Contribution To Hyperpolarizability Research Articles

Nonlinear chiral molecular photonics using twisted light: hyper-Rayleigh and hyper-Raman optical activity

Chiroptical and optical activity effects involve differential interactions between matter and light. Generally this involves chiral molecules absorbing or scattering right- and left-handed circularly polarized photons at different rates due to the chiroptical interplay of molecular and optical chirality. Laser light which propagates with a helical phase and twisted wavefront possesses optical orbital angular momentum. These optical vortices can twist either clockwise or anticlockwise, and as such they exhibit an optical handedness or chirality completely distinct from that of circular polarization. It has recently been established that the linear optical effects of single-photon absorption and scattering can exhibit optical activity and chiroptical interactions with respect to the optical vortex handedness. Here a fundamental mechanism of optical activity for twisted light is exhibited in nonlinear processes, with specific emphasis on hyper-Rayleigh and hyper-Raman scattering. In comparison to unstructured or plane-wave light, it is shown that using twisted photons produces novel scattering mechanisms dependent on parameters unique to optical vortex beams. Specifically, the scattered intensity for both hyper-Rayleigh and hyper-Raman optical activity is dependent on the sign and magnitude of the OAM of the incident twisted photons, as well as the transverse position of the chiral scatterer. Moreover, symmetry analysis reveals that, unlike the recently discovered linear optical activity effects with optical vortices, nonlinear scattering of twisted light by chiral molecules leads to a modification of scattering through uniquely weighted individual hyperpolarizability contributions.

Coherence Preservation of a Single Neutral Atom Qubit Transferred between Magic-Intensity Optical Traps.

We demonstrate that the coherence of a single mobile atomic qubit can be well preserved during a transfer process among different optical dipole traps (ODTs). This is a prerequisite step in realizing a large-scale neutral atom quantum information processing platform. A qubit encoded in the hyperfine manifold of an ^{87}Rb atom is dynamically extracted from the static quantum register by an auxiliary moving ODT and reinserted into the static ODT. Previous experiments were limited by decoherences induced by the differential light shifts of qubit states. Here, we apply a magic-intensity trapping technique which mitigates the detrimental effects of light shifts and substantially enhances the coherence time to 225±21 ms. The experimentally demonstrated magic trapping technique relies on the previously neglected hyperpolarizability contribution to the light shifts, which makes the light shift dependence on the trapping laser intensity parabolic. Because of the parabolic dependence, at a certain "magic" intensity, the first order sensitivity to trapping light-intensity variations over ODT volume is eliminated. We experimentally demonstrate the utility of this approach and measure hyperpolarizability for the first time. Our results pave the way for constructing scalable quantum-computing architectures with single atoms trapped in an array of magic ODTs.

The electric quadrupole moment of O2

Room-temperature measurements of the Buckingham effect (electric-field-gradient-induced birefringence, EFGIB) for gaseous oxygen are presented. The traceless electric quadrupole moment of the oxygen molecule has been deduced from these data, with the assumption that the temperature-independent hyperpolarizability contribution to the EFGIB is negligibly small. The value obtained is Θ=(−1.033±0.027)×10−40Cm2. This value is compared with the best available ab initio quantum computational values in the literature.

Ultrafast Quantum Mechanics/Molecular Mechanics Monte Carlo simulations using generalized multipole polarizabilities

A fast and accurate Quantum Mechanics/Molecular Mechanics method is described for thermodynamic simulation of solutes (or active sites in flexible molecules) in polar environments. The solute is described quantum mechanically and is held fixed during averaging over solvent configurations, which are described by Molecular Mechanics. Quantum calculations during simulation are replaced by the evaluation of the response of the solute to the long range electric field of the solvent, using precalculated generalized electric moments and polarizabilities. This results in huge decrease of computational time without affecting the accuracy of the QM/MM results. Implementation in a Monte Carlo program accelerated the simulations of guanine and the phenylalanine dipeptide in TIP3P water by over four orders of magnitude. Polarizability is essential for accuracy. Its inclusion decreases the average signed energy error and its standard deviation from 5.69 to 0.003 and 1.22 to 0.013kcal/mol, respectively, for the dipeptide. Hyperpolarizability contributions are insignificant.

