Browsing by Author "Cheng, Szu-Cheng"

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Calculation of spontaneous emission from a V-type three-level atom in photonic crystals using fractional calculus
(2011-07-05)
Huang, Chih-Hsien
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Wu, Jing-Nuo
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Li, Yen-Yin
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Cheng, Szu-Cheng
;
Hsieh, Wen-Feng
Fractional time derivative, an abstract mathematical operator of fractional calculus, is used to describe the real optical system of a V-type three-level atom embedded in a photonic crystal. A fractional kinetic equation governing the dynamics of the spontaneous emission from this optical system is obtained as a fractional Langevin equation. Solving this fractional kinetic equation by fractional calculus leads to the analytical solutions expressed in terms of fractional exponential functions. The accuracy of the obtained solutions is verified through reducing the system into the special cases whose results are consistent with the experimental observation. With accurate physical results and avoiding the complex integration for solving this optical system, we propose fractional calculus with fractional time derivative as a better mathematical method to study spontaneous emission dynamics from the optical system with non-Markovian dynamics.
Coherent Coupling Between a Three-Level Atom and a Structured Reservoir
(2008-12-01)
Wu, Jing-Nuo
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Yang, Tzong-Jer
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Cheng, Szu-Cheng
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光電工程學系
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Department of Photonics
We study the spontaneous emission (SE) spectra of a three-level A-type atom in photonic crystals. The air-band, the dielectric-band and the free-space vacuum reservoirs coupled with the atom are considered. With the consideration of the phase difference between the air-band and the dielectric-band fields, two band reservoirs become coherent and can interfere with each other. This interference effect depends on the embedded position of the atom and the band-gap width and can affect the SE spectrum. The effect of this interference on the SE spectrum is shown.
Collective excitations, Nambu-Goldstone modes, and instability of inhomogeneous polariton condensates
(2013-11-08)
Chen, Ting-Wei
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Cheng, Szu-Cheng
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Hsieh, Wen-Feng
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光電工程學系
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Department of Photonics
We study nonequilibrium polariton condensates in a harmonic potential trap. After finding the steady-state density and supercurrent distributions of nonequilibrium condensates, we calculate the collective excitations of the system. From collective excitation spectra, we can identify the bifurcation of the stable and unstable modes in terms of the pumping spot size and power. There exist Nambu-Goldstone modes that reveal the pattern of the spontaneous symmetry breaking of the system. Moreover, the unstable mechanism associated with the inward supercurrent flow is characterized by the existence of a supersonic region within the condensate.
Coupling theory of asymmetric photonic-crystal waveguides
(2008)
Huang, Chih-Hsien
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Hsieh, Wen-Feng
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Cheng, Szu-Cheng
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光電工程學系
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Department of Photonics
The physical properties of asymmetric photonic-crystal directional couplers axe studied by using the tight-binding theory, which considers that the field distributions of photonic-crystal waveguides (PCWs) are localized around the periodic defects. From this model, the analytic formulas which describe the dispersion of the coupler and the eigenmode patterns were derived. By considering coupling up to the third nearest-neighboring between two PCWs, analytic expressions of the dispersion relations of asymmetric photonic crystal coupler are consistent with the results from the plane wave expansion method (PWEM). Due to the broken symmetry, two dispersion curves will never cross. Nevertheless, the eigenmode patterns switch their parity as the symmetric coupler does when wavevector k passes over the decoupling point.
Dark solitons in a spinor microcavity-polariton condensate
(2016-10)
Chen, Ting-Wei
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Jheng, Shih-Da
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Hsieh, Wen-Feng
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Cheng, Szu-Cheng
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物理研究所
Dark solitons of a two-component condensate occurring in nonresonantly-pumped microcavity polaritons (spinor MPCs) with integer vorticities, referred to as integer dark solitons (IDSs), can be excited by a laser beam with tunable polarization and power. We investigate the physical properties of stationary IDSs in a pure spinor MPCs without defects. From the excitations of a IDS, we show that the soliton is stable when the pump power is higher than a critical value. When the pump polarization is in favor of one component, we find that the critical pump power for the stabilization becomes higher. The stable IDS exists below a critical pump polarization. A stable phase diagram of IDSs in terms of the pump condition, i.e., pump polarization and power, is thus obtained. (C) 2016 Elsevier Ltd. All rights reserved.
