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DOE OSTI2023

A New Plasma Radar Concept for Simultaneous Magnetic and Density Measurements

An innovative, compact 288GHz interferometer has been fabricated, tested, installed and successfully demonstrated on the LAPD-U magnetized plasma at UCLA. The system takes advantage of frequency modulated (FM) radar techniques to deliver a compact heterodyne system. In addition, the reflected power from the source is taken advantage of to eliminate the need for additional quasi-optical components. Electron density in LAPD-U plasma has recently been increased substantially thereby requiring a higher frequency/shorter wavelength interferometer to avoid deleterious refractive effects. This system satisfies those needs. The system uses a 96GHz varactor tuned Gunn oscillator which passes to a passive tripler. This tripler has ~3% conversion efficiency. The 288GHz radiation is then coupled to free space using a so-called dual-mode or Pickett horn. The output 288GHz beam is then coupled to an aspheric lens manufactured from low-loss, high-density polyethylene. This lens is employed to collimate the emerging beam. Small axial adjustment of the lens position can also be used to create a slowly focusing beam so as to optimize the measured signal. In addition, up-down or side-to-side adjustment of the lens can be utilized to steer the beam vertically or horizontally – again to optimize alignment. The propagating beam passes through a beam splitter and then through a water-free, bubble-free fused quartz window into the LAPD-U vacuum vessel. The beam-splitter is a thin sheet of G10 which reflects a small fraction of the incident power (~5 %) towards a zero-bias detector optimized for the frequency range from 220 to 300GHz. Note that waveguides at this frequency have dimensions of ~0.9mm x 0.45mm and so have very large conductive losses. This drives the use of quasi-optical propagation. The detector requires no DC bias and is very responsive (> 1V/mW into 1MΩ). Radiation is coupled to the detector via a similar lens-horn arrangement used for the launch. This reflected beam acts as the local oscillator or reference millimeter-wave beam for the detector. The remainder of the launched source beam then enters the LAPD-U vacuum vessel and passes through the plasma at the mid-plane until reaching the opposing port which is closed off with an aluminum flange. This flange is used as a mirror to retroreflect the incident 288GHz beam back along its path. The retroreflected beam exits the input port but does NOT couple directly into the zero-bias detector. Instead, the majority of the return power continues towards the 288GHz source. As mentioned above the transmitted beam enters the source a second time. This would appear undesirable. However, at these frequencies multipliers are highly non-linear elements which results in a significant portion of the return beam (~20%) re-emerging from the multiplier and horn and then coupling via the G10 beam-splitter to the zero-bias detector. This approach eliminated the need for a second quasi-optical beam-splitter. The system is extremely compact measuring approximately 28 inches x 20 inches. The above did not explain how heterodyne operation was achieved. As mentioned above the Gunn oscillator is able to be varactor tuned. This allows a low voltage to be applied to control the operating frequency of the Gunn oscillator. During heterodyne operation a sawtooth shaped voltage is applied to the varactor at 750kHz using an 80MHz Arbitrary Waveform Generator (AWG). This voltage changes the Gunn frequency linearly during the up-sweep which is then reset abruptly at the sawtooth crash to be immediately followed by another linear sweep. Passage through the 288GHz multiplier triples the frequency change experienced by the electromagnetic wave. These frequency changes are small – tens of megahertz. This FM radar approach results in the launched electromagnetic wave frequencies at the detector for the reference and plasma wave to be different. The approximately 10 ns delay propagation delay for the plasma beam results in the local oscillator and plasma beams NOT having an identical frequency – there is in fact a fixed difference frequency. The frequency tuning level of the Gunn oscillator is then adjusted so that there is ONE cycle of this difference frequency during each linear ramp. During the sawtooth crash or downward re-sweep this one cycle replays in reverse but on a very fast timescale. The process then repeats. Low-pass filtering eliminates the fast re-sweep to leave a pure sine wave heterodyne signal. When the plasma is present it introduces a phase delay in the sine wave (caused by the extremely small Doppler shift resulting from the optical path length change). Of course, to measure this phase change we need a reference. This is simply obtained from an arbitrary waveform generator which provides a synchronized output pulse train which again is low pass filtered to obtain a 750kHz sinusoidal voltage reference for the interferometer. The interferometer was installed on LAPD-U where it has worked reliably and has established that electron densities exceeding 1x10 13 cm -3 are routinely achieved. In addition, the system sensitivity was able to easily observe density fluctuation at frequencies up to 50kHz. FM Radar techniques have enabled a full demonstration of a compact, sensitive, high frequency (288GHz/1mm) heterodyne interferometer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1986

