Two-photon Transition Research Articles

Anisotropic dynamics of two-photon ionization: An attosecond movie of photoemission.

Imaging in real time the complete dynamics of a process as fundamental as photoemission has long been out of reach because of the difficulty of combining attosecond temporal resolution with fine spectral and angular resolutions. Here, we achieve full decoding of the intricate angle-dependent dynamics of a photoemission process in helium, spectrally and anisotropically structured by two-photon transitions through intermediate bound states. Using spectrally and angularly resolved attosecond electron interferometry, we characterize the complex-valued transition probability amplitude toward the photoelectron quantum state. This allows reconstructing in space, time, and energy the complete formation of the photoionized wave packet.

Generation of Greenberger-Horne-Zeilinger states for silicon-vacancy centers using a decoherence-free subspace

Generating Greenberger-Horne-Zeilinger (GHZ) states of solid-state spins is of great significance for quantum metrology and quantum error correction. We propose here an efficient scheme for generating high fidelity GHZ states in a solid-state setup where multiple silicon-vacancy (SiV) centers are embedded in a quasi-one-dimensional acoustic diamond waveguide. The lattice distortion gives rise to a strong strain coupling between the orbital degree of freedom of SiV centers and the continuum phonon modes. Due to the permutation symmetry, we can take advantage of the decoherence-free subspace to avoid dissipation. Under the quantum Zeno regime, two control fields are used to achieve a ladderlike coupling structure in decoherence-free subspace along with an off-resonant two-photon Raman transition process. We calculate the pulse sequences for $N=4$ and at the same time analyze the effect of different collective decay rates. Moreover, we consider the disorder in the imperfect position of SiV centers and the inhomogeneous strain coupling. This paper may provide a feasible protocol for the generation of GHZ states in a solid-state system.

Measurement of Optical Rubidium Clock Frequency Spanning 65 Days.

Optical clocks are emerging as next-generation timekeeping devices with technological and scientific use cases. Simplified atomic sources such as vapor cells may offer a straightforward path to field use, but suffer from long-term frequency drifts and environmental sensitivities. Here, we measure a laboratory optical clock based on warm rubidium atoms and find low levels of drift on the month-long timescale. We observe and quantify helium contamination inside the glass vapor cell by gradually removing the helium via a vacuum apparatus. We quantify a drift rate of /day, a 10 day Allan deviation less than , and an absolute frequency of the Rb-87 two-photon clock transition of 385,284,566,371,190(1970) Hz. These results support the premise that optical vapor cell clocks will be able to meet future technology needs in navigation and communications as sensors of time and frequency.

Isolating Attosecond Electron Dynamics in Molecules where Nuclei Move Fast.

Capturing electronic dynamics in real time has been the ultimate goal of attosecond science since its beginning. While for atomic targets the existing measurement techniques have been thoroughly validated, in molecules there are open questions due to the inevitable copresence of moving nuclei, which are not always mere spectators of the phototriggered electron dynamics. Previous work has shown that not only can nuclear motion affect the way electrons move in a molecule, but it can also lead to contradictory interpretations depending on the chosen experimental approach. In this Letter we investigate how nuclear motion affects and eventually distorts the electronic dynamics measured by using two of the most popular attosecond techniques, reconstruction of attosecond beating by interference of two-photon transitions and attosecond streaking. Both methods are employed, in combination with abinitio theoretical calculations, to retrieve photoionization delays in the dissociative ionization of H_{2}, H_{2}→H^{+}+H+e^{-}, in the region of the Q_{1} series of autoionizing states, where nuclear motion plays a prominent role. We find that the experimental reconstruction of attosecond beating by interference of two-photon transitions results are very sensitive to bond softening around the Q_{1} threshold (27.8eV), even at relatively low infrared (IR) intensity (I_{0}∼1.4×10^{11} W/cm^{2}), due to the long duration of the probe pulse that is inherent to this technique. Streaking, on the other hand, seems to be a better choice to isolate attosecond electron dynamics, since shorter pulses can be used, thus reducing the role of bond softening. This conclusion is supported by very good agreement between our streaking measurements and the results of accurate theoretical calculations. Additionally, the streaking technique offers the necessary energy resolution to accurately retrieve the fast-oscillating phase of the photoionization matrix elements, an essential requirement for extending this technique to even more complicated molecular targets.

