Transport control in a deterministic ratchet system.

We study the control of transport properties in a deterministic inertia ratchet system via the extended delay feedback method. A chaotic current of a deterministic inertia ratchet system is controlled to a regular current by stabilizing unstable periodic orbits embedded in a chaotic attractor of the unperturbed system. By selecting an unstable periodic orbit, which has a desired transport property, and stabilizing it via the extended delay feedback method, we can control transport properties of the deterministic inertia ratchet system. Also, we show that the extended delay feedback method can be utilized for separation of particles in the deterministic inertia ratchet system as a particle's initial condition varies.

Secure quantum key distribution with a single not-so-weak coherent pulse.

We propose a secure quantum key distribution (QKD) protocol using a single not-so-weak coherent qubit. With two preprocesses for random rotation and compensation, a key bit is encoded to a randomly polarized not-so-weak coherent qubit. We analyze the security of the QKD protocol, which counters the photon number splitting and the impersonation attacks. The estimated mean number of photon, which is less than 6.0, guarantees security. Additionally, we discuss the possibility of quantum secure direct communication.

Survival probability time distribution in dielectric cavities.

We study the survival probability time distribution (SPTD) in dielectric cavities. In a circular dielectric cavity the SPTD has an algebraic long time behavior, approximately t(-2) in both the TM and TE cases, but shows different short time behaviors due to the existence of the Brewster angle in the TE case where the short time behavior is exponential. The SPTD for a stadium-shaped cavity decays exponentially, and the exponent shows a relation of gamma approximately n(-2), n is the refractive index, and the proportional coefficient is obtained from a simple model of the steady probability distribution. We also discuss the SPTD for a quadrupolar deformed cavity and show that the long time behavior can be algebraic or exponential depending on the location of islands.

Lasing modes in a spiral-shaped dielectric microcavity.

The resonance patterns and lasing modes in a spiral-shaped dielectric microcavity are investigated through passive and active medium calculations. We find that the high-Q resonance modes are whispering-gallery-like modes, and these resonance modes can be easily excited as lasing modes. We also find that the quasi-scarred resonance mode, which shows strong directional emission beams from the cavity boundary, can be excited with selectively applied external pumping. Through a spectral analysis of the time evolution of the light field, the competition between these lasing modes is discussed.

Phase synchronization of chaotic lasers.

We experimentally investigate phase synchronization between two electronically coupled diode laser pumped Nd:YAG lasers. As the coupling strength increases, the phase of the two chaotic laser outputs develops from a nonsynchronous state to a phase synchronous one through a phase jump state. We find that there are 2pi phase jumps and a pi/2 phase shift between the two laser outputs unlike in optically coupled Nd:YAG lasers. To clarify the transition to phase synchronization with a pi/2 phase shift, we analyze the phenomenon of phase synchronization by using a phase portrait, phase difference dynamics, and frequency variation depending on the coupling strength and obtain the scaling rule of the average phase locking time in the intermittent phase jump state.

Quantum key distribution with blind polarization bases.

We propose a new quantum key distribution scheme that uses the blind polarization basis. In our scheme the sender and the receiver share key information by exchanging qubits with arbitrary polarization angles without basis reconciliation. As only random polarizations are transmitted, our protocol is secure even when a key is embedded in a not-so-weak coherent-state pulse. We show its security against the photon-number splitting attack and the impersonation attack.

Encryption with synchronized time-delayed systems.

We propose a new communication scheme that uses time-delayed chaotic systems with delay time modulation. In this method, the transmitter encodes a message as an additional modulation of the delay time and then the receiver decodes the message by tracking the delay time. We demonstrate our communication scheme in a system of coupled logistic maps. Also we discuss the error of the transferred message due to an external noise and present its correction method.

Synchronization of chaotic oscillators due to common delay time modulation.

We have found a synchronization behavior between two identical chaotic systems when their delay times are modulated by a common irregular signal. This phenomenon is demonstrated both in two identical chaotic maps whose delay times are driven by a common chaotic or random signal and in two identical chaotic oscillators whose delay times are driven by a signal of another chaotic oscillator. We analyze the phenomenon by using the Lyapunov exponents and discuss it in relation to generalized synchronization.

Effects of time-delayed feedback on chaotic oscillators.