Feasibility study of optical boundary layer transition detection method

A high sensitivity differential interferometer was developed to locate the region where the boundary layer flow undergoes transition from laminar to turbulent. Two laboratory experimental configurations were used to evaluate the performance of the interferometer: open shear layer, and low speed wind tunnel turbulent spot configuration. In each experiment, small temperature fluctuations were introduced as the signal source. Simultaneous cold wire measurements were compared with the interferometer data. The comparison shows that the interferometer is sensitive to very weak phase variations in the order of 0.001 the laser wavelength. An attempt to detect boundary layer transition over a flat plate at NASA-Langley Unitary Supersonic Wind Tunnel using the interferometer system was performed. The phase variations during boundary layer transition in the supersonic wind tunnel were beyond the minimum signal-to-noise level of the instrument.

Azzazy, M.↗

NASA NTRS1990

Amplitude and intensity spatial interferometry; Proceedings of the Meeting, Tucson, AZ, Feb. 14-16, 1990

Attention is given to such topics as ground interferometers, space interferometers, speckle-based and interferometry-based astronomical observations, adaptive and atmospheric optics, speckle techniques, and instrumentation. Particular papers are presented concerning recent progress on the IR Michelson array; the IOTA interferometer project; a space interferometer concept for the detection of extrasolar earth-like planets; IR speckle imaging at Palomar; optical diameters of stars measured with the Mt. Wilson Mark III interferometer; the IR array camera for interferometry with the cophased Multiple Mirror Telescope; optimization techniques appliesd to the bispectrum of one-dimensional IR astronomical speckle data; and adaptive optical iamging for extended objects.

Breckinridge, Jim B.↗

NASA NTRS1991

Dual frequency along-track interferometry

In recent months, the JPL Airborne Synthetic Aperture Radar (AIRSAR) System has had a C-band Along-Track Interferometer installed. This, in addition to the L-band interferometer already operating in the system, makes it possible to simultaneously acquire two frequency interferometer data. Also, another upgrade involving the radar digital system allows each interferometer to be operated in such a way as to obtain two along-track interferometric baselines differing by a factor of 2 in length. An engineering checkout flight has demonstrated the ability to acquire and process both frequencies to high-resolution velocity maps of the ocean surface. The status of these interferometers and some initial data are presented.

Carande, R. E.↗

NASA NTRS1991

A real time interferometry system for unsteady flow measurements

A simple real-time interferometer system was developed for use in dynamic stall and other unsteady flow research at compressible flow speeds. A conventional schlieren system was modified to operate as a point diffraction interferometer. The implementation of this interferometer is discussed, and results of trials with different point diffractors are presented in this paper. The performance of the interferometer under various flow conditions was investigated. Results are presented which show the effects of the interferometer parameters such as pinhole size and pinhole-plate optical density on the performance of the system.

Brock, N. J.↗

NASA NTRS1993

Remote sounding of tropospheric minor constituents

The etalon interferometer, or Fabry-Perot interferometer (FPI), with its high throughput and high spectral resolution was widely used in the remote-sensing measurements of the earth's atmospheric composition, winds, and temperatures. The most recent satellite instruments include the Fabry-Perot interferometer flown on the Dynamics Explorer-2 (DE-2) and the High Resolution Doppler Imager (HRDI) to be flown on the Upper Atmosphere Research Satellite (UARS). These instruments measure the Doppler line profiles of the emission and absorption of certain atmospheric species (such as atomic oxygen) in the visible spectral region. The successful space flight of DE-FPI and the test and delivery of UARS-HRDI demonstrated the extremely high spectral resolution and ruggedness of the etalon system for the remote sensing of earth and planetary atmospheres. Recently, an innovative FPI focal plane detection technique called the Circle-to-Line Interferometer Optical (CLIO) system was invented at the Space Physics Research Laboratory (SPRL). The CLIO simplifies the FPI focal plane detection process by converting the circular rings or fringes into a linear pattern similar to that produced by a conventional spectrometer, while retaining the throughput advantage of the etalon interferometer. CLIO makes the use of linear array detectors more practical and efficient with FPI, the combination of FPI and CLIO represents a very promising new technique for the remote sensing of the lower atmospheres of Earth, Mars, Venus, Neptune, and other planets. The Multiorder Etalon Spectrometer (MOES), as a combination of the rugged etalon and the CLIO, compares very favorably to other spaceborne optical instruments in terms of performance versus complexity. The feasibility of an advanced etalon spectrometer for the remote sensing of tropospheric trace species, particularly carbon monoxide (CO), nitrous oxide (N2O), and methane (CH4) was discussed. The etalon atmospheric spectroscopy techniques are described, instrument design and related technical issues are discussed. The primary objective is to establish the concept of atmospheric spectroscopy with the CLIO and etalon system and its applications for the measurements of tropospheric trace species analyze system requirements and performance, determine the feasibility of components and subsystem implementation with available technology, and develop inversion algorithm for retrieval simulation and data analysis.