Rashba splitting in organic\u2013inorganic lead\u2013halide perovskites revealed through two-photon absorption spectroscopy

The Rashba splitting in hybrid organic–inorganic lead–halide perovskites (HOIP) is particularly promising and yet controversial, due to questions surrounding the presence or absence of inversion symmetry. Here we utilize two-photon absorption spectroscopy to study inversion symmetry breaking in different phases of these materials. This is an all-optical technique to observe and quantify the Rashba effect as it probes the bulk of the materials. In particular, we measure two-photon excitation spectra of the photoluminescence in 2D, 3D, and anionic mixed HOIP crystals, and show that an additional band above, but close to the optical gap is the signature of new two-photon transition channels that originate from the Rashba splitting. The inversion symmetry breaking is believed to arise from ionic impurities that induce local electric fields. The observation of the Rashba splitting in the bulk of HOIP has significant implications for the understanding of their spintronic and optoelectronic device properties.

Resonant enhancement of two-photon absorption in rubidium with crossed polarizations

The rubidium 52S1/2→52D3/2 and 52S1/2→52D5/2 two-color two-photon transitions were examined with a variety of detunings in the region 758–798 nm to reveal the transition rates. Two cw lasers with crossed linear polarizations were overlapped and counterpropagated through a vapor cell, with the transition rate monitored by side fluorescence from 6P. Resonant enhancement via the 5P states results in intensity variations of over 6 orders of magnitude across the detuning range. No destructive interference zeros were seen, as expected from the polarization dependent calculation of the third-order susceptibility. Zeros occur from interference between two intermediate states, but due to the contributions from both symmetric and antisymmetric susceptibility tensors the zero of one is hidden by a non-zero value of the other. The polarization dependence was explicitly seen by fixing the detuning and iterating the linear polarizations from crossed to parallel.

Angle-resolved one and Two-Photon absorption spectrum in twisted bilayer graphene quantum dots

In this paper, one-photon absorption (OPA) spectrum and two-photon absorption (TPA) spectrum and its electronic excitation, charge transfer, partial density of states (PDOS) and magnetic induction current density of zigzag edge twisted bilayer graphene quantum dots (Z-TwBLG-QDs) with different twisted angles which were divide into two pattern of Moiré superlatrate (MS) are qualitativly and quantitativly analyed by using density functional theory (DFT), excited state wave function, single electron approximation, and gauge-invariant atomic orbital (GIAO) method. The inter-layer local excitation in the electronic transition and intra-layer charge transfer dominated by MS and anti-symmetric electron-hole pair density induced by PDOS are discussed. The twisted angle is decisive to the absorption spectrum, large twisted angle will lead to the red shift of the absorption spectrum. The two-photon transition shows that the twisted angle can regulate the TPA cross section and the boundary effect of Z-TwBLG-QDs in a specific wavelength range. The edge effect of two-step transition can be enhanced by MS with specific twisted angles. The physical mechanism of twisted angle regulating electron transition behavior is revealed by magnetic induction current density analysis.

Pulse shaping for on-demand emission of single Raman photons from a quantum-dot biexciton

Semiconductor quantum dots embedded in optical cavities are promising on-demand sources of single photons. Here, we theoretically study single photon emission from an optically driven two-photon Raman transition between the biexciton and the ground state of a quantum dot. The advantage of this process is that it allows all-optical control of the properties of the emitted single photon with a laser pulse. However, with the presence of other decay channels and excitation-induced quantum interference, on-demand emission of the single Raman photon is generally difficult to achieve. Here we show that laser pulses with non-trivial shapes can be used to maintain excitation conditions for which with increasing pulse intensities the on-demand regime is reached. To provide a realistic picture of the achievable system performance, we include phonon-mediated processes in the theoretical caluclations. While preserving both high photon purity and indistinguishability, we find that although based on a higher-order emission process, for realistic system parameters on-demand Raman photon emission is indeed achievable with suitably tailored laser pulses.

