Two-photon Spontaneous Emission Research Articles

General framework for two-photon spontaneous emission near plasmonic nanostructures

General framework for two-photon spontaneous emission near plasmonic nanostructures

Enhancing two-photon spontaneous emission in rare earths using graphene and graphene nanoribbons

The enhancement of two-photon spontaneous emission (2PSE) from trivalent and divalent rare earth ions in proximity to graphene and graphene nanoribbons is calculated for achievable experimental conditions using a combination of finite difference time domain simulations and direct computation of transition rates between energy levels in rare earths. For Er$^{3+}$, we find that the 2PSE rate is initially 8 orders lower than the single-photon spontaneous emission rate but that, with enhancement, 2PSE can reach 2.5% of the overall decay. When graphene nanoribbons are used, we also show that the emission of free-space photon pairs from Er$^{3+}$ at 3 - 3.2 $\mu$m via 2PSE can be increased by $\sim 400$. Our calculations show significantly less relative graphene-enhanced 2PSE than previous works, and we attribute this variation to differences in emitter size and assumed graphene mobility. We also show that the internal energy structure of the ion can have an impact on degree of 2PSE enhancement achievable and find that divalent rare earths are more favorable.

Two-photon spontaneous emission of an atom in a cosmic string background

It is well known that the vicinities of an atomic system may substantially affect its radiative properties. In this work, we consider the influence of a cosmic string background in the spontaneous emission of an excited atom. We start by computing the one-photon spontaneous emission rate of a quantum emitter, which is a narrow band process, and then we analyze the more complex case of the two-photon spontaneous emission, which is a broadband and much richer phenomenon. In the former case, we analyze not only the behavior of the decay rate with the distance from the atom to the string, but also with the deficit angle associated with the cosmic string metric. In the latter case, we show that the spectral distribution of the emitted photons is substantially affected by the cosmic string background.

Aperiodic bandgap structures for enhanced quantum two-photon sources

In this paper, we propose a novel approach to enhance the efficiency of the two-photon spontaneous emission process that is driven by the multifractal optical mode density of photonic structures based on the aperiodic distributions of Eisenstein and Gaussian primes. In particular, using the accurate Mie–Lorenz multipolar theory in combination with multifractal detrended fluctuation analysis, we compute the local density of states of periodic and aperiodic systems and demonstrate the formation of complete bandgaps with distinctive fractal scaling behavior for scattering arrays of dielectric nanocylinders. Moreover, we systematically study the Purcell enhancement and the most localized optical mode resonances in these novel aperiodic photonic systems and compute their two-photon spontaneous emission rates based on the general Green’s tensor approach. Our results demonstrate that excitation of the highly resonant critical states of Eisenstein and Gaussian photonic arrays across broadband multifractal spectra gives rise to significantly enhanced emission rates compared to what is possible at the band edges of periodic structures with comparable size. Besides defining a novel approach for enhanced quantum two-photon sources on the chip, the engineering of aperiodic bandgap structures with multifractal mode density may provide access to novel electromagnetic resonant phenomena in a multi-scale-invariant vacuum for quantum nanophotonics applications.

Two-Photon Spontaneous Emission in Atomically Thin Plasmonic Nanostructures.

The ability to harness light-matter interactions at the few-photon level plays a pivotal role in quantum technologies. Single photons-the most elementary states of light-can be generated on demand in atomic and solid state emitters. Two-photon states are also key quantum assets, but achieving them in individual emitters is challenging because their generation rate is much slower than competing one-photon processes. We demonstrate that atomically thin plasmonic nanostructures can harness two-photon spontaneous emission, resulting in giant far field two-photon production, a wealth of resonant modes enabling tailored photonic and plasmonic entangled states, and plasmon-assisted single-photon creation orders of magnitude more efficient than standard one-photon emission. We unravel the two-photon spontaneous emission channels and show that their spectral line shapes emerge from an intricate interplay between Fano and Lorentzian resonances. Enhanced two-photon spontaneous emission in two-dimensional nanostructures paves the way to an alternative efficient source of light-matter entanglement for on-chip quantum information processing and free-space quantum communications.

