Abstract: An optical module of an atomic oscillator using a quantum interference effect includes a light source to generate first light including a fundamental wave having a center wavelength, and including a first sideband wave and a second sideband wave having wavelengths that are different from each other, a wavelength selection unit that emits second light by selecting the first sideband wave and the second sideband wave of the first light and by allowing them to pass through, a gas cell in which an alkali metal gas is sealed and to which the second light is irradiated, and a light detection unit that detects an intensity of the second light passing through the gas cell.

Abstract: Oscillators and methods of operating the same, the oscillators include a pinned layer having a fixed magnetization direction, a first free layer over the pinned layer, and a second free layer over the first free layer. The oscillators are configured to generate a signal using precession of a magnetic moment of at least one of the first and second free layers.

Abstract: Some demonstrative embodiments include devices, systems and/or methods of generating a frequency reference using a solid-state atomic resonator formed by a solid-state material including an optical cavity having color centers. A device may include a solid-state atomic clock to generate a clock frequency signal, the solid-state atomic dock including a solid state atomic resonator formed by a solid-state material including an optical cavity having color centers, which are capable of exhibiting hyperfine transition, wherein the solid-state atomic clock may generate the clock frequency signal based on a hyperfine resonance frequency of the color centers.

Abstract: An atomic oscillator using an electromagnetically induced transparency phenomenon caused by irradiation of a resonant light pair to an alkali metal atom, includes: a light source that generates a first light having a center frequency f1 and a plurality of frequency components different from each other in frequency by ?f, and a second light having a center frequency f2 and a plurality of frequency components different from each other in frequency by ?f; a light detection unit that detects intensities of lights including the first light and the second light passing through the alkali metal atom; and a control unit that controls, based on a detection result of the light detection unit, to cause a frequency difference between a specified frequency component of the first light and a specified frequency component of the second light to be equal to a frequency corresponding to an energy difference between two ground levels of the alkali metal atom, wherein a frequency difference between the center frequency f1 of th

Abstract: A solid state atomic clock may utilize quantum states capable of exhibiting a hyperfine resonance in order to generate a frequency standard. A device capable of coupling a free running oscillator to the hyperfine resonance frequency in order to generated output signal is described herein. In some aspect of the invention, the atomic clock may be fabricated on a silicon substrate and it may be integrated, in chip scale, as part of an electronic integrated circuit. The principal of operation, the method of making and system which utilized a solid state atomic clock are also disclosed.

Abstract: A quantum interference device causing electromagnetically induced transparency in an alkali metal atom includes: a light source generating first and second resonant lights with frequency differences ??; a magnetic field generator applying a magnetic field to the atom; a light detector detecting intensities of the first and second resonant lights passing through the atom; and a controller causing a frequency difference between specified first and second resonant lights to equal a frequency difference corresponding to an energy difference between two ground levels of the atom based on the detected light. The controller causes the frequency ?? or magnetic field intensity to satisfy 2×?×n=?? or ??×n=2×?. The frequency ? corresponds to an energy difference between two Zeeman split levels differentiated by one magnetic quantum number and generated in the two ground levels of the atom by energy splitting.

Abstract: The present invention relates to an atomic frequency acquisition device comprising a gas cell (400) filled with an atomic gas, a laser light source (100) emitting a laser beam which enters the gas cell (40) and excites a first energy transition of the atomic gas, a local oscillator (700) for generating an oscillator frequency in a frequency range including a frequency of a HFS transition of the atomic gas, and a modulator (600) modulating the laser light source (100) so as to emit laser radiation modulated with the oscillator frequency. An optical reflector (500) is arranged behind the gas cell (400) to reflect the laser beam after passage through the atomic gas so as to re-enter the laser cavity. A photodetector (200) detects beat frequencies caused by self-mixing interference within the laser cavity.

Abstract: A system is disclosed for charging a compact vapor cell, including placing an alkali-filled capillary into a reservoir cell formed in a substrate, the reservoir cell in vapor communication with an interrogation cell in the substrate and bonding a transparent window to the substrate on a common face of the reservoir cell and the interrogation cell to form a compact vapor cell. Capillary action in the capillary delays migration of alkali in the alkali-filled capillary from the reservoir cell into the interrogation cell during the bonding.

Abstract: A method of controlling an atomic oscillator includes generating a resonant light pair in response to a center frequency signal and a sideband signal, and setting the sideband signal so that an electromagnetically induced transparency (EIT) phenomenon does not occur in a gas cell of the atomic oscillator. The method includes applying the resonant light pair to the gas cell and detecting an intensity level of light transmitted through the gas cell. While the sideband signal is set so that the EIT phenomenon is not occurring, the center frequency signal is varied until a minimum value of the intensity level is identified. A first frequency is calculated by subtracting a predetermined frequency offset from the center frequency at which the intensity level was equal to the minimum value. A center frequency of the resonant light pair is set to the first frequency for operation of the atomic oscillator.

