Symmetric Interferometer Research Articles

Design optical surface as the measurement datum in measuring gear tooth flank by symmetrical laser interferometer

Laser interferometry is a promising method to measure the form deviation of gear tooth flanks. The lack of measurement datum is the bottleneck problem of measuring a gear tooth flank by laser interferometry. Manufacturing a physical reference gear tooth flank as the measurement datum has many drawbacks which restrain the application prospect of measuring gear by laser interferometry. Optical surfaces are more mature to manufacture and have much higher processing accuracy compared with the physical reference tooth flank. Thus, we design and use an optical surface as the measurement datum. First, we invent a symmetrical oblique incidence laser interferometer (SOILI) to reduce the interference fringe’s density and enhance the tractability of interferograms. Second, we propose a design method for calculating the measured tooth flank’s similar optical surface. Lastly, we propose the nonparallel plate model which is a general form of the parallel plate model and can be used to calculate the situations where the normal directions of the measured surface and the reference surface are different. Experimental results verify that an optical surface can be designed and used as the measurement datum. Furthermore, this research provides some references for the measurement datum in the relevant comparative measurements processes by laser interferometry.

Sensitivity of Quantum-Enhanced Interferometers

We review various schemes of quantum-enhanced optical interferometers, both linear (SU(2)) and non-linear (SU(1,1)) ones, as well as hybrid SU(2)/SU(1,1) options, using the unified modular approach based on the Quantum Cramèr–Rao bound (QCRB), and taking into account the practical limitations pertinent to all real-world highly-sensitive interferometers. We focus on three important cases defined by the interferometer symmetry: (i) the asymmetric single-arm interferometer; (ii) the symmetric two-arm interferometer with the antisymmetric phase shifts in the arms; and (iii) the symmetric two-arm interferometer with the symmetric phase shifts in the arms. We show that while the optimal regimes for these cases differ significantly, their QCRBs asymptotically correspond to the same squeezing-enhanced shot noise limit (2), which first appeared in the pioneering work by C. Caves in 1981.We show also that in all considered cases the QCRB can be asymptotically saturated by the standard (direct or homodyne) detection schemes.

Testing complementarity on a transmon quantum processor

We propose quantum circuits to test interferometric complementarity using symmetric two-way interferometers coupled to a which-path detector. First, we consider the two-qubit setup in which the controlled transfer of path information to the detector subsystem depletes interference on the probed subspace, testing the visibility-distinguishability tradeoff via minimum-error state discrimination measurements. Next, we consider the quantum eraser setup, in which reading out path information in the right basis recovers an interference pattern. These experiments are then carried out in an IBM superconducting transmon processor. A detailed analysis of the results is provided. Despite finding good agreement with theory at a coarse level, we also identify small but persistent systematic deviations preventing the observation of full particlelike and wavelike statistics. We understand them by carefully modeling two-qubit gates, showing that even small coherent errors in their implementation preclude the observation of Bohr's strong formulation of complementarity.

Visible Fourier transform absorption spectrum measurement method based on dual interferometer configuration

We introduce an absorption spectrum measurement method in the visible regime based on dual interferometer configuration. The proposed method can realize the measurement of the absorption spectrum by addition and calculation of the alternating current (AC) components of interferograms from dual symmetrical interferometers in one measurement, with no need to subtract twice-measured spectrum data with or without samples in the traditional single interferometer method, thus expanding the dynamic range of measurement, especially suitable for weak absorption. The absorption spectra of FB570-10 bandpass filter and NF533-17 notch filter measured by this method conform to the official data.

Parity-Protected Superconductor-Semiconductor Qubit.

Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parity-protected qubit based on voltage-controlled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energy-phase relation of few-channel junctions. A symmetric interferometer formed by two such junctions, gate-tuned into balance and frustrated by a half-quantum of applied flux, yields a cos(2φ) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate that relaxation of the qubit can be suppressed tenfold by tuning into the protected regime.

Features of correlation measurements of the parameters of pulsed hyperspectral optical fields using an asymmetric interferometer

Differences in correlation measurements of the parameters of pulsed hyperspectral optical fields using symmetric and asymmetric interferometers are considered. It is shown analytically that the resulting cross-correlation function is sensitive to phase perturbations in the original wave field. The considered setup, which contains a telescopic reflective 4f system of parabolic mirrors in one arm, demonstrates that in the case of an asymmetric interferometer, the presence of aberrations leads to degradation of the reconstructed image, whereas in the case of symmetric interferometers these aberrations do not affect the result.

