Vibration-induced phase noise in Mach–Zehnder atom interferometers

The high inertial sensitivity of atom interferometers has been used to build accelerometers and gyrometers, but this property makes these interferometers very sensitive to the laboratory seismic noise. This seismic noise induces a phase noise which is large enough to reduce the fringe visibility in many cases. We develop here a model calculation of this phase noise applicable to a wide class of Mach–Zehnder atom interferometers and we apply this model to our thermal lithium interferometer. We are thus able to explain the observed dependence of the fringe visibility on the diffraction order. The dynamical model developed in the present paper should be very useful to further reduce this phase noise in atom interferometers and this reduction should open the way to improved interferometers. PACS 03.75.Dg; 39.20.+q; 42.50.Vk     

Performance study and assessment of phase noise suppression by incoherent addition in a mode-locked fiber laser system

This paper investigates the effectiveness of phase noise suppression by incoherent addition in a passively mode-locked fiber laser. Incoherent addition is achieved by using an interferometer external to the mode-locked laser. Two different types of interferometers, Mach–Zehnder and ring, are investigated experimentally for different background phase noise levels. Measurements show that both types of interferometers can achieve good phase noise reduction for a background phase noise level above ? 130 dBc/Hz. Effects of dispersion management and pulse train intensity ratio in the interferometers are also discussed. Multi-stage cascaded interferometers are proposed for supermode noise suppression of harmonically actively mode-locked lasers.     

Interferometry based on the lau effect

Two interferometers are described for investigating phase structures. In both an extended white light source is used for illumination. The operation of the interferometers is based on the Lau effect, which is briefly explained.     

Analysis on the laser beam pointing instability induced fringe shift and contrast dilution from different interferometers used for writing fiber Bragg grating

This paper presents an analysis on the effect of laser beam pointing instability on the fringe shift and hence the contrast dilution of superposed fringes from two beam interferometers. The interferometers analyzed are those commonly used in writing fiber Bragg grating (FBG) such as phase mask, bi-prism and phase mask based Talbot/Holographic type. The beam pointing instability is incorporated as slight change in the angle between two interfering beams. The relative immunity of different interferometers to laser beam pointing is discussed vs location of FBG writing plane from the beam splitter. The effect of the beam pointing was minimum in proximity FBG writing by phase mask. The effect, in terms of fringes contrast dilution, was worst in case of large length interferometers e.g. phase mask based-Talbot interferometer. For intermediate length prism interferometers, the effect was moderate. For a given length interferometer, the fringe shift was directly proportional to beam pointing angle and inversely proportional to fringe separation. Theoretical analysis is verified experimentally by studying the fringe instability of interference pattern formed by a bi-prism of angle 2^o with the copper vapour laser (CVL, λ = 510 nm) beams of different beam pointing instabilities.     

Limitations of atom interferometry for gravitational wave observations in space

A paper published recently (Hogan et al. in Gen. Relativ. Gravit. 43:1953–2009, 2011) suggests the use of atom interferometry between satellites in Earth orbit to observe gravitational waves. The proposed altitude and satellite separation are about 1,000 and 30 km respectively. The difference in acceleration between clouds of ultracold atoms in atom interferometers near the two satellites would be detected by using laser beams between the interferometers. Because of the measurement path being very short compared with the million km or longer measurement path for a proposed laser interferometer gravitational wave antenna in space, the sensitivity to differential fluctuations in the laser phase as seen by the atoms in the two atom interferometers is very high. Problems introduced by this high sensitivity to spurious laser beam phase changes will be described in the first part of this paper. Then other limitations on the performance and on the suggested types of sources that could be observed will be discussed.     

Gravitational wave detection with single-laser atom interferometers

We present a new general design approach of a broad-band detector of gravitational radiation that relies on two atom interferometers separated by a distance L. In this scheme, only one arm and one laser will be used for operating the two atom interferometers. We consider atoms in the atom interferometers not only as perfect inertial reference sensors, but also as highly stable clocks. Atomic coherence is intrinsically stable and can be many orders of magnitude more stable than a laser. The unique one-laser configuration allows us to then apply time-delay interferometry to the responses of the two atom interferometers, thereby canceling the laser phase fluctuations while preserving the gravitational wave signal in the resulting data set. Our approach appears very promising. We plan to investigate further its practicality and detailed sensitivity analysis.     

