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Journal of Physics Conference Series

Geometry of the Quantum States of Light in a Mach-Zehnder Interferometer

Alejandro Romero-Osnaya

Published Mar 1, 2016• 1 citation
Publisher

Abstract

A geometric approach to the quantum states of light that is injected into a Mach- Zehnder interferometer is discussed. It is based on the Jordan-Schwinger representation of angular momentum and permits the identification of the photon states with cones in the threedimensional space that are rotated by the action of the optical devices. Some cases of the evolution loops, dynamical processes for which any state evolves cyclically, are presented.

DOI
10.1088/1742-6596/698/1/012014

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A geometric approach to the quantum states of light that is injected into a Mach- Zehnder interferometer is discussed. It is based on the Jordan-Schwinger representation of angular momentum and permits the identification of the photon states with cones in the threedimensional space that are rotated by the action of the optical devices. Some cases of the evolution loops, dynamical processes for which any state evolves cyclically, are presented.
In this paper, we present a coherent state-vector method which can explain the results of a nested linear Mach-Zehnder Interferometric experiment. Such interferometers are used widely in Quantum Information and Quantum Optics experiments and also in designing quantum circuits. We have specifically considered the case of an experiment by Danan \emph{et al.} (Phys. Rev. Lett. \textbf{111}, 240402 (2013)) where the outcome of the experiment was spooky by our intuitive guesses. However we have been able to show by our method that the results of this experiment is indeed expected within the standard formalism of Quantum Mechanics using any classical state of a single-mode radiation field as the input into the nested interferometric set-up of the aforesaid experiment and thereby looking into the power spectrum of the output beam.
In the Schrödinger evolution of a quantum state, time enters as a real parameter representing the coordinate. In a more consistent approach, time should be defined as a quantum observable, with the evolution taking place in a four-dimensional spacetime. This is possible in the projection evolution model in which the wave function is defined in both space and time. This allows to construct the time operator and discuss the temporal structure of the quantum processes. In this paper, we discuss a photon travelling through a Mach-Zehnder interferometer, focusing the description on the temporal profile of the wave function. We show that in this approach the delayed-choice experiments can be explained by the temporal overlap of the photon and the devices in the interferometer.
In the Schrödinger evolution of a quantum state time enters as a real parameter representing the coordinate. In a more consistent approach time should be defined as a quantum observable, with the evolution taking place in a four-dimensional spacetime. This is possible in the projection evolution model in which the wave function is defined in both space and time. This allows to construct the time operator and discuss the temporal structure of quantum processes. In this paper we discuss a photon travelling through a Mach-Zehnder interferometer, focusing the description on the temporal profile of the wave function. We show that in this approach the delayed-choice experiments can be explained by the temporal overlap of the photon and the devices in the interferometer.
We consider an oscillating micromirror replacing one of the two fixed mirrors of a Mach-Zehnder interferometer. In this ideal optical set-up the quantum oscillator is subjected to the radiation pressure interaction of traveling light waves, no cavity is involved. The aim of this configuration is to show that squeezed light can be generated by pure scattering on a quantum system, without involving a cavity. The squeezing can be detected at the output ports of the interferometer either by direct detection or by measuring the spectrum of the difference current. We use the quantum-stochastic Schr\"odinger equation (Hudson-Parthasarathy equation) to model the global evolution. Indeed, it can describe the scattering of photons and the resulting radiation pressure interaction on the quantum oscillator. Moreover, it allows us to consider also the interaction with a thermal bath, so that it can describe also the damping of the harmonic oscillator and non-Markovian thermal effects. In this way we have a unitary dynamics giving the evolution of oscillator and fields. The Bose fields of quantum stochastic calculus and the related generalized Weyl operators allow us to describe the whole optical circuit. By working in the Heisenberg picture, the quantum Langevin equations for position and momentum and the output fields arise, which are used to describe the monitoring in continuous time of the light at the output ports. In the case of strong laser and weak radiation pressure interaction highly nonclassical light is produced, and this can be revealed either by direct detection (a negative Mandel QQQ-parameter is found) or by the intensity spectrum of the difference current of two photodetector; in the second case a nearly complete cancellation of the shot noise can be reached. In this last case it appears that the Mach-Zehnder configuration together with the detection of the difference current corresponds to an homodyne detection scheme, so that we can say that the apparatus is measuring the ``spectrum of squeezing.''
Linear-optical interferometers play a key role in designing circuits for quantum information processing and quantum communications. Even though nested Mach-Zehnder interferometers appear easy to describe, there are occasions when they provide unintuitive results. This paper explains the results of a highly discussed experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013).] using a standard approach. We provide a simple and intuitive one-state vector formalism capable of interpreting their experiment. Additionally, we cross-checked our model with a classical-physics-based approach and found that both models are in complete agreement. We argue that the quantity used in the mentioned experiment is not a suitable which-path witness, producing seemingly contraintuitive results. To circumvent this issue, we establish a more reliable which-path witness and show that it yields well-expected outcomes of the experiment.