Swapan Mandal

Rate-determining factors in the chain polymerization of molecules initiated by local single-molecule excitation.

Spontaneous chain polymerization of molecules initiated by a scanning tunneling microscope tip is studied with a focus on its rate-determining factors. Such chain polymerization that happens in self-assembled monolayers (SAM) of diacetylene compound molecules, which results in a π-conjugated linear polydiacetylene nanowire, varies in its rate P depending on domains in the SAM and substrate materials. While the arrangement of diacetylene molecules is identical in every domain on a graphite substrate, it varies in different domains on a MoS(2) substrate. This structural variation enables us to investigate how P is affected by molecular geometry. An important determining factor of P is the distance between two carbon atoms which are to be bound by polymerization reaction, R; as R decreases by 0.1 nm, P increases ∼2 times. P for a MoS(2) substrate is ∼4 times higher (with the same value of R) than that for a graphite substrate because of higher mobility of molecules. The exciting correlation of the chain polymerization rate to the geometrical structure of the diacetylene molecules brings a deeper understanding of the mechanism of chain polymerization kinetics. In addition, the fabrication of one-dimensional conjugated polymer nanowires on a semiconducting MoS(2) substrate as demonstrated here may be of immense importance in the realization of future molecular devices.

Classical and quantum oscillators of quartic anharmonicities: second-order solution

Abstract An analytical solution up to the second order in the coupling constant λ is obtained for a classical quartic anharmonic oscillator by using Taylor series method. Our solution yields, as a special instance, the corresponding results obtained by using Laplace transform. With the help of correspondence principle, the classical solution is used to obtain the solution corresponding to a quantum quartic anharmonic oscillator. In the weak coupling regime (i.e., anharmonic constant λ⪡1), the so-called secular terms in classical and quantum solutions are tucked in (summed up) to avoid the nonconvergence. Both the classical and quantum solutions are used to obtain the frequency shifts of the quartic oscillators. It is found that these frequency shifts coincide exactly with those of the earlier results obtained by other methods. From the quantum field theoretic point of view, our solution exhibits the so-called Lamb shift. As an application of the solution for the quantum oscillator, we examine the possibility of getting squeezed states out of the input coherent light interacting with a nonlinear medium of inversion symmetry.

Quantum oscillator of quartic anharmonicity

A Taylor series method is derived to construct an analytical solution for the quantum anharmonic oscillator. The expression presented is found to yield in a rather natural way the corresponding special result obtained by using perturbation theoretic techniques. Attempts are made to give a possible physical interpretation for the various terms originating from nonlinear effects. Numerical results are presented to develop a feeling for their relative importance.

Classical and quantum oscillators of sextic and octic anharmonicities

Classical oscillators of sextic and octic anharmonicities are solved analytically up to the linear power of λ (anharmonic constant) by using Taylor series method. These solutions exhibit the presence of secular terms which are summed up for all orders. The frequency shifts of the oscillators for small anharmonic constants are obtained. It is found that the calculated shifts agree nicely with the available results to-date. The solutions for classical anharmonic oscillators are used to obtain the solutions corresponding to quantum anharmonic oscillators by imposing fundamental commutation relations between position and momentum operators.

Squeezed states in spontaneous Raman and in stimulated Raman processes

The Hamiltonian and the equations of motion for various modes involving spontaneous and stimulated Raman processes are derived. The coupled differential equations involving these modes are solved analytically by using an intuitive approach (IA). The solution of the present paper does not require any short time approximation. As a matter of fact, the present solution for field operators and hence the squeezing for various modes are valid for all interaction time t. In this way, the present paper is more general compared to the earlier investigations where short-time approximations were found a must. By exploiting the solutions for the field operators, we obtain the squeezing effects of input coherent light for pure and for mixed field modes. The IA employs the perturbation theory and hence we came across the secular terms in the solution. Of course, for small coupling constants these secular terms could be summed for all orders. To establish our claim, we remove the secular terms at least for one occasion.

