Equal Coupling Research Articles

Antiferromagnetic order in a semiconductor quantum well with spin–orbit coupling

An argument is made on the existence of a low-temperature itinerant antiferromagnetic (AF) spin alignment, rather than persistent helical (PH), in the ground state of a two dimensional electron gas in a semiconductor quantum well with linear spin–orbit Rashba–Dresselhaus interaction at equal coupling strengths, α. This result is obtained on account of the opposite-spin single-particle state degeneracy at k=0 that makes the spin instability possible. A theory of the resulting magnetic phase is formulated within the Hartree–Fock approximation of the Coulomb interaction. In the AF state the direction of the fractional polarization is obtained to be aligned along the displacement vector of the single-particle states.

Analysis of Flocking of Cooperative Multiple Inertial Agents via A Geometric Decomposition Technique

In this paper, we consider flocking of multiple inertial agents with second-order dynamics. For a single agent, its state is therefore velocity and position. There exists both velocity coupling and position coupling between agents that are not necessarily equal. The nonequal couplings are distinguished here, instead of the common assumption of the equal velocity coupling and position coupling in most literature, since they play different roles in the system dynamics. The main contributions are in two aspects: first, we provide a general geometric decomposition approach for analyzing such systems of the agents. Then, we provide some stability results via Lyapunov analysis as a function of couplings and gains that generalize existing results in this area, which are especially useful when the couplings are partially known. Although the stability results are only sufficient, they serve as important complements of the eigenvalue analysis, which generally requires complete knowledge of the couplings in the eigenvalue analysis.

Improving the performance of Mach–Zehnder interferometer with the dispersion response of the add-drop ring resonator

We use the add-drop ring resonator (ADRR) to produce the normal and anomalous dispersion simultaneously and apply these two dispersion responses to enhance the sensitivity of the Mach–Zehnder interferometer (MZI). To estimate the sensing ability of the ADRR assisted MZI, the dispersion sensitivity of the structure is theoretically and experimentally demonstrated. For two equal amplitude coupling coefficients, a 19.2-fold increase in the dispersion sensitivity is experimentally achieved, a little lower than 19.5-fold predicted in theory. This value can be futher increased by minimizing the attenuation or by choosing different amplitude coupling coefficient settings at different coupling regions. To acquire better dispersion sensitivity, only output port one should be utilized at the over-coupling region, and two output ports should be adopted at the under-coupling region.

Coupling spin ensembles via superconducting flux qubits

We study a hybrid quantum system consisting of spin ensembles and superconducting flux qubits, where each spin ensemble is realized using the nitrogen-vacancy centers in a diamond crystal and the nearest-neighbor spin ensembles are effectively coupled via a flux qubit.We show that the coupling strengths between flux qubits and spin ensembles can reach the strong and even ultrastrong coupling regimes by either engineering the hybrid structure in advance or tuning the excitation frequencies of spin ensembles via external magnetic fields. When extending the hybrid structure to an array with equal coupling strengths, we find that in the strong-coupling regime, the hybrid array is reduced to a tight-binding model of a one-dimensional bosonic lattice. In the ultrastrong-coupling regime, it exhibits quasiparticle excitations separated from the ground state by an energy gap. Moreover, these quasiparticle excitations and the ground state are stable under a certain condition that is tunable via the external magnetic field. This may provide an experimentally accessible method to probe the instability of the system.

Nonlinear Modes and Symmetries in Linearly Coupled Pairs of ‐Invariant Dimers

The subjects of the work are pairs of linearly coupled ‐symmetric dimers. Two different settings are introduced, namely, straight‐coupled dimers, where each gain site is linearly coupled to one gain and one loss site, and cross‐coupled dimers, with each gain site coupled to two lossy ones. The latter pair with equal coupling coefficients represents a ‐hypersymmetric quadrimer. We find symmetric and antisymmetric solutions in these systems, chiefly in an analytical form, and explore the existence, stability, and dynamical behavior of such solutions by means of numerical methods. We thus identify bifurcations occurring in the systems, including spontaneous symmetry breaking and saddle‐center bifurcations. Simulations demonstrate that evolution of unstable branches typically leads to blowup. However, in some cases, unstable modes rearrange into stable ones.

