Search

Optomechanical thermometry is a precise and reference-free method to measure absolute temperature. While pumping high optical power is needed to overcome noise and reduce the integration time, there is actually an upper limit to the useful optical power regardless of all other nonideal effects. Side-band inequivalence is a nonlinear effect obtained by higher-order operator algebra in quantum optomechanics and equivalent experiments, which causes asymmetric frequency shifts in side-bands and also an additional difference in their population. This chapter discusses previously unnoticed nonlinear effects arising from side-band inequivalence in optomechanical and Raman thermometry, which determines an upper bound in available optical power for temperature readout.

The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum optomechanics and quantum computing have a highly nonlinear nature, which makes their analysis extraordinarily difficult using classical schemes. Typically, modern quantum systems of interest nowadays come with four basic properties: (i) quantumness, (ii) openness, (iii) randomness, and (iv) nonlinearity. The newly introduced method of higher-order operators targets analytical solutions to such systems, and while providing at least mathematically approximate expressions with improved accuracy over the fully linearized schemes, some cases admit exact solutions. Many different applications of this method in quantum and classically nonlinear systems are demonstrated throughout. This review is purposed to provide the reader with ease of access to this recent and well-established operator algebra, while going over a moderate amount of literature review. The reader with basic knowledge of quantum mechanics and quantum noise theory should be able to start using this scheme to his or her own problem of interest.

Frequency shifts of red- and blue-scattered (Stokes/anti-Stokes) side-bands in quantum optomechanics are shown to be counter-intuitively inequal, resulting in an unexpected symmetry breaking. This difference is referred to as Side-band Inequivalenve (SI), which normally leans towards red, and being a nonlinear effect it depends on optical power or intracavity photon number. Also there exists a maximum attainable SI at an optimal operation point. The mathematical method employed here is a combination of operator algebra equipped with harmonic balance, which allows a clear understanding of the associated nonlinear process. This reveals the existence of three distinct operation regimes in terms of pump power, two of which have immeasurably small SI. Compelling evidence from various experiments sharing similar interaction Hamiltonians, including quantum optomechanics, ion/Paul traps, electrooptic modulation, Brillouin scattering, and Raman scattering unambiguously confirm existence of a previously unnoticed SI., Comment: This is the final version including Supplementary Information; Comments are utmostly welcome

In this letter, it is proposed that cryogenic quantum bits can operate based on the nonlinearity due to the quantum capacitance of two-dimensional Dirac materials, and in particular graphene. The anharmonicity of a typical superconducting quantum bit is calculated, and the sensitivity of quantum bit frequency and anharmonicity with respect to temperature are found. Reasonable estimates reveal that a careful fabrication process can reveal expected properties, putting the context of quantum computing hardware into new perspectives., Comment: Published: 2 July 2018

We present a full operator approach to treatment of the cross-Kerr interaction combined with parametric amplification. It is shown that this problem can be exactly integrated using the method of higher-order operators. While the initial basis is infinite-dimensional, an orthogonal transformation can reduce the problem exactly into a six-dimensional basis which can be integrated conveniently.

This chapter summarizes the recent progress in the theory and analytical tools of quadratic optomechanical interactions, as one of the prominent domains of contemporary nonlinear quantum optics. Emphasis has been put here first to show what types of nonlinear interactions do exist, and what physical interpretations follow each. The standard quadratic interactions between light and mechanical motion is expressed as the product of cavity light intensity and squared mirror position. However, there exists a non-standard quadratic optomechanical interaction as well, which assumes a mathematically different form and appears as the squared product of field and mirror momenta. This non-standard type of quadratic interaction originates from two corrections: the momentum exchange and conservation among mirror and field, as well as relativistic corrections due to different mechanisms. Both these types of non-standard interactions become relevant when the ratio of mechanical to optical frequency is no longer negligible. Next, we turn to the solution technique of such interactions, and introduce a formal higher-order operator method to tackle the nonlinear evolution of quantum systems. This enables one to accurately study any type of quantum nonlinear interaction using the analysis tools of linear algebra. In order to employ the analytical power of higher-order operator method, one first needs to identify a closed Lie algebra, which should satisfy closedness property under commutation either exactly or approximately, and is referred to as the basis. Having the basis of higher-order operators known, one may proceed to construct the corresponding Langevin equations, which can be now conveniently analyzed using the existing mathematical toolbox of linear algebra to yield the spectral densities, moments, and expectation values.

