Zero-phonon Transitions Research Articles

Cavity-assisted resonance fluorescence from a nitrogen-vacancy center in diamond

The nitrogen-vacancy center in diamond is an attractive resource for the generation of remote entangled states owing to its optically addressable and long-lived electronic spin. However, its low native fraction of coherent photon emission, ~3%, undermines the achievable spin-photon entanglement rates. Here, we couple a nitrogen-vacancy center with a narrow extrinsically-broadened linewidth (159 MHz), hosted in a micron-thin membrane, to an open microcavity. The resulting Purcell factor of ~1.8 increases the zero-phonon line fraction to over 44%. Operation in the Purcell regime, together with an efficient collection of the zero-phonon-line photons, allows resonance fluorescence to be detected for the first time without any temporal filtering. We achieve a >10 signal-to-laser background ratio. This selective enhancement of the center’s zero-phonon transitions could increase spin-spin entanglement success probabilities beyond an order of magnitude compared to state-of-the-art implementations, and enable powerful quantum optics techniques such as wave-packet shaping or all-optical spin manipulation.

Vibrational anharmonicity of A-band related optical center and its temperature dependence studied by femtosecond laser excitation in bulk natural diamond

Unusual A-band spectra with well-resolved quasi-periodical phonon progressions of multiple peaks (N\(\sim \)9) were excited in a natural diamond by 515-nm, 300-fs laser pulses at variable pre-heating temperatures of 24-200oC. The non-radiative multi-phonon part of the relaxation path was comparable with the total relaxation energy (zero-phonon line energy), pointing out some extended defects (e.g., dislocations) as the recombination center of the A-band emission. The derived temperature dependences of the peak intensities, separations and half-widths of the separate spectral peaks in the A-band phonon progressions indicate the different trends for vibration-free zero-phonon transition and vibration-related lower-energy transitions to high vibrational levels of the bottom state – lower thermal damping and more softened phonon for the zero-phonon transition, also implying the extended defect origin of the A-band photoluminescence.

Charge state transition levels of Ni in β-Ga2O3 crystals from experiment and theory: An attractive candidate for compensation doping

Nickel-doped β-Ga2O3 crystals were investigated by optical absorption and photoconductivity, revealing Ni-related deep levels. The photoconductivity spectra were fitted using the phenomenological Kopylov and Pikhtin model to identify the energy of the zero-phonon transition (thermal ionization), Franck–Condon shift, and effective phonon energy. The resulting values are compared with the predicted ones by first-principle calculations based on the density functional theory (DFT). An acceptor level (0/−) of 1.9 eV and a donor level (+/0) of 1.1 eV above the valence band minimum are consistently determined for NiGa, which preferentially incorporates on the octahedrally coordinated Ga site. Temperature-dependent resistivity measurements yield a thermal activation energy of ∼2.0 eV that agrees well with the determined Ni acceptor level. Conclusively, Ni is an eminently suitable candidate for compensation doping for producing semi-insulating β-Ga2O3 substrates due to the position of the acceptor level (below and close to the mid-bandgap).

Cobalt as a promising dopant for producing semi-insulating β-Ga2O3 crystals: Charge state transition levels from experiment and theory

Optical absorption and photoconductivity measurements of Co-doped β-Ga2O3 crystals reveal the photon energies of optically excited charge transfer between the Co related deep levels and the conduction or valence band. The corresponding photoionization cross sections are fitted by a phenomenological model considering electron–phonon coupling. The obtained fitting parameters: thermal ionization (zero-phonon transition) energy, Franck–Condon shift, and effective phonon energy are compared with corresponding values predicted by first principle calculations based on density functional theory. A (+/0) donor level ∼0.85 eV above the valence band maximum and a (0/−) acceptor level ∼2.1 eV below the conduction band minimum are consistently derived. Temperature-dependent electrical resistivity measurement at elevated temperatures (up to 1000 K) yields a thermal activation energy of 2.1 ± 0.1 eV, consistent with the position of the Co acceptor level. Furthermore, the results show that Co doping is promising for producing semi-insulating β-Ga2O3 crystals.

Nonperturbative theory of zero-phonon transitions

A nonperturbative theory of zero-phonon transitions in impurity centers in crystals is proposed in the case of arbitrary linear and quadratic vibronic interaction with a phonon continuum. Formulas for the temperature dependence of frequency, width, Huang-Rhys facto and asymmetry parameter are obtained. It was found that linear and quadratic vibronic interactions jointly contribute to the frequency, the Huang-Rice factor and the asymmetry parameter of these transitions. However, the width is completely determined by the purely quadratic part of this interaction. The obtained formulas can be used to verify the simulation of tunneling by the quantum Monte Carlo method.