Measurement of the electric quadrupole moment of CO

Measurements of the temperature dependence of the Buckingham effect (electric-field-gradient-induced birefringence, EFGIB) for gaseous carbon monoxide are presented. The measurements span the temperature range 301.2-473.9 K, which allows for separation of the temperature-independent hyperpolarizability contribution from the temperature-dependent quadrupole contribution. It is demonstrated that in the case of carbon monoxide, quantization of the rotational motion of the molecules needs to be considered, the analysis yielding a quadrupole moment of Θ = (-8.77 ± 0.31) × 10(-40) C m(2) and a hyperpolarizability term of b' = (-0.1243 ± 0.0078) × 10(-60) C(3) m(4) J(-2). For dipolar molecules, the quadrupole moment is origin dependent, and the value reported here is referred to an origin called the effective quadrupole center. Comparison of this value with the center-of-mass quadrupole moment obtained from other experiments yields information about the dynamic dipole-quadrupole and dipole-magnetic dipole polarizabilities. The temperature-independent term, which contributes (7.0 ± 0.6)% to the EFGIB at room temperature, is by no means insignificant, and must necessarily be accounted for if the quadrupole moment is to be definitively established. The measured Θ and b' are compared with the best available ab initio calculated values.

Erratum: “Density-functional and electron correlated study of five linear birefringences—Kerr, Cotton–Mouton, Buckingham, Jones and magnetoelectric—in gaseous benzene” [J. Chem. Phys. 121, 8814 (2004)]; “Density-functional study of electric and magnetic properties of hexafluorobenzene in the vapor phase” [J. Chem. Phys. 122, 234314 (2005)]; and “A computational study of some electric and magnetic properties of gaseous BF3 and BCl3” [J. Chem. Phys.

wecame to discover the occurrence of an unfortunate mistake inthe determination of the sign of the paramagnetic contribu-tion para to the anisotropy of the hypermagnetizability published in the studies of Refs. 2–4. In the latter,moreover, the sign of the hyperpolarizability contribution toBuckingham birefringence

Fifth-order nonlinear Raman processes in molecular liquids using quasi-cw noisy light. I. Theory

Fifth-order nonlinear Raman processes using broadband, incoherent light are treated for a multiply resonant, multicomponent mixture. In particular, the theoretical development of the direct and the sequential fifth-order analogs of coherent Raman scattering is presented. Of the complete formalism, only the dominant doubly Raman resonant hyperpolarizability contributions to the signal intensity are discussed in this article. Furthermore, application is made to simulate fifth-order signals from a variety of hypothetical molecular liquids. It is seen how the direct and the sequential processes can distinguish themselves in a mixture, in a neat liquid with more than one Raman coherence, and also whenever the Raman active modes are taken to be anharmonic. This theoretical treatment anticipates experimental results presented in the following paper.

Coherent Raman scattering with incoherent light for a multiply resonant mixture: A factorized time correlator diagram analysis

Coherent Raman scattering using broadband, incoherent (noisy) light (termed ${\mathrm{I}}^{(2)}\mathrm{CRS}$---the I for interferometric and the superscript 2 for twice acting noisy fields) is treated for a multiply resonant, multicomponent mixture of molecules. Both the resonant-resonant and resonant-nonresonant hyperpolarizability contributions to the signal intensity are included in this formalism. The emphasis is on the physical understanding of this spectroscopy. To this end, factorized time correlator (FTC) diagram analysis is used to characterize the ${\mathrm{I}}^{(2)}\mathrm{CRS}$ signal. The FTC diagram technique also serves to organize the terms that arise through the stochastic averaging of the noise at the intensity level. In addition to the FTC diagram analysis, a spectral filter analogy is employed to provide further insight into the physics behind ${\mathrm{I}}^{(2)}\mathrm{CRS}.$

Coherent Raman scattering with incoherent light for a multiply resonant mixture: Theory

The theory for coherent Raman scattering (CRS) with broadband incoherent light is presented for a multiply resonant, multicomponent mixture of molecules that exhibits simultaneous multiple resonances with the frequencies of the driving fields. All possible pairwise hyperpolarizability contributions to the signal intensity are included in the theoretical treatment---(resonant-resonant, resonant-nonresonant, and nonresonant-nonresonant correlations between chromophores) and it is shown how the different types of correlations manifest themselves as differently behaved components of the signal intensity. The Raman resonances are modeled as Lorentzians in the frequency domain, as is the spectral density of the incoherent light. The analytic results for this multiply resonant mixture are presented and applied to a specific binary mixture. These analytic results will be used to recover frequencies and dephasing times in a series of experiments on multiply resonant mixtures.