This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second order operators which constitute an exactly closed commutators. We consider both types of standard position-field and the recently predicted non-standard momentum-field quadratic interactions, which is significant when the ratio of mechanical frequency to optical frequency is not negligible. This unexplored regime of large mechanical frequency can be investigated in few platforms including the superconducting electromechanics and simulating quantum cavity electrodynamic circuits. It has been shown that the existence of non-standard quadratic interaction could be observable under appropriate conditions.

We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises from nonlinear higher-order processes leading to inequal detunings. Similarly, a higher-order resonance shift exists appearing as changes in both of the optical and mechanical resonances. We provide the first known method to explicitly estimate the population of coherent phonons. We also calculate corrections to spring effect due to higher-order interactions and coherent phonons, and show that these corrections can be quite significant in measurement of single-photon optomechanical interaction rate. It is shown that there exists non-unique and various choices for the higher-order operators to solve the optomechanical interaction with different multiplicative noise terms, among which a minimal basis offers exactly linear Langevin equations, while decoupling one Langevin equation and thus leaving the whole standard optomechanical problem exactly solvable by explicit expressions. We finally present a detailed treatment of multiplicative noise as well as nonlinear dynamic stability phases by the method of higher-order operators. Similar approach can be used outside the domain of standard optomechanics to quadratic and all other types of nonlinear interactions in quantum physics., Comment: 16 equations, 11 pages, 88 references, with 21 pages of Supplementary Information. Experimental observations were dropped. This final version with total restructuring under a new title appears in Scientific Reports

Most electromechanical devices are in two-dimensional metallic drums under high tensile stress, which causes increased mechanical frequency and quality factor. However, high mechanical frequencies lead to small zero-point displacements $x_{\rm zp}$, which limits the single-photon interaction rate $g_0$. For applications which demand large $g_0$, any design with increased $x_{\rm zp}$ is desirable. It is shown that a patterned drum by spiral shape can resolve this difficulty, which is obtained by a reduction of mechanical frequency while the motion mass is kept almost constant. An order of magnitude increase in $g_0$, and agreement between simulations and interferometric measurements is observed.

We present a detailed calculation of the linear and nonlinear optical response of four types of monolayer Two-Dimensional (2D) Transition-Metal Dichalcogenides (TMDCs), having the formula $\textrm{MX}_2$ with M=Mo,W and X=S,Se. The calculations are based on 6-band tight-binding model of TMDCs, and then performing a semiclassical perturbation analysis of response functions. We numerically calculate the linear $\chi_{\mu\nu}^{(1)}(-\omega;\omega)$ and nonlinear surface susceptibility tensors $\chi_{\mu\nu\zeta\eta}^{(3)} (-\omega_\Sigma;\omega_r,\omega_s,\omega_t)$ with $\omega_\Sigma=\omega_r+\omega_s+\omega_t$. Both non-degenerate and degenerate cases are studied for third-harmonic generation and nonlinear refractive index, respectively. Computational results obtained \textit{with no external fitting parameters} are discussed regarding two recent reported experiments on ${\rm MoS}_2$, and thus we can confirm the extraordinarily strong optical nonlinearity of TMDCs. As a possible application, we demonstrate generation of a $\frac{\pi}{4}-$rotated squeezed state by means of nonlinear response of TMDCs, in a silica micro-disk resonator covered with the 2D material. Our proposed method will enable accurate calculations of nonlinear optical response, such as four-wave mixing and high-harmonic generation in 2D materials and their heterostructures, thus enabling study of novel functionalities of 2D photonic integrated circuits.

