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Annual Meeting Optical Society of America

A Fabry-Perot interferometer for atoms

Byron B. Taylor, E. Goldstein, M. Wilkens, P. Meystre

Published Jan 1, 1992• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1992.tuaaa3

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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.
In the optical masers realized so far a Perot-Fabry device is used as a multimode cavity. It may be interesting to investigate the general properties of such a device when the emitting or the absorbing atoms are put inside the reflecting mirrors. Even in the case when this device works below the threshold of maser action it shows remarkable properties which are worthwhile studying experimentally. The following aspects are considered in the paper: In the case of external illumination, the distribution of light intensity inside a Perot-Fabry interferometer is calculated. It is shown that the local light intensity in the stationary waves inside can be much higher than the intensity of the incident light beam. The properties of light emitted by atoms inside the Perot-Fabry and emerging from it are investigated. Narrow fringes of very strong intensity can be obtained. If the emitting atoms are located in an atomic beam the central fringe has natural line width, the Doppler broadening being suppressed. The realization of a fluorescent medium of lamellar structure is discussed. This structure favors one special mode of emission fringes. Finally, the absorption of atoms inside the interferometer is studied. It is shown that this device is equivalent to a long absorption path in an ordinary light beam.
In the optical masers realized so far a Perot-Fabry device is used as a multimode cavity. It may be interesting to investigate the general properties of such a device when the emitting or the absorbing atoms are put inside the reflecting mirrors. Even in the case when this device works below the threshold of maser action it shows remarkable properties which are worthwhile studying experimentally. The following aspects are considered in the paper: In the case of external illumination, the distribution of light intensity inside a Perot-Fabry interferometer is calculated. It is shown that the local light intensity in the stationary waves inside can be much higher than the intensity of the incident light beam. The properties of light emitted by atoms inside the Perot-Fabry and emerging from it are investigated. Narrow fringes of very strong intensity can be obtained. If the emitting atoms are located in an atomic beam the central fringe has natural line width, the Doppler broadening being suppressed. The realization of a fluorescent medium of lamellar structure is discussed. This structure favors one special mode of emission fringes. Finally, the absorption of atoms inside the interferometer is studied. It is shown that this device is equivalent to a long absorption path in an ordinary light beam.
In the optical masers realized so far a Perot-Fabry device is used as a multimode cavity. It may be interesting to investigate the general properties of such a device when the emitting or the absorbing atoms are put inside the reflecting mirrors. Even in the case when this device works below the threshold of maser action it shows remarkable properties which are worthwhile studying experimentally. The following aspects are considered in the paper: In the case of external illumination, the distribution of light intensity inside a Perot-Fabry interferometer is calculated. It is shown that the local light intensity in the stationary waves inside can be much higher than the intensity of the incident light beam. The properties of light emitted by atoms inside the Perot-Fabry and emerging from it are investigated. Narrow fringes of very strong intensity can be obtained. If the emitting atoms are located in an atomic beam the central fringe has natural line width, the Doppler broadening being suppressed. The realization of a fluorescent medium of lamellar structure is discussed. This structure favors one special mode of emission fringes. Finally, the absorption of atoms inside the interferometer is studied. It is shown that this device is equivalent to a long absorption path in an ordinary light beam.
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.
We propose to engineer the atomic band structure in optical lattices in order to design a Fabry-Perot interferometer with large mode spacing and strong nonlinear coupling to be employed in atom optics. The use of an optical lattice allows for a significant reduction of the atomic effective mass, while the slow modulation of its parameters spatially confines the matter waves on a length scale of a few dozen optical wavelengths. As a consequence, the mode spacing in such a cavity would be as high as one-tenth of the recoil energy, allowing for a very efficient filter action, while the nonlinear coupling due to interatomic interactions could lead to bistability and limiting effects in the transmission of the atomic beam.
Interferometers are ubiquitous devices in optics, consisting of arrangements of totally reflective and semitransparent mirrors, fiber optics, detectors, etc . The smallest possible mirror consists of a single atom, and with recent advances in nanotechnology it is possible to fabricate them and couple them to transmission lines. This can be realized for example with superconducting qubits and superconducting coplanar waveguide resonators or with dipole emitters coupled to surface-plasmon nanowires. Based on a recent proposal [G S Paraoanu, Phys. Rev. A 82 , 023802 (2010)], here we give a brief overview of the two-atom Mach-Zender interferometer. Here we show that both the phase and the amplitude of the output field can be used to extract information about the phase difference between the two arms of the interferometer. Also, we point out that this device can be used as well in the reflection mode.