Upconversion Yb3+/Er3+:La2Ti2O7 phosphors for solid-state lighting and optical thermometry

The solid-state reaction was employed as a suitable method to produce orthorhombic Yb3+/Er3+ co-doped La2Ti2O7 phosphors. The pump power and temperature dependencies of spectra of the Yb3+/Er3+ co-doped La2Ti2O7 were studied for color tunability and optical thermometry.The pump power significantly affected the color coordinates of the phosphors. The upconversion green light transformed to the broad white light at higher pump power. A two-photon transition was proposed to explain the upconversion energy transfer process. The fluorescence intensity ratio technique was used to calculate the optical temperature sensor sensitivities. The ΔE energy difference obtained from the intensity ratios of the thermally coupled 2H11/2 and 4I15/2 energy levels of Er3+ are 763.64 ± 76.62 cm−1, 777.77 ± 44.62 cm−1, 640.71 ± 137.39 cm−1 for La1.95Yb0.04Er0.01Ti2O7, La1.94Yb0.04Er0.02Ti2O7, and La1.93Yb0.04Er0.03Ti2O7, respectively. Absolute temperature sensitivities of the phosphors decreased with increasing Er3+ concentration. The maximum absolute sensitivity was determined to be 0.51x10-2 K−1 at 553 K for La1.95Yb0.04Er0.01Ti2O7, 0.64x10-2 K−1 at 571 K for La1.94Yb0.04Er0.02Ti2O7, and 0.38x10-2 K−1 at 457 K for La1.93Yb0.04Er0.03Ti2O7.

Dynamics in direct two-photon transition by frequency combs

Based on the proposed theoretical model of a three-level system, the optical Bloch equations including the direct two-photon transition (DTPT) process using the optical frequency comb (OFC) were derived and the population distribution of particles in the upper states varying with the velocity of the atoms was obtained. Comparing to the resonance two-photon transition process, that population was increased by a factor of 1.4 without the Doppler shift, which is consistent with our previous experimental results. Simultaneously, the relationships between momentum transfers, and atomic velocity and pulse number were analyzed. When applied to a multi-level system it was found that the population of particles in the excited states increased by a few percentages. The novel approach of DTPT using OFC improved the utilization of comb teeth and atoms, increased the momentum transfer path, reduced the reachable Doppler temperature limit, and encouraged us to use OFC to cool multiple elements simultaneously through the DTPT process. By analyzing the Doppler temperature of 133Cs and 87Rb in one dimension, it was found that this process can lower a temperature below 100 mK and generate dipolar molecules 133Cs87Rb via photoassociation, which provides us with a new tool to create dipolar molecules and to investigate their complex rovibrational spectra in ultra-cold chemistry.

Precise measurement of attosecond dynamics of NO molecular shape resonance

Shape resonance is an important and ubiquitous phenomenon in the process of molecular scattering and photoionization. The study of the attosecond photoemission time delay in the vicinity of the shape resonance is of great significance for understanding its intrinsic origin on a nature time scale of electron motion. In this paper, an advanced attosecond coincidence interferometer consisting of a near-infrared femtosecond light source and an extreme ultraviolet attosecond pulse train is used to study the shape resonance process of the 4σ electron of nitric oxide molecules via reconstructing attosecond harmonic beating by measuring the interference of two-photon transitions (RABBIT). The energy dependent effective ionization time delay in the vicinity of the resonance energy region is reported. By comparing the relationship between the two-photon transition delay and the one-photon transition delay, it is found that the Wigner delay of the single-photon process is the main reason for the two-photon transition delay changing with energy. The effect of continuum-continuum delay is further explored. Theoretical calculations of the initial state (bound state) and final state (resonance state) electron wave function orbits of the resonance show that the shape resonance assisted time delay is dominated by the electrons trapped in the centrifugal potential barrier.

Two-Photon Bound-Bound Atomic Transitions Induced by Lg Beams

Two-Photon Bound-Bound Atomic Transitions Induced by Lg Beams

Межзонный двухфотонный линейно-циркулярный дихроизм в полупроводниках в приближении Кейна

Interband two-photon optical transitions are classified and expressions are obtained for the matrix elements in a narrow-gap semiconductor depending on the band parameters, degree of polarization, and light frequency. It is shown that the main contribution to two-photon linear-circular dichroism in narrow-gap semiconductors is made by optical transitions proceeding from the subband of light holes to the conduction band. The dependences of the partial coefficients of interband two-photon absorption of light, which differ from each other by the types of optical transitions, are analyzed depending on the degree of polarization of the light, and a quantitative analysis of the coefficient of linear-circular dichroism of two-photon absorption of light is carried out. Expressions are obtained for the spectral dependence of the coefficient of interband two-photon absorption of light in narrow-gap semiconductors in the Kane model.