Simultaneous Wireless Power Transfer via Magnetic Resonant Coupling to Multiple Receiving Coils

An optimal design for a simultaneous wireless power transfer system is difficult to achieve, as the effect of multiple coils on the total efficiency is unclear. The power loss increases with the number of coils when they are arranged in a straight line. On the other hand, simultaneous wireless power transfer to multiple receiving coils surrounded by a large transmitting coil has not been studied. In this paper, the simultaneous wireless power transfer system is represented by an equivalent circuit, and a detailed study of the total efficiency and optimal load is carried out. The number of coils is increased, and an analysis is performed for both the equal coupling coefficient case and the unequal coupling coefficient case. From the theoretical analysis and experimental results, the total efficiency improves when more coils are added. Nevertheless, the final efficiency is bounded by the internal resistance and the load values at the receiving coils. The proposed equivalent circuit model also demonstrates that the maximum efficiency is achievable by using the optimal resistance for wireless power transfer containing a specific number of coils.

Control of Turing patterns and their usage as sensors, memory arrays, and logic gates

We study a model system of three diffusively coupled reaction cells arranged in a linear array that display Turing patterns with special focus on the case of equal coupling strength for all components. As a suitable model reaction we consider a two-variable core model of glycolysis. Using numerical continuation and bifurcation techniques we analyze the dependence of the system's steady states on varying rate coefficient of the recycling step while the coupling coefficients of the inhibitor and activator are fixed and set at the ratios 100:1, 1:1, and 4:5. We show that stable Turing patterns occur at all three ratios but, as expected, spontaneous transition from the spatially uniform steady state to the spatially nonuniform Turing patterns occurs only in the first case. The other two cases possess multiple Turing patterns, which are stabilized by secondary bifurcations and coexist with stable uniform periodic oscillations. For the 1:1 ratio we examine modular spatiotemporal perturbations, which allow for controllable switching between the uniform oscillations and various Turing patterns. Such modular perturbations are then used to construct chemical computing devices utilizing the multiple Turing patterns. By classifying various responses we propose: (a) a single-input resettable sensor capable of reading certain value of concentration, (b) two-input and three-input memory arrays capable of storing logic information, (c) three-input, three-output logic gates performing combinations of logical functions OR, XOR, AND, and NAND.

Synthetic gauge field with highly magnetic lanthanide atoms

We present a scheme for generating a synthetic magnetic field and spin-orbit coupling via Raman coupling in highly magnetic lanthanide atoms such as dysprosium. Employing these atoms offers several advantages for realizing strongly correlated states and exotic spinor phases. The large spin and narrow optical transitions of these atoms allow the generation of synthetic magnetic fields that are an order of magnitude larger than those in the alkali metals, but with considerable reduction of the heating rate for equal Raman coupling. The effective Hamiltonian of these systems differs from that of the alkali metals' by an additional nematic coupling term, which leads to a phase transition in the dressed states as detuning varies. For high-spin condensates, spin-orbit coupling leads to a spatially periodic structure, which is described in a Majorana representation by a set of points moving periodically on a unit sphere. We name this a ``Majorana spinor helix,'' in analogy to the persistent spin-$\frac{1}{2}$ helix observed in electronic systems.

Time-optimal unitary operations in Ising chains: unequal couplings and fixed fidelity

We analytically determine the minimal time and the optimal control laws required for the realization, up to an assigned fidelity and with a fixed energy available, of entangling quantum gates (CNOT) between indirectly coupled qubits of a trilinear Ising chain. The control is coherent and open loop, and it is represented by a local and continuous magnetic field acting on the intermediate qubit. The time cost of this local quantum operation is not restricted to be zero. When the matching with the target gate is perfect (fidelity equal to 1), we provide exact solutions for the case of equal Ising coupling. For the more general case when some error is tolerated (fidelity smaller than 1), we give perturbative solutions for unequal couplings. Comparison with previous numerical solutions for the minimal time to generate the same gates with the same Ising Hamiltonian but with instantaneous local controls shows that the latter are not time optimal.

Manifestation of bound states and coupling to leads in coherent transmission through multiterminal molecular conductors

We examine analytically a rarely if ever addressed issue: the effects of scattering at the conductor-lead interfaces on the transmittivity of N-terminal molecular conductors. The feeding leads are not one-dimensional and the strength of wire-lead coupling is allowed to be arbitrary. The conductor imbedded into a circuit is supposed to be a Y junction of three identical molecular wires or of two identical wires and one different wire. The wire connector is a C-H group and wires are conjugated and/or saturated oligo(hydro)carbons. The spectrum of branched oligo(hydro)carbons is rationalized in terms of extended and bound states. The junctions, where identical wires are equally coupled to the respective leads (all-symmetric junctions), are compared with hybrid junctions, where nonequivalence of terminal-to-terminal transmission appears due to either not identical wires or not equal coupling, or both. These model systems reveal incredible potentials of branched oligo(hydro)carbons for engineering a variety of molecular electronic devices. In addition, the role of wire connectors, atomic and molecular, is briefly discussed. Some of the obtained results are valid for N-terminal starlike junctions. © 2012 American Physical Society.

