Showing papers on "Parametric oscillator published in 1986"

Preparation, measurement and information capacity of optical quantum states

Abstract: The preparation, or generation of coherent states, squeezed states, and photon number states is discussed. The quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadrature measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier. A quantum nondemolition measurement followed by a measurement of the conjugate variable is also categorized as a simultaneous measurement. It is shown that, for all of these schemes, the minimum uncertainty product of the measured variables is exactly equal to that required for a simultaneous measurement of two noncommuting variables. On the other hand, measurements of a single quadrature component are noise-free. Such measurements are degenerate heterodyning, degenerate parametric amplification, and cavity degenerate four-wave mixing and photon counting by a photomultiplier or avalanche photodiode. The Heisenberg uncertainty principle and the quantum-mechanical channel capacity of Shannon are discussed to address the question "How much information can be transmitted by a single photon?" The quantum-mechanical channel capacity provides an upper bound on the achievable information capacity and is ideally realized by photon number states and photon counting detection. Its value is $\frac{\ensuremath{\hbar}\ensuremath{\omega}}{(\mathrm{ln}2)kT}$ bit per photon. The use of coherent or squeezed states and a simultaneous measurement of two quadrature field components or the measurement of one single quadrature field component does not achieve the ultimate limit.

Amplitude squeezing in a pump-noise-suppressed laser oscillator.

Abstract: This paper clarifies the origins of the standard quantum limit for the amplitude noise of a laser-oscillator outgoing field. The amplitude noise within the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\le}\ensuremath{\omega}/Q, is ultimately caused by the pump amplitude fluctuation, while that above the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\ge}\ensuremath{\omega}/Q, is due to the field zero-point fluctuation. The uncertainty product of the amplitude- and phase-noise spectra at an extremely high pumping level is still larger than the Heisenberg minimum-uncertainty product because of the presence of nonstationary phase-diffusion noise. In this sense, an ordinary laser oscillator is not a quantum-limited device. This paper suggests that a laser oscillator can produce an amplitude-squeezed state in itself if the pump amplitude fluctuation is suppressed below the ordinary shot-noise level. The paper discusses possible schemes for suppressing pump fluctuation, commutator bracket preservation without pump fluctuation, and resulting amplitude and phase spectra. The similarity of and difference between a pump-noise-suppressed laser and a cavity degenerate parametric amplifier are delineated.

Broadly tunable infrared parametric oscillator using AgGaSe2

Abstract: The first successful operation of a AgGaSe2 infrared parametric oscillator is reported. Continuous tuning ranges of 1.6–1.7 μm, 6.7–6.9 μm, and 2.65–9.02 μm were achieved using 1.34‐μm neodymium and 2.05‐μm holmium pump lasers. Pulse energies exceeding 3 mJ, peak powers near 100 kW, and conversion efficiencies of 18% were obtained. Operation of the parametric oscillator was possible well below the 13–40 MW/cm2 surface damage threshold of this nonlinear material.

Small-signal amplification in bifurcating dynamical systems

Abstract: Near the onset of a dynamical instability, any time-periodic system can act to amplify small periodic perturbations. The details of this small-signal sensitivity depend solely on the type of bifurcation involved: Explicit expressions are derived for the power spectra in the vicinity of the simplest classes of codimension-1 bifurcations. Results obtained from analog simulations of a period-doubling system are in good agreement with the theory. We propose that the superconducting Josephson-junction parametric amplifier is an example of this amplification process.

Brownian motion of a parametric oscillator: A model for ion confinement in radio frequency traps

Abstract: The distribution function for Brownian motion of a parametric oscillator is calculated exactly with the help of continued fraction expansions in the long time limit. We derive expressions for the energy and the widths of the spatial and velocity distribution. Our results are relevant to understand confinement of particles in radio frequency ion traps.

Theory of feedback-generated squeezed states.

Abstract: Conservation of commutator brackets imposes constraints on the response of linear systems. From these constraints the minimum uncertainties of in-phase and quadrature field components in linearized parametric and oscillator systems can be determined. In this paper, a cavity containing a ``degenerate parametric wall'' is analyzed and the resulting equations are found to be identical with those of a saturated oscillator. The ideal parametric wall resonator has lower noise than the saturated oscillator. Feedback is put onto an oscillator formed by the parametric wall, and onto the saturated oscillator, by degenerate heterodyne (homodyne) detection of the oscillator output. It is shown in both cases that the field fluctuations incident upon the photodetector in the feedback loop are ``squeezed,'' i.e., the photodetector current fluctuation level is below shot noise. A semiclassical analysis arrives at the same expression for the detector current fluctuations in the limit of a highly saturated oscillator, thus permitting an alternative interpretation of these results. However, a quantum nondemolition measurement via a nonlinear interferometer ``extracts'' the squeezed states, predicted by the quantum analysis, from the feedback loop. This result has no semiclassical interpretation.

