N-photon Process Research Articles

Up-to-Five-Photon Upconversion from Near-Infrared to Ultraviolet Luminescence Coupled to Aluminum Plasmonic Lattices.

The incorporation of upconversion luminescence (UCL) materials into various plasmonic structures promotes light-matter interactions in nanophotonic systems. It has been experimentally demonstrated that UCL enhancement entailing two photons exhibits a quadratic dependence on the excitation intensity. However, in the field of plasmonics, there have not been sufficient studies on high-order multi-photon upconversion processes. We report up-to-five-photon UCL, wherein λ = 1550 nm near-infrared light is converted to 382 nm ultraviolet light, from core-inert shell nanoparticles coupled to aluminum plasmonic lattices. The five-photon UCL intensity of nanoparticles on the plasmonic lattice is over 800 times stronger than that on the flat glass. We demonstrate that the enhancement of UCL scales with the nth power of the local field enhancement for n-photon process. These findings give a strategy to obtain high-order multi-photon UPL with aluminum plasmonic nanostructures and can contribute to anti-counterfeiting application.

High resolution energy-time of flight spectrometer: Dehydrogenation of fluorene cation as case study

Testing and performance validation of a new multipurpose time-of-flight mass spectrometer followed by an energy analyzer is presented. The instrument with high mass and energy resolution is primarily designed to study cations of polycyclic aromatic hydrocarbons (PAHs) and their dehydrogenation process. The energy correlated time-of-flight measurement is supplemented by Monte Carlo simulation to probe the dehydrogenation process in a relatively small PAH cation. The experiment is carried out on fluorene+ on a timescale of several microseconds. Fluorene cations with high internal energies were produced using UV multiphoton ionization. Specific n-photon processes leading to ionization as well as H-loss reaction were identified. The average value of dehydrogenation rate is estimated by fitting the measured data to the outcome of simulations. The quantification of H loss decay rate is in agreement with previously reported decay rate measurement. This corresponds to the internal energy available by inner valence electron emission caused by three photon process. The effectiveness of the instrument to access a range of decay rates (103–107 s−1) in a single measurement is demonstrated.

Probability amplitudes for broadband N-photon processes in linear optics

Advances in the production of multiple-photon states with a broadband spectrum and its subsequent processing through linear optical systems demand simple rules to automate the calculation of probability amplitudes. A methodology to write down directly the probability amplitude of any broadband multi-photon process in linear optics is proved. A physically intuitive notion of multi-photon paths is derived from Wick’s theorem and amplitudes are formulated as sums over paths. Every permutation of the out-state photon frequencies over the photon occupation indices that the in-state wavepacket assigns to the inports contributes a path. A simple general rule is provided to compute them. Broadband two-photon processes in the interferometers by Hong, Ou and Mandel (HOM) and by Mach and Zehnder (MZ) are considered. We provide a rigorous description of the HOM interferometer as a probe of the amount of frequency entanglement contained in some two-photon wavepackets, establishing an integral transform between the interference profile and the spectral density of frequency-entangled photon pairs. For the MZ interferometer, our method provides the exact rate of coincidence counts for a broadband two-photon process that is relevant for pairs produced with a wide two-dimensional spectral bandwidth by spontaneous parametric downconversion.

Model of multiphoton transitions in a current-biased Josephson junction

We present a simple model to describe multiphoton transitions between the quasi-bound states of a currentdriven Josephson junction. The transitions are induced by applying an ac voltage with controllable frequency and amplitude across the junction. The voltage induces transitions across the junction when the frequency satisfies n =E10, where E10 is the splitting between the ground and first excited quasi-bound state of the junction. We calculate the matrix elements of the transitions as a function of the dc bias current I, and the frequency and amplitude Vac of the microwave voltage, for representative junction parameters. We also calculate the frequency-dependent absorption coefficient by solving the relevant Bloch equations when the ac voltage is sufficiently weak. In this regime, the absorption coefficient is a sum of Lorentzian lines centered at the n-photon absorption frequency, of strength proportional to the squared matrix elements. For fixed Vac, the transition rate for an n-photon process usually decreases with increasing n. We also find a characteristic even-odd effect: The absorption coefficient typically increases with I for n even but decreases for n odd. Our results agree qualitatively with recent experiments.

