Quantum coherence and entangled states in intracavity third subharmonic generation process

The dynamics of correlation of photon number fluctuations of interacting modes for the process of intracavity third subharmonic generation is investigated. It is shown that the entangled field states by the variables of photon number can be obtained in this system. The quantum dynamics of the photons number, the quantum entropy and the Wigner function of the stationary states of the fundamental mode and the third subharmonic mode have also been studied. It is found that the dynamics of these quantities depends highly on the value of the coupling coefficient of the interacting modes. It is shown that at long interaction times and for the large values of the coupling coefficient of the modes, the mode of the third subharmonic is localized in the three-component state with the same probability of detection of the mode in each component of the state. The quantum entropy of the state is less than the maximal entropy of the three-component state ln3, which points out the presence of quantum mechanical interference between the components of the state of third subharmonic mode.     

Quantum dynamics of intracavity third-subharmonic generation

The quantum dynamics of the mean number of photons and quantum entropy of interacting modes, as well as the Wigner function of the stationary state of the fundamental mode and the third subharmonic mode has been investigated for the intracavity third-subharmonic generation. It is shown that the quantum dynamics of the system depends strongly on the nonlinear coupling coefficient between the modes. It is also demonstrated that, in the steady-state limit, depending on the intermodal coupling coefficient, the fundamental mode can be either in a pure coherent state, or in a squeezed state, or in a pure vacuum state. The third subharmonic mode in the subthreshold regime of generation of this mode is in the vacuum state. The Wigner function is squeezed over three sides of an equilateral triangle (squeezed vacuum). The quantum entropy of this state is nonzero. It is also shown that the third subharmonic mode, depending on the nonlinear coupling coefficient in the steady-state limit, can be localized in the three-component state with the same probability of detecting a field in each coherent component of the state and with the presence of quantummechanical interference between the state components. The mean number of photons in this state is smaller than unity. Depending on the nonlinear coupling coefficient, the third subharmonic mode can also be localized in the three-component state, which is a statistical mixture of three squeezed states.     

Quantum dynamics of formation of an unstable field state in the process of intracavity third-harmonic generation

The dynamics of the Wigner functions and quantum entropy of the fundamental and third-harmonic modes is studied for the process of intracavity third-harmonic generation. It is shown that quantum dynamics of the system strongly depends on the coupling coefficient of the interacting modes. The dynamics of the transition of the system from a stable to an unstable state is investigated.     

Correlation of fluctuations of the quadrature amplitudes of interacting modes in the instability region of intracavity third-harmonic generation

Correlation of fluctuations of quadrature amplitudes of interacting modes is studied for the process of intracavity third-harmonic generation in the region of instability. It is shown that this correlation strongly depends on the value of the nonlinear mode coupling coefficient. For small values of the coupling coefficient, correlation of fluctuations of quadrature amplitudes is small. With increasing coupling coefficient, the correlation increases (states of the subsystems become entangled). Then, starting from a certain value of the coupling coefficient, it starts decreasing gradually, tending to zero (entanglement of states of the subsystems decreases). Correlation of fluctuations of quadrature amplitudes decreases also when the amplitude of the fundamental mode perturbing field is decreased.     

Quantum signatures in the dynamics of two dipole-dipole interacting soft dimers

The quantum covariances of physically transparent pairs of observables relative to two dimers hosted in a solid matrix are exactly investigated in the temporal domain. Both dimers possess fermionic and bosonic degrees of freedom and are dipolarly coupled. We find out and describe clear signatures traceable back to the presence and persistence of quantum coherence in the time evolution of the system. Manifestations of a competition between intramolecular and intermolecular energy migration mechanisms are brought to light. The experimental relevance of our results is briefly commented.     

内腔二次谐波过程中光场强度自脉冲振荡的增强

本文利用宏观非线性极化模型,分析了相干驱动内腔二次谐波过程中光场的动力学演化行为.发现了光场的一种新的动力学不稳定性.在此基础上,提出了一个增强光场强度自脉冲振荡的可能途径.     

Evolution dynamics of initial coherent states of a field in an unstable region of the behavior in the process of intracavity third harmonic generation

The quantum dynamics of the state of a field is studied for the process of intracavity third harmonic generation in the region of unstable behavior of the system in the case in which the interacting modes are developed from initial coherent states. It is shown that the Wigner functions of the states of the modes and mean values of the quadrature amplitudes of the fields can have oscillations disappearing with the transition of the system to a stable region.     

Quantum noise in intracavity laser spectroscopy

The limitations on the intracavity laser spectroscopy (ILS) method are considered which are caused by the statistical character of the multimode laser radiation. Stochastic processes (shot photon noise) are shown to result in a heavily “jagged” function, instead of a smooth one, which describes a specific realization of the generation spectrum. The increase of fluctuations with time between two successive measurements of the spectrum has also been investigated. The threshold sensitivity for the ILS method has been found which is determined by the stochastic character of the multimode generation.     