Equal coupling strength approach to spin precession effects concerning Rashba and Dresselhaus spin–orbit interactions in the presence of in-plane magnetic fields

The influence of Rashba and Dresselhaus spin–orbit interactions on the electronic properties of quasi one-dimensional systems like InAs quantum wires is discussed in the presence of in-plane magnetic fields. One shows that equal coupling strength conditions are provided specifically by the commutativity of two-dimensional constituents of velocity and current operators. The interesting point is that equal strength spin–orbit couplings one deals with proceed in conjunction with related spin conservations, which amounts to account for selected orientations of the magnetic field. Accordingly, the in-plane magnetic fields should be directed solely along the bisectrices. Other angles may be conceivable, but in this case spin conservations alluded to above are lost. Such results open the way to a consistent derivation of the equal coupling strength limit of the energy, which leads in turn to the derivation of novel spin-precession effects. A related effective gyromagnetic factor has also been established.

Entanglement transfer between bipartite systems

The problem of a controlled transfer of an entanglement initially encoded into two two-level atoms that are successively sent through two single-mode cavities is investigated. The atoms and the cavity modes form a four-qubit system and we demonstrate the conditions under which the initial entanglement encoded into the atoms can be completely transferred to other pairs of qubits. We find that in the case of non-zero detuning between the atomic transition frequencies and the cavity mode frequencies, no complete transfer of the initial entanglement is possible to any of the other pairs of qubits. In the case of exact resonance and equal coupling strengths of the atoms to the cavity modes, an initial maximally entangled state of the atoms can be completely transferred to the cavity modes. Complete transfer of the entanglement is restricted to the cavity modes, with transfer to the other pairs being limited to 50%. We find that complete transfer of an initial entanglement to other pairs of qubits may take place if the initial state is not the maximally entangled state and the atoms couple to the cavity modes with unequal strengths. Depending on the ratio between the coupling strengths, optimal entanglement can be created between the atoms and one of the cavity modes.

The NMR line shape of a system of nuclear spins with equal spin-spin coupling constants

We obtain an expression for the NMR line at low temperatures for a system of nuclear spins described by a Hamiltonian with equal spin-spin coupling constants. We show that in the case of “easy axis” anisotropy, the line has a logarithmic low-frequency singularity and an exponentially decreasing high-frequency asymptotic behavior at the temperature of an anomalous peak of heat capacity. In the case of “easy plane” anisotropy, the line has the traditional Gaussian form. We discuss the possibility of using NMR data to discover specific thermodynamic and magnetic properties of the considered model system.

El estudio y enseñanza de los modos vibracionales de la molécula triatómica

En este trabajo se muestra que a través del dominio de la teoría general de pequeñas oscilaciones es posible resolver analíticamente los modos vibracionales de la molécula triangular, y que a la luz de resultados comparativos entre la molécula lineal y triangular se puede evaluar la dinámica de la molécula triangular y simplificar el análisis. Para ilustrar lo anterior, se modela mecánicamente una molécula triatómica, utilizando la formulación de Lagrange y asumiendo un tipo de molécula en la cual las masas (átomos) están ubicadas en los vértices de un triángulo rectángulo. Para un desarrollo analítico del problema se utiliza la teoría de pequeñas oscilaciones, considerando las masas y las constantes de acoplamiento iguales. Esto último permite escribir el Lagrangiano del sistema en forma adecuada y posteriormente determinar las ecuaciones diferenciales de movimiento, que describen el comportamiento de la molécula y permiten determinar las frecuencias propias de vibración. También se analiza y discute el caso de una molécula triatómica lineal, determinando los correspondientes modos normales de vibración. Finalmente, se comparan las soluciones de ambos sistemas.