Drayson, S. Roland↗

NASA NTRS1993

Multiorder etalon sounder (MOES) development and test for balloon experiment

The Fabry-Perot interferometer (FPI), with its high throughput and high spectral resolution has been used in the remote-sensing measurements of the earth's atmospheric composition, winds, and temperatures. The most recent satellite instruments include the Fabry-Perot interferometer flown on the Dynamics Explorer-2 (DE-2), the High Resolution Doppler Imager (HRDI), and the Cryogenic Limb Array Etalon Spectrometer (CLAES) flown on the Upper Atmosphere Research Satellite (UARS). These instruments measure the Doppler line profiles of the emission and absorption of certain atmospheric species (such as atomic oxygen) in the visible and infrared spectral region. The successful space flight of DE-FPI, HRDI, and CLAES on UARS demonstrated the extremely high spectral resolution and ruggedness of the etalon system for the remote sensing of earth and planetary atmospheres. Recently, an innovative FPI focal plane detection technique called the Circle-to-Line Interferometer Optical (CLIO) system was invented at the Space Physics Research Laboratory. The CLIO simplifies the FPI focal plane detection process by converting the circular rings or fringes into a linear pattern similar to that produced by a conventional spectrometer, while retaining the throughput advantage of the etalon interferometer. The combination of FPI and CLIO allows the development of more sensitive Fabry-Perot interferometers in the infrared for the remote sensing of the lower atmospheres of Earth and possibly other planets. The Multiorder Etalon Sounder (MOES), a combination of the rugged etalon and the CLIO, compares very favorably to other space-borne optical instruments in terms of performance versus complexity. The new instrument is expected to be rugged, compact, and very suitable for an operational temperature and moisture sounder. With this technique, the contamination of radiance measurements by emissions of other gases is also minimized. At the Space Physics Research Laboratory (SPRL), the MOES concept and laboratory experiments were worked on for the past several years. Both theoretical studies and laboratory prototype experiments showed that MOES is very competitive compared with other high resolution sounders in terms of complexity and performance and has great potential as a compact and rugged high resolution atmospheric temperature and trace species sounder from the polar platform or the geostationary platform. The logical next step is to convert our laboratory prototype to a balloon instrument, so that field test of MOES can be carried out to prove the feasibility and capability of this new technology. Some of the activities related to the development of MOES for a possible balloon flight demonstration are described. Those research activities include the imaging quality study on the CLIO, the design and construction of a MOES laboratory prototype, the test and calibration of the MOES prototype, and the design of the balloon flight gondola.