Three-Path Atom Interferometry with Large Momentum Separation.

We demonstrate the scale up of a symmetric three-path contrast interferometer to large momentum separation. The observed phase stability at separation of 112 photon recoil momenta exceeds the performance of earlier free-space interferometers. In addition to the symmetric interferometer geometry and Bose-Einstein condensate source, the robust scalability of our approach relies on the suppression of undesired diffraction phases through a careful choice of atom optics parameters. The interferometer phase evolution is quadratic with number of recoils, reaching a rate as high as 7×10^{7} rad/s. We discuss the applicability of our method towards a new measurement of the fine-structure constant and a test of QED.

Thermal Drift of Optics in Separated-Beam Heterodyne Interferometers

Designs of next-generation interferometers tend to place most of their emphasis on periodic nonlinearities rather than on thermal drift of the optics, which can contribute more than the well-known periodic errors to the overall error. In this paper, a novel model for analyzing the mechanism of thermal drift in a separated-beam heterodyne interferometer (SBHI) is developed. To verify the proposed model, an SBHI with symmetric optical configuration is constructed, and an asymmetric SBHI is realized by inserting a glass plate into the measuring arm of the symmetric interferometer. Comparison tests are carried out between these two SBHIs. Experimental results show that the symmetric SBHI achieves a thermal stability of 1.2 nm/°C, and the thermal coefficient obtained from experiments, for the asymmetric SBHI, is close to the theoretical value calculated based on the proposed model.

Coherence recovery mechanisms of quantum Hall edge states

The work is motivated by the puzzling results of the recent experiment [S. Tewari et al., Phys. Rev. B 93, 035420 (2016)], where a robust coherence recovery from a certain energy was detected for an electron injected into the quantum Hall edge at the filling factor 2. After passing through a quantum dot the electron then tunnels into the edge with a subsequent propagation towards a symmetric Mach-Zender interferometer, after which the visibility of Aharonov-Bohm (AB) oscillations is measured. According to conventional understanding its decay with the increasing energy of the injected electron was expected, which was confirmed theoretically in the bosonization framework. Here we analyze why such a model fails to account for the coherence recovery and show that the reason is essentially the destructive interference of the two quasiparticles (charge and neutral modes) forming at the edge out of the incoming electron. This statement is robust with respect to the strength of Coulomb interaction. We firstly exploit the idea of introducing an imbalance between the quasiparticles, by creating different conditions of propagation for them. It can be done by taking into account either dispersion or dissipation, which indeed results in the partial coherence recovery. The idea of imbalance can also be realized by applying a periodic potential to the arms of interferometer. We discuss such an experiment, which might also shed light on the internal coherence of the two edge excitations. Another scenario relies on the lowering of the energy density of the electron wave packet by the time it arrives at the interferometer in presence of dissipation or dispersion. This energy density is defined by a certain parameter, which is completely independent of the injected energy, which naturally explains the emergence of a threshold energy in the experiment.

Highly thermal-stable heterodyne interferometer with minimized periodic nonlinearity.

Heterodyne interferometers suffer from thermal drift of optics (TDO), which may introduce error even up to several micrometers. In this paper, we propose a symmetric heterodyne interferometer with spatially separated beams, which realizes completely balanced optical paths between probe and reference beams and simultaneously avoids the optical mixing, and thereby is theoretically capable of eliminating TDO and the periodic nonlinearity (PNL). To validate the performance of the proposed interferometer, first a special experimental setup is constructed, with which the TDO test can be conducted in vacuum, and the result shows that a thermal coefficient of 1.2nm/°C is achieved. Next, the PNL of the proposed interferometer is measured by both the frequency domain method and the phase quadrature method, which demonstrates an undetectable PNL at a noise level of 13pm.