NTH-ORDER AMPLITUDE SQUEEZING EFFECTS OF RADIATION IN MULTIPHOTON PROCESSES

Squeezing of the electromagnetic field is a purely quantum mechanical phenomenon and this quantum effect is expected to manifest itself in optical processes in which the nonlinear response of the system to the radiation field plays an important role. It has generated a great deal of interest in view of the possibility of reducing the noise of an optical signal below the vacuum limit i.e. zero-point oscillations. In this paper the concept of nth-order amplitude squeezing is introduced in the fundamental mode in four- and six-wave mixing processes as a generalization of the higher-order squeezing under short-time approximation based on a fully quantum mechanical approach. It established the coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators. The condition for occurrence of nth-order squeezing is obtained from which higher-order squeezing upto n=3 are studied. Dependence of squeezing on photon number is also established. The conditions for obtaining maximum and minimum squeezing are obtained. The method of present investigation can be applied to any higher-order non-linear optical processes and the technique can also be extended for studying squeezing in any N-photon process in general. Further, nth-order squeezing of radiation in N-photon process can also be investigated. The results obtained may help in selecting a suitable process to generate optimum squeezing in the radiation field.

Deceleration of atoms in an n-photon process by means of a laser-travelling wave in the Dirac representation

A detailed theoretical study is made of the slowing down of the atomic beam by resonant laser radiation. By using the density matrix technique in the interaction representation, employing optical Bloch equations, one can obtain the average radiation force, with respect to the coherent state of the laser mode, represented in the complex plane. It is revealed that all the relevant variables are explicit functions of time via the average photon number. It is shown under the conditions which can be attained in practice that the behavior of the velocity and diffusion coefficients in both the longitudinal and transverse directions is consistent with previous works on such phenomenon.

The multiphoton AC Stark effect

We study the interaction of a two-level atom with two intense lasers: a strong laser of Rabi frequency 2Ω on resonance with the atomic transition, and a weaker laser detuned by 2Ω/n, i.e. by a subharmonic of the Rabi frequency of the first. The second laser “dresses” the dressed states created by the first in an n-photon process. We calculate the energy levels and eigenstates of this “doubly-dressed” atom, and find a new phenomenon: the splitting of the energy levels due to an n-photon coupling between them, resulting in a multiphoton AC Stark effect. We illustrate this effect in the fluorescence spectrum, and show that the spectrum contains triplets at the subharmonic as well as harmonic resonance frequencies with a clear dependence on the order n of the resonance and the ratio α of the Rabi frequencies of the lasers

Low-energy laser-assisted electron-helium collisions

Laser-assisted electron-helium scattering is studied by perturbation theory for electron energies \ensuremath{\leqslant}2.6 eV and ${\mathrm{CO}}_{2}$ laser intensities \ensuremath{\leqslant}1\ifmmode\times\else\texttimes\fi{}${10}^{6}$ W/${\mathrm{cm}}^{2}$. A model potential is adopted that gives a good description of the field-free elastic scattering. Results are presented for one- and two-photon processes. It is found that absorption cross sections are larger than those for emission. The dependences on electron energy at zero energy for absorption and at the n\ensuremath{\omega} thresholds for emission are analyzed. The elastic scattering within the laser pulse is discussed and related to a general sum rule involving the n-photon process probabilities.

Asymptotic approximations for the Q function in the Jaynes-Cummings model.

The Q function in the undamped Jaynes-Cummings model for a coherent initial state in the rotating-wave approximation is investigated. By applying the method of steepest decent and saddle-point integration in the limit of high photon numbers, closed analytic expressions for the Q function at different times are given, from which analytic expressions for the Rabi frequency, revival times, envelope shapes of the inversion, beat frequencies, etc. are derived. As Eiselt and one of us have shown [J. Eiselt and H. Risken, Phys. Rev. A 43, 346 (1991)], the Q function first splits into two peaks which counterrotate in the complex plane and then collide on the opposite side of the plane. This behavior of the Q function leads to an interpretation of the collapses and revivals of the Rabi oscillations and a better understanding of expressions for the Rabi frequency, revival times, envelope shapes of the inversion, beat frequencies, etc. The results are generalized to N-photon processes; in particular, the cases N=2 and 4 are treated in some detail.