We present quantum yield measurements of single layer $\textrm{WSe}_2$ (1L-$\textrm{WSe}_2$) integrated with high-Q ($Q>10^6$) optical microdisk cavities, using an efficient ($\eta>$90%) near-field coupling scheme based on a tapered optical fiber. Coupling of the excitonic emission is achieved by placing 1L-WSe$_2$ to the evanescent cavity field. This preserves the microresonator high intrinsic quality factor ($Q>10^6$) below the bandgap of 1L-WSe$_2$. The nonlinear excitation power dependence of the cavity quantum yield is in agreement with an exciton-exciton annihilation model. The cavity quantum yield is $\textrm{QY}_\textrm{c}\sim10^{-3}$, consistent with operation in the \textit{broad emitter} regime (i.e. the emission lifetime of 1L-WSe$_2$ is significantly shorter than the bare cavity decay time). This scheme can serve as a precise measurement tool for the excitonic emission of layered materials into cavity modes, for both in plane and out of plane excitation.

Phoxonic crystal as a means of guiding and confining electromagnetic and elastic waves has already attracted attentions. Lack of exact knowledge on how these two types of waves interact inside this crystal and how electromagnetic wave evolves through this interaction has increased this field complexity. Here we explain how an elastic wave affects an electromagnetic wave through photo-elasticity and interface displacement mechanisms in a phoxonic crystal slab waveguide. We obtain a master equation which can describe electromagnetic wave evolution. In this equation we define a coupling parameter and calculate its value for different modes of electromagnetic and elastic waves and show it vanishes for some types of modes . Finally we solve the master equation for a typical phoxonic crystal slab waveguide and illustrate the electromagnetic wave evolution.

Today's standard fabrication processes are just capable of manufacturing slab of photonic and phononic crystals, so an efficient method for analysis of these crystals is indispensable. Plane wave expansion (PWE) as a widely used method in studying photonic and phononic (phoxonic) crystals in full three dimensions is not suitable for slab analysis in its standard form, because of convergence and stability issues. Here, we propose a modification to this method which overcomes these limitations. This improved method can be utilized for calculation of both photonic and phononic modes in phoxonic slabs. While in the standard three-dimensional PWE, Fourier series are used to estimate the field dependence across the normal component of the slab, we expand the fields across the third dimension using eigenmodes of a plain unstructured slab. Despite its approximate nature, this approach is observed to be both much faster and more accurate than the conventional PWE method and can give a very accurate estimation of confined propagating modes. As an application example of the proposed method we investigate a non-reciprocal photonic device. This device is a phoxonic slab waveguide which changes modes of optical waves by elastic waves and can be used as an optical insulator or mode converter., Comment: accepted to Journal of Lightwave Technology

A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While, the zeroth order linearization approximation to the operators is normally used, here first and second order truncation perturbation schemes are proposed. These schemes employ higher-order system operators, and then approximate number operators with their corresponding mean boson numbers, only where needed. Spectral densities of higher-order operators are derived, and an expression for the second-order correlation function at zero time-delay has been found, which reveals that the cavity photon occupation of an ideal laser at threshold reaches $\sqrt{6}-2$, in good agreement with extensive numerical calculations. As further applications, analysis of the quantum anharmonic oscillator, calculation of $Q-$functions, analysis of quantum limited amplifiers, and nondemoliton measurements.

A system scheme is presented which allows non-reciprocal wave transmission or directional amplification of electromagnetic signals, using a boxed four-node method. Edges represent strong hopping interactions and diagonals stand for weak parametric interactions. Using careful optimization of values for design parameters, we are able to obtain non-reciprocity in excess of 12dB and 130dB for intrinsic and extrinsic configurations at identical input/output frequencies. For the directional amplification, an isolation as high as 40dB is demonstrated with forward/backward gains of $\pm$20dB. Cascading two such systems potentially can offer high isolations at high gains., Comment: accepted to IEEE Journal of Quantum Electronics

Owing to its peculiar energy dispersion, the quantum capacitance property of graphene can be exploited in a two-dimensional layered capacitor configuration. Using graphene and boron nitride respectively as the electrodes and the insulating dielectric, a strongly nonlinear behavior at zero bias and small voltages is obtained. When the temperature is sufficiently low, the strong nonlinear interaction emerging from the quantum capacitance exhibits a diverse range of phenomena. The proposed structure could take over the functionalities of nonlinear elements in many cryogenic quantum systems, and in particular, quantum electro-optics. It is shown that ultrastrong coupling is easily reached with small number of pump photons at temperatures around 1K and capacitor areas of the order of $1\mu{\textrm{m}}^2$. A measure of anharmonicity is defined and as potential applications, a qubit design as well as schemes for non-reciprocal devices such as an electromagnetic frequency circulator are discussed., Comment: Accepted to Nature 2D Materials & Applications

The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order interactions, do not vanish under any possible choice of canonical parameters, and lead to coupling of momentum and field. The existence of quadratic mechanical parametric interaction is then demonstrated rigorously, which has been so far assumed phenomenologically in previous studies. Corrections to the quadratic terms are particularly significant when the mechanical frequency is of the same order or larger than the electromagnetic frequency. Further discussions on the squeezing as well as relativistic corrections are presented.