Generalized analysis of quantum noise and dynamic backaction in signal-recycled Michelson-type laser interferometers

We analyze the radiation pressure induced interaction of mirror motion and light fields in Michelson-type interferometers used for the detection of gravitational waves and for fundamental research in table-top quantum optomechanical experiments, focusing on the asymmetric regime with a (slightly) unbalanced beamsplitter and a (small) offset from the dark port. This regime, as it was shown recently, provides new interesting features, in particular a stable optical spring and optical cooling on cavity resonance. We show that generally the nature of optomechanical coupling in Michelson-type interferometers does not fit into the standard dispersive/dissipative dichotomy. In particular, a symmetric Michelson interferometer with signal-recycling but without power-recycling cavity is characterized by a purely dissipative optomechanical coupling; only in the presence of asymmetry, additional dispersive coupling arises. In gravitational waves detectors possessing signal- and power-recycling cavities, yet another, "coherent" type of optomechanical coupling takes place. We develop here a generalized framework for the analysis of asymmetric Michelson-type interferometers which also covers the possibility of the injection of carrier light into both ports of the interferometer. Using this framework, we analyze in depth the "anomalous" features of the Michelson-Sagnac interferometer which where discussed and observed experimentally in previous works [1-3].

Analyzing refractive index profiles of confined fluids by interferometry part II: Multilayer and asymmetric systems

Methods for determining the substrate properties and the optical thickness of thin films or any variation in the refractive index of a fluid or film near a surface for unknown 5-layer symmetric and 3-layer asymmetric interferometers are presented. Both systems can be fully resolved without any known layer properties and without contact or confining the films. The method was tested using realistic simulated interferometer data, and was found to consistently yield accurate values for all desired properties. The method was experimentally validated through analysis of an asymmetric three layer interferometer system of linear polyethyleneimine (LPEI) adsorbed onto mica substrates of differing thickness and identical refractive index. The results were in excellent agreement with the dry polymer film properties measured using conventional SFA contact measurements. More complicated systems were also evaluated for feasibility, and any additional parameter specifications required for analysis were determined. The utility of this method is broad, as a single experiment in a laboratory setting can independently provide non-contact film properties and the effects of confinement on the film structure, which can be correlated to a simultaneously measured interaction force profile.

Temperature Sensitivity of a Waveguide Young Interferometer

The temperature sensitivity of a waveguide Young interferometer is investigated experimentally and using numerical simulations. With different materials on the two arms of the interferometer, the output phase is linear with temperature, making the device suitable for on-chip temperature sensing. A symmetric interferometer with the same material on both arms is almost insensitive to hotspots and temperature steps applied to the bottom of the substrate, while it is still sensitive to the asymmetric heating of the top surface. For biological or chemical sensing, it must be assured that any heating of the top surface, e.g. from liquid or gas flow, is symmetric with respect to the interferometer, both for asymmetric and symmetric devices. For a 20mm long device, the difference in temperature between the two arms must be limited to a few millikelvin in order not to influence the performance of the device.

Double Bragg Interferometry.

We employ light-induced double Bragg diffraction of delta-kick collimated Bose-Einstein condensates to create three symmetric Mach-Zehnder interferometers. They rely on (i)first-order, (ii)two successive first-order, and (iii) second-order processes which demonstrate the scalability of the corresponding momentum transfer. With respect to devices based on conventional Bragg scattering, these symmetric interferometers double the scale factor and feature a better suppression of noise and systematic uncertainties intrinsic to the diffraction process. Moreover, we utilize these interferometers as tiltmeters for monitoring their inclination with respect to gravity.

Quantum test of the equivalence principle and space-time aboard the International Space Station

We describe the Quantum Test of the Equivalence principle and Space Time (QTEST), a concept for an atom interferometry mission on the International Space Station (ISS). The primary science objective of the mission is a test of Einstein’s equivalence principle with two rubidium isotope gases at a precision of better than 10−15, a 100-fold improvement over the current limit on equivalence principle violations, and over 1,000,000 fold improvement over similar quantum experiments demonstrated in laboratories. Distinct from the classical tests is the use of quantum wave packets and their expected large spatial separation in the QTEST experiment. This dual species atom interferometer experiment will also be sensitive to time-dependent equivalence principle violations that would be signatures for ultralight dark-matter particles. In addition, QTEST will be able to perform photon recoil measurements to better than 10−11 precision. This improves upon terrestrial experiments by a factor of 100, enabling an accurate test of the standard model of particle physics and contributing to mass measurement, in the proposed new international system of units (SI), with significantly improved precision. The predicted high measurement precision of QTEST comes from the microgravity environment on ISS, offering extended free fall times in a well-controlled environment. QTEST plans to use high-flux, dual-species atom sources, and advanced cooling schemes, for N > 106 non-condensed atoms of each species at temperatures below 1 nK. Suppression of systematic errors by use of symmetric interferometer configurations and rejection of common-mode errors drives the QTEST design. It uses Bragg interferometry with a single laser beam at the ‘magic’ wavelength, where the two isotopes have the same polarizability, for mitigating sensitivities to vibrations and laser noise, imaging detection for correcting cloud initial conditions and maintaining contrast, modulation of the atomic hyperfine states for reduced sensitivity to magnetic field gradients, two source-regions for simultaneous time reversal measurements and redundancy, and modulation of the gravity vector using a rotating platform to reduce otherwise difficult systematics to below 10−16.

