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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2019

Bell Inequality Experiment for a High Brightness Time-Energy Entangled Source

A periodically poled MgO doped LiNbO3 (MgO:LN) non-degenerate photon pair source is utilized for spontaneous parametric down-conversion of 532 nm photons into time-energy entangled pairs of 800 and 1600 nm photons. The entangled photons are separated using previously detailed sorting optics, such that each wavelength is independently directed through one of two modified Mach-Zehnder interferometers also known as a Franson interferometer after which they are fiber-optically guided to high-efficiency photon detectors. Output from the detectors is sent to a high resolution time tagger, where coincidences between the entangled photons are recorded. By varying the length of the long path in one Mach-Zehnder interferometer, it is possible to observe high visibility sinusoidal fringes in the measured coincidence rates (while no variation is seen in single photon detection rates). These fringes due to interference between the photon probability amplitudes are indicative of a violation of the Bell inequality, and confirm inconsistencies with local hidden variable theory for the correlations of the time-energy entangled photon pairs.

time-energy entanglement↗
NASA NTRS2019

Bell Inequality Experiment for a High Brightness Time-Energy Entangled Source

A periodically poled MgO - doped LiNbO3 (MgO:LN) non-degenerate photon pair source is utilized for spontaneous parametric down-conversion of 532-nanometer photons into time-energy entangled pairs of 800- and 1600-nanometer photons. The entangled photons are separated using previously detailed sorting optics, such that each wavelength is independently directed through one of two modified Mach-Zehnder interferometers - also known as a Franson interferometer - after which they are fiber-optically guided to high-efficiency photon detectors. Output from the detectors is sent to a high resolution time tagger, where coincidences between the entangled photons are recorded. By varying the length of the long path in one Mach-Zehnder interferometer, it is possible to observe high visibility sinusoidal fringes in the measured coincidence rates (while no variation is seen in single photon detection rates). These fringes - due to interference between the photon probability amplitudes - are indicative of a violation of the Bell inequality, and confirm inconsistencies with local hidden variable theory for the correlations of the time-energy entangled photon pairs.

Time-Energy Entanglement↗
NASA NTRS1965

Necessary conditions for a multistage bolza- mayer problem involving control variables and having inequality and finite equation constraints

A multiplier rule and analogues of the Weierstrass and Clebsch conditions are developed for a multistage Bolza-Meyer calculus of variations problems. The number of stages is fixed, but partition points defining state boundaries are variable. Discontinuities are allowed in variables finite equations and inequalities, as well as differential equations, all of which involve control variables. An appendix summarizes some of the results obtained by C. H. Denbow, as modified by R. W. hunt, for a generalized Bolza problem. The appendix is independent of the rest of the paper.

Differential equation↗