Suppression of period-doubling and nonlinear parametric effects in periodically perturbed systems.

Abstract: We consider the effect on a generic period-doubling bifurcation of a periodic perturbation, whose frequency ${\ensuremath{\omega}}_{1}$ is near the period-doubled frequency ${\ensuremath{\omega}}_{0}$/2. The perturbation is shown to always suppress the bifurcation, shifting the bifurcation point and stabilizing the behavior at the original bifurcation point. We derive an equation characterizing the response of the system to the perturbation, analysis of which reveals many interesting features of the perturbed bifurcation, including (1) the scaling law relating the shift of the bifurcation point and the amplitude of the perturbation, (2) the characteristics of the system's response as a function of bifurcation parameter, (3) parametric amplification of the perturbation signal including nonlinear effects such as gain saturation and a discontinuity in the response at a critical perturbation amplitude, (4) the effect of the detuning (${\ensuremath{\omega}}_{1}$-${\ensuremath{\omega}}_{0}$/2) on the bifurcation, and (5) the emergence of a closely spaced set of peaks in the response spectrum. An important application is the use of period-doubling systems as small-signal amplifiers, e.g., the superconducting Josephson parametric amplifier.

Voltage controlled oscillator with frequency sensitivity control

Abstract: A voltage controlled oscillator is tuned with a network comprising two varactor diodes and two transmission lines. By selecting appropriate values of varactor capacitance and transmission line length and width the overall reactance of the network is such that, when a varactor tuning voltage is varied, the output frequency of the voltage controlled oscillator will vary in an fashion with respect to the tuning voltage. Such a voltage controlled oscillator is gain compensated and exhibits a controlled modulation sensitivity over a range of frequencies. If the required frequency range of the oscillator is known beforehand, an alternate embodiment of the invention may be employed in which one of the varactor diodes is replaced with a fixed capacitor having a suitable value for the desired frequency range.

Canonical treatment of harmonic oscillator with variable mass.

Abstract: By the use of a canonical transformation the problem of the harmonic oscillator with a time-dependent mass has been transformed to that of an oscillator with a time-dependent frequency. Pseudostationary and quasicoherent states are discussed.

Algebraic time-ordering techniques and harmonic oscillator with time-dependent frequency.

Abstract: The Wei-Norman algebraic techniques for time-ordering problems are applied to the study of the evolution of quantum states ruled by a harmonic-oscillator Hamiltonian with a time-dependent frequency. The slowly varying frequency case is studied; the adiabatic theorem is rederived together with higher-order corrections. The analogy with the propagation of a paraxial beam through a self-focusing fiber is also pointed out.

Improved oscillator phase locking by use of a modulated electron beam in a gyrotron.

Abstract: A new method of microwave oscillator phase locking, exploiting the extended nature of the gyroklystron configuration, is accomplished by modulation of the electron beam before it reaches the cavity oscillator. The amount of power required to give phase locking in a gyrotron is decreased by more than an order of magnitude from that predicted by Adler's theory. In addition, oscillator priming is observed at drive powers far below all other systems tested to date. These new methods provide the coherence required of rf sources for linear accelerators and may enhance gyrotron performance for fusion heating.

New cavity design for a LiNbO3 optical parametric oscillator

Abstract: A new cavity design for a Nd–YAG‐pumped LiNbO3 optical parametric oscillator has been developed for resonating the low‐frequency component between 2.2 and 4.0 μ. The design allows for rapid conversion between medium (0.8 cm−1) and high (0.06 cm−1) resolution configurations. The use of digital feedback servocontrols enables computer scanning over a range of 400 and 4 cm−1 in medium‐ and high‐resolution modes, respectively.

High-gain, long-pulse free-electron-laser oscillator.

Abstract: We report the first operation of a high-gain, long-pulse (>1 ..mu..sec), free-electron-laser oscillator. The growth rate is measured by variation of the interaction length of the electron beam within the oscillator cavity. The observed power gain per pass of up to 10/sup 4/ and the buildup of cavity power to multimegawatt levels are in agreement with high-gain oscillator theory. Growth rates have also been measured as a function of wiggler field strength.

Quantizing the damped harmonic oscillator

Abstract: A damped harmonic oscillator can be modeled as a manifestly conservative system by replacing the dissipative element with a string or transmission line of infinite extent. This conservative system can be quantized in a straightforward manner using the standard techniques of canonical quantization. The system may be used to illustrate various aspects of the quantum mechanics of a particle interacting with a field.

