Photon-atom Bound State Research Articles

Manipulation of fluorescence from Gaussian distributed atoms in a coherent photonic-band-gap reservoir

Effects of position and density distribution of atoms on spontaneous emission (SE) from excited two-level atoms in an anisotropic and two-band photonic crystal (PC) are investigated. By considering these atoms with a Gaussian distribution in the PC, which acts as a coherent photonic-band-gap reservoir, we find that a photon-atom bound state occurring in the single-band model becomes a decay state as the center of atomic distribution is moved from the void region toward the dielectric region. The strong coupling between the atom and electromagnetic (EM) modes from both the air and dielectric bands leads to one of the enhanced decay behaviors. This effect is position-dependent and is dominant for a narrow atomic density distribution. The other decay behavior comes from the collective emission through the tunnel processes of the localized photons, which is dominant for a wide atomic density distribution. Therefore, for the wider atomic distribution, the collective effect on SE is stronger than the position-dependent one. By tuning the position and atomic density distribution, we can thus control the fluorescence of atoms in PC systems effectively.

Dynamics of the Energy Relaxation and Decoherence of a Photon-Atom Bound State in an Anisotropic Photonic Crystal

An atom embedded inside photonic crystals can form a photon-atom bound state if the emission frequency of the excited atom is lying inside the photonic-band gap of photonic crystals. We studied the dynamics of the energy relaxation and decoherence of a QPAB, qubit made by a photon-atom bound state in photonic crystals. Dynamics of these measurements are solved analytically through the fractional calculus which has been shown to be appropriate mathematical method for the optical systems with non-Markovian dynamics. From these dynamics, we find that the losses of energy, coherence, and information of a QPAB are inhibited. As compared with those qubits without forming photon-atom bound states, the energy relaxation and decoherence rates of these QPABs are strongly suppressed. Other systems suitable for realizing these properties are discussed.

Quantum dynamics of two quantum dots in the vicinity of a photonic band edge: role of structured reservoirs and phonons

We study the population and disentanglement dynamics of two identical quantum dots placed inside the structured electromagnetic reservoir of a photonic crystal and coupled to an independent bath of thermal phonons. A formalism based on the method of generalized-Laplace transforms is developed to study the population and disentanglement dynamics. The effect of resonant dipole dipole interaction between the two quantum dots on the population dynamics in the presence of phonons and shows that the two two-level atoms can have a residual population at long times in the structured reservoir of a photonic crystal due to the formation of a photon-atom bound state. The disentanglement dynamics of the two quantum dots (assumed to be initially entangled) is studied using concurrence as a measure and is computed from the reduced two two-level system density matrix using the method of generalized-Laplace transforms. We show that partial disentanglement results from the interaction of the two quantum dots with the electromagnetic and phonon reservoirs. However, substantial entanglement is preserved in the fractionalized steady state formed if the transition frequency of two the quantum dots lies in the vicinity of the photonic band edge. We also discuss in detail the role of acoustic phonons on the population and disentanglement dynamics and the long time residual entanglement.

Microscopic theory of multiple-phonon-mediated dephasing and relaxation of quantum dots near a photonic band gap

We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption line shape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored'' electromagnetic vacuum of a photonic band-gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to an enhanced lifetime of a photon-atom bound state in a PBG. This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (breakup of phonons into lower energy phonons) and purely nonradiative decay. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption line shapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.

Spontaneous emission near the band edge of a three-dimensional photonic crystal: afractional calculus approach

We suggest a better mathematical method, fractional calculus, for studying the behavior ofthe atom–field interaction in photonic crystals. By studying the spontaneous emission of anatom in a photonic crystal with a one-band isotropic model, we found that the long-timeinducing memory of the spontaneous emission is a fractional phenomenon. This behaviorcould be well described by fractional calculus. The results show no steady photon–atombound state for the atomic resonant transition frequency lying in the proximity of theallowed band edge which was encountered in a previous study (Woldeyohannes and John2003 J. Opt. B: Quantum Semiclass. Opt. 5 R43). The correctness of this result is validatedby the ‘cut-off smoothing’ density of photon states (DOS) with fractional calculus. Byobtaining a rigorous solution without the multiple-valued problem for the system,we show that the method of fractional calculus has a logically concise property.

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.

