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Acta Sinica Quantum Optica

Manipulations of Quantum Information by a Type II Second Harmonic Generation Process

Juan Guo

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

We have studied theoretically quantum noise fluctuation of type Ⅱsecond harmonic generation(SHG) process.The dependence of generated quantum fields by the input quantized fields is calculated.The results indicate that the SHG optical cavity can realize manipulation of quantum fluctuations when the pump beams are quantum fields.This manipulation of quantum fluctuations is essential in quantum information processing and quantum networking.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 8, 2013•5 citations
We have studied theoretically quantum noise fluctuation of type Ⅱsecond harmonic generation(SHG) process.The dependence of generated quantum fields by the input quantized fields is calculated.The results indicate that the SHG optical cavity can realize manipulation of quantum fluctuations when the pump beams are quantum fields.This manipulation of quantum fluctuations is essential in quantum information processing and quantum networking.
The quantum fluctuations and correlations of the output signal and idler beams from a type-II polarization nondegenerate optical parametric amplifier (NOPA) inside an optical cavity are investigated theoretically, which is driven by the different kinds of quantized fields such as the two-mode thermal field, the phase-conjugate state, and a pair of EPR beams at the signal and idler frequency. Spectral line shapes due to quantum interferences between the input quantum fields and the generated down-converted subharmonic fields of NOPA are studied by scanning the length of the NOPA cavity. The entanglement degree of the EPR entangled beams injected into the NOPA as signal and idler beams can be increased or decreased, which are realized by controlling the relative phase between the pump beam and the injected beams for the NOPA. The results demonstrate coherent phenomena of NOPA in the quantum regime and show phase-sensitive manipulations of quantum entanglement for quantum information processing.
This work presents a quantum theory of the nonlinear optical process of second-harmonic generation (SHG) in one-dimensional microresonators. More specifically, we show how the manipulation of vacuum field fluctuations in high-confinement systems, leading to a spectrally (and spatially) modulated commutation relation for the photon's generalized formulations of their creation and annihilation operators, deeply affects SHG behavior and gives rise to a threshold level. The two main effects the modulated commutator has on this optical process are an inhibition of the SHG process at low pumping level and a significant (cubic) amplification of the second-harmonic signal production rate once the threshold is overcome (finally reaching the usual quadratic dependence at sufficiently high pumping level). Our predictions, which represent a concrete picture of a fractional quantum system, could be used to probe vacuum field fluctuations present in high-confinement microresonators and emphasize the fundamental importance of vacuum field fluctuations.
In this paper, tripartite entanglement among the two pump fields and the second-order harmonic field is established in the process of type-II second-order harmonic generation (SHG) with a triply resonant optical cavity below threshold. A sufficient inseparability criterion for continuous-variable tripartite entanglement proposed by van Loock and Furusawa is used to evaluate the degree of the quadrature--phase-amplitude correlations between the three modes. The dependence of the entanglement on the pump parameter and analysis frequency is also discussed. It is shown that the best entanglement appears at the appropriate pump power and analysis frequency. These three entangled states with different frequencies generated directly from a simple SHG process make the scheme useful for the application in quantum communication and network.
We analyze squeezing of both the fundamental and harmonic fields undergoing traveling-wave, second-harmonic generation (SHG) in second-order (${\mathrm{\ensuremath{\chi}}}^{(2)}$) nonlinear media. We take into account depletion of the fundamental field as well as the phase mismatch between the fundamental and harmonic fields. The behavior of the quantum noises on the propagating fields is studied by linearizing the nonlinear operator equations around the mean-field values. We first consider the degenerate case that is applicable to type-I phase-matching geometries, obtaining expressions for squeezing in both the fundamental and harmonic fields under the conditions of perfect phase matching and large phase mismatch. We show that in the case of a large phase mismatch, the intensity-dependent self-phase shift of the fundamental field, arising due to cascading of the ${\mathrm{\ensuremath{\chi}}}^{(2)}$ nonlinearity, is responsible for the squeezing generation. We also numerically solve the linearized quadrature-operator equations together with the nonlinear mean-field equations. We find that in the case of a finite phase mismatch the harmonic field can be highly squeezed. This is in contrast to the perfectly phase-matched case where the maximum squeezing is limited to 50%. Finally, we analyze the nondegenerate case that applies to type-II phase-matching geometries. Here we show that the commonly used type-II phase-matched SHG process with the input harmonic field in the vacuum state is equivalent to a type-I SHG process in parallel with a degenerate optical-parametric process. The latter causes squeezing in the mode that is polarized orthogonal to the fundamental beam. In the perfect phase-matching case, the squeezing in the orthogonally polarized mode follows the simple expression S=1-\ensuremath{\gamma}, where \ensuremath{\gamma} is the harmonic conversion frequency.
The interest toward strong electromagnetic confinement structures through the use of microcavities is of great interest, from both the fundamental understanding and the technological application sides. Here, we focus our attention to second order nonlinear processes inside such structures. From a basic point of view, electromagnetic confinement leads, physically, to the manipulation of vacuum field fluctuations and, formally, to an anomalous commutation relation [Ueda, M. and Imoto, N., "Anomalous commutation relation and modified spontanenous emission inside a microcavity," Phys. Rev. A, 50(1), 89-92 (1994)]. However, an attempt to probe the resulting anomaly with a beam splitter located inside a cavity is theoretically proved inadequate for this task. For this reason, parametric fluorescence (PF, parametric down conversion) and second harmonic generation (SHG) are considered as potential tools to probe vacuum field fluctuations in confinement structures. Indeed, it was recently showed that PF can be strongly intensified, by two orders of magnitude or more, when it occurs inside a high confinement (open) cavity. Therefore, PF could efficiently be used to probe the expected anomaly. Additionally, in consideration of the simplest possible experimental scheme to probe the anomaly and because it is generally admitted that SHG is the time reversal of degenerate parametric fluorescence, here our attention is also directed toward SHG. Formally, we show that the equations describing SHG and PF are not symmetrical regarding quantum noise. It turns out that, conversely to the case of PF, the intensification of vacuum field fluctuations tends to inhibit SHG. We interpret this result as due to the reduction of waves coherence induced by stronger quantum noise. In conclusion, albeit both processes could be used as probes to prove or disprove the realm of quantum anomalies, PF appears as a more convenient tool.