Polarization controlled tunable multiwavelength SOA-fiber laser based on few-mode polarization maintaining fiber loop mirror

A tunable multiwavelength fiber ring laser based on a semiconductor optical amplifier and few-mode polarization maintaining fiber (FM-PMF) loop mirror is proposed and experimentally demonstrated. It is accomplished by simply adjusting a polarization controller (PC) next to the FM-PMF in the loop arm for the polarization-dependent mode excitation in the FM-PMF and the resulting effective refractive index change. In addition, the undesirable dependence of the transmission loss of the FM-PMF loop mirror on the rotation angle of the PC in the loop arm can be reduced by using a fiber coupler with unequal coupling ratio instead of equal coupling ratio. Stable and tunable multiwavelength operation with up to 11 lasing lines at about 1.5 nm interval is achieved with the power deviation less than 2 dB and optical signal to noise extinction ratio over 35 dB.

Parity detection and entanglement with a Mach-Zehnder interferometer

A parity meter projects the state of two qubits onto two subspaces with different parities, the states in each parity class being indistinguishable. It has application in quantum information for its entanglement properties. In our work we consider the electronic Mach-Zehnder interferometer (MZI) coupled capacitively to two double quantum dots (DQDs), one on each arm of the MZI. These charge qubits couple linearly to the charge in the arms of the MZI. A key advantage of an MZI is that the qubits are well separated in distance so that mutual interaction between them is avoided. Assuming equal coupling between both DQDs and the arms and the same bias for each DQD, this setup usually detects three different currents, one for the odd states and two for each even state. Controlling the magnetic flux of the MZI, we can operate the MZI as a parity meter: only two currents are measured at the output, one for each parity class. In this configuration, the MZI acts as an ideal detector, its Heisenberg efficiency being maximal. For a class of initial states, the initially unentangled DQDs become entangled through the parity measurement process with probability one.

Photon-energy qubit generation by spontaneous emission in a V-type system

We propose a scheme for generating arbitrary pure-sate photon-energy qubits by adiabatic manipulations of a cavity-embedded v-type level system. The dynamics of the system is analyzed as well as the effect of various parameters including decoherence. Our calculations indicate that an equal coupling constant v-type system is the preferable choice. The realization of the proposed scheme is possible in Rb-based implementations-–aimed at applications in fiber-optical quantum communication.

Chaos synchronization and communication of mutual coupling lasers ring based on incoherent injection

A chaos secure communication system of mutual coupling lasers ring based on incoherent optical injection is proposed, in which fine tuning of optical frequency is not required compared with other schemes based on coherent optical injection. Therefore the secure communication scheme is attractive for experimental investigation. The dynamics of semiconductor lasers in the coupling ring are examined. Numerical investigations indicate that zero lag synchronization can be achieved under equal coupling time and strength of mutual coupling. Furthermore, by chaos shift keying (CSK), secure communication is simulated with a random bit stream of 1.0 Gbit/s. The results confirm the possibility of applying incoherent schemes of mutual coupling lasers ring to realize chaotic secure communication.

Spin-orbit coupling effects in two-dimensional circular quantum rings: Elliptical deformation of confined electron density

We study electron states confined in two-dimensional circular quantum rings in the presence of spin-orbit coupling due to both structure and crystal inversion asymmetry in the external magnetic field. It is demonstrated that the confined electron density loses the circular symmetry of the confinement potential provided that both Rashba and Dresselhaus coupling constants are nonzero, with the exception of a special case of equal coupling constants and absence of the spin Zeeman interaction. An elliptical deviation from the circular symmetry---present already for a single confined electron---is for two electrons strengthened by the Coulomb repulsion. We discuss signatures of the charge-density deformation in the experimentally accessible quantities: magnetization and charging properties of the ring. Relevance of the results of one-dimensional ring models for description of spin-orbit coupling effects is also discussed.

Tubuloglomerular Feedback-Mediated Dynamics in Three Coupled Nephrons

A model of three coupled nephrons branching from a common cortical radial artery is developed to further understand the effects of equal and unequal coupling on tubuloglomerular feedback. The integral model of Pitman et al. (2002), which describes the fluid flow up the thick ascending limb of a single, short-looped nephron of the mammalian kidney, is extended to a system of three nephrons through a model of coupling proposed by Pitman et al. (2004). Analysis of the system, verified by numerical results, indicates that stable limit-cycle oscillations emerge for sufficiently large feedback gain magnitude and time delay through a Hopf bifurcation, similar to the single nephron model, yet generally at lower values. Previous work has demonstrated that coupling induces oscillations at lower values of gain, relative to uncoupled nephrons. The current analysis extends this earlier finding by showing that asymmetric coupling among nephrons further increases the likelihood of the model nephron system being in an oscillatory state.