Measurement of the electric quadrupole moments of CO2, CO, N2, Cl2 and BF3

The electric quadrupole moments of a number of molecules have been determined from measurement of the birefringence induced in a gas by an electric field gradient. The values obtained are: carbon dioxide (− 14·27 ± 0·61)x 10−40 C m2, carbon monoxide (− 9·47 ± 0·15)x 10−40 C m2, nitrogen (− 4·65±0·08)x 10−40 C m2 and boron trifluoride (12·6±0·7)x 10−40 C m2. In the calculation of the moments for carbon monoxide and boron trifluoride the small hyperpolarizability contribution was neglected in the absence of known values. By means of the Jones calculus a detailed analysis was made of the effects of strain birefringence in the cell windows and imperfect orientation of polarizing components in the light path. This analysis led to a measurement procedure which yielded results significantly different from previously reported ones obtained with essentially the same apparatus. The probable error in the earlier procedure is identified.

Measurement of the electric quadrupole moments of CO2, CO, N2, Cl2 and BF3

The electric quadrupole moments of a number of molecules have been determined from measurement of the birefringence induced in a gas by an electric field gradient. The values obtained are: carbon dioxide (− 14·27 ± 0·61)x 10−40 C m2, carbon monoxide (− 9·47 ± 0·15)x 10−40 C m2, nitrogen (− 4·65±0·08)x 10−40 C m2 and boron trifluoride (12·6±0·7)x 10−40 C m2. In the calculation of the moments for carbon monoxide and boron trifluoride the small hyperpolarizability contribution was neglected in the absence of known values. By means of the Jones calculus a detailed analysis was made of the effects of strain birefringence in the cell windows and imperfect orientation of polarizing components in the light path. This analysis led to a measurement procedure which yielded results significantly different from previously reported ones obtained with essentially the same apparatus. The probable error in the earlier procedure is identified.

Push−Pull Phthalocyanines: A Hammett Correlation between the Cubic Hyperpolarizability and the Donor−Acceptor Character of the Substituents

The nonlinear optical (NLO) properties at the molecular level of a family of unsymmetrically substituted metal-free phthalocyanines (3−9) have been studied for the first time. NLO characterization has been performed by electric field-induced second harmonic (EFISH) generation and third harmonic generation (THG) experiments in solution at 1.064 and 1.34 mm, respectively. The NLO response has been investigated for different types of substituents. Although no experimental evidence of a quadratic hyperpolarizability (β) contribution to γEFISH has been obtained, a significant influence of intramolecular charge transfer (ICT) on the cubic nonlinear response has been evidenced and correlated to the relative strengths of donor and acceptor substituents. Thus, γTHG shows a clear absolute minimum for low Hammett parameters values of the substituents and becomes maximal for high values, i.e., for compounds having strong donor or acceptor groups such as alkoxy (3) or nitro (8) substituents. Such an enhancement effect of the γTHG values due to the high dipolar moment associated with strong donor or acceptor substituents follows the trend previously observed in some porphyrin and phthalocyanine systems.

Theory of coherent Raman scattering with quasi-cw noisy light for a general line shape function

The theory of electronically nonresonant coherent Raman scattering (CRS) with quasi-cw noisy light (I(2) CRS) is developed for a general material response. The (Raman) resonant–resonant and resonant–nonresonant hyperpolarizability contributions to the I(2) CRS signal are interferometrically separable. It is found that, in general, the interferometric decay of each of these terms exposes the Raman line shape function in a different manner. Only for a Lorentzian line is their decay identical. Thus, in principle, I(2) CRS provides a new way to explore the line shape function that is analytically distinct from frequency domain and time domain methods. By way of illustration, the general theory is applied to three common line shapes: Lorentzian (as in the original I(2) CRS theory), Gaussian, and Voigt. The results are shown to be consistent with the principles of factorized time correlation diagram analysis.

