Journal Article•
Laser gyro at quantum limit
01 Jan 1991-SPIE milestone series (Society of Photo-Optical Instrumentation Engineers)-Vol. 28, pp 365-368
TL;DR: In this article, it was shown that a certain fundamental limit applies to the accuracy of all optical rotation sensors which use laser light as a probe, and the same relationship is obtained from a spontaneous-emission noise formulation.
Abstract: We show that a certain fundamental limit applies to the accuracy of all optical rotation sensors which use laser light as a probe. We derive this fundamental rotation-rate uncertainty from the Heisenberg uncertainty relations and Glauber's minimum uncertainty states. The same relationship is obtained from a spontaneous-emission noise formulation. We present experimental data on a (nondithered) four-frequency ring laser gyroscope for which this limit is attained.
Citations
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TL;DR: In this article, the capability of ring-laser gyros for measurements of geodesic interest, including seismometry and earth tides, and for detection of other sources of non-reciprocal refractive indices, including axions and CP violation, are discussed.
Abstract: HeNe ring-laser gyros are standard sensors in inertial guidance; mirror reflectances now reach 99.9999%. Present research instruments have an area of , a passive quality factor of , and a resolution of the frequency difference of counter-rotating optical beams approaching microhertz. In the Sagnac effect, this difference is proportional to the angular velocity. Present resolution is limited by thermal drifts in frequency pulling, itself reflecting mirror backscatter. The capability of ring lasers for measurements of geodesic interest, including seismometry and earth tides, and for detection of other sources of non-reciprocal refractive indices, including axions and CP violation, are discussed. In standard polarization geometries the observable is necessarily time-reversal odd. Scaling rules for dimensions, finesse etc summarizing past progress and suggesting future potential are given.
349 citations
TL;DR: In this paper, the quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadratures measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier.
Abstract: The preparation, or generation of coherent states, squeezed states, and photon number states is discussed. The quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadrature measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier. A quantum nondemolition measurement followed by a measurement of the conjugate variable is also categorized as a simultaneous measurement. It is shown that, for all of these schemes, the minimum uncertainty product of the measured variables is exactly equal to that required for a simultaneous measurement of two noncommuting variables. On the other hand, measurements of a single quadrature component are noise-free. Such measurements are degenerate heterodyning, degenerate parametric amplification, and cavity degenerate four-wave mixing and photon counting by a photomultiplier or avalanche photodiode. The Heisenberg uncertainty principle and the quantum-mechanical channel capacity of Shannon are discussed to address the question "How much information can be transmitted by a single photon?" The quantum-mechanical channel capacity provides an upper bound on the achievable information capacity and is ideally realized by photon number states and photon counting detection. Its value is $\frac{\ensuremath{\hbar}\ensuremath{\omega}}{(\mathrm{ln}2)kT}$ bit per photon. The use of coherent or squeezed states and a simultaneous measurement of two quadrature field components or the measurement of one single quadrature field component does not achieve the ultimate limit.
340 citations
TL;DR: In this article, a review of methods for generating sub-Poissonian light and related concepts is presented. But the authors focus on the conceptual foundations and developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-poissonic light generation in lasers and masers.
Abstract: The author reviews methods for generating sub-Poissonian light and related concepts. This light has energy fluctuations reduced below the level which corresponds to a classical Poissonian process (shot-noise level). After an introduction to the concept of nonclassical light, an overview is given of the main methods of quantum-noise reduction. Sub-Poissonian processes are exemplified in different areas of optics, ranging from single-atom resonance fluorescence to nonlinear optics, laser physics, and cavity quantum electrodynamics. Emphasis is placed on the conceptual foundations, and on developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-Poissonian light generation in lasers and masers. The sources of quantum noise in these devices are analyzed, and four noise-suppression methods are discussed in detail: regularization of the pumping, suppression of spontaneous-emission noise, nonadiabatic evolution of the atomic variables, and twin-beam generation.
319 citations
Cites background from "Laser gyro at quantum limit"
...…(Grangier et al., 1987; Xiao et al., 1987), on the application of squeezed light to increase the sensitivity of gyroscopes (Ezekiel et al., 1978; Dorschner et al., 1980; Chow et al., 1985), and on spectroscopy with resolution below the natural linewidth (Gardiner, 1986; Gardiner et al., 1987;…...
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TL;DR: In this paper, the authors describe a resonator-based optical gyroscope whose sensitivity for measuring absolute rotation is enhanced via use of the anomalous dispersion characteristic of superluminal light propagation.
Abstract: We describe a resonator-based optical gyroscope whose sensitivity for measuring absolute rotation is enhanced via use of the anomalous dispersion characteristic of superluminal light propagation. The enhancement is given by the inverse of the group index, saturating to a bound determined by the group velocity dispersion. We also show how the offsetting effect of the concomitant broadening of the resonator linewidth may be circumvented by using an active cavity. For realistic conditions, the enhancement factor is as high as ${10}^{6}$. We also show how normal dispersion used for slow light can enhance relative rotation sensing in a specially designed Sagnac interferometer, with the enhancement given by the slowing factor.
270 citations
TL;DR: In this article, the role of integrated optics and photonic integrated circuit technology in the enhancement of gyroscope performance and compactness is broadly discussed, and the architecture of new slow-light integrated angular rate sensors is described.