It is first shown that the Dirac's equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint $4\times 4$ relativistic time operator for spin-$\frac{1}{2}$ particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli's objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.

Acousto-optic interaction in optomechanical crystals allows unidirectional control of elastic waves over optical waves. However, as a result of this nonlinear interaction, infinitely many optical modes are born. This article presents an exact formulaion of coupled mode theory for interaction between elastic and photonic Bloch waves moving along an optomechanical waveguide. In general, an optical wavefront is strongly diffracted by an elastic wave in frequency and wavevector, and thus infinite modes with different frequencies and wavevectors appear. We discuss resonance and mode conversion conditions, and present a rigorous method to derive coupling rates and mode profiles. We also find a conservation law which rules over total optical power from interacting individual modes. We present application examples to the theory to optomechanical waveguides and cavities, as well as non-reciprocal transmission of light and optomechanical switches., Comment: to appear in IEEE Journal of Quantum Electronics

The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The result for real-valued systems are simplified and a pair of basis functions is found. These bases are a bit less accurate than WKB solutions but much easier to work with because of their algebraic form. Furthermore, these bases exactly satisfy the initial conditions and may go over the turning points without the divergent behavior of WKB solutions. The findings of this paper allow explicit evaluation of eigenvalues of confined modes with high precision, as demonstrated by few examples.

We present an explicit solution of carrier and field distributions in abrupt PN junctions under equilibrium. An accurate logarithmic numerical method is implemented and results are compared to the analytical solutions. Analysis of results shows reasonable agreement with numerical solution as well as the depletion layer approximation. We discuss extensions to the asymmetric junctions. Approximate relations for differential capacitance and I-V characteristics are also found under non-zero external bias.

We introduce a new scalable cavity quantum electrodynamics platform which can be used for quantum computing. This system is composed of coupled photonic crystal (PC) cavities which their modes lie on a Dirac cone in the whole super crystal band structure. Quantum information is stored in quantum dots that are positioned inside the cavities. We show if there is just one quantum dot in the system, energy as photon is exchanged between the quantum dot and the Dirac modes sinusoidally. Meanwhile the quantum dot becomes entangled with Dirac modes. If we insert more quantum dots into the system, they also become entangled with each other.

Bloch theorem for a periodic operator is being revisited here, and we notice extra orthogonality relationships. It is shown that solutions are bi-periodic, in the sense that eigenfunctions are periodic with respect to one argument, and pseudo-periodic with respect to the other. An additional kind of symmetry between r-space and k-space exists between the envelope and eignfunctions not apparently noticed before, which allows to define new invertible modified Wannier functions. As opposed to the Wannier functions in r-space, these modified Wannier functions are defined in the k-spaces, but satisfy similar basic properties. These could result in new algorithms and other novel applications in the computational tools of periodic structures.

We propose a new method based on variational principle for analysis of photonic crystal (PC) slabs. Most of the methods used today treat PC slab as a three-dimensional (3D) crystal and this makes them very time and/or memory consuming. In this method we use Bloch theorem to expand the field on infinite plane waves which their amplitudes depend on the component perpendicular to the slab surface. By approximating these amplitudes with appropriate functions, we can find modes of PC slabs almost as fast as we can find modes of a two-dimensional (2D) crystal. Besides this advantage, we can also calculate radiation modes with this method which is not feasible with 3D Plane Wave Expansion (PWE) method., Comment: accepted to Materials Research Express

The widely accepted approach to the foundation of quantum mechanics is that the Poisson bracket, governing the non-commutative algebra of operators, is taken as a postulate with no underlying physics. In this manuscript, it is shown that this postulation is in fact unnecessary and may be replaced by a few deeper concepts, which ultimately lead to the derivation of Poisson bracket. One would only need to use Fourier transform pairs and Kramers-Kronig identities in the complex domain. We present a definition of Hermitian time-operator and discuss some of its basic properties.