Model studies of collective atomic excitations by intense laser fields

Abstract: A quantum version of the Drude-Lorentz model of the atom is used to study abnormally large energy transfers found in recent ionization experiments by strong laser fields It is argued that collective excitations greatly enhanced by parametric resonance may lead to an exponential growth of the atomic energy with time It is shown that the repulsion between the electrons plays an essential role, reducing the frequency at which parametric resonance occurs

Injection locking and tuning circuit for microwave diode oscillator

Abstract: A four-diode bridge is positioned within the cavity of a Gunn diode oscillator. A subharmonic signal is applied to the diode bridge and the diode bridge couples an odd harmonic of the injected signal into the cavity. The cavity is thus caused to resonate at the odd harmonic of the injected signal. The injected signal can be changed using a frequency synthesizer in order to provide a microwave oscillator with multiple-channel operation. The diode bridge provides a feedback signal indicative of the phase of cavity oscillation. The feedback signal is applied to a varactor which pretunes the Gunn diode oscillator and thereby provides phase-locked control.

The modified Poschl-Teller Oscillator

Abstract: Anharmonic potential energy surfaces are often needed for a realistic description of molecular dynamics. In some cases the dominant channels of decay are accessible only due to anharmonic terms in the potential energy surface.

Dissipation of energy in the damped harmonic oscillator.

Abstract: A canonical description of a harmonic oscillator with energy dissipation is sought which combines the advantages of the Kanai-Caldirola Hamiltonian and a simple model of strangulation previously considered by the authors. The treatment is in the Heisenberg picture of quantum mechanics or alternatively in classical mechanics. A strangulation \ensuremath{\beta} is superimposed on the damping (or growth) \ensuremath{\gamma}, represented by an oscillator mass m(t)=${m}_{0}$exp(2\ensuremath{\gamma}t). In general, the expected dissipation of energy occurs only if \ensuremath{\beta}g\ensuremath{\Vert}\ensuremath{\gamma}\ensuremath{\Vert}. If \ensuremath{\beta}l\ensuremath{\Vert}\ensuremath{\gamma}\ensuremath{\Vert} the attempted strangulation induces a long-term growth in energy unless a special initial motion is chosen. A slight deviation from this initial motion results in a temporary decay in energy followed by growth. \ensuremath{\beta}l0 always induces a growth in energy.

New active-R sinusoidal oscillator

Abstract: A new active-R sinusoidal oscillator circuit is presented. The circuit uses two operational amplifiers and a single resistor at most. Experimental results are included.

Generalized Langevin equation for an oscillator.

Abstract: A central oscillator coupled to a bath of harmonic oscillators with a two-dimensional Debye spectrum is set up as a model for the dynamics of strongly coupled linear systems. The bath oscillators are eliminated from the central oscillator's equation of motion, other than for initial conditions. The resulting Langevin equation is solved analytically for two different initial conditions for the bath. In one case, the bath oscillators are started at finite temperature and the coupling is turned on suddenly, and in the other they are adiabatically heated with constant coupling. The problem of equipartitioning of the kinetic energy, the velocity autocorrelation function of the central oscillator, and its spectral distribution are examined for various values of the physical parameters. The analytical results of the sudden case are compared with molecular-dynamics calculations and excellent agreement is found.

On the quantisation of the two-dimensional harmonic oscillator with 2:1 resonance

Abstract: Exact eigenfunctions, which simultaneously diagonalise the Hamiltonian of a 2:1 resonant, two-dimensional harmonic oscillator and an additional constant of the motion, cubic in the cartesian displacement coordinates and momenta, are found by direct solution of the Schrodinger equation in parabolic coordinates. The connection with the usual harmonic-oscillator cartesian basis is established and used in the formulation of a second-order perturbation theory for the oscillator with a particular form of nonlinear coupling. Uniform semiclassical quantisation of the unperturbed oscillator is discussed.

Nonlinear vibrations of offshore structures under random wave excitation

Abstract: An account is given of some mathematical methods which have been used to analyse the response of offshore structures to random wave excitation. The analysis of nonlinear phenomena and the assessment of related nongaussian probability distributions are emphasized. The following problems are analysed in some depth: probability distributions for Morison-type wave loading; response near resonance of nonlinearly damped systems to random excitation; parametric resonance and instability of nonlinearly damped systems with randomly fluctuating restoring force coefficient. Solutions to each of these problem areas are illustrated by practical examples.

Motion of a Gaussian wave packet in a periodically pulsed harmonic oscillator.

Abstract: We point out that the Hamiltonian for the periodically pulsed harmonic oscillator considered by Hogg and Huberman [Phys. Rev. A 28, 22 (1983)] preserves ordinary coherent states under time evolution. The expectation values of x and p then follow the classical motion in phase space.