Sharp luminescence system in titanium dioxide with zero-phonon transition at 1.573 eV

In this paper, we discuss near-IR steady-state and time-resolved low-temperature (5 K) luminescence of crystalline titanium dioxide (TiO2) powders with different particle sizes. Upon optical excitation with quantum energy close to 3.1 eV, the near-IR luminescence of all the powders reveals a very similar characteristic spectrum, which includes a narrow 1.573 eV line, a set of wider peaks in 1.565–1.545 eV range, and a broad band at ∼1.42 eV. The spectrum remains unchanged when using different excitation quanta, thus indicating that all components are governed by the same luminescence system. It is also confirmed by identic two-exponential luminescence decays with characteristic decay times 70 μs and 400 μs observed for all parts of the spectrum. The properties of the luminescent system are not sensitive to the crystallite size reduction to 10 nm, and its intensity sharply increases after annealing converting the anatase phase into rutile. A comparison of the spectrum with TiO2 phonon density of states indicates that 1.573 eV peak is a zero-phonon transition, and 1.545–1.565 eV structure is due to interaction with bulk phonons of rutile phase. The band at 1.42 eV seems to be due to non-adiabatic electron-phonon coupling. The data obtained clearly indicates that the luminescent system is governed by inner shells of transition elements located in rutile lattice. This transition element can be vanadium as it follows from ICP-MS data and theoretical modeling. The detected luminescent system provides a convenient optical marker of TiO2, including nanoform, and thus can be useful for some applications related to medicine, biology, as well as the food industry.

Plasmonic Photocatalysis: Principles and Application

The efficient narrow band emission of Eu2+ in Cs2MP2O7 (M = Ca2+, Sr2+) is characterized by a large Stokes shift and a high quenching temperature which makes the material promising for application in warm white LEDs. The unusual Eu2+ luminescence properties were reported recently but an explanation for the peculiar behavior is lacking. In this paper we aim at providing new insights in the luminescence of the Eu2+ emission in Cs2MP2O7 through measurements at cryogenic temperatures (down to 4 K) and by comparison with the d–f luminescence of Ce3+ and Yb2+ in the same host. The results reveal a sharp onset of the Eu2+ emission and excitation bands at 4 K. Usually the sharp onset for narrow excitation and emission bands coincide at an energy corresponding to the zero-phonon (purely electronic) transition, but for Eu2+ in Cs2MP2O7 there is a large shift of 3500 cm−1 between the onsets, consistent with the large Stokes shift observed. The onset shift can be explained by emission from a lower energy distorted excited 4f65d1 state. For Ce3+, the f–d absorption bands are at energies expected based on the relation between the absorption energies for Eu2+ and Ce3+ reported by Dorenbos. Contrary to Eu2+, the emission for Ce3+ shows a normal Stokes shift and therefore the emission bands are at much higher energies than predicted from the energy of the Eu2+ emission and the Dorenbos relations. Based on the present results the unusually large Stokes shift for the Eu2+ emission in Cs2MP2O7 is assigned to a Jahn–Teller like deformation in the excited 4f65d1 state of Eu2+ that is not present in the 5d state of Ce3+.

Off-diagonal electron-phonon coupling effects on two-level system dynamics

Electromagnetically coupled two-level systems play a central role in several condensed matter components being considered for quantum information processing applications. If the states couple to phonon excitations, their electromagnetic response is altered via phonon-assisted transitions and lifetime broadening. The former has been treated extensively for a number of specific two-level systems (e.g., excitons in artificial quantum dots, localized states associated with impurities or defects, etc.), but the latter has received less attention. Here we study a microscopic model of the dipole transition of a two-level system under the influence of both diagonal and nondiagonal interactions with a bath of phonons. Our results capture both the influence of the frequency distribution of phonons on the relative spectral weight of the zero-phonon transition and the phonon sidebands, and the broadening of the zero-phonon line due to nondiagonal electron-phonon coupling. We use a formalism that includes non-Markovian effects related to the feedback mechanism between the two-level system and the phonon bath. For simplified forms of the phonon spectral functions we provide analytical expressions up to second order in the coupling strength that demonstrate the importance of including both forms of electron-phonon coupling in studies of these systems. Our formalism can be generalized to higher orders of coupling and for realistic phonon spectral functions.

Strong Zero-Phonon Transition from Point Defect-Stacking Fault Complexes in Silicon Carbide Nanowires.