Generation of photon-number squeezed states with a fiber-optic symmetric interferometer.

We numerically and experimentally demonstrate photon-number squeezed state generation with a symmetric fiber interferometer in an 800-nm wavelength and compared with an asymmetric fiber interferometer, although photon-number squeezed pulses have been generated only with asymmetric interferometers. Even though we obtain -1.0dB squeezing with an asymmetric fiber interferometer, since perfect spectral phase and intensity matching between displacement and signal pulses are achieved with a symmetric fiber interferometer, we obtain better squeezing of -3.1dB. We also numerically calculate and clarify this scheme's usefulness at a 1.55-μm wavelength.

Composite-light-pulse technique for high-precision atom interferometry.

We realize beam splitters and mirrors for atom waves by employing a sequence of light pulses rather than individual ones. In this way we can tailor atom interferometers with improved sensitivity and accuracy. We demonstrate our method of composite pulses by creating a symmetric matter-wave interferometer which combines the advantages of conventional Bragg- and Raman-type concepts. This feature leads to an interferometer with a high immunity to technical noise allowing us to devise a large-area Sagnac gyroscope yielding a phase shift of 6.5 rad due to the Earth's rotation. With this device we achieve a rotation rate precision of 120 nrad s(-1) Hz(-1/2) and determine the Earth's rotation rate with a relative uncertainty of 1.2%.

Generation of second-order vortex arrays with six-pinhole interferometers under plane wave illumination

We propose a method based on six-pinhole interferometers to generate vortex arrays with topological charge 2, only with plane wave illumination. The six-pinhole interferometer is composed of two concentric symmetrical three-pinhole interferometers with different radial distances of the pinholes and a relative rotation of 60 deg from each other. In the Fourier domain, the vortices with second-order topological charge are generated when the radial distances of the two three-pinhole interferometers satisfy some certain ratios. Due to the symmetry of the six-pinhole interferometer, such vortices are distributed at the vertices of some symmetrically distributed regular hexagons. The experimental results obtained in a focal-to-focal system show satisfactory coincidence with the calculations.

Double Bragg diffraction: A tool for atom optics

The use of retro-reflection in light-pulse atom interferometry under microgravity conditions naturally leads to a double-diffraction scheme. The two pairs of counterpropagating beams induce simultaneously transitions with opposite momentum transfer that, when acting on atoms initially at rest, give rise to symmetric interferometer configurations where the total momentum transfer is automatically doubled and where a number of noise sources and systematic effects cancel out. Here we extend earlier implementations for Raman transitions to the case of Bragg diffraction. In contrast with the single-diffraction case, the existence of additional off-resonant transitions between resonantly connected states precludes the use of the adiabatic elimination technique. Nevertheless, we have been able to obtain analytic results even beyond the deep Bragg regime by employing the so-called "method of averaging," which can be applied to more general situations of this kind. Our results have been validated by comparison to numerical solutions of the basic equations describing the double-diffraction process.

State-labeling Wannier-Stark atomic interferometers

Using cold 87Rb atoms trapped in a 1D-optical lattice, atomic interferometers involving coherent superpositions between different Wannier-Stark atomic states are realized. Two di fferent kinds of trapped interferometer schemes are presented: a Ramsey-type interferometer sensitive both to clock frequency and external forces, and a symmetric accordion-type interferometer, sensitive to external forces only. We evaluate the limits in terms of sensitivity and accuracy of those schemes and discuss their application as force sensors. As a first step, we apply these interferometers to the measurement of the Bloch frequency and the demonstration of a compact gravimeter.