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Annals of Physics

Photon wave function formalism for analysis of Mach–Zehnder interferometer and sum-frequency generation

Atirach Ritboon, Chalongrat Daengngam, Teparksorn Pengpan

Published Apr 13, 2016• 0 citations
Publisher
DOI
10.1016/j.aop.2016.04.004

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In this paper, a Mach–Zehnder interferometer is analyzed with a single photon Gaussian wave packet at one of its input ports and vacuum state at the other input port. Various noises arising in the Mach–Zehnder interferometer such as photon flux noise and quadrature noise are mathematically analyzed. The effect of variation in device parameters on the power spectral density at the output ports of the Mach–Zehnder interferometer is studied. It is observed that the power spectral density of photon flux noise autocorrelation at the output ports of a Mach–Zehnder interferometer is a function of phase shift, whereas the power spectral density of quadrature noise autocorrelation at the output ports of a Mach–Zehnder interferometer is a function of frequency of a single photon wave packet and the phase shift. The analysis carried out in this paper will be helpful in understanding the quantum fluctuations in the design of quantum logic devices and circuits where the Mach–Zehnder interferometer is a core building block.
The two-state vector formalism (TSVF) describes a quantum system between two measurements, with a pre- and post-selected states evolving forward and backward in time, respectively. In this paper, we investigate the which-path information and the TSVF analysis considering the polarization and path states in a polarization-based nested Mach-Zehnder interferometer (NMZI). By adjusting photon polarization in the multipath via polarization optics, we can investigate the which-path information of the photons after the polarization beam splitter in the polarization-based NMZI under conditions of constructive or destructive interference conditions. Considering the incomplete polarization states of photons in the NMZI, the interpretation of our experimental results does not contradict the TSVF analysis.
Most of the experimental interferometric setup are based on the Mach-Zehnder geometry. Usually in the experimental configurations the photons travel in air, at a speed v independent of λ. An integrated optics approach appears necessary both for practical applications and because it can be useful for fundamental optics studies because the transmitted photons are in a spatial coherent state. We exploited a hybrid setup integrating optical fibres and monolithic optical waveguides to implement an asymmetric nonlinear Mach-Zehnder Interferometer (ANLI). One arm of the interferometer was equipped with a single mode Er:LiNbO3 waveguide, acting as nonlinear component whereas the other arm was an undoped LiNbO3 single mode waveguide, used to obtain a phase shift through the application of a voltage ramp. We injected in the ANLI a 980 nm laser radiation to collect interferograms that could be ascribed exclusively to the pump photons, as all frequency conversion events are localized only in one arm of the interferometer. The Fourier Transform analysis of the experimental data allowed us to perform a n Interaction-Free Quantum Optics experiment. This is a novel approach that can be used because in quantum mechanics the wave functions of a state, expressed in terms of two conjugate variables, are Fourier Transform pairs. In fact, operating in the Fourier Transform time-frequency space-domain, we recovered the spectral composition, in the wavenumber space-domain, of the photons generated by the excitation of an Er3+ doped crystal placed in one arm of the interferometer.