Drag and critical velocities in a nonresonantly pumped trapped polariton condensate with a rotating defect
(2016-01-19)
Cheng, Szu-Cheng
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Chen, Ting-Wei
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Jheng, Shih-Da
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Hsieh, Wen-Feng
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物理研究所
We model the superfluid properties of a trapped exciton-polariton condensate under non-resonant excitation subjected to a rotating defect. With increasing the linear velocity of rotating defect, the density modulation can be classified into superfluid-like regime, parabolic-like regime, Cherenkov regime and over-Cherenkov regime. The threshold-like behavior of drag force and the onset of turbulent fringes can define the critical velocity for the superfluidity. Based on the perturbative drag force in the Bogoliubov-type analysis, the rigid modes with gapped excitation spectrum have higher critical velocity than that of the soft modes. (C) 2015 Elsevier Ltd. All rights reserved.
Dynamics of the Energy Relaxation and Decoherence of a Photon-Atom Bound State in an Anisotropic Photonic Crystal
(2013)
Wu, Jing-Nuo
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Hsieh, Wen-Feng
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Huang, Hsin-Chien
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Cheng, Szu-Cheng
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光電工程學系
An atom embedded inside photonic crystals can form a photon-atom bound state if the emission frequency of the excited atom is lying inside the photonic-band gap of photonic crystals. We studied the dynamics of the energy relaxation and decoherence of a QPAB, qubit made by a photon-atom bound state in photonic crystals. Dynamics of these measurements are solved analytically through the fractional calculus which has been shown to be appropriate mathematical method for the optical systems with non-Markovian dynamics. From these dynamics, we find that the losses of energy, coherence, and information of a QPAB are inhibited. As compared with those qubits without forming photon-atom bound states, the energy relaxation and decoherence rates of these QPABs are strongly suppressed. Other systems suitable for realizing these properties are discussed.
Fractional dynamics of the spontaneous emission of an atom in photonic crystals
(2008-08-01)
Cheng, Szu-Cheng
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Tsai, Ming-Rung
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Hsleh, Wen-Feng
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光電工程學系
;
Department of Photonics
We studied the spontaneous emission of an atom in a photonic crystal with an isotropic band structure. We show that a fractal phenomenon induces the long-time memory of the spontaneous emission in the photonic crystal. The natural mathematics of describing the fractal phenomenon is fractional calculus. From fractional calculus, we show that no multiple-valued problem and no fractionalized steady-state inversion was encountered in the previous study [J. Opt. 13: Quantum Semiclass. Opt. 5, R43 (2003)] when the atomic transition frequency was within the allowed band.
Instabilities of Bose-Einstein condensates in optical lattices
(2007-04-01)
Kuan, W. H.
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Jiang, T. F.
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Cheng, Szu-Cheng
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物理研究所
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Institute of Physics
We study the instabilities, Landau and dynamical instabilities, that are two mechanisms responsible for the breakdown of superfluidity in Bose-Einstein condensates interacting with a one-dimensional optical lattice. An effective-mass Gross-Pitaevskii equation was used to calculate the excitation spectrum and the condensate density of Bose-Einstein condensates in a weak periodic potential. After the condensate velocities greater than the speed of sound, we observe a decreasing of the condensate density, which is the onset of Landau instability. The condensate is dissipated, but not completely, from colliding with the thermal atom cloud. For even higher velocities of the condensate, we find a fast decreasing of the condensate density until full removal of the condensate. The regime of totally removing of the condensate is happened at the inverse effective mass of the condensate becoming zero or negative, where the condensate is on the dynamical instability.