There has been a rapidly growing interest in optoelectronic properties of graphene and associated structures. Despite the general belief on absence of spontaneous emission in graphene, which is normally attributed to its unique ultrafast carrier momentum relaxation mechanisms, there exist a few recent evidences of strong optical gain and spontaneous light emission from mono-layer graphene, supported by observations of dominant role of out-of-plane excitons in polycyclic aromatic hydrocarbons. In this article, we develop a novel concept of light emission and optical gain from simple vertical graphene/dielectric tunnel junctions. It is theoretically shown that the possible optical gain or emission spectrum will be easily tunable by the applied voltage. We present details of quantum mechanical calculations and perform an exact analysis of field-assisted tunneling using transfer matrices combined with expansion on Airy's functions.

In this note we extend the Differential Transfer Matrix Method (DTMM) for a second-order linear ordinary differential equation to the complex plane. This is achieved by separation of real and imaginary parts, and then forming a system of equations having a rank twice the size of the real-valued problem. The method discussed in this paper also successfully removes the problem of dealing with essential singularities, which was present in the earlier formulations. Then we simplify the result for real-valued problems and obtain a new set of basis functions, which may be used instead of the WKB solutions. These basis functions not only satisfy the initial conditions perfectly, but also, may approach the turning points without the divergent behavior, which is observed in WKB solutions. Finally, an analytical transformation in the form of a matrix exponential is presented for improving the accuracy of solutions., Comment: to appear in Proc. SPIE, vol. 8619

Cavity quantum electrodynamics of multipartite systems is studied in depth, which consist of an arbitrary number of emitters in interaction with an arbitrary number of cavity modes. The governing model is obtained by taking the full field-dipole and dipole-dipole interactions into account, and is solved in the Schr\"odinger picture without assumption of any further approximation. An extensive code is developed which is able to accurately solve the system and track its evolution with high precision in time, while maintaining sufficient degrees of arbitrariness in setting up the initial conditions and interacting partitions. Using this code, we have been able to numerically evaluate various parameters such as probabilities, expectation values (of field and atomic operators), as well as the concurrence as the most rigorously defined measure of entanglement of quantum systems. We present and discuss several examples including a seven-partition system consisting of six quantum dots interacting with one cavity mode. We observe for the first time that the behavior of quantum systems under ultrastrong coupling is significantly different than the weakly and strongly coupled systems, marked by onset of a chaos and abrupt phase changes. We also discuss how to implement spin into the theoretical picture and thus successfully simulate a recently reported spin-entanglement experiment., Comment: 21 figures, PACS 42.50.Gy, 42.50.Pq, 05.45.Mt, 42.65.Sf

We analyze the interaction of a propagating guided electromagnetic wave with a quantum well embedded in a dielectric slab waveguide. First, we design a quantum well based on InAlGaAs compounds with the transition energy of 0.8eV corresponding to a wavelength of 1.55um. By exploiting the envelope function approximation, we derive the eigenstates of electrons and holes and the transition dipole moments, through solution of the Luttinger Hamiltonian. Next, we calculate the electrical susceptibility of a three-level quantum system (as a model for the two-dimensional electron gas trapped in the waveguide), by using phenomenological optical Bloch equations. We show that the two-dimensional electron gas behaves as a conducting interface, whose conductivity can be modified by controlling the populations of electrons and holes the energy levels. Finally, we design a slab waveguide in which a guided wave with the wavelength of 1.55um experiences a strong coupling to the conducting interface. We calculate the propagation constant of the wave in the waveguide subject to the conducting interface, by exploiting the modified transfer matrix method, and establish it linear dependence on the interface conductivity. By presenting a method for controlling the populations of electrons and holes, we design a compact optical modulator with an overall length of around 60um.