Precision measurement of quasi-bound resonances in H2 and the H + H scattering length

Quasi-bound resonances of are produced via two-photon photolysis of S molecules as reactive intermediates or transition states and detected before decay of the parent molecule into three separate atoms. As was previously reported [K. F. Lai et al., Phys. Rev. Lett. 127, 183001 (2021)] four centrifugally bound quantum resonances with lifetimes of multiple μs, lying energetically above the dissociation limit of the electronic ground state of , were observed as , , , and , while also the short-lived ( ns) quasi-bound resonance was probed. The present paper gives a detailed account on the identification of the quasi-bound or shape resonances, based on laser detection via - two-photon transitions, and their strongly enhanced Franck-Condon factors due to the shifting of the wave function density to large internuclear separation. In addition, the assignment of the rotational quantum number is verified by subsequent multi-step laser excitation into autoionisation continuum resonances. Existing frameworks of full-fledged ab initio computations for the bound region in , including Born-Oppenheimer, adiabatic, non-adiabatic, relativistic and quantum-electrodynamic contributions, are extended into the energetic range above the dissociation energy. These comprehensive calculations are compared to the accurate measurements of energies of quasi-bound resonances, finding excellent agreement. They show that the quasi-bound states are in particular sensitive to non-adiabatic contributions to the potential energy. From the potential energy curve and the correction terms, now tested at high accuracy over a wide range of energies and internuclear separations, the s-wave scattering length for singlet H+H scattering is determined at . It is for the first time that such an accurate value for a scattering length is determined based on fully ab initio methods including effects of adiabatic, non-adiabatic, relativistic and QED with contributions up to .

Investigation of 6S 1/2–8S 1/2 two-photon transition of cesium atoms by a single 822 nm laser

We experimentally investigate the 6S 1/2–8S 1/2 two-photon transition in cesium vapor by a single laser. A blue (455.5 and 459.3 nm) fluorescence signal is observed as a result of 822.5 nm laser beams illuminating the Cs vapor with a counter-propagating configuration. The dependences of the fluorescence intensity on the polarization combinations of the laser beams, laser power and vapor temperature are studied to obtain optimal experimental parameters. The frequency difference between the two hyperfine components of 4158 (7) MHz is measured with a Fabry–Perot interferometer as a frequency reference. Such a large spectral isolation and the insensitivity to the Earth’s magnetic field enable the 6S 1/2–8S 1/2 transition to be a stable frequency standard candidate for a frequency-doubled 1644 nm laser in the U-band window for quantum telecommunication.

Strong-field control by reverse engineering

Based on the idea of reverse engineering, we design an optimal laser pulse to control strong-field multiphoton atomic transitions. Starting from the time-dependent Schr\"odinger equation of the full system, we adiabatically eliminate the nonessential states and apply the rotating-wave approximation to arrive at an effective two-state representation that involves dynamic Stark shifts and multiphoton coupling. Solving this equation inversely for the field, we obtain an analytical laser pulse shape that is expected to induce the full system's evolution according to user-defined quantum pathways. In our procedure, the amplitude and phase of the laser pulse are engineered such that the dynamically shifted electronic states are resonantly coupled during the action of the pulse at each moment of time. As a result, the driven system evolves from an arbitrary initial population distribution to any desired final quantum state superposition at a predefined rate. The proposed scheme is demonstrated using the example of the $3s\ensuremath{\rightarrow}4s$ two-photon transition of atomic sodium. By solving the time-dependent Schr\"odinger equation of the single-active electron with two different methods, either propagating time-dependent coefficients of many field-free states or directly propagating the three-dimensional electronic wave packet on a grid, we demonstrate the robustness as well as the limitations of the presented reverse engineering scheme.