Instability of a spontaneously formed multiple-flux vortex in polariton condensates
(2015-07-01)
Chen, Ting-Wei
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Cheng, Szu-Cheng
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Hsieh, Wen-Feng
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光電工程學系
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Department of Photonics
A spontaneously formed vortex can occur in an incoherently pumped microcavity-polariton condensate which is a non-equilibrium system. The stability of this vortex depends on the flux quanta that the vortex owns. In this paper, we have investigated the dynamics of spontaneously formed vortices with multiple-flux quanta in incoherently pumped microcavity-polariton condensates. From the excitation spectra of a spontaneously formed vortex, we can study the stability of the vortex under different pump strength. The vortices with flux quanta less than four are dynamically stable within a wide range of pump strength. However, when the flux quanta of a vortex is greater than three and the pump power is above a critical pump strength, some imaginary parts of excitation modes of the vortex become positive. The vortex then becomes dynamically unstable and Lends to split into several vortices with smaller flux quanta. (C) 2015 Elsevier Ltd. All rights reserved.
Modulation instability in nonlinear coupled resonator optical waveguides and photonic crystal waveguides
(2009-02-02)
Huang, Chih-Hsien
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Lai, Ying-Hsiuan
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Cheng, Szu-Cheng
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Hsieh, Wen-Feng
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光電工程學系
Modulation instability (MI) in a coupled resonator optical waveguide (CROW) and photonic-crystal waveguide (PCW) with nonlinear Kerr media was studied by using the tight-binding theory. By considering the coupling between the defects, we obtained a discrete nonlinear evolution equation and termed it the extended discrete nonlinear Schrodinger (EDNLS) equation. By solving this equation for CROWs and PCWs, we obtained the MI region and the MI gains, G(p,q), for different wavevectors of the incident plane wave (p) and perturbation (q) analytically. In CROWs, the MI region, in which solitons can be formed, can only occur for pa being located either before or after square/2, where a is the separation of the cavities. The location of the MI region is determined by the number of the separation rods between defects and the sign of the Kerr coefficient. However, in the PCWs, pa in the MI region can exceed the square/2. For those wavevectors close to square/2, the MI profile, G(q), can possess two gain maxima at fixed pa. It is quite different from the results of the nonlinear CROWs and optical fibers. By numerically solving the EDNLS equation using the 4(th) order Runge-Kutta method to observe exponential growth of small perturbation in the MI region, we found it is consistent with our analytic solutions. (C) 2009 Optical Society of America
Nonequilibrium and nonlinear defect states in microcavity-polariton condensates
(2016-05-18)
Chen, Ting-Wei
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Jheng, Shih-Da
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Hsieh, Wen-Feng
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Cheng, Szu-Cheng
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物理研究所
The nonequilibrium and nonlinear defect modes (NNDMs), localized by a defect in a nonequilibrium microcavity-polariton condensate (MPC), are studied. There are three analytic solutions of NNDMs in a point defect: the bright NNDM, a bound state with two dark solitons for an attractive potential, and a gray soliton bound by a defect for a repulsive potential. We find that the stable NNDMs in a nonequilibrium MPC are the bright NNDM and gray soliton bound by a defect. The bright NNDM, which has the hyperbolic cotangent form, is a bright localized state existing in a uniform MPC. The bright NNDM is a unique state occurring in a nonequilibrium MPC that has pump-dissipation and repulsive-nonlinearity characters. No such state can exist in an equilibrium system with repulsive nonlinearity.
Phase diagram of microcavity polariton condensates with a harmonic potential trap
(2014-01-01)
Chen, Ting-Wei
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Wei, Ming-Dar
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Cheng, Szu-Cheng
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Hsieh, Wen-Feng
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光電工程學系
We theoretically explore the phase transition in inhomogeneous exciton-polariton condensates with variable pumping conditions. Through Bogoliubov excitations to the radial-symmetric solutions of complex Gross-Pitaevskii equation, we determine not only the bifurcation of stable and unstable modes by the sign of fluid compressibility but also two distinct stable modes which are characterized by the elementary excitations and the stability of singly quantized vortex. One state is the quasi-condensate BKT phase with Goldstone flat dispersion; the other state is the localized-BEG phase which exhibits linear-type dispersion and has an excitation energy gap at zero momentum. (C) 2013 Elsevier Ltd. All rights reserved.