Exciton dressing and capture by a photonic band edge

We demonstrate electromagnetically induced anomalous quantum dynamics of an exciton in a photonic band gap (PBG)-quantum well (QW) heterostructure. Within the engineered electromagnetic vacuum of the PBG material, the exciton can propagate through the QW by the emission and reabsorption of virtual photons in addition to the conventional electronic hopping mechanism. When the exciton wave vector and recombination energy nearly coincide with a photonic band edge, the exciton kinetic energy is lowered by $1--10\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ through coherent radiative hopping. This capture of the exciton by the photonic band edge is accompanied by strong electromagnetic dressing in which exciton's renormalized effective mass is 4--5 orders of magnitude smaller than in the absence of the PBG environment. This dressed exciton exhibits a long radiative lifetime characteristic of a photon-atom bound state and is robust to phonon-assisted recombinative decay. By inheriting properties of the PBG electromagnetic vacuum, the bound electron-hole pair becomes a stable, ultramobile quantum excitation.

Method of collective operators for resonance fluorescence near a photonic band edge

In this work a formalism of collective atom-field operators is described and applied to study the dynamics of a classically driven two-level atom inside a band-gap material. We show that if a photon-atom bound state can exist when driving is absent, then it is possible to assume mutual independence of collective operators and develop an effective approximation for the case when driving is present.

Single-atom switching in photonic crystals

We describe the role of first non-Markovian corrections to resonance fluorescence in photonic crystals, using a perturbative expansion of the Heisenberg equations of motion in powers of the atom-field reservoir coupling strength. Non-Markovian effects arise from the rapid variation of the photonic density of states with frequency. Our method recaptures the physics of the photon-atom bound state in the presence of a full photonic band gap. For the anisotropic three-dimensional photonic band gap, it predicts remarkable features in the resonance fluorescence, such as atomic population inversion and switching behavior in a two-level atom for moderate values of the applied laser field. The magnitude of the switching effect depends sensitively on the external laser intensity and its detuning frequency from the atomic transition. The robustness of this effect against nonradiative decay and dephasing mechanisms is also investigated.

Resonance Raman scattering in photonic band-gap materials

We study the resonance Raman scattering of light from a three-level atom embedded in a photonic band-gap material or in a frequency dispersive medium whose photon spectrum exhibits a gap due to photon coupling to medium excitations such as excitons and optical phonons. We demonstrate that the one-particle spectrum of the system consists of either a continuous part with energy lying outside the gap or a single discrete mode with energy lying inside the gap. The discrete mode, which occurs when both of the allowed atomic transitions of the $\ensuremath{\Lambda}$ configuration lie inside the gap, can be treated as a photon-atom bound state in which the radiation is localized in the vicinity of the atom. In the case of the continuous spectrum, the Rayleigh and Stokes lines are shifted as well as narrowed (or broadened) as the corresponding transition frequencies are shifted relative to the upper band edge, providing a distinctive experimental signature of atom-photon interactions near a photonic band edge.

Trapping an atom with single photons

The creation of a photon-atom bound state was first envisaged for the case of an atom in a long-lived excited state inside a high-quality microwave cavity. In practice, however, light forces in the microwave domain are insufficient to support an atom against gravity. Although optical photons can provide forces of the required magnitude, atomic decay rates and cavity losses are larger too, and so the atom-cavity system must be continually excited by an external laser. Such an approach also permits continuous observation of the atom's position, by monitoring the light transmitted through the cavity. The dual role of photons in this system distinguishes it from other single-atom experiments such as those using magneto-optical traps, ion traps or a far-off-resonance optical trap. Here we report high-finesse optical cavity experiments in which the change in transmission induced by a single slow atom approaching the cavity triggers an external feedback switch which traps the atom in a light field containing about one photon on average. The oscillatory motion of the trapped atom induces oscillations in the transmitted light intensity; we attribute periodic structure in intensity-correlation-function data to 'long-distance' flights of the atom between different anti-nodes of the standing-wave in the cavity. The system should facilitate investigations of the dynamics of single quantum objects and may find future applications in quantum information processing.

Quantum optics of localized light in a photonic band gap.

We describe the quantum electrodynamics of photons interacting with hydrogenic atoms and molecules in a class of strongly scattering dielectric materials. These dielectrics consist of an ordered or nearly ordered array of spherical scatterers with real positive refractive index and exhibit a complete photonic band gap or pseudogap for all directions of electromagnetic propagation. For hydrogenic atoms with a transition frequency in the forbidden optical gap, we demonstrate both the existence and stability of a photon-atom bound state. For a band gap to center frequency ratio \ensuremath{\Delta}\ensuremath{\omega}/${\mathrm{\ensuremath{\omega}}}_{0}$\ensuremath{\sim}5%, the photon localization length ${\ensuremath{\xi}}_{\mathrm{loc}}$\ensuremath{\ge}10L, where L is the lattice constant of dielectric array. This strong self-dressing of the atom by its own localized radiation field leads to anomalous Lamb shifts and a splitting of the excited atomic level into a doublet when the transition frequency lies near a photonic band edge. We estimate the magnitude of this splitting to be ${10}^{\mathrm{\ensuremath{-}}6}$ at the vacuum transition energies.