Hays, Paul B.↗

NASA NTRS1977

Measurement of the Specific Refractivities of CF4 and C2F6

In order to relate the measured fringe shift of an interferometer to density, the relation between density rho and refractive index n must be known. For gases where the refractive index is close to unity, this relation between density and refractive index is very closely approximated by (n - 1) = K rho where K is the specific refractivity, or the Gladstone-Dale constant. The specific refractivity, which is weakly dependent on wavelength and temperature, is readily available for a number of common test gases such as N2 and air. For more unique test gases such as CF4 and C2F6 for which refractive index data at optical wavelengths is not readily available, the constants can be estimated from the atomic refractivities of carbon and fluorine. In order to verify this estimation, a two-beam interferometer was used to experimentally determine the specific refractivities of CF4 and C2F6. This data was required for holographic interferometric measurements made at the Langley Hypersonic CF4 Tunnel. A Twyman-Green interferometer with a He-Ne laser light source of vacuum wavelength lambda equal to 633 nm was used to measure the constants. One beam of the two-beam interferometer passed through an optical cell of known inside length l which could be evacuated and slowly filled with the test gas to a density of 7.2 kg/cu m for CF4 or 5.7 kg/cu m for C2F6. If the refractive index (and hence density) is constant along the optical path through the cell, the fringe shift M and density change Delta rho are related M = 2Kl Delta rho/lambda for the double pass interferometer. Thus K can be determined by measuring the fringe shift as the density is changed. The output of a photodiode used to detect the fringe shift was recorded on a strip chart recorder. The rate of pressure increase of the test gas in the cell was controlled such that the fringes shifted at a rate of 0.5 to 1 fringe per sec. The pressure in the test cell was measured with a high accuracy quartz crystal pressure transducer and recorded approximately every 20 fringe peaks. The temperature of the cell was measured with a thermocouple and recorded at the start, midpoint, and end of each test.

Burner, A. W.↗

NASA NTRS2006

Optical Interferometry Motivation and History

A history and motivation of stellar interferometry is presented. The topics include: 1) On Tides, Organ Pipes, and Soap Bubbles; 2) Armand Hippolyte Fizeau (1819-1896); 3) Fizeau Suggests Stellar Interferometry 1867; 4) Edouard Stephan (1837-1923); 5) Foucault Refractor; 6) Albert A. Michelson (1852-1931); 7) On the Application of Interference Methods to Astronomy (1890); 8) Moons of Jupiter (1891); 9) Other Applications in 19th Century; 10) Timeline of Interferometry to 1938; 11) 30 years goes by; 12) Mount Wilson Observatory; 13) Michelson's 20 ft Interferometer; 14) Was Michelson Influenced by Fizeau? 15) Work Continues in the 1920s and 30s; 16) 50 ft Interferometer (1931-1938); 17) Light Paths in the 50 ft Interferometer; 18) Ground-level at the 50 ft; 19) F.G. Pease (1881-1938); 20) Timeline of Optical Interferometry to 1970; 21) A New Type of Stellar Interferometer (1956); 22) Intensity Interferometer (1963- 1976; 23) Robert Hanbury Brown; 24) Interest in Optical Interferometry in the 1960s; 25) Interferometry in the Early 1970s; and 26) A New Frontier is Opened up in 1974.

history↗

NASA NTRS2005

Fiber-Optic Sensor Would Monitor Growth of Polymer Film

A proposed optoelectronic sensor system would measure the increase in thickness of a film of parylene (a thermoplastic polymer made from para-xylene) during growth of the film in a vapor deposition process. By enabling real-time monitoring of film thickness, the system would make it possible to identify process conditions favorable for growth and to tailor the final thickness of the film with greater precision than is now possible. The heart of the sensor would be a pair of fiber-optic Fabry-Perot interferometers, depicted schematically in the figure. (In principle, a single such interferometer would suffice. The proposal calls for the use of two interferometers for protective redundancy and increased accuracy.) Each interferometer would include a light source, a fiber-optic coupler, and photodetectors in a control box outside the deposition chamber. A single-mode optical fiber for each interferometer would run from inside the control box to a fused-silica faceplate in a sensor head. The sensory tips of the optical fibers would be polished flush with the free surface of the faceplate. In preparation for use, the sensor head would be mounted with a hermetic seal in a feed-through port in the deposition chamber, such that free face of the faceplate and the sensory tips of the optical fibers would be exposed to the deposition environment. During operation, light would travel along each optical fiber from the control box to the sensor head. A small portion of the light would be reflected toward the control box from the end face of each fiber. Once growth of the parylene film started, a small portion of the light would also be reflected toward the control box from the outer surface of the film. In the control box, the two reflected portions of the light beam would interfere in one of the photodetectors. The difference between the phases of the interfering reflected portions of the light beam would vary in proportion to the increasing thickness of the film and the known index of refraction of the film, causing the photodetector reading to vary in proportion to a known sinusoidal function of film thickness. Electronic means of monitoring this variation and the corresponding variation in phase and thickness are well established in the art of interferometry. Hence, by tracking the cumulative change in phase difference from the beginning of deposition, one could track the growing thickness of the film to within a small fraction of a wavelength of light.