We study the effects of time-delayed feedback on chaotic systems where the delay time is both fixed (static case) and varying (dynamic case) in time. For the static case, typical phase coherent and incoherent chaotic oscillators are investigated. Detailed phase diagrams are investigated in the parameter space of feedback gain ( K ) and delay time ( tau ). Linear stability analysis, by assuming the time-delayed perturbation, varies as e(lambdat) where lambda is the eigenvalue, gives the boundaries of the stability islands and critical feedback gains ( K(c) ) for both Rössler oscillators and Lorenz oscillators. We also found that the stability island are found when the delay time is about tau= (n+ 1 / 2 ) T , where n is an integer and T is the average period of the chaotic oscillator. It is shown that these analytical predictions agree well with the numerical results. For the dynamic case, we investigate Rössler oscillator with periodically modulated delay time. Stability regimes are found for parameter space of feedback gain and modulation frequency in which it was impossible to be stabilized for a fixed delay time. We also trace the detailed routes to the stability near the island boundaries for both cases by investigating bifurcation diagrams.

Characteristics of a delayed system with time-dependent delay time.

The characteristics of a time-delayed system with time-dependent delay time is investigated. We demonstrate that the nonlinearity characteristics of the time-delayed system are significantly changed depending on the properties of time-dependent delay time and especially that the reconstructed phase trajectory of the system is not collapsed into simple manifold, differently from the delayed system with fixed delay time. We discuss the possibility of a phase space reconstruction and its applications.

Chaotic behaviors of operational amplifiers.

We investigate nonlinear dynamical behaviors of operational amplifiers. When the output terminal of an operational amplifier is connected to the inverting input terminal, the circuit exhibits period-doubling bifurcation, chaos, and periodic windows, depending on the voltages of the positive and the negative power supplies. We study these nonlinear dynamical characteristics of this electronic circuit experimentally.

Experimental observation of characteristic relations of type-III intermittency in the presence of noise in a simple electronic circuit.

We investigate the characteristic relations of type-II and -III intermittencies in the presence of noise. The theoretically predicted characteristic relation is that approximately exp[/epsilon/(2)] for a negative regime of epsilon and approximately epsilon(-nu) for the positive regime of epsilon (1/2 is the average laminar length and (1+epsilon) is the slope of the local Poincaré map around the tangent point. We experimentally confirm these relations in a simple electronic circuit.

Periodic phase synchronization in coupled chaotic oscillators.

We investigate the characteristics of temporal phase locking states observed in the route to phase synchronization. It is found that before phase synchronization there is a periodic phase synchronization state characterized by periodic appearance of temporal phase-locking state and that the state leads to local negativeness in one of the vanishing Lyapunov exponents. By taking a statistical measure, we present the evidences of the phenomenon in unidirectionally and mutually coupled chaotic oscillators, respectively. And it is qualitatively discussed that the phenomenon is described by a nonuniform oscillator model in the presence of noise.

Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers.

Using mutually coupled nonidentical continuous-wave Nd:YAG lasers, we experimentally confirmed the recently proposed transition route from phase synchronization to complete synchronization. As evidence of this transition we obtained the probability distribution of the intermittent synchronization time near the threshold of the complete synchronization transition.

Current reversal with type-I intermittency in deterministic inertia ratchets.

The intermittency is investigated when the current reversal occurs in a deterministic inertia ratchet system. To determine which type the intermittency belongs to, we obtain the return map of velocities of particle by using stroboscopic recordings, and by numerically calculating the distribution of the average laminar length . The distribution follows the scaling law of proportional to epsilon(-1/2), the characteristic relation of type-I intermittency.

Routes to complete synchronization via phase synchronization in coupled nonidentical chaotic oscillators.

We study the transition route to complete synchronization through phase synchronization in generic coupled nonidentical chaotic oscillators. Through numerical studies, two routes are found, i.e., one, via lag synchronization, the other, via the intermittent chaotic burst state without lag synchronization. We claim that these two routes are universal. As evidence, we analyze several examples on the basis of the conventional theory of intermittency in the presence of noise.

Experimental observation of the characteristic relations of type-I intermittency in the presence of noise.

Recently, it has been reported that the characteristic relation of type-I intermittency in the presence of noise is deformed nontrivially as the channel width epsilon changes from the positive region to the negative. In order to verify it experimentally as a real phenomenon, we study the characteristic relations both for epsilon<0 and for epsilon>0 in a simple inductor-resistor-diode circuit that is under noisy circumstances. The experimental results agree well with the theoretical expectation that the characteristic relations are proportional to epsilon(-1/4) for epsilon>0 and proportional to exp(alpha/epsilon/(3/2)) for epsilon<0.