No Arabic abstract
We report the first observation of the quantum effects of competing $chi^{(2)}$ nonlinearities. We also report new classical signatures of competition, namely clamping of the second harmonic power and production of nondegenerate frequencies in the visible. Theory is presented that describes the observations as resulting from competition between various $chi^{(2)}$ upconversion and downconversion processes. We show that competition imposes hitherto unsuspected limits to both power generation and squeezing. The observed signatures are expected to be significant effects in practical systems.
A shaped doublet pump pulse is proposed for simultaneous octave-spanning soliton Kerr frequency comb generation and second-harmonic conversion in a single microresonator. The temporal soliton in the cavity is trapped atop a doublet pulse pedestal, resulting in a greatly expanded soliton region compared to that with a general Gaussian pulse pump. The possibility of single-microresonator comb self-referencing in a single silicon nitride microring, which can facilitate compact on-chip optical clocks, is demonstrated via simulation.
We analyze both theoretically and by means of numerical simulations the phenomena of filamentation and dynamical formation of self-guided nonlinear waves in media featuring competing cubic and quintic nonlinearities. We provide a theoretical description of recent experiments in terms of a linear stability analysis supported with simulations, showing the possibility of experimental observation of the modulational instability suppression of intense light pulses travelling across such nonlinear media. We also show a novel mechanism of indirect excitation of {em light condensates} by means of coalescence processes of nonlinear coherent structures produced by managed filamentation of high power laser beams.
Optical $chi^{(2)}$ non-linearity can be used for parametric amplification and producing down-converted entangled photon pairs that have broad applications. It is known that weak non-linear media exhibit dispersion and produce a frequency response. It is therefore of interest to know how spectral effects of a strong $chi^{(2)}$ crystal affect the performance. Here we model the spectral effects of the dispersion of a strong $chi^{(2)}$ crystal and illustrate how this affects its ability to perform Bell measurements and influence the performance of a quantum gates that employ such a Bell measurement. We show that a Dyson series expansion of the unitary operator is necessary in general, leading to unwanted spectral entanglement. We identify a limiting situation employing periodic poling, in which a Taylor series expansion is a good approximation and this entanglement can be removed.
The density matrix in quantum mechanics parameterizes the statistical properties of the system under observation, just like a classical probability distribution does for classical systems. The expectation value of observables cannot be measured directly, it can only be approximated by applying classical statistical methods to the frequencies by which certain measurement outcomes (clicks) are obtained. In this paper, we make a detailed study of the statistical fluctuations obtained during an experiment in which a hypothesis is tested, i.e. the hypothesis that a certain setup produces a given quantum state. Although the classical and quantum problem are very much related to each other, the quantum problem is much richer due to the additional optimization over the measurement basis. Just as in the case of classical hypothesis testing, the confidence in quantum hypothesis testing scales exponentially in the number of copies. In this paper, we will argue 1) that the physically relevant data of quantum experiments is only contained in the frequencies of the measurement outcomes, and that the statistical fluctuations of the experiment are essential, so that the correct formulation of the conclusions of a quantum experiment should be given in terms of hypothesis tests, 2) that the (classical) $chi^2$ test for distinguishing two quantum states gives rise to the quantum $chi^2$ divergence when optimized over the measurement basis, 3) present a max-min characterization for the optimal measurement basis for quantum goodness of fit testing, find the quantum measurement which leads both to the maximal Pitman and Bahadur efficiency, and determine the associated divergence rates.
Quantum optics plays a central role in the study of fundamental concepts in quantum mechanics, and in the development of new technological applications. Typical experiments employ non-classical light, such as entangled photons, generated by parametric processes. The standard characterization of the sources by quantum tomography, which relies on detecting the pairs themselves and thus requires single photon detectors, limits both measurement speed and accuracy. Here we show that the spectral characterization of the quantum correlations generated by two-photon sources can be directly performed classically with an unprecedented spectral resolution. This streamlined technique has the potential to speed up design and testing of massively parallel integrated sources by providing a fast and reliable quality control procedure. Adapting our method to explore other degrees of freedom would allow the complete characterization of biphoton states generated by parametric processes.