Linear and nonlinear polarizabilities of polydiacetylene and polybutatriene chains: An ab initio coupled Hartree–Fock investigation

Ab initio Hartree–Fock 6-31G longitudinal polarizabilities and second hyperpolarizabilities of polydiacetylene and polybutatriene oligomers are computed and, then, extrapolated to the infinite polymer limit. Both the electronic and vibrational components are obtained with the latter evaluated in the double harmonic approximation. For static fields the electronic hyperpolarizability of the butatrienic form is almost 50 times larger than the acetylenic form; the ratio of the vibrational to the electronic component is 0.86 for the latter and 3.3 for the former. Thus, the two components are sensitive to the difference in bond length alternation (BLA) in different ways. Depending upon the particular nonlinear process it is shown that the vibrational hyperpolarizability may remain large even at optical frequencies. Three intense Raman-active k=0 modes dominate the vibrational component. At the level of theory used here these modes occur in the frequency range 1000–2500 cm−1 and they consist of changes in the BLA as well as hydrogen wagging motions. For polydiacetylene, there is a 1:1 relation with the corresponding vibrations that make the most important hyperpolarizability contributions in polyacetylene and polyyne.

Depolarized light scattering by CF 4

Tetrafluoromethane gas depolarized scattering has been recorded at 294·5 K and 20·3 amagat in the frequency range 2-340 cm−1. Two-body depolarized scattered intensities have been measured in absolute units up to 150 cm−1. The theoretical intensities taking into account multipolar polarizabilities and several hyperpolarizability contributions have been calculated. From comparison with experiment, the independent components of the dipole-quadrupole and the dipole-octopole polarizability tensors have been estimated and checked with recent ab initio theoretical values.

Calculation of solvation energies: the self-consistent multipole moment reaction field method

The self-consistent multipole moment reaction field (SCMMRF) method is proposed as a simple alternative to the conventional self-consistent reaction field (SCRF) technique for the calculation of solvation energies within the confines of the dielectric continuum model. The SCMMRF method represents a straight forward generalization of the original Kirkwood method by the inclusion of the solute's polarizability. Formally, the SCMMRF method is identical to SCRF through second order in the reaction field in its present formulation, i.e., hyperpolarizability contributions are neglected. The SCMMRF method is particularly cost-effective when applied in conjunction with correlated wavefunctions, since it requires only multipole moments and their polarizabilities to be computed. Test calculations for the water and pyrimidine molecules and for several H2O clusters demonstrate that the SCMMRF technique is a numerically reliable alternative to SCRF. Using a composite discrete-continuum approach, the hydration energy o...

A theoretical study of hyperpolarizability effects in the measurement of molecular quadrupole moments

Calculations are made of the hyperpolarizability contribution to the electric-field-gradient-induced birefringence which is used to measure the quadrupole moments of non-dipolar molecules. It is concluded that hyperpolarizability effects are small for most, but not all, molecules.

The quadrupole moments of carbon dioxide and carbon disulphide

The electric quadrupole moments of carbon dioxide and carbon disulphide have been measured through the birefringence induced in gaseous samples over a range of temperature. The value for CO2, Θ = (-14·98 ± 0·50) × 10-40 C m2, is consistent with earlier measurements, showing that the temperature-independent hyperpolarizability contribution to the birefringence is insignificant. For CS2, Θ = (+12·0 ± 0·6) × 10-40 C m2. The positive sign reflects the increased importance of the π electron contribution to Θ in CS2.

An atom–dipole interaction theory of the hyperpolarizability contribution to the optical activity of molecules

The atom–dipole interaction model formulation of the polarizability theory of optical activity is generalized to include hyperpolarizability effects. This is done by considering the response of the optical rotation of a high frequency light signal to the intensity and orientation of the electric vector of another low frequency but intense light signal. The molecular polarizabilities are written in terms of the two-, three-, and four-atom relay tensors and the electric vector of the low frequency field. Expressions are derived for the electric displacement and magnetic induction vectors, and values for the refractive indices of two different elliptically polarized light waves are extracted from Maxwell’s equations. Lastly, expressions for the optical rotation rate and the ellipticity rate are derived, and a sample calculation is performed on the halomethane CHFClBr.

Kerr constants, depolarization ratios, and hyperpolarizabilities of substituted methanes

The static Kerr constants of eight substituted methanes in the gas phase have been measured by a low-frequency null technique. Combining these results with gas phase depolarization ratio measurements we show that the hyperpolarizability contributions to the Kerr constant are small except for CH3F. The magnitudes of the hyperpolarizabilities obtained are in good agreement with the values obtained from second harmonic generation measurments. In the case of nitromethane the electric birefringence and depolarization ratio measurements are combined to obtain the three principal values of the polarizability tensor.