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Physical Review Applied

Quantum Fabry-Perot Resonator: Extreme Angular Selectivity in Matter-Wave Tunneling

Constantinos A. Valagiannopoulos

Published Nov 18, 2019• 29 citations
Publisher

Abstract

The simple quantum setup of the Fabry-Perot interferometer from optics is found to exhibit very strong directional preference for impinging particle beams. Two types of resonances are identified, the different mechanisms of which are demonstrated through the spatial distribution of wave-function magnitude and probability current. These findings offer additional degrees of freedom when designing architectures for a broad range of quantum engineering applications involving beam tunneling, from e-beam steering to matter-wave filtering and quantum sensing. They also provide a set of limits for the angular selectivity that can be achieved with the considered geometry.

DOI
10.1103/physrevapplied.12.054042

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The simple quantum setup of the Fabry-Perot interferometer from optics is found to exhibit very strong directional preference for impinging particle beams. Two types of resonances are identified, the different mechanisms of which are demonstrated through the spatial distribution of wave-function magnitude and probability current. These findings offer additional degrees of freedom when designing architectures for a broad range of quantum engineering applications involving beam tunneling, from e-beam steering to matter-wave filtering and quantum sensing. They also provide a set of limits for the angular selectivity that can be achieved with the considered geometry.
Recent progress in atom optics has culminated in several demonstrations of atom interferometers. These rely on the passage of atoms through mechanical or light gratings and may be roughly characterized as Mach–Zehnder interferometers. In this communication, we propose a scheme to realize a Fabry–Perot interferometer for atoms. The mirrors are realized by the field gradient resulting from the spatial mode structure in optical or microwave cavities. When ultra- cold atoms impinge on such cavities, they experience quantum mechanical reflection and transmission that result in the appearance of longitudinal modes for the atomic wave function. We present a model of such a Fabry–Perot interferometer for two-level atoms. We discuss the intra-cavity matter–wave mode structure as well as the transmittivity and reflectivity characteristics of the interferometer. The potential generation of macroscopic quantum waves using such a device, as well as its potential as a sensitive photon detector, will be addressed.
We examine the prospects of utilizing matter-wave Fabry-Pérot interferometers for enhanced inertial sensing applications. Our study explores such tunneling-based sensors for the measurement of accelerations in two configurations: (a) a transmission setup, where the initial wave packet is transmitted through the cavity and (b) an out-tunneling scheme with intra-cavity generated initial states lacking a classical counterpart. We perform numerical simulations of the complete dynamics of the quantum wave packet, investigate the tunneling through a matter-wave cavity formed by realistic optical potentials and determine the impact of interactions between atoms. As a consequence we estimate the prospective sensitivities to inertial forces for both proposed configurations and show their feasibility for serving as inertial sensors.
Selecting the quantum signals with respect to features like direction of propagation or impinging energy makes a ubiquitous operation that is employed in a variety of quantum engineering applications. The conditions for optimally selective angular and energy filtering via homogeneous planar inclusions are determined and the derived designs exhibit substantial robustness with respect to fabrication defects. The reported findings may open new uncharted directions towards the efficient design of integrated devices exploiting quantum filtering from sharp sensors and tuners to multiport networks and quantum circuits.
This communication has considered the case of a Fabry-Perot cavity with light impinging on one end while the field distribution on the other end is observed. It has been shown that if one starts with a wave that can be expanded into the modes of the integral operator, and if the medium in the cavity is passive, more than one mode would be observed at the other end although the amplitude of the dominant mode can be much greater than that of the other modes. It was further shown that if there is present an active medium with sufficient gain there will be only a single mode, and the single mode is necessary and sufficient for complete spatial coherency.
We have investigated nonlinear atom optical effects which arise from atom-atom collisional interactions in a single-mode atomic Fabry-Perot cavity driven by a coherent cw atom laser beam. When the nonlinear interaction energy per single atom is small, the exact numerical solution of the master equation is well reproduced by a mean-field treatment in which quantum fluctuations are included linearizing the stochastic equations of the Positive-P representation. On the other hand, when the damping of the cavity mode is very weak and its wave-function is tightly confined in space, a regime of strong nonlinearity can be achieved. For the specific case of an incident atom laser frequency at resonance with the empty cavity, the numerical calculations predict a sort of atom blockade effect, which is a sort of atom optical analog of the well-known Coulomb blockade effect of electronic transport through microscopic structures: only one atom can occupy the cavity mode at a time and the statistical properties of the transmitted beam, being very similar to the resonance fluorescence from a single two-level system, show definitely nonclassical behaviors such as antibunching. Only at very large incident intensities, more than one atom can be simultaneously forced inside the cavity mode: in this regime, the results of the numerical calculations can be successfully interpreted using a dressed cavity model. From the formal analogy between atomic matter waves and optical light waves in nonlinear media, it follows that the same results hold for photonic systems.