Detection of atomic bromine (4p5 2PJ; J = 1/2, 3/2) by two-photon laser-induced vacuum ultraviolet emission

Two ultraviolet photons (250–282 nm) excited atomic bromine, Br(4p52PJ;J=1/2,3/2), to the terms built from the 4p45p electronic configuration. Through visible and infrared (VIS–IR) transitions and/or collisions with ambient gases, the terms transfer to the 2,4DJ and 2,4PJ states in the 4p44d and 4p45s electronic configurations. The vacuum ultraviolet (VUV) emission (125–163 nm) from the 4p44d and 4p45s states to the 4p52PJ state was detected. Twenty in 25 allowed two-photon transitions were observed; however, no VUV or VIS–IR emission from the other five transitions was detected. The findings differ from those by the previous reports on the two-photon resonance-enhanced ionization.

Linear and Nonlinear Optical Processes Controlling S2 and S1 Dual Fluorescence in Cyanine Dyes.

We report on the changes in the dual fluorescence of two cyanine dyes IR144 and IR140 as a function of viscosity and probe their internal conversion dynamics from S2 to S1 via their dependence on a femtosecond laser pulse chirp. Steady-state and time-resolved measurements performed in methanol, ethanol, propanol, ethylene glycol, and glycerol solutions are presented. Quantum calculations reveal the presence of three excited states responsible for the experimental observations. Above the first excited state, we find an excited state, which we designate as S1', that relaxes to the S1 minimum, and we find that the S2 state has two stable configurations. Chirp-dependence measurements, aided by numerical simulations, reveal how internal conversion from S2 to S1 depends on solvent viscosity and pulse duration. By combining solvent viscosity, transform-limited pulses, and chirped pulses, we obtain an overall change in the S2/S1 population ratio of a factor of 86 and 55 for IR144 and IR140, respectively. The increase in the S2/S1 ratio is explained by a two-photon transition to a higher excited state. The ability to maximize the population of higher excited states by delaying or bypassing nonradiative relaxation may lead to the increased efficiency of photochemical processes.

Proposal for suppressing the ac Stark shift in the He(2 3S1→ 3 3S1 ) two-photon transition using magic wavelengths

Motivated by recent direct measurement of the forbidden $2\,^3S_1\rightarrow3\,^3S_1$ transition in helium [K. F. Thomas et al., Phys. Rev. Lett. 125, 013002(2020)], where the ac Stark shift is one of the main systematic uncertainties, we propose a dichroic two-photon transition measurement for $2\,^3S_1\rightarrow3\,^3S_1$ which could effectively suppress the ac Stark shift by utilizing magic wavelengths: one magic wavelength is used to realize state-insensitive optical trapping, the other magic wavelength is used as one of the two lasers driving the two-photon transition. Carrying out calculations based on the no-pair Dirac-Coulomb-Breit Hamiltonian with mass shift operator included, we report the magic wavelength of 1265.615 9(4) nm for $^4$He [or 1265.683 9(2) nm for $^3$He] can be used to design an optical dipole trap; the magic wavelength of 934.234 5(2) nm for $^4$He [or 934.255 4(4) nm for $^3$He] can be as one excitation laser in the two-photon process, and the ac Stark shift can be reduced to less than 100 kHz, as long as the intensity of the other excitation laser does not exceed $1\times10^4~W/cm^2$. Alternatively, by selecting detuning frequencies relative to the $2\,^3P$ state in the region of 82$\sim$103 THz, as well as adjusting the intensity ratios of the two lasers, the ac Stark shift in the $2\,^3S_1\rightarrow3\,^3S_1$ two-photon transition can be cancelled.

High-performance, compact optical standard.

We describe a high-performance, compact optical frequency standard based on a microfabricated Rb vapor cell and a low-noise, external cavity diode laser operating on the Rb two-photon transition at 778 nm. The optical standard achieves an instability of 1.8×10-13τ-1/2 for times less than 100 s and a flicker noise floor of 1×10-14 out to 6000 s. At long integration times, the instability is limited by variations in optical probe power and the ac Stark shift. The retrace was measured to 5.7×10-13 after 30 h of dormancy. Such a simple, yet high-performance optical standard could be suitable as an accurate realization of the meter or, if coupled with an optical frequency comb, as a compact atomic clock comparable to a hydrogen maser.