Quantum two-photon emission in a photonic cavity

We derive a new expression for the two-photon spontaneous emission (TPSE) rate of an excited quantum emitter in the presence of arbitrary bodies in its vicinities. After investigating the influence of a perfectly conducting plate on the TPSE spectral distribution (Purcell effect), we demonstrate the equivalence of our expression with the more usual formula written in terms of the corresponding dyadic Green's function. We establish a general and convenient relation between the TPSE spectral distribution and the corresponding Purcell factors of the system. Next, we consider an emitter close to a dielectric medium and show that, in the near field regime, the TPSE spectral distribution is substantially enhanced and changes abruptly at the resonance frequencies. Finally, motivated by the suppression that may occur in the one-photon spontaneous emission of an excited atom between two parallel conducting plates, we discuss the TPSE for this same situation and show that complete suppression can never occur for $s \rightarrow s$ transitions.

Periodic revival of frustrated two-photon creation via interference.

It has been known that suitably placed external mirrors can enhance and suppress emission of entangled photon pairs in spontaneous parametric down-conversion (SPDC), known as frustrated two-photon creation via interference. In this work, we report periodic revival of frustrated two-photon creation via interference with SPDC pumped by a continuous-wave (cw) multi-mode laser. As the mirrors are translated relative to the position of the SPDC source, the effect of frustrated two-photon creation via interference gradually dies off. However, as the mirrors are translated even further, the effect of frustrated two-photon creation via interference re-appears periodically. Our theoretical and numerical analyses show that this revival phenomenon is due to the nature of cw multi-mode pump laser. This work clearly demonstrates how the properties of the pump laser, in addition to suitably placed external mirrors, can be used to modify the process of spontaneous two-photon emission.

Cavity Quantum Electrodynamics and Lasing Oscillation in Single Quantum Dot-Photonic Crystal Nanocavity Coupled Systems

Our recent advances in solid-state cavity quantum electrodynamics and lasing oscillation in single quantum dot (QD)photonic crystal (PhC) nanocavity coupled systems are discussed. These include the fabrication of high-quality 2-D PhC nanocavities (Q >; 50 000), which enabled the generation of spontaneous two-photon emission from a single QD, and the realization of lasing oscillation with single QD gain in the strong coupling regime. Moreover, we have fabricated high-quality 3-D PhC nanocavities (Q ~ 38 500), which have facilitated the realization of both lasing oscillation and the Purcell effect. Lasing oscillation in a 1-D PhC nanobeam cavity with gain produced by a few QDs has also been demonstrated.

Parametrization of the angular correlation and degree of linear polarization in two-photon decays of hydrogenlike ions

The spontaneous two-photon emission in hydrogenlike ions is investigated within the framework of second-order perturbation theory and Dirac's equation. Special attention is paid to the angular correlation of the emitted photons as well as to the degree of linear polarization of one of the two photons, if the second is just observed under arbitrary angles. Expressions for the angular correlation and the degree of linear polarization are expanded in powers of cosine functions of the two-photon opening angle, whose coefficients depend on the atomic number and the energy sharing of the emitted photons. The effects of including higher (electric and magnetic) multipoles upon the emitted photon pairs beyond the electric-dipole approximation are also discussed. Calculations of the coefficients are performed for the transitions $2{s}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}$, $3{d}_{3/2}\ensuremath{\rightarrow}1{s}_{1/2}$, and $3{d}_{5/2}\ensuremath{\rightarrow}1{s}_{1/2}$, along the entire hydrogen isoelectronic sequence ($1\ensuremath{\le}Z\ensuremath{\le}100$).