In this paper, a new method based on Greens function theory and Fourier transform analysis has been proposed for calculating band structure with high accuracy and low processing time. This method utilizes sampling of potential energy in some points of crystals unit cell with Dirac delta functions, then through lattice Fourier transform gives us a simple and applicable formula for most of nanostructures. Sampling of potential in a crystal lattice of any kind contains accurate approximation of actual potential energy of atoms in the crystal. The step forward regarding the method concentrated on two novel ideas, Firstly, the potential was sampled and approximated by delta functions spread over the unit cell. Secondly, the principal equation of lattice is translated into reciprocal lattice and resulted in a huge reduction of calculations. By this method, it is possible to extract the band structure of any one, two or three dimensional crystalline structure., Comment: 6 pages, 4 figures

We discuss the deflection of light and Shapiro delay under the influence of gravity as described by Schwarzschild metric. We obtain an exact expression based on the coordinate velocity, as first set forth by Einstein, and present a discussion on the effect of velocity anisotropy. We conclude that the anisotropy in the coordinate velocity, as the velocity apparent to a distant observer, gives rise to a third order error in the deflection angle, so that the practical astronomical observations from gravitational lensing data remain inconclusive on the anisotropy. However, measurement of Shapiro delay provides a fairly convenient way to determine whether the spacetime is optically anisotropic for a distant observer or not. We calculate the Shapiro delay for a round trip path between Earth and Venus and observe excellent agreement to two experimentally reported values measured during a time span of six months in 1967, without any need to extra fitting parameters. This is while the expected delay obtained from an isotropic light velocity as described by Einstein's model suffers from much larger errors under similar conditions. This article illustrates the usefulness of the equivalent medium theory in understanding of general theory of relativity., Comment: To appear in Proceedings of SPIE, vol. 8480

Here, approximate, but accurate expressions for calculation of wavefunctions and tunneling rates are obtained using the method of uniform asymptotic expansion.

We have performed a numerical solution for band structure of an Abrikosov vortex lattice in type-II superconductors forming a periodic array in two dimensions for applications of incorporating the photonic crystals concept into superconducting materials with possibilities for optical electronics. The implemented numerical method is based on the extensive numerical solution of the Ginzburg-Landau equation for calculating the parameters of the two-fluid model and obtaining the band structure from the permittivity, which depends on the above parameters and the frequency. This is while the characteristics of such crystals highly vary with an externally applied static normal magnetic field, leading to nonlinear behavior of the band structure, which also has nonlinear dependence on the temperature. The similar analysis for every arbitrary lattice structure is also possible to be developed by this approach as presented in this work. We also present some examples and discuss the results., Comment: 2 pages, 2 figures

We have developed a simulation system for nanoscale high-electron mobility transistors, in which the self-consistent solution of Poisson and Schr\"odinger equations is obtained with the finite element method. We solve the exact set of nonlinear differential equations to obtain electron wave function, electric potential distribution, electron density, Fermi surface energy and current density distribution in the whole body of the device. For more precision, local dependence of carrier mobility on the electric field distribution is considered. We furthermore compare the simulation to a recent experimental measurement and observe perfect agreement. We also propose a graded channel design to improve the transconductance and thereby the threshold frequency of the device., Comment: 8 pages, 19 figures

We revisit the mathematical formulation of the famous Jaynes-Cummings-Paul Hamiltonian, which describes the interaction of a two-level atom with a single mode of an electromagnetic cavity reservoir. We rigorously show that under the condition of Ultrastrong coupling between the atom and cavity, in which the transition frequency is comparable to the coupling frequency, the bosonic field operators undergo non-sinusoidal time variations. As a result, the well-known solutions to the Jaynes-Cummings-Paul model are no longer valid, even when the rotating wave approximation is not used. We show how a correct mathematical solution could be found instead., Comment: 13 pages, 7 figures

Here, we investigate the possible optical anisotropy of vacuum due to gravitational field. In doing this, we provide sufficient evidence from direct coordinate integration of the null-geodesic equations obtained from the Lagrangian method, as well as ray-tracing equations obtained from the Plebanski's equivalent medium theory. All calculations are done for the Schwarzschild geometry, which results in an anisotropic (pseudo-isotropic) optical equivalent medium when Cartesian coordinates are taken. We confirm that the results of ray-tracing in the equivalent medium and null geodesics are exactly the same, while they are in disagreement with the results of integration in the conventional isotropic equivalent medium of Schwarzschild geometry. Based on the principle invariance of physical due to coordinate transformation, there exist just one result. This Contradiction will be solved by tensor algebra and it will be shown that the conventional isotropic approach is wrong, and even by making isotropic of the metric, the optical behavior of vacuum will remain anisotropic. Hence, we conclude that the true optical behavior of curved spacetime must be anisotropic, and it is an intrinsic property of vacuum in the presence of gravitational field. We provide further discussions on how to detect this possible anisotropy, and what further consequences might be expected in the interpretation of gravtiational lensing data., Comment: accepted for publication in International Journal of Optics and Photonics