Electron Sagnac gyroscope in an array of mesoscopic quantum rings

The Sagnac effect is an important phase coherent effect in optical and atom interferometers where rotations with respect to an inertial frame are measured in the interference pattern. We analyze the Sagnac effect in a serial array of mesoscopic ring shaped electron interferometers comprised of rings with half-circumferences comparable to the mean free path. The entire array is, however, much larger than the phase coherence length. Phase coherent transport at the level of individual rings leads to a measurable Sagnac effect in the conductance of the chain. We use the signal to noise ratio (SNR) to determine the number of rings needed to measure a desired rotation rate.     

Thermodynamic phase noise in fibre interferometers

Phase noise due to thermodynamic fluctuations in the optical path length is evaluated in this paper for basic fibre interferometers. In Mach-Zehnder and Michelson interferometers, where the temperature phase fluctuation (TPF) is that intrinsic to the fibre, this noise has been reported to be comparable to shot noise and a possible limit to sensor sensitivity in practical cases. We show that in Sagnac interferometers, used in fibre gyro and in Faraday current sensors, the TPF noise is decreased with respect to that intrinsic to the fiber because propagation in the same optical path leads to a correlation of the phase fluctuations. In addition, we show that in Fabry-Perot and ring resonators, as multiple reflections increase the effective path length, TPF noise is enhanced and can be dominant over shot noise even for moderate fibre lengths.     

Andreev probe of persistent current states in superconducting quantum circuits

Using the extraordinary sensitivity of Andreev interferometers to the superconducting phase difference associated with currents, we measure the persistent current quantum states in superconducting loops interrupted by Josephson junctions. Straightforward electrical resistance measurements of the interferometers give a continuous readout of the states, allowing us to construct the energy spectrum of the quantum circuit. The probe is estimated to be more precise and faster than previous methods, and can measure the local phase difference in a wide range of superconducting circuits.     

5D optics for atomic clocks and gravito-inertial sensors

A new framework is proposed to compare and unify photon and atomoptics, which rests on the quantization of proper time. A common waveequation written in five dimensions reduces both cases to 5D-optics ofmassless particles. The ordinary methods of optics (eikonal equation, Kirchhoff integral, Lagrange invariant, Fermat principle, symplectic algebraand ABCD matrices,...) are used to solve this equation in practical cases.The various phase shift cancellations, which occur in atom interferometers, and the quantum Langevin twin paradox for atoms, are then easily explained.A general phase-shift formula for interferometers is derived in fivedimensions, which applies to clocks as well as to gravito-inertial sensors.The application of this formula is illustrated in the case of atomicfountain clocks.     

Ring interferometer on the basis of 2D electron gas in a double quantum well

Magnetotransport properties of submicron rings fabricated on the basis of 2D electron gas in a GaAs double quantum well are studied. It is shown that, in such interferometers, the Aharonov-Bohm effect is caused by coherent processes in two weakly coupled rings, which have different widths of electron channels. In these interferometers, a phase inversion of h/e oscillations is observed under the action of the parallel component of a tilted magnetic field. This phenomenon is qualitatively explained by a redistribution of charge carriers in the two rings.     

Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system

A highly stabilised vibration-displacement measurement system, which employs fiber Bragg gratings (FBGs) to interleave two fiber Michelson interferometers that share the common-interferometric-optical path, is presented. The phase change in the interferometric signals of the two fiber Michelson interferometers have been tracked, respectively, with two electronic feedback loops. One of the fiber interferometers is used to stabilise the system by the use of an electronic feedback loop to compensate the environmental disturbances. The second fiber interferometer is used to perform the measurement task and employs another electronic feedback loop to track the phase change in the interferometric signal. The measurement system is able to measure vibration-displacement and provide the sense of direction of the displacement. The frequency range of the measured vibration-displacement is from 0.1 to 200 Hz and the measurement resolution is 10 nm.     

Holographic interferometry with wavefront shearing

Application of the common path shearing interferometric techniques to holography to study the phase variations in transparent specimens is described. These shearing interferometers are less susceptible to vibration and other external disturbances. Real-time reconstructed interferograms are shown.     

Using time-reversal symmetry for sensitive incoherent matter-wave Sagnac interferometry

We present a theory of the transmission of guided matter-waves through Sagnac interferometers. Interferometer configurations with only one input and one output port have a property similar to the phase rigidity observed in the transmission through Aharonov-Bohm interferometers in coherent mesoscopic electronics. This property enables their operation with incoherent matter-wave sources. High rotation sensitivity is predicted for high finesse configurations.     

Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers

We describe fiber-based quadrature low-coherence interferometers that exploit the inherent phase shifts of 3 x 3 and higher-order fiber-optic couplers. We present a framework based on conservation of energy to account for the interferometric shifts in 3 x 3 interferometers, and we demonstrate that the resulting interferometers provide the entire complex interferometric signal instantaneously in homodyne and heterodyne systems. In heterodyne detection we demonstrate the capability for extraction of the magnitude and sign of Doppler shifts from the complex data. In homodyne detection we show the detection of subwavelength sample motion. N x N (N > 2) low-coherence interferometer topologies will be useful in Doppler optical coherence tomography (OCT), optical coherence microscopy, Fourier-domain OCT, optical frequency domain reflectometry, and phase-referenced interferometry.     

Internal Reflection Spectroscopy

Abstract

This review‐type article deals with small, stable, compact, inexpensive, and low‐resolution interferometers mainly based on continuous or back and forth rotational motion to create the optical path difference. These interferometers are suitable for low‐resolution Fourier Transform Infrared (FTIR) spectroscopy. The paper introduces the most typical interferometers illustrated with figures. For example, interferometers with retroreflectors such as corner cubes are presented. This work aims at developing a tilt compensated optical design where the optical path difference of the interferometer will be achieved with rotational scanning. The most important property of this optical design is large mechanical tolerances to make manufacturing easy and inexpensive. New interferometers based on rotational motion are described. The mechanical angle tolerances of these interferometers can be up to three orders of magnitude larger than the angle tolerances in commonly used corner cubes.     

Real-time visualisation of deformation fields using speckle interferometry and temporal phase unwrapping

A real-time system for analysing data from speckle interferometers, and speckle shearing interferometers, has been developed. Interferograms are continuously recorded by a digital camera at a rate of 60 frames s⁻¹ with temporal phase shifting carried out at the same rate. The images are analysed using a pipeline image processor. With a standard 4-frame phase-shifting algorithm (phase steps of π/2), wrapped phase maps are calculated and displayed at 15 frames s⁻¹. These are unwrapped using a temporal phase unwrapping algorithm to provide a real-time colour-coded display of the relevant displacement component. Each camera pixel (or cluster of pixels) behaves in effect as an independent displacement sensor. The reference speckle interferogram is updated automatically at regular user-defined intervals, allowing arbitrarily large deformations to be measured and errors due to speckle decorrelation to be minimised. The system has been applied to the problem of detecting sub-surface delamination cracks in carbon fibre composite panels.     

Interferometry with independent Bose-Einstein condensates: parity as an EPR/Bell quantum variable

When independent Bose-Einstein condensates (BEC), described quantum mechanically by Fock (number) states, are sent into interferometers, the measurement of the output port at which the particles are detected provides a binary measurement, with two possible results ±1. With two interferometers and two BEC’s, the parity (product of all results obtained at each interferometer) has all the features of an Einstein-Podolsky-Rosen quantity, with perfect correlations predicted by quantum mechanics when the settings (phase shifts of the interferometers) are the same. When they are different, significant violations of Bell inequalities are obtained. These violations do not tend to zero when the number N of particles increases, and can therefore be obtained with arbitrarily large systems, but a condition is that all particles should be detected. We discuss the general experimental requirements for observing such effects, the necessary detection of all particles in correlation, the role of the pixels of the CCD detectors, and that of the alignments of the interferometers in terms of matching of the wave fronts of the sources in the detection regions. Another scheme involving three interferometers and three BEC’s is discussed; it leads to Greenberger-Horne-Zeilinger (GHZ) sign contradictions, as in the usual GHZ case with three particles, but for an arbitrarily large number of them. Finally, generalizations of the Hardy impossibilities to an arbitrarily large number of particles are introduced. BEC’s provide a large versality for observing violations of local realism in a variety of experimental arrangements.     

Gravitational decoherence of atomic interferometers

We study the decoherence of atomic interferometers due to the scattering of stochastic gravitational waves. We evaluate the “direct” gravitational effect registered by the phase of the matter waves as well as the “indirect” effect registered by the light waves used as beam-splitters and mirrors for the matter waves. Considering as an example the space project HYPER, we show that both effects are negligible for the presently studied interferometers. Received 15 February 2002 / Received in final form 12 April 2002 Published online 19 July 2002     

Reconstruction method for weak-phase optical interferometry

Current optical interferometers are affected by unknown turbulent phases on each telescope. We account for this lack of phase information by introducing system aberration parameters, and we solve the image reconstruction problem by minimizing an original joint criterion in the aberrations and in the object. We validate this method by means of simulations. Tests on experimental data are under way.