Tailoring and enhancing spontaneous two-photon emission using resonant plasmonic nanostructures

The rate of spontaneous emission is known to depend on the environment of a emitter, and the enhancement of one-photon emission in a resonant cavity is known as the Purcell effect. Here we develop a theory of spontaneous two-photon emission for a general electromagnetic environment including inhomogeneous dispersive and absorptive media. This theory is used to evaluate the two-photon Purcell enhancement in the vicinity of metallic nanoparticles and demonstrates that the surface-plasmon resonances supported by these particles can increase the emission rate by more than two orders of magnitude. The control over two-photon Purcell enhancement given by tailored nanostructured environments could provide an emitter with any desired spectral response and may serve as an ultimate route for designing light sources with novel properties.

Langevin and generalized Langevin types of spontaneous emission of quantum particles

In the effective Hamiltonian representation, we have obtained a quantum stochastic differential equation of a generalized Langevin type for the evolution operator of an atomic ensemble in a microcavity in an external broadband quantized field and in a nonresonant field of the microcavity. We show that, depending on the number of particles in the atomic ensemble, its dynamics demonstrates both the Langevin and the generalized Langevin types of the two-photon spontaneous decay. In this case, one photon is emitted into the cavity mode, whereas the other photon is emitted into the external broadband electromagnetic field. The Langevin type is determined by a considerable Stark interaction of the atomic ensemble with the broadband photon-free quantized field. We show that, here, the Stark interaction is represented by a quantized Poisson process and, depending on its magnitude (at certain numbers of atoms in the ensemble), the two-photon collective spontaneous emission of microcavity atoms can be completely suppressed. In this case, the two-photon spontaneous emission of the singly excited atomic ensemble is described by the two-level model, while the atom-photon cluster of the microcavity under the described conditions is an artificial two-level quantum particle with a strong Stark interaction.

Spontaneous Two-Photon Emission from a Single Quantum Dot

Spontaneous two-photon emission from a solid-state single quantum emitter is observed. We investigated photoluminescence from the neutral biexciton in a single semiconductor quantum dot coupled with a high Q photonic crystal nanocavity. When the cavity is resonant to the half energy of the biexciton, the strong vacuum field in the cavity inspires the biexciton to simultaneously emit two photons into the mode, resulting in clear emission enhancement of the mode. Meanwhile, the suppression of other single photon emission from the biexciton was observed, as the two-photon emission process becomes faster than the others at the resonance.

Plasmonic Nanoantennas for Broad-Band Enhancement of Two-Photon Emission from Semiconductors

We demonstrate experimentally and theoretically a broad-band enhancement of the spontaneous two-photon emission from AlGaAs at room temperature by plasmonic nanoantenna arrays fabricated on the semiconductor surface. Plasmonic structures with inherently low quality factors but very small effective volumes are shown to be optimal. A 20-fold enhancement was achieved for the entire antenna array, corresponding to an enhancement of nearly 3 orders of magnitude for charge carriers emitting at the near field of a plasmonic antenna.

Enhanced two-photon processes in single quantum dots inside photonic crystal nanocavities

We show that the two-photon transition rates of quantum dots coupled to nanocavities are enhanced by up to several orders of magnitude relative to quantum dots in bulk host. We then propose how to take advantage of this enhancement to implement coherent quantum-dot excitation by two-photon absorption, entangled photon pair generation by two-photon spontaneous emission, and single-photon generation at telecom wavelengths by two-photon stimulated and spontaneous emission.

Atom microscopy via two-photon spontaneous emission spectroscopy

We study subwavelength position measurement via spontaneous emission spectroscopy with two photons. Our model systems are a single $\ensuremath{\Lambda}$-type three-level atom, in which a dual interaction generates two independent photons, and an $M$-type five-level atom, which emits two photons in a double-Raman process. The difference is that the $M$-type system emits correlated pairs of photons, while the photon pairs from the $\ensuremath{\Lambda}$ system are uncorrelated. In order to evaluate the performance of the position measurement, we introduce an analysis scheme motivated by a possible experimental measurement procedure. We find characteristic differences in the spontaneous emission spectra of the two systems arising from the photon correlation in the $M$-type system. But interestingly, the effect of this photon pair correlation on the conditional position probability distribution does not lead to an increase in the position information of the single atom. Nevertheless, both schemes allow for an efficient measurement of the particle position with unambiguous position determination over a wide range of parameters.