Abstract: Photonics for angular rate sensing is a well-established research field having very
important industrial applications, especially in the field of strapdown inertial
navigation. Recent advances in this research field are reviewed. Results obtained in
the past years in the development of the ring laser gyroscope and the fiber optic
gyroscope are presented. The role of integrated optics and photonic integrated
circuit technology in the enhancement of gyroscope performance and compactness is
broadly discussed. Architectures of new slow-light integrated angular rate sensors
are described. Finally, photonic gyroscopes are compared with other solid-state
gyros, showing their strengths and weaknesses.
200 citations
References
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TL;DR: In this article, the photon statistics of arbitrary fields in fully quantum-mechanical terms are discussed, and a general method of representing the density operator for the field is discussed as well as a simple formulation of a superposition law for photon fields.
Abstract: Methods are developed for discussing the photon statistics of arbitrary fields in fully quantum-mechanical terms. In order to keep the classical limit of quantum electrodynamics plainly in view, extensive use is made of the coherent states of the field. These states, which reduce the field correlation functions to factorized forms, are shown to offer a convenient basis for the description of fields of all types. Although they are not orthogonal to one another, the coherent states form a complete set. It is shown that any quantum state of the field may be expanded in terms of them in a unique way. Expansions are also developed for arbitrary operators in terms of products of the coherent state vectors. These expansions are discussed as a general method of representing the density operator for the field. A particular form is exhibited for the density operator which makes it possible to carry out many quantum-mechanical calculations by methods resembling those of classical theory. This representation permits clear insights into the essential distinction between the quantum and classical descriptions of the field. It leads, in addition, to a simple formulation of a superposition law for photon fields. Detailed discussions are given of the incoherent fields which are generated by superposing the outputs of many stationary sources. These fields are all shown to have intimately related properties, some of which have been known for the particular case of blackbody radiation.
5,372 citations
TL;DR: In this paper, the concept of two-photon coherent states is introduced for applications in quantum optics, which is a simple generalization of the well-known minimum-uncertainty wave packets.
Abstract: The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.
1,661 citations
TL;DR: In this article, the capability of ring-laser gyros for measurements of geodesic interest, including seismometry and earth tides, and for detection of other sources of non-reciprocal refractive indices, including axions and CP violation, are discussed.
Abstract: HeNe ring-laser gyros are standard sensors in inertial guidance; mirror reflectances now reach 99.9999%. Present research instruments have an area of , a passive quality factor of , and a resolution of the frequency difference of counter-rotating optical beams approaching microhertz. In the Sagnac effect, this difference is proportional to the angular velocity. Present resolution is limited by thermal drifts in frequency pulling, itself reflecting mirror backscatter. The capability of ring lasers for measurements of geodesic interest, including seismometry and earth tides, and for detection of other sources of non-reciprocal refractive indices, including axions and CP violation, are discussed. In standard polarization geometries the observable is necessarily time-reversal odd. Scaling rules for dimensions, finesse etc summarizing past progress and suggesting future potential are given.
349 citations
TL;DR: In this paper, the quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadratures measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier.
Abstract: The preparation, or generation of coherent states, squeezed states, and photon number states is discussed. The quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadrature measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier. A quantum nondemolition measurement followed by a measurement of the conjugate variable is also categorized as a simultaneous measurement. It is shown that, for all of these schemes, the minimum uncertainty product of the measured variables is exactly equal to that required for a simultaneous measurement of two noncommuting variables. On the other hand, measurements of a single quadrature component are noise-free. Such measurements are degenerate heterodyning, degenerate parametric amplification, and cavity degenerate four-wave mixing and photon counting by a photomultiplier or avalanche photodiode. The Heisenberg uncertainty principle and the quantum-mechanical channel capacity of Shannon are discussed to address the question "How much information can be transmitted by a single photon?" The quantum-mechanical channel capacity provides an upper bound on the achievable information capacity and is ideally realized by photon number states and photon counting detection. Its value is $\frac{\ensuremath{\hbar}\ensuremath{\omega}}{(\mathrm{ln}2)kT}$ bit per photon. The use of coherent or squeezed states and a simultaneous measurement of two quadrature field components or the measurement of one single quadrature field component does not achieve the ultimate limit.
340 citations
TL;DR: In this article, a review of methods for generating sub-Poissonian light and related concepts is presented. But the authors focus on the conceptual foundations and developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-poissonic light generation in lasers and masers.
Abstract: The author reviews methods for generating sub-Poissonian light and related concepts. This light has energy fluctuations reduced below the level which corresponds to a classical Poissonian process (shot-noise level). After an introduction to the concept of nonclassical light, an overview is given of the main methods of quantum-noise reduction. Sub-Poissonian processes are exemplified in different areas of optics, ranging from single-atom resonance fluorescence to nonlinear optics, laser physics, and cavity quantum electrodynamics. Emphasis is placed on the conceptual foundations, and on developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-Poissonian light generation in lasers and masers. The sources of quantum noise in these devices are analyzed, and four noise-suppression methods are discussed in detail: regularization of the pumping, suppression of spontaneous-emission noise, nonadiabatic evolution of the atomic variables, and twin-beam generation.
319 citations