Physical properties of asymmetric photonic crystal waveguides
(2009-01-01)
Huang, Chih-Hsien
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Hsieh, Wen-Feng
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Cheng, Szu-Cheng
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光電工程學系
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Department of Photonics
By considering the next nearest neighboring defects between two photonic crystal waveguides (PCWs) and analytic formulae derived from the tight binding theory, we will explain the physical properties of an asymmetric directional coupler made from two coupled PCWS: (1) The dispersion curves of a photonic crystal coupler will decouple into the dispersion curves of a single line defect, and the electric field will only be localized in one waveguide of the coupler at a particular point, which we name a decoupling point. (2) The parities of the eigenmodes switch at the decoupling point, even though the dispersion curves are not crossing. (3) The eigenfield at a higher (lower) dispersion curve is always mainly localized in the waveguides that have higher (lower) eigenfrequencies of single line defects, even though the eigenmodes are switched. As a given frequency is incident into the coupler, the energy transfer between two waveguides and the coupling length can be expressed analytically. Due to there being no dispersion curve crossing, the coupling length is no longer infinite at the decoupling point in asymmetric PCWs, but it still has the minimal energy transfer between two waveguides when the frequency of the incident wave is close to the decoupling point.
Physical Realization of von Neumann Lattices in Rotating Bose Gases with Dipole Interatomic Interactions
(2016-08-22)
Cheng, Szu-Cheng
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Jheng, Shih-Da
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物理研究所
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Institute of Physics
This paper reports a novel type of vortex lattice, referred to as a bubble crystal, which was discovered in rapidly rotating Bose gases with long-range interactions. Bubble crystals differ from vortex lattices which possess a single quantum flux per unit cell, while atoms in bubble crystals are clustered periodically and surrounded by vortices. No existing model is able to describe the vortex structure of bubble crystals; however, we identified a mathematical lattice, which is a subset of coherent states and exists periodically in the physical space. This lattice is called a von Neumann lattice, and when it possesses a single vortex per unit cell, it presents the same geometrical structure as an Abrikosov lattice. In this report, we extend the von Neumann lattice to one with an integral number of flux quanta per unit cell and demonstrate that von Neumann lattices well reproduce the translational properties of bubble crystals. Numerical simulations confirm that, as a generalized vortex, a von Neumann lattice can be physically realized using vortex lattices in rapidly rotating Bose gases with dipole interatomic interactions.
Quantum fluctuations and stability of vortex lattices in a nonresonantly pumped exciton-polariton condensate
(2017-03-01)
Chen, Ting-Wei
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Jheng, Shih-Da
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Jiang, T. F.
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Cheng, Szu-Cheng
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物理研究所
The dynamics of an exciton-polariton condensate (EPC) subject to harmonic confinement can cause spontaneously formed vortices to arrange into a triangular vortex lattice. The stability of such a spontaneously formed vortex lattice is still unknown. We investigate the quantum fluctuations of vortex lattices in a rapidly rotating EPC with a rotation frequency close to the harmonic trap. In such a large condensate, we find that a vortex lattice with a triangular structure is stable, whereas one with a square structure becomes unstable. This result indicates that a driven-dissipative vortex array with strong quantum fluctuations can occur in an EPC.
Roton instabilities and correlated Wigner crystals of rotating dipolar fermions in the fractional quantum Hall regime
(2013-11-04)
Jheng, Shih-Da
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Jiang, T. F.
