the resulting optical diodes against the fabrication error is discussed. Furthermore, it is revealed that the figure of merit, which is defined as the product of the threshold transmission and the transmission contrast, can be greatly improved by dropping the use of air defects. Some abnormal and intriguing transmission behaviors are observed in the PC molecules without using air defects.

Investigation and Modification of Coupling of Photonic CrystalDefects

We investigate the coupling of photonic crystal (PC) defects by usingcoupled-mode theory. The PC molecules formed by the coupling of twoidentical PC atoms are the focus of our study. It is revealed that theflatness of the transmission spectra of the PC molecules is determineduniquely by the phase shift of the travelling wave between the twocoupled PC atoms. By properly adjusting the distance between the twoconstitutional PC atoms, we are able to modify the transmissionspectrum of the resulting PC molecule. Theoretical analyses based onthe coupled-mode theory are in good agreement with the simulationresults obtained by the transfer matrix method and thefinite-difference time-domain technique.

Dynamics of nonlinear photonic crystal atoms characterized by numerical simulations in a pump-probe scheme

We investigate the dynamics of nonlinear photonic crystal (PC) atoms by use of numerical simulations in a pump-probe scheme based on a finite-difference time-domain technique. A two-dimensional nonlinear PC atom with multimode is intentionally employed for the numerical simulations. The use of the multimode PC atom makes it possible that the pump and probe waves are set at different frequencies, ensuring the clear identification of the dynamics of the nonlinear PC atom. The physical model for the dynamics of nonlinear PC atoms has been established and very good agreement between the analytical and simulation results has been achieved.

Physical origin of the ultrafast response of nonlinear photonic crystal atoms to the excitation of ultrashort pulses

The physical origin of the ultrafast response of nonlinear photonic crystal (PC) atoms to the excitation of ultrashort pulses is investigated in detail. It is found that the dynamic shift of PC defect modes is responsible for the dramatic shortening of the photon lifetime in nonlinear PC atoms. The transmission spectra for nonlinear PC atoms that resulted from the dynamic shift are calculated and they are in good agreement with the simulation results.

Spontaneous emission and lame shift in photonic crystals

Being motivated by the controversial results based on two dispersion models and Weisskopf–Wigner approximation (WWA), we introduce, for the first time to our knowledge, the position-dependent photon-atom interaction into the Green function method of the evolution operator and develop a universal theoretical approach to study spontaneous emission of atoms in photonic crystals (PCs). A position-sensitive generalized Lorentzian formalism (non-Lorentzian shape) for the decay of an excited atom in PCs is derived, and an exact numerical method for calculating the local coupling strength, proportional to the photonic local density of state (LDOS), is presented. For weak interaction PCs with pseudo gaps, the generalized Lorentzian formalism may be reduced to the famous Lorentzian spectrum. In this case, we introduce a lifetime distribution function for an assembly of atoms and find that it depends strongly on the atomic configuration in space, which clarifies successfully the tremendous discrepancy between different experiments. For the PCs with large full gaps, we find that the atomic position can fundamentally change the decay behavior of an excited atom: in strong interaction positions, the atomic decay is non-classical or exhibits an envelope-damped Rabi oscillation, while in weak interaction positions the WWA is valid. Recently, we also predicted giant Lamb shifts for hydrogen atoms in PCs, and revealed that in inhomogeneous electromagnetic environment, the dominant contribution to the Lamb shift comes from real photon emission, while the contribution from emission and reabsorption of virtual photon is negligible, in vast contrast with the case of free space where the virtual photon processes play a key role.