Crystallographic defects such as vacancies and stacking faults engineer electronic band structure at the atomic level and create zero- and two-dimensional quantum structures in crystals. The combination of these point and planar defects can generate a new type of defect complex system. Here, we investigate silicon carbide nanowires that host point defects near stacking faults. These point-planar defect complexes in the nanowire exhibit outstanding optical properties of high-brightness single photons (>360 kcounts/s), a fast recombination time (<1 ns), and a high Debye-Waller factor (>50%). These distinct optical properties of coupled point-planar defects lead to an unusually strong zero-phonon transition, essential for achieving highly efficient quantum interactions between multiple qubits. Our findings can be extended to other defects in various materials and therefore offer a new perspective for engineering defect qubits.

Simultaneous high Q/V-ratio and optimized far-field emission pattern in diamond slot-bridge nanobeam cavity

We present a design for a slot-bridge nanobeam cavity that supports ultrahigh Q/V and optimized far-field emission pattern, and operates at the zero-phonon transition (637nm) of the nitrogen-vacancy color centers in diamond. The slot-bridge cavity is formed by introducing a diamond bridge at the center of the air region of a slotted cavity. As a result of the boundary condition on the parallel component of the electric field, the electric field in the bridge region is the same as that in the slot. This results in a further reduction of the mode volume. Optimized slot-bridge cavities with a calculated Q factor of 6×106 and mode volume of Veff=0.28(λ/n)3have been realized. In comparison to nanobeam cavities, the mode volume is reduced by a factor of 139. The far-field pattern of a slot-bridge cavity is optimized by using the band folding method and by adding small air-slot extensions to the two closest air-holes surrounding the cavity. A high Q of 9.8×105 and a small mode volume of Veff=0.011(λ/n)3 is realized for this design. Therefore, this type of cavities would allow for the realization of efficient single-photon sources. Our results are important for fundamental studies, like cavity quantum electrodynamics, as well as applications in quantum information processing based on diamond where high quality-factor and ultrasmall mode volume are required.

Electron-vibrational coupling on the absorption spectrum of dithienyl-diketopyrrolopyrrole dye

The S1←S0 electronic spectrum of DPP2T in a chloroform solution was investigated using the vertical gradient (VG) and adiabatic shift (AS) models, which were compared with experimental results. The solvent effects were accounted through the polarizable continuum model (PCM) in non-equilibrium regime. Using the Condon approximation, linear coupling contribution for DPP2T's spectrum is mainly composed of zero-phonon and fundamental transitions. The most intense fundamental transition is related to symmetrical and in-plane normal mode stretching of carbon-carbon bonds belonging π-conjugated skeleton of DPP2T, which is quinoidized upon S1←S0 electronic transition. DPP2T's low-frequency torsional modes couple quadratically to the transition. Their thermal excitation at room temperature broadens the spectrum, shifting it slightly to higher energies.

Chemical stabilization of Eu2+ in LuPO4 and YPO4 hosts and its peculiar sharp line luminescence

The efficient 4f65d→4f7 (d-f) luminescence from Eu2+ is well-known for host lattices where Eu2+ is substituted on a divalent (e.g. Ca2+, Sr2+) or monovalent (e.g. Na+, K+) cation site. Only recently some studies appeared concerning d-f emission from Eu2+ on a trivalent cation site. The stable Eu2+ emission was observed in X-ray irradiated LuPO4:Eu3+ crystals where Eu2+ is produced through trapping of conduction band electrons generated by X-ray absorption. Here, we demonstrated that Eu2+ can also be chemically stabilized in YPO4 and LuPO4 through co-doping with a tetravalent charge compensator: Hf4+. In orthophosphate crystals doubly doped with Eu and Hf, the characteristic Eu2+ emission is observed at low temperatures without the need for X-ray irradiation. The excitation and emission spectra show strong and narrow zero-phonon lines and a rich vibronic structure. In the excitation spectra a multitude of zero-phonon transitions to individual crystal field components of 7FJ multiplets in the 4f6(7FJ)5d excited state was observed for Eu2+ in both LuPO4 and YPO4. Analysis of the spectra is consistent with a slightly larger crystal field splitting for Eu2+ on the smaller Lu3+ site (compared to Y3+). The observation of many 4f6(7FJ)5d electronic origins make these systems to be model compounds for testing the validity of theoretical models for energy level calculations of 4f65d states of Eu2+.