We generalized the squeeze and displacement operators of the one-dimensional harmonic oscillator to the three-dimensional case and based on these operators we construct the corresponding coherent and squeezed states. We have also calculated the Wigner function for the three-dimensional harmonic oscillator and from the analysis of time evolution of this function, the quantum Liouville equation is also presented. Further properties of the quantum states including Mandel's Q and quadrature squeezing parameters are discussed as well., Comment: Accepted for publication in the International Journal of Optics and Photonics

In this article, the interaction of an arbitrary number of quantum dots, behaving as artificial molecules, with different energy levels and multi-mode electromagnetic field is studied. We make the assumption that each quantum dot can be represented as an atom with zero kinetic energy, and that all excitonic effects except dipole-dipole interactions may be disregarded. We use Jaynes-Cummings-Paul model with applications to quantum systems based on a time-dependent Hamiltonian and entangled states. We obtain a system of equations describing the interaction and present a method to solve the equations analytically for a single mode field within the Rotating-Wave Approximation. As an example of the applicability of this approach, we solve the system of two two-level quantum dots in a lossless cavity with two modes of electromagnetic field. We furthermore study the evolution of entanglement by defining and computing the concurrency., Comment: accepted for publication in Scientia Iranica

The exact numerical solution of the nonlinear Ginzburg-Landau equation for Josephson junctions is obtained, from which the nontrivial current density and effective potential of the Josephson junction are accurately found. Tunneling probabilities of the calculated bound states in the resulting potential well are computed. The effects of junction and bias parameters such as thickness of the insulating barrier, cross sectional area, bias current and magnetic field are fully investigated using a successive perturbation approach. We define and compute figures of merit for achieving optimal operation of phase qubits and measurement of states. Particularly, it is predicted that Josephson junctions with thicker barriers yield better performance in measurement of the phase qubit. The proportion of other parameters is also studied and discussed for the right situation of the setup. Results are in complete agreement with reported experimental data.

A new method for calculation of band structure has been proposed based on the Green's function theory and local sampling. Potential energy in the Hamiltonian of Schrodinger's equation is approximated with a series of sampled Dirac delta functions weighted by appropriate factors. These factors are found from multipole expansion of atomic potentials in the crystal lattice, with considering effects such as screening. Fourier transform was then applied to describe the wave function in reciprocal space. Sampling can be uniform or non-uniform throughout space; however rate and interval optimization is essential. Theory was implemented for Silicon, Germanium and Graphene sheet individually, while results were compared with the ab-initio non-local pseudopotential (AINLPS) method. Also for Silicon, the pseudopotential used in orbital-free density functional theory (OF-DFT) was employed as a suitable sampling source. Phase variations of the dispersion formula are analyzed, introducing adapting parameters to improve compatibility with ab-initio results. Local analysis with low order truncation in real space, reduces implementation time while giving acceptable results., Comment: Accepted to Physical Review B

We report a new analytical method for solution of a wide class of second-order differential equations with eigenvalues replaced by arbitrary functions. Such classes of problems occur frequently in Quantum Mechanics and Optics. This approach is based on the extension of the previously reported differential transfer matrix method with modified basis functions. Applications of the method to boundary value and initial value problems, as well as several examples are illustrated., Comment: 14 pages, 19 references

