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Register a new userSpectral Effects of Strong Chi-2 Non-Linearity for Quantum Processing
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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.
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According to idealized models, a strong Kerr non-linearity may be used to build optical quantum gates for optical quantum information processing by inducing conditional phase shifts on quantum states. Recently, Shapiro (PRA 73, 062305 (2006)) argued that for a Kerr medium with non-instantaneous but fast response, essentially no phase shift is induced on two-single-photon input states, and thus a quantum gate build from such a medium cannot work. Here we show that a fast response Kerr medium induces some but very little phase shifts on a two-single-photon input state, and it is insufficient for high fidelity quantum computation. We point out that this is caused by the medium imparting spectral entanglement to the input photons. We further show that a way to circumvent this problem and achieve a high fidelity gate, is to engineer the dispersion properties of the medium to give a dominant spectral effect over the non-instantaneous response, in addition to satisfying a phase matching condition.
Any optical quantum information processing machine would be comprised of fully-characterized constituent devices for both single state manipulations and tasks involving the interaction between multiple quantum optical states. Ideally for the latter, would be an apparatus capable of deterministic optical phase shifts that operate on input quantum states with the action mediated solely by auxiliary signal fields. Here we present the complete experimental characterization of a system designed for optically controlled phase shifts acting on single-photon level probe coherent states. Our setup is based on a warm vapor of rubidium atoms under the conditions of electromagnetically induced transparency with its dispersion properties modified through the use of an optically triggered N-type Kerr non-linearity. We fully characterize the performance of our device by sending in a set of input probe states and measuring the corresponding output via balanced homodyne tomography and subsequently performing the technique of coherent state quantum process tomography. This method provides us with the precise knowledge of how our optical phase shift will modify any arbitrary input quantum state engineered in the mode of the reconstruction.
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.
We analytically treat the scattering of two counter-propagating photons on a two-level emitter embedded in an optical waveguide. We find that the non-linearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could be quantified via a reduction in coincident clicks in a Hong-Ou-Mandel measurement setup, analogous to a linear beam splitter. Changes to the spectra and phase of the scattered photons, however, would lead to reduced interference with other photons when implemented in a larger optical circuit. We introduce suitable fidelity measures which account for these changes, and find that high values can still be achieved even when accounting for all properties of the scattered photonic state.
We analyse the minimum quantum resources needed to realise strong non-locality, as exemplified e.g. by the classical GHZ construction. It was already known that no two-qubit system, with any finite number of local measurements, can realise strong non-locality. For three-qubit systems, we show that strong non-locality can only be realised in the GHZ SLOCC class, and with equatorial measurements. However, we show that in this class there is an infinite family of states which are pairwise non-LU-equivalent that realise strong non-locality with finitely many measurements. These states have decreasing entanglement between one qubit and the other two, necessitating an increasing number of local measurements on the latter.
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