Ultrabright single-photon emission from germanium-vacancy zero-phonon lines: deterministic emitter-waveguide interfacing at plasmonic hot spots

Abstract Striving for nanometer-sized solid-state single-photon sources, we investigate atom-like quantum emitters based on single germanium-vacancy (GeV) centers isolated in crystalline nanodiamonds (NDs). Cryogenic characterization indicated symmetry-protected and bright (&gt;106 counts/s with off-resonance excitation) zero-phonon optical transitions with up to 6-fold enhancement in energy splitting of their ground states as compared to that found for GeV centers in bulk diamonds (i.e. up to 870 GHz in highly strained NDs vs. 150 GHz in bulk). Utilizing lithographic alignment techniques, we demonstrate an integrated nanophotonic platform for deterministic interfacing plasmonic waveguides with isolated GeV centers in NDs, which enables 10-fold enhancement of single-photon decay rates along with the emission direction control by judiciously designing and positioning a Bragg reflector. This approach allows one to realize the unidirectional emission from single-photon dipolar sources, thereby opening new perspectives for the realization of quantum optical integrated circuits.

First-principles calculations of Stark shifts of electronic transitions for defects in semiconductors: the Si vacancy in 4H-SiC

Point defects in solids are promising single-photon sources with application in quantum sensing, computing and communication. Herein, we describe a theoretical framework for studying electric field effects on defect-related electronic transitions, based on density functional theory calculations with periodic boundary conditions. Sawtooth-shaped electric fields are applied perpendicular to the surface of a two-dimensional defective slab, with induced charge singularities being placed in the vacuum layer. The silicon vacancy (V Si) in 4H-SiC is employed as a benchmark system, having three zero-phonon lines in the near-infrared (V1, V1′ and V2) and exhibiting Stark tunability via fabrication of Schottky barrier or p-i-n diodes. In agreement with experimental observations, we find an approximately linear field response for the zero-phonon transitions of V Si involving the decay from the first excited state (named V1 and V2). However, the magnitude of the Stark shifts are overestimated by nearly a factor of 10 when comparing to experimental findings. We discuss several theoretical and experimental aspects which could affect the agreement.

Zero-Phonon Transition Frequency in Diffuse Electronic Spectra of Color Centers in Crystals and Glasses

The method for determining frequencies of purely electronic molecular transitions from diffuse electronic absorption or emission spectra that is based on an adiabatic approximation and thermal equilibrium in the initial transition state is shown to be applicable to color centers and F-centers in crystals and glasses. The experimental results showed that the method can be used, in particular, to monitor the homogeneity of chromophores and, possibly, the media containing them.

Compact design of a gallium phosphide nanobeam cavity for coupling to diamond germanium-vacancy centers

A design for an ultrahigh Q/V nanobeam cavity engineered to interact with Germanium-vacancy (GeV) centers is presented. The nanobeam cavity supports a mode with Q/V>108 with transmission over 70%. The proposed design is based on a new scalable approach developed to reduce the footprint of nanobeam cavities by more than 50% without losing the cavity Q/V value and transmission. Cavity quantum electrodynamics analysis reveals that strong coupling between the zero-phonon line transition of GeV centers and the cavity mode can be achieved for a range of nanobeam dimensions.

Lead-related quantum emitters in diamond

We report on quantum emission from Pb-related color centers in diamond following ion implantation and high temperature vacuum annealing. First-principles calculations predict a negatively-charged Pb-vacancy center in a split-vacancy configuration, with a zero-phonon transition around 2.3 eV. Cryogenic photoluminescence measurements performed on emitters in nanofabricated pillars reveal several transitions, including a prominent doublet near 520 nm. The splitting of this doublet, 2 THz, exceeds that reported for other group-IV centers. These observations are consistent with the PbV center, which is expected to have the combination of narrow optical transitions and stable spin states, making it a promising system for quantum network nodes.

Sub-Band Gap Absorption Mechanisms Involving Oxygen Vacancies in Hydroxyapatite

Hydroxyapatite (HAp) is a widely used biomaterial for the preparation of bone and dental implants. Despite the relevance of HAp in medicine, exciting applications involving this material as a bio-compatible photocatalyst, depend on how well we understand its fundamental properties. Experimental evidence suggests that oxygen vacancies play a critical role in the production of surface radicals upon exposure of HAp to ultra-violet (UV) light. However, very little is known about the underlying physical and chemical details. We present a hybrid density-functional study of the structural and electronic properties of oxygen vacancies in large HAp supercells within the plane-wave formalism. We find that under equilibrium conditions, vacancies occur either as a simple vacant oxygen site (in the neutral charge state), or as extended structures replacing several crystalline moieties (in the double plus charge state). Large atomic relaxations upon ionization make the oxygen vacancy a negative-$U$ defect, where the single plus charge state is metastable, being only accessible under UV excitation. From inspection of the transition levels, we find that electron promotion from the valence band top to the donor state of the vacancy, involves a zero-phonon transition of 3.6-3.9 eV. This mechanism is the most likely explanation to the 3.4-4.0 eV absorption onset for the observation of photocatalysis using HAp under persistent UV illumination.