An intuitive approach to the higher order solutions for classical and quantum oscillators of quartic anharmonicity

An intuitive approach is used to propose the most general form of the solution of a classical quartic anharmonic oscillator. The proposed (assumed) solution is a direct outcome of perturbation theory and contains time-dependent parameters. Under suitable boundary conditions, the exact functional form of these parameters are obtained by solving differential equations. Knowing the solution for zeroth order in λ (anharmonic constant), the solution first order in λ is obtained. In a similar manner, the solution first order in λ is used to obtain the solution corresponding to the second order in λ. Both the first and second order solutions in λ are in good agreement with the solutions obtained by using a Taylor series method. The iterative approach, though tedious, is useful for the generalization of the solution for all orders in λ. By using the correspondence principle, the solution of a quantum quartic oscillator is obtained from the knowledge of the solution of its classical counterpart. The present solutions for all orders in λ may be useful to frame an algorithm for the purpose of getting numerical solutions to the quantum anharmonic oscillator problem.

Phase fluctuations of coherent light coupled to a nonlinear medium of inversion symmetry

Abstract An analytical approach is being adopted for the calculation of phase fluctuations of coherent light interacting with a nonlinear medium of inversion symmetry. The useful parameters for such calculations are expressed in closed analytical forms (up to the linear power of coupling constant). It is found that the presence of non-conserving energy terms in the model Hamiltonian lead to enhancement and reduction of phases compared to their initial values.

On the possibility of continuous generation of squeezed states in a quartic anharmonic oscillator

Coherent light interacting with a nonlinear nonabsorbing medium of inversion symmetry is modelled as a quartic anharmonic oscillator if the lowest (i.e. third) order of nonlinearity is considered. The equation of motion of the quadrature operators of such an oscillator is solved approximately in a closed analytical form. The corresponding solution is used to investigate the possibility of finding the continuous squeezed states. It is found that the amount of squeezing is increased with the increase of intensity of the applied field. An improvement of the squeezing is also possible if the coupling strength is increased. We report the squeezing effect of the input vacuum field. The possibility of generating continuous squeezing in an absolute sense (i.e. 100%) of the input radiation field is also discussed.

High Ferromagnetic Transition Temperature in PbS and PbS:Mn Nanowires

Spontaneous magnetization measured in the temperature range 5-300 K with high ferromagnetic transition temperature (T(c)) has been observed in both undoped and Mn doped (2-8 mol %) PbS nanowires (diameter 30 nm) in polymer. For undoped sample, we find T(c) ~ 290 K while for doped samples T(c) varies between 310-340 K depending on Mn concentrations. Both T(c) and coercive fields are critically dependent on Mn concentrations. Coercive fields show a T(0.5) dependence with temperature for a moderate concentration of Mn (4 mol %) in PbS while it deviates from T(0.5) behavior for higher Mn concentrations. Anionic defects arising out of nonstoichiometric growth is solely responsible for the observed magnetism in undoped PbS nanowires. The role of intrinsic strain along with reduced dimensionality in determining such high T(c) and overall magnetizations has been discussed.

Ordered Monomolecular Layers as a Template for the Regular Arrangement of Gold Nanoparticles

Ordered arrays of metal nanoparticles are important for nanoelectronic and nanophotonic applications. Here, we report the formation of self-assembled arrays of gold nanoparticles on molecular layers of diacetylene compounds on a MoS2(0001) substrate. The arrangement of gold nanoparticles is observed using scanning tunneling microscopy. When gold is deposited on a self-assembled monolayer of 10,12-nonacosadiynoic acid or 10,12-octadecadiynoic acid on a MoS2(0001) substrate, the ordered array of diacetylene moieties in the molecular layer serves as a template for the formation of ordered arrays of gold nanoparticles. In contrast, when gold is deposited on a pristine MoS2(0001) surface or on a molecular layer of stearic acid, the gold nanoparticles are randomly distributed on the surface. It is found that the arrangement of gold nanoparticles is largely determined by the deposition rate; faster deposition results in more ordered arrays of gold nanoparticles. Our observations confirm the role of unsaturated π systems in molecules acting as a template for the regular arrangement of gold nanoparticles; this work will open up new possibilities for interfacial nanoarchitectonics.