Beamesderfer, Michael↗

NASA NTRS2004

Aligning Arrays of Lenses and Single-Mode Optical Fibers

A procedure now under development is intended to enable the precise alignment of sheet arrays of microscopic lenses with the end faces of a coherent bundle of as many as 1,000 single-mode optical fibers packed closely in a regular array (see Figure 1). In the original application that prompted this development, the precise assembly of lenses and optical fibers serves as a single-mode spatial filter for a visible-light nulling interferometer. The precision of alignment must be sufficient to limit any remaining wavefront error to a root-mean-square value of less than 1/10 of a wavelength of light. This wavefront-error limit translates to requirements to (1) ensure uniformity of both the lens and fiber arrays, (2) ensure that the lateral distance from the central axis of each lens and the corresponding optical fiber is no more than a fraction of a micron, (3) angularly align the lens-sheet planes and the fiber-bundle end faces to within a few arc seconds, and (4) axially align the lenses and the fiber-bundle end faces to within tens of microns of the focal distance. Figure 2 depicts the apparatus used in the alignment procedure. The beam of light from a Zygo (or equivalent) interferometer is first compressed by a ratio of 20:1 so that upon its return to the interferometer, the beam will be magnified enough to enable measurement of wavefront quality. The apparatus includes relay lenses that enable imaging of the arrays of microscopic lenses in a charge-coupled-device (CCD) camera that is part of the interferometer. One of the arrays of microscopic lenses is mounted on a 6-axis stage, in proximity to the front face of the bundle of optical fibers. The bundle is mounted on a separate stage. A mirror is attached to the back face of the bundle of optical fibers for retroreflection of light. When a microscopic lens and a fiber are aligned with each other, the affected portion of the light is reflected back by the mirror, recollimated by the microscopic lens, transmitted through the relay lenses and the beam compressor/expander, then split so that half goes to a detector and half to the interferometer. The output of the detector is used as a feedback control signal for the six-axis stage to effect alignment.

Liu, Duncan↗

NASA NTRS2016

Characterization of the JWST Pathfinder Mirror Dynamics Using the Center of Curvature Optical Assembly (CoCOA)

The JWST (James Webb Space Telescope) Optical Telescope Element (OTE) consists of a 6.6 meter clear aperture, 18-segment primary mirror, all-reflective, three-mirror anastigmat operating at cryogenic temperatures. To verify performance of the primary mirror, a full aperture center of curvature optical null test is performed under cryogenic conditions in Chamber A at NASA Johnson Space Center using an instantaneous phase measuring interferometer. After phasing the mirrors during the JWST Pathfinder testing, the interferometer is utilized to characterize the mirror relative piston and tilt dynamics under different facility configurations. The correlation between the motions seen on detectors at the focal plane and the interferometer validates the use of the interferometer for dynamic investigations. The success of planned test hardware improvements will be characterized by the multi-wavelength interferometer (MWIF) at the Center of Curvature Optical Assembly (CoCOA).

Wells, Conrad↗

NASA NTRS2016

Characterization of the JWST Pathfinder Mirror Dynamics Using the Center of Curvature Optical Assembly (CoCOA)

Wells, C.↗

NASA NTRS2004

White light modeling, algorithm development, and validation on the micro-arcsecond metrology testbed

The Space Interferometry Mission (SIM), scheduled for launch in early 2010, is an optical interferometer that will perform narrow angle and global wide angle astrometry with unprecedented accuracy, providing differential position accuracies of 1uas, and 4uas global accuracies in position, proper motion and parallax. SIM astrometric measurements are synthesized from pathlength delay measurements provided by three Michelson-type, white light interferometers. Two of the interferometers are used for making precise measurements of variations in the spacecraft attitude, while the third interferometer performs the science measurement. The ultimate performance of SIM relies on a combination of precise fringe measurements of the interfered starlight with picometer class relative distance measurements made between a set of fiducials that define the interferometer baseline vectors. The focus of the present paper is on the development and analysis of algorithms for accurate white light fringe estimation, and on the preliminary validation of these algorithms on the Micro-Arcsecond Testbed (MAM).