Experimental Study and Analysis of Absorption Spectra of Ni2+ Ions in Nickel Orthoborate Ni3(BO3)2

The results of studies of the absorption spectra of nickel orthoborate Ni3(BO3)2 in the range of electronic d–d-transitions are reported. The obtained data are analyzed in the framework of the crystal field theory. The Ni2+ ions are located in two crystallographically nonequivalent positions 2a and 4f with point symmetry groups C2h and C2, respectively, surrounded by six oxygen ions forming deformed octahedra. The absorption spectra exhibit three intense bands corresponding to spin-resolved transitions from the ground state of nickel ion 3A2g (3F) to the sublevels of the 3T2g (3F), 3T1g (3F) and 3T1g (3P) triplets split by the spinorbit interaction and the rhombic component of the crystal field. At temperatures below 100 K, the spectra exhibit a thin structure, in which phonon-free lines can be distinguished. Comparison of the calculated frequencies of the zero-phonon transitions with the experimental data allows estimating parameters of the crystal field acting on the nickel ions in the 2a- and 4f-positions, as well as the parameters of electrostatic interaction between the 3d electrons and spin-orbit interaction constants.

Circularly polarized zero-phonon transitions of vacancies in diamond at high magnetic fields

We study the circularly polarized photoluminescence of negatively charged (${\mathrm{NV}}^{\ensuremath{-}}$) and neutral (${\mathrm{NV}}^{0}$) nitrogen-vacancy ensembles and neutral vacancies (${\mathrm{V}}^{0}$) in diamond crystals exposed to magnetic fields of up to 10 T. We determine the orbital and spin Zeeman splitting as well as the energetic ordering of their ground and first-excited states. The spin-triplet and -singlet states of the ${\mathrm{NV}}^{\ensuremath{-}}$ are described by an orbital Zeeman splitting of about 9 $\ensuremath{\mu}\mathrm{eV}/\mathrm{T}$, which corresponds to a positive orbital $g$-factor of ${g}_{L}=0.164$ under application of the magnetic field along the (001) and (111) crystallographic directions, respectively. The zero-phonon line (ZPL) of the ${\mathrm{NV}}^{\ensuremath{-}}$ singlet is defined as a transition from the ${}^{1}{E}^{\ensuremath{'}}$ states, which are split by ${g}_{L}{\ensuremath{\mu}}_{\text{B}}B$, to the ${}^{1}{A}_{1}$ state. The energies of the zero-phonon triplet transitions show a quadratic dependence on intermediate magnetic field strengths, which we attribute to a mixing of excited states with nonzero orbital angular momentum. Moreover, we identify slightly different spin Zeeman splittings in the ground (gs) and excited (es) triplet states, which can be expressed by a deviation between their spin $g$-factors: ${g}_{S,\text{es}}={g}_{S,\text{gs}}+\mathrm{\ensuremath{\Delta}}g$ with values of $\mathrm{\ensuremath{\Delta}}g=0.014$ and 0.029 in the (001) and (111) geometries, respectively. The degree of circular polarization of the ${\mathrm{NV}}^{\ensuremath{-}}$ ZPLs depends significantly on the temperature, which is explained by an efficient spin-orbit coupling of the excited states mediated through acoustic phonons. We further demonstrate that the sign of the circular polarization degree is switched under rotation of the diamond crystal. A weak Zeeman splitting similar to $\mathrm{\ensuremath{\Delta}}g{\ensuremath{\mu}}_{\text{B}}B$ measured for the ${\mathrm{NV}}^{\ensuremath{-}}$ ZPLs is also obtained for the ${\mathrm{NV}}^{0}$ zero-phonon lines, from which we conclude that the ground state is composed of two optically active states with compensated orbital contributions and opposite spin-1/2 momentum projections. The zero-phonon lines of the ${\mathrm{V}}^{0}$ show Zeeman splittings and degrees of the circular polarization with opposite signs. The magnetophotoluminescence data indicate that the electron transition from the $^{1}T_{2}$ states to the $^{1}A$ ground state defines the zero-phonon emission at 1.674 eV, while the $^{1}T_{2}\ensuremath{\rightarrow}^{1}E$ transition is responsible for the zero-phonon line at 1.666 eV. The $^{1}T_{2}$ ($^{1}E$) states are characterized by an orbital Zeeman splitting with ${g}_{L}=0.071$ (0.128).