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arXiv:2405.00132 · AVS Quantum Science

Engineering superpositions of N00N states using an asymmetric non-linear Mach–Zehnder interferometer

Richard J. Birrittella, Paul M. Alsing, James Schneeloch, Christopher C. Gerry, Jihane Mimih, P. L. Knight

Published Mar 1, 2023• 1 citation
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Abstract

We revisit a method for mapping arbitrary single-mode pure states into superpositions of N00N states using an asymmetric non-linear Mach–Zehnder interferometer (ANLMZI). This method would allow one to tailor-make superpositions of N00N states where each axis of the two-mode joint-photon number distribution is weighted by the statistics of any single-mode pure state. The non-linearity of the ANLMZI comes in the form of a χ(3) self-Kerr interaction occurring on one of the intermediary modes of the interferometer. Motivated by the non-classical interference effects that occur at a beam splitter, we introduce inverse-engineering techniques aimed toward extrapolating optimal transformations for generating N00N state superpositions. These techniques are general enough so as to be employed to probe the means of generating states of any desired quantum properties.

DOI
10.1116/5.0137099

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We revisit a method for mapping arbitrary single-mode pure states into superpositions of N00N states using an asymmetric non-linear Mach–Zehnder interferometer (ANLMZI). This method would allow one to tailor-make superpositions of N00N states where each axis of the two-mode joint-photon number distribution is weighted by the statistics of any single-mode pure state. The non-linearity of the ANLMZI comes in the form of a χ(3) self-Kerr interaction occurring on one of the intermediary modes of the interferometer. Motivated by the non-classical interference effects that occur at a beam splitter, we introduce inverse-engineering techniques aimed toward extrapolating optimal transformations for generating N00N state superpositions. These techniques are general enough so as to be employed to probe the means of generating states of any desired quantum properties.
A method for producing macroscopic quantum superposition states (generally known as Schr\"odinger cat) states for optical fields is presented. The proposed method involves two modes of the field interacting dispersively in a Kerr medium where one of the modes is an arm of a Mach-Zehnder interferometer and the other mode is external to it. If the external mode initially contains a macroscopic quantum state, such as a coherent state, and the vacuum and a single photon state are the inputs to the interferometer, the external field state becomes entangled with the number states associated with the two paths of the interferometer. Selective measurement at the output ports of the interferometer project the external mode into the desired cat states. It is pointed out that the method can also be used to generate cat states out of multimode states initially containing correlations.
It is generally believed that the “mystery” behind understanding Quantum Mechanics (QM) and the global drives to construct quantum computers using “Entanglement”, can be understood from how the two-beam superposition effect (SE) emerges out of a 2-slit, and a Mach-Zehnder Interferometer (MZI). This chapter rehabilitates the classical analyses of these two superposition effects, while exploiting functional asymmetries, either deliberately introduced or intrinsic in the two-beam apparatuses. We are using mathematical formalism already well-established in classical optics since 1800’s, but with the extra emphasis that any final data generation requires some real physical interaction between the detector and the two light signals simultaneously stimulating the detecting molecules. This critical step of physical interaction process is not explicitly underscored by either the classical or the quantum physics. However, the asymmetry, either in the propagation or in the interaction process, is utilized to bring out the contradictions with the QM interpretations. For the 2-slit system, we deliberately introduce asymmetry on one of the slits. For MZI, the asymmetry is already built into the classical reflection property of a typical beams splitter.
We suggest an all-optical scheme to generate entangled superposition of a single photon with macroscopic entangled states for testing macroscopic realism. The scheme consists of source of single photons, a Mach-Zehnder interferometer in routes of which a system of coupled-down converters with type-I phase matching is inserted, and a beam splitter for the other auxiliary modes of the scheme. We use quantization of the pumping modes, depletion of the coherent states passing through the system, and interference effect in the pumping modes in the process of erasing which-path information of the single-photon on exit from the Mach-Zehnder interferometer. We show the macroscopic fields of the output superposition are distinguishable states. This scheme generates macroscopic entangled state that violates Bell's inequality. Moreover, the detailed analysis concerning change of amplitudes of entangled superposition by means of repeating this process many times is accomplished. We show our scheme works without photon number resolving detection and it is robust to detector inefficiency.
Nonlinear interferometers are Mach-Zehnder interferometers with Kerr media in either one or both arms. We refer to these devices, respectively, as the asymmetric and symmetric nonlinear interferometers. In the asymmetric case, with one input mode in the vacuum, it is possible to generate maximally entangled photonic states or superpositions of such states. We consider the device as a resource of entangled states for applications to Heisenberg-limited interferometry. Interferometry with the maximally entangled states cannot be performed by simply subtracting the output photocounts as in standard interferometry. Instead, one must perform parity measurements on only one of the output beams. We show that the symmetric nonlinear interferometer, with one input mode in the vacuum, may be used to perform such parity measurements. The same device is shown to produce, with an input coherent state and upon projective measurements, even or odd coherent states, examples of the Schr\"odinger-cat states.