Mode-coupling phenomena in intracavity second harmonic generation

The dependence of intracavity second harmonic generation efficiency on the linear phase detunings in crystal and air is studied both theoretically and experimentally. It is shown that in the presence of feedback at the second harmonic frequency an optimum conversion efficiency can be achieved by a mutually correlated choice of phase mismatch in a nonlinear crystal and the position of the latter inside the cavity.     

Distribution of numbers of photons in the region of unstable behavior in the process of intracavity second harmonic generation

For the process of intracavity second harmonic generation we investigate in positive P-representation with simulation of Langevin noise sources the distribution functions of numbers of photons in fundamental and second harmonic modes in the region of unstable behavior of the system. It is shown that in the unstable region, as distinct from the stable, the functions of distribution have two-peak structure. We also study the joint function of distribution of photon numbers in interacting modes.     

Efficient output coupling of intracavity high-harmonic generation

We demonstrate a novel technique for coupling extreme-ultraviolet (XUV) harmonic radiation out of a femtosecond enhancement cavity. We use a small-period diffraction grating etched directly into the surface of a dielectric mirror. For the fundamental light, this element acts as a high reflector. For harmonic wavelengths, it acts as a diffraction grating, coupling XUV radiation out of the cavity. Using this method, we observed the third through twenty-first odd harmonics with a dramatic increase in usable power over previous results of high-harmonic generation at high repetition rates.     

Harmonic and subharmonic acoustic wave generation in finite structures

The generation of harmonic and subharmonic vibrations is considered in a finite monodimensional structure, as it is produced by the nonlinear acoustic characteristics of the medium. The equation of motion is considered, where a general function of the displacement and its derivatives acts as the forcing term for (sub)harmonic generation and a series of 'selection rules' is found, depending on the sample constrains. The localization of the nonlinear term is also considered that mimics the presence of defects or cracks in the structure, together with the spatial distribution of subharmonic modes. Experimental evidence is given relative to the power law dependence of the harmonic modes vs. the fundamental mode displacement amplitude, and subharmonic mode distribution with hysteretic effects is also reported in a cylindrical sample of piezoelectric material.     

Generation of localized modes in an electrical lattice using subharmonic driving

We show experimentally and numerically that an intrinsic localized mode (ILM) can be stably produced (and experimentally observed) via subharmonic, spatially homogeneous driving in the context of a nonlinear electrical lattice. The precise nonlinear spatial response of the system has been seen to depend on the relative location in frequency between the driver frequency, ω(d), and the bottom of the linear dispersion curve, ω(0). If ω(d)/2 lies just below ω(0), then a single ILM can be generated in a 32-node lattice, whereas, when ω(d)/2 lies within the dispersion band, a spatially extended waveform resembling a train of ILMs results. To our knowledge, and despite its apparently broad relevance, such an experimental observation of subharmonically driven ILMs has not been previously reported.     

Fluctuations in number of photons in region of unstable behavior in process of intracavity generation of second harmonic

Quantum fluctuations of the number of photons of the fundamental mode and of the second harmonic in the process of intracavity generation of the second harmonic in the unstable region of the system are studied. The distribution functions of the number of photons of interacting modes are calculated in the positive P-representation. The functions of the joint distribution of the number of photons of the fundamental mode and the number of photons in the second harmonic are also studied.     

Observation of spatial modulation instability in intracavity second-harmonic generation

We report the observation of spatial instabilities in singly resonant intracavity second-harmonic generation. Self-focusing as well as spatially ordered near- and far-field structures are observed. Experimental results are compared with mean-field analysis as well as three-dimensional numerical simulations.     

Wigner distribution of bistable steady states in optical subharmonic generation

The phase sensitive bistability occuring in subharmonic generation has long been known, but may only now find applications in the optical domain. We extend our earlier theories of additive and multiplicative noise in quantum optics and determine the Wigner distributions for the bistable subharmonic mode which is controlled by an external coherent signal, both for the case of a coherent and a partially incoherent pump at the fundamental frequency.     

A dynamical model of subharmonic generation in ultrasonic infrared thermography

Subharmonics are often observed in ultrasonic infrared thermography (UIR) system as samples are excited by ultrasonic transducers, and it is testified that, as the subharmonics appear, the detectability of cracks or defects in the sample is greatly enhanced in the UIR system. A dynamical model to explore the generation mechanism of the subharmonics and simulate the sample motion excited by an ultrasonic transducer in the UIR system is presented in this paper. In the model, the sample is continuously impacted by the transducer as the transducer is pushed to the sample by a constant force, in which the sample is simplified as a damped oscillator and the transducer is simplified as an active oscillator with constant frequency and amplitude. The impact process is also taken into account, in which the acting force is assumed to vary linearly during the impact process. A stable waveform of subharmonics in the sample can be obtained in appropriate conditions.