High-rate entanglement source via two-photon emission from semiconductor quantum wells

We propose a compact high-intensity room-temperature source of entangled photons based on the efficient second-order process of two-photon spontaneous emission from electrically-pumped semiconductor quantum wells in a photonic microcavity. Two-photon emission rate in room-temperature semiconductor devices is determined solely by the carrier density, regardless of the residual one-photon emission. The microcavity selects two-photon emission for a specific signal and idler wavelengths and at a preferred direction without modifying the overall rate. Pair-generation rate in GaAs/AlGaAs quantum well structure is estimated using a 14-band model to be 3 orders of magnitude higher than for traditional broadband parametric down-conversion sources.

Two-photon interference spectra at the sum-frequency generation of a bichromatic field interacting with a three-level atom

We have calculated the spectral functions for a number of induced excitations near the sum-frequency generation of a bichromatic field interacting with a three-level atom in the cascade configuration. Although the two-photon spontaneous emission is electric dipole forbidden, there are induced peaks whose subnatural line widths and spectral heights depend on the intensities of the bichromatic field. At low intensities of both laser fields, the maximum heights of the induced peaks take positive, zero, and negative values, indicating that the physical processes of absorption (attenuation), dark resonance (nonabsorbing state), and stimulated emission (amplification) are likely to occur at the sum-frequency generation of the two laser fields, respectively. The derived results are graphically presented and discussed.

Application of B-splines finite basis sets to relativistic two-photon decay rates of $\mathsf{2s}$ level in hydrogenic ions

A theoretical study of the one- and two-photon spontaneous emission rates from the 2s1/2 state of one-electron ions is presented. High-precision values of the relativistic emission rates for ions with nuclear charge Z up to 100 are obtained through the use of finite basis sets for the Dirac equation constructed from B-splines. Furthermore, we analyze the influence of the inclusion of quantum electrodynamics corrections in the initial and final state energies.

Two-photon cooperative emission in the presence of athermal electromagnetic field

The possibility of cooperative spontaneous two-photon emission of an extended radiators system and the influence of the external thermal electromagnetic field on the spontaneous emission rate, in such a system, are investigated. It is concluded that, in an external electromagnetic field, the two-photon cooperative emission rate increases significantly. The importance of this effect on the emission of gamma rays from inverted long-lived isomers triggered by X-ray thermal fields, is emphasized.

Magnetic-field-enhanced spontaneous two-photon emission of hydrogenic atoms.

Two-photon transitions for hydrogen and hydrogenlike ions in arbitrary magnetic fields are investigated using currently available nonrelativistic energy levels and one-photon dipole transition probabilities. For hydrogen, the 2s-1s two-photon spontaneous-decay rate is shown to increase rapidly with the strength of the applied field from its field-free value of 8.2284 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ to a maximum of 1.537\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 1.41\ifmmode\times\else\texttimes\fi{}${10}^{6}$ T, approaching that of the 2p-1s one-photon rate, and to drop slightly to 1.055\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 4.7\ifmmode\times\else\texttimes\fi{}${10}^{8}$ T. The transition rate is shown to scale as ${\mathit{Z}}^{4}$ for hydrogenic ions with nuclear charge Z in fields \ensuremath{\ge}3300${\mathit{Z}}^{2}$ T. The spectral distribution of the photons for the 2s-1s transition in a large field reveals interesting features including resonances due to migration of the 2${\mathit{p}}_{0}$ and 2${\mathit{p}}_{\mathrm{\ensuremath{-}}1}$ energy levels between the 1s and 2s levels and the appearance of minima resulting from destructive interference between the intermediate-state dipole terms. In the field-free case, these spectral features are only present for high-lying-state transitions, i.e., 3s-1s, 4s-1s, etc.