Shen, Janice TsaePyng↗

DOE OSTI2014

Talbot-Lau X-ray Phase-Contrast Research at Johns Hopkins

The Talbot-Lau (T-L) grating interferometer enables X-ray differential phase-contrast (DPC) imaging with low coherence conventional X-ray tubes, being thus attractive for medical and other applications. We studied several variations of the conventional T-L interferometer design. First, to extend the T-L method to high X-ray energy we developed a symmetric interferometer having gratings inclined at a glancing angle (GAI). This simple setup enables achieving high fringe contrast up to 80 kVp or more. The high GAI contrast in turn enabled demonstrating for the first time DPC-CT of soft tissues with clinically compatible X-ray dose and energy. Industrial and security applications of the GAI appear also possible. Further on, we studied high magnification T-L interferometry for electron density diagnostic in high energy density plasmas. High magnification refraction radiography with laser driven backlighters can help understand inertial confinement fusion experiments for instance. For plasma diagnostic using a single radiographic image we develop Moiré fringe deflectometry. We also extended the T-L method below 10 keV using membrane and free standing gratings. Lastly, we explored using grazing incidence micro-periodic mirrors instead of gratings in the T-L interferometers. These enable in principle achieving very small interferometer periods over a broad energy range, at the price of a narrow field of view in one dimension. The possibility of using these designs for DPC imaging of materials under extreme conditions will also be examined.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2014

Digital holographic interferometry: A novel optical calorimetry technique for radiation dosimetry

Purpose: To develop and demonstrate the proof-of-principle of a novel optical calorimetry method to determine radiation absorbed dose in a transparent medium. Methods: The calorimetric property of water is measured during irradiation by means of an interferometer, which detects temperature-induced changes in the refractive index that can be mathematically related to absorbed dose. The proposed method uses a technique called digital holographic interferometry (DHI), which comprises an optical laser interferometer setup and consecutive physical reconstruction of the recorded wave fronts by means of the Fresnel transform. This paper describes the conceptual framework and provides the mathematical basis for DHI dosimetry. Dose distributions from a high dose rate Brachytherapy source were measured by a prototype optical setup to demonstrate the feasibility of the approach. Results: The developed DHI dosimeter successfully determined absorbed dose distributions in water in the region adjacent to a high dose rate Brachytherapy source. A temperature change of 0.0381 K across a distance of 6.8 mm near the source was measured, corresponding to a dose of 159.3 Gy. The standard deviation in a typical measurement set was ±3.45 Gy (corresponding to an uncertainty in the temperature value of ±8.3 × 10{sup −4} K). The relative dose fall off was in agreement with treatment planning system modeled data. Conclusions: First results with a prototype optical setup and a Brachytherapy source demonstrate the proof-of-principle of the approach. The prototype achieves high spatial resolution of approximately 3 × 10{sup −5} m. The general approach is fundamentally independent of the radiation type and energy. The sensitivity range determined indicates that the method is predominantly suitable for high dose rate applications. Further work is required to determine absolute dose in all three dimensions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2020

Interference in between the acts of pre- and postselection

As an alternative approach for measuring the weak effects associated with the artificial preparation of rare events in quantum metrology, we propose the study of the interference pattern generated by acts of pre- and postselection of a quantum system. An example of two Mach – Zehnder interferometers connected by a cross-Kerr nonlinearity is considered. Postselection of photon states at the output of one of the interferometers and the application of a controlled phase shift in one of its arms induces interference phenomena in the photodetection statistics at the output of the second interferometer. The nonlinearity parameter determines the shift and width of the structures in the interference pattern. The main features of this pattern are studied depending on the magnitude of the Kerr nonlinearity and the number of photons at the input of the interferometers. (paper)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2011

Dynamical phase interferometry of cold atoms in optical lattices

We study the propagation of cold-atom wave packets in an interferometer with a Mach-Zehnder topology based on the dynamical phase of Bloch oscillation in a weakly forced optical lattice with a narrow potential barrier that functions as a cold-atom wave-packet splitter. We calculate analytically the atomic wave function, and show that the expected number of atoms in the two outputs of the interferometer oscillates rapidly as a function of the angle between the potential barrier and the forcing direction with period proportional to the external potential difference across a lattice spacing divided by the lattice band energy scale. The interferometer can be used as a high-precision force probe whose principle of operation is different from current interferometers based on the overall position of Bloch oscillating wave packets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