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Cheng, Szu-Cheng
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物理研究所
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Institute of Physics
We point out that the Wigner crystal (WC) state of rotating dipolar fermions in the lowest Landau level is strongly correlated. From intra-Landau-level excitations of the fractional quantum Hall effect (FQHE) liquid, we find that the roton minimum of the excitation spectrum at. nu = 1/7 becomes negative, indicating an absence of the FQHE state, which is supposed to be the ground state of the system. Therefore, we show that the Hartree-Fock theory of the WC does not predict the correct ground-state energy in the lowest Landau level. There exists a strong correlation effect on the Wigner crystallization of rotating dipolar gases.
Spontaneous emission dynamics in an omnidirectional waveguide made of photonic crystals
(2011-06-08)
Huang, Chih-Hsien
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Cheng, Szu-Cheng
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Wu, Jing-Nuo
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Hsieh, Wen-Feng
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光電工程學系
The spontaneous emission dynamics of atoms embedded in an omnidirectional waveguide (ODWG), a novel optical waveguide, is studied on the basis of the complete reflection of one-dimensional photonic crystals. With the dispersion curve of the single waveguide mode within the photonic band gap and various extents of background dissipation, we characterize the photon-atom interaction in the ODWG. The photon emitter of the system is a two-level atom embedded in the low-index medium of the multilayer-film ODWG or the atom-ODWG system. Fractional calculus, an innovative mathematical method in optical systems, is applied to solve the equation of motion for this atom-ODWG system. Two kinds of states with different group velocities exhibit totally distinctive dynamical behavior. The high frequency waveguide mode with a fast group velocity shows fast exponential decay in propagation while the band-edge mode with a slow group velocity displays non-Markovian dynamics with non-exponential oscillating time evolution. We therefore suggest different functions of this atom-ODWG system for these two kinds of states. The richness of the physical content of the system is also revealed through investigating the dynamical behavior of the band-edge mode. These results aid in further application and fundamental understanding of the atom-ODWG system.
Spontaneous emission from a two-level atom in anisotropic one-band photonic crystals: A fractional calculus approach
(2010-02-01)
Wu, Jing-Nuo
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Huang, Chih-Hsien
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Cheng, Szu-Cheng
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Hsieh, Wen-Feng
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光電工程學系
Spontaneous emission ( SE) from a two-level atom in an anisotropic photonic crystal ( PC) is investigated by the fractional calculus. Physical phenomena of the SE are studied analytically by solving the fractional kinetic equations of the SE. There is a dynamical discrepancy between the SE of anisotropic and isotropic PCs. We find that, contrary to the SE phenomenon of the isotropic PC, the SE near the band edge of an anisotropic PC shows no photon-atom bound state. It is consistent with the experimental results of Barth, Schuster, Gruber, and Cichos [Phys. Rev. Lett. 96, 243902 ( 2006)] that the anisotropic property of the system enhances the SE. We also study effects of dispersion curvatures on the changes of the photonic density of states and the appearance of the diffusion fields in the SE.
Spontaneous emission near the band edge of a three-dimensional photonic crystal: a fractional calculus approach
(2009-01-07)
Cheng, Szu-Cheng
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Wu, Jing-Nuo
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Tsai, Ming-Rung
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Hsieh, Wen-Feng
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光電工程學系
We suggest a better mathematical method, fractional calculus, for studying the behavior of the atom-field interaction in photonic crystals. By studying the spontaneous emission of an atom in a photonic crystal with a one-band isotropic model, we found that the long-time inducing memory of the spontaneous emission is a fractional phenomenon. This behavior could be well described by fractional calculus. The results show no steady photon-atom bound state for the atomic resonant transition frequency lying in the proximity of the allowed band edge which was encountered in a previous study (Woldeyohannes and John 2003 J. Opt. B: Quantum Semiclass. Opt.5 R43). The correctness of this result is validated by the 'cut-off smoothing' density of photon states (DOS) with fractional calculus. By obtaining a rigorous solution without the multiple-valued problem for the system, we show that the method of fractional calculus has a logically concise property.