This overview presents a tutorial introduction to the theory of magnetic plasma confinement in toroidal confinement systems with particular emphasis on axisymmetric equilibrium geometries, and tokamaks. The discussion covers three important aspects of plasma physics: Equilibrium, Stability, and Transport. The section on equilibrium will go through an introduction to ideal magnetohydrodynamics, curvilinear system of coordinates, flux coordinates, extensions to axisymmetric equilibrium, Grad-Shafranov Equation (GSE), Green's function formalism, as well as analytical and numerical solutions to GSE. The section on stability will address topics including Lyapunov Stability in nonlinear systems, energy principle, modal analysis, and simplifications for axisymmetric machines. The final section will consider transport in toroidal systems. We present the flux-surface-averaged system of equations describing classical and non-classical transport phenomena. Applications to the small-sized high-aspect-ratio Damavand tokamak will be described., Comment: 105 pages, to be publised in Tokamaks: Tokamak Theory, Design and Types, and Plasma Heating by Nova Science Publishers

In contrast to graphene which is a gapless semiconductor, graphane, the hydrogenated graphene, is a semiconductor with an energy gap. Together with the two-dimensional geometry, unique transport features of graphene, and possibility of doping graphane, p and n regions can be defined so that 2D p-n junctions become feasible with small reverse currents. This paper introduces a basic analysis to obtain current-voltage characteristics of such a 2D p-n junction based on graphane. As we show, within the approximation of Shockley law of junctions, an ideal I-V charactristic for this p-n junction is to be expected.

In this paper, we present an envelope function analysis in order to design the emission spectra of a white quantum well light emitting diode. The nanometric heterostructure that we are dealing with is a multiple quantum well, consisting periods of three single quantum wells with various well thicknesses. With the aid of 6x6 Luttinger Hamiltonian, we employ the combination of two methods, k.p perturbation and transfer matrix method, to acquire electron and hole wavefunctions analytically. The envelope function approximation was considered to obtain these wavefunctions for a special basis set. While adjacent valence subbands have been studied exactly, the conduction bands are approximated as parabolic. The effect of Stokes shift has been also taken into account. The dipole moment matrix elements for interband atomic transitions are evaluated via correlation between electron and hole envelope functions, for both orthogonal polarizations. This has simplified the calculation of photoluminescence intensity. Spatial variations in hole/electron wavefunctions have been examined with the introduction of piezoelectric and spontaneous polarizations internal field. We theoretically establish the possibility of a highly efficient InGaN red emitter, resulting in a uniform luminescence in red, green and blue emissions from the while light emitting diode, through adjusting material composition, potential slope, and thickness.

It is has been long known that the curved space in the presence of gravitation can be described as a non-homogeneous anisotropic medium in flat geometry with different constitutive equations. In this article, we show that the eigenpolarizations of such medium can be exactly solved, leading to a pseudo-isotropic description of curved vacuum with two refractive index eigenvalues having opposite signs, which correspond to forward and backward travel in time. We conclude that for a rotating universe, time-reversal symmetry is broken. We also demonstrate the applicability of this method to Schwarzschild metric and derive exact forms of refractive index. We derive the subtle optical anisotropy of space around a spherically symmetric, non-rotating and uncharged blackhole in the form of an elegant closed form expression, and show that the refractive index in such a pseudo-isotropic system would be a function of coordinates as well as the direction of propagation. Corrections arising from such anisotropy in the bending of light are shown and a simplified system of equations for ray-tracing in the equivalent medium of Schwarzschild metric is found., Comment: 22 pages, 45 references, accepted for publication in Optics Communications

We present a detailed analysis of exciton-photon interaction in a microcavity made out of a photonic crystal slab. Here we have analyzed a disk-like quantum dot where an exciton is formed. Excitonic eigen-functions in addition to their eigen-energies are found through direct matrix diagonalization, while wave functions corresponding to unbound electron and hole are chosen as the basis set for this procedure. In order to evaluate these wave functions precisely, we have used Luttinger Hamiltonian in the case of hole while ignoring bands adjacent to conduction band for electron states. After analyzing Excitonic states, a photonic crystal based microcavity with a relatively high quality factor mode has been proposed and its lattice constant has been adjusted to obtain the prescribed resonant frequency. We use finite-difference time-domain method in order to simulate our cavity with sufficient precision. Finally, we formulate the coupling constants for exciton-photon interaction both where intra-band and inter-band transitions occur. By evaluating a sample coupling constant, it has been shown that the system can be in strong coupling regime and Rabi oscillations can occur for Excitonic state population., Comment: Journal of Physics B: Atomic and Molecular Physics (to appear)