New Lie-algebraic structures in nonlinear problems of quantum optics and laser physics

New Lie-algebraic structures (polynomial deformations of Lie algebras) are revealed in some problems of quantum optics and laser physics. Specifically, deformations of oscillator algebras due to extensions of unitary algebras by their symmetric and skew-symmetric tensors are shown to be algebras of dynamic symmetry (ADS) in models of n-photon processes with internal symmetries. Similarly, deformed algebras sud(2) are found as ADS in the context of generalized Dicke models and frequency conversion models. We also briefly discuss some possible schemes of employing the results to solving physical problems.

1/n expansion for n-photon processes. Quasiclassical approach

The aim of this paper is to show that the 1/n expansion for n-photon processes can be considered as a quasiclassical one. We discuss qualitatively the domain of validity of the leading term of this expansion and show how corrections to it can be accounted for in a systematic and univocal way. Applications to photoionisation processes in strong laser or microwave fields are also discussed.

Asymmetric Light and Multiphoton Processes

Abstract In a previous paper it was found that the squeezed vacuum light is (2n−1)!!-fold more efficient in an n-photon process than coherent light of the same intensity. It is shown here that this is true not only for the squeezed vacuum but also for light with more complicated statistics if the variances of the quadratures used in describing squeezing are sufficiently different, even in the case when both variances are above the vacuum noise level. It is found that such light can be generated more easily than the squeezed light. It is also shown that, in contrast to squeezing, this high efficiency is not destroyed by a usual linear amplifier even during very strong amplification.

Amplification of squeezed light and multiphoton processes

It is shown that a wide class of state of light related to squeezed light has high, (2 n−1)!!-fold efficiency in n-photon processes. In contrast to squeezing this high efficiency is not destroyed by a usual linear amplifier even during a very strong amplification.

1/n Expansion for n-Phonon Processes. Scattering

In recent experiments on photoionization and electron-atom collisions a great number of photons absorbed or emitted were reported. These experiments justify the consideration of the limit of large n for n-photon processes. In this paper a new approximation scheme is developed, which consists in 1/n expansion for the measured quantities. In particular, a complementary region where the low-frequency approximation is applicable is found. It appears that the Kroll-Watson formula is valid even at the very small initial energy provided that the final one is sufficiently large with respect to the laser photon energy.

Multiple Bifurcations in Coherent n-photon Processes

We consider a new class of bifurcations that may arise in multiphoton processes inside a coherently driven optical cavity involving more than one mode of the radiation field. For a non-saturable, non-linear medium, a single bifurcation point exists where the symmetric solution bifurcates into a number of non-symmetric solutions. The nature of the bifurcation ranges from a simple pitchfork bifurcation, in the case of four-wave mixing, to more complicated phenomena in higher-order processes. A saturable non-linear medium exhibits similar behaviour for low-input intensities; however, as the input intensity is increased the medium saturates, and at a second bifurcation point the symmetric branch regains its stability. The presence of fluctuations assures the accessibility of the symmetric branch. Thus, for example, for a two-photon absorbing medium we have the possibility of optical tristability involving one symmetric solution and two non-symmetric solutions.

A correction factor for experimental multiphoton absorption cross section

The experimental absorption cross section δ n of an n-photon process induced by pulsed laser radiation is shown to be dependent in a simple way on the distribution of the laser intensity. A gaussian radial distribution of the intensity leads to a correction factor of n −1 and a gaussain temporal distribution of the intensity within the pulse leads to a correction factor of n − 1 2 . Values for δ n derived from fluorescence intensity data without taking into account spatial and temporal intensity distributions should therefore be multiplied by a correction factor n 3 2 .