Abstract: An atomic oscillator, attention is paid to the fact that the degree of change of the energy difference between the two ground levels of the alkali metal atom with respect to the change of the magnetic field intensity is specific to each of the magnetic quantum numbers, a resonant light pair to cause a transition between the two ground levels corresponding to each of the plural magnetic quantum numbers is sequentially generated, plural pieces of profile information capable of specifying the energy difference between the two ground levels corresponding to each of the magnetic quantum numbers are sequentially acquired based on the detection signal, the change amount of the magnetic field intensity is specified based on the acquired plural pieces of profile information, and the control is performed so that the intensity of the magnetic field becomes constant.

Abstract: A method to construct a chip-scale atomic clock is provided. The method comprises providing a scaffolding for components in a chip-scale atomic clock. The components include a laser and at least one other component. The method also includes operationally positioning the components on the scaffolding so that an emitting surface of the laser is non-parallel to partially reflective surfaces of the at least one other component.

Abstract: A quantum interference device includes: gaseous alkali metal atoms; and a light source for causing a resonant light pair having different frequencies that keep a frequency difference equivalent to an energy difference between two ground states of the alkali metal atoms, the quantum interference device causing the alkali metal atoms and the resonant light pair to interact each other to cause an electromagnetically induced transparency phenomenon (EIT), wherein there are a plurality of the resonant light pairs, and center frequencies of the respective resonant light pairs are different from one another.

Abstract: One embodiment of the invention includes a magneto-optical trap (MOT) housing substantially surrounding atoms in an atom trapping region. The housing includes a first end that is substantially open to receive light that is substantially collimated and a second end opposite the first end that includes an aperture that emits a cold atom beam from the atom trapping region. The housing also includes a housing section surrounding and extending along a substantially central axis having a substantially reflective interior peripheral surface that reflects the light to generate an optical force on the atoms. The housing further includes an optical mask located substantially at the first end and along the substantially central axis that is configured to occlude the atom trapping region from the light to substantially prevent direct illumination of the atoms by unreflected light.

Abstract: An atomic clock comprises endohedral fullerene systems which provide the standard frequency oscillations. A magnet device applies a magnetic field to the endohedral fullerenes. The applied magnetic field is adjustable. An excitation device both excites each endohedral fullerene system to cause it to undergo transitions which generate the time-keeping oscillations, and also probes the systems such that the oscillations can be measured and the device controlled. A detection device senses the response of the systems induced by the excitation device. The output of the detection device is fed to a controller. The controller produces the atomic clock output, which is the clock signal or frequency standard, and also controls the magnet device and the excitation device.

Abstract: A terahertz oscillator may include a first insulating layer, an electron emitter on the first insulating layer, adapted to emit an electron beam, and including a cathode, an anode, an oscillating circuit, and a collector sequentially disposed, spaced apart from each other, on the first insulating layer in a direction in which the electron beam is emitted from the electron emitter, wherein the oscillating circuit converts energy of the electron beam to energy of an electromagnetic wave, and wherein the collector collects the electron beam, an output unit adapted to emit the electromagnetic wave from the oscillating circuit to outside of the terahertz oscillator, and an electron emitting material layer. The cathode may include a first curved portion that extends in a direction perpendicular to the first insulating layer. The electron emitting material layer may be on an inner surface of the first curved portion of the cathode.

Abstract: A spin transfer oscillator (STO) device is disclosed with a giant magnetoresistive (GMR) junction comprising a magnetic resistance layer (MRL)/spacer/magnetic oscillation layer (MOL) configuration, and a MR sensor including a sensing layer/junction layer/reference layer configuration. MOL and sensing layer are magnetostatically coupled and separated by a conductive spacer. MRL has perpendicular magnetic anisotropy while MOL and sensing layer have a Mst (saturation magnetization×thickness) value within ±50% of each other. When a magnetic field is applied perpendicular to the planes of the MOL and a high density current flows from the conductive spacer to the MRL, a MOL oscillation state with a certain frequency is induced. Consequently, the sensing layer oscillates with a similar RF frequency and when a low density current flows across the MR sensor, an AC voltage signal is generated to determine the sensing layer frequency that can be varied by adjusting the applied field.

Abstract: An atomic clock comprises helium 3 plasma as measurement medium, which is taken to the plasma state to exploit the metastable state of the material and the levels of the hyperfine structure, the lifetime of which is long and which thus enable an easier measurement than the excitations of gaseous atoms.

Abstract: The application relates to a calibration apparatus and calibration method for a tuneable resonator of a delta-sigma modulator of the continuous time, band pass type. The calibration apparatus comprises: a resonator driver capable of causing an oscillating behavior in a resonator output signal, a reference signal source that provides a reference signal, a frequency detector that provides a frequency relation signal corresponding to the frequency relation between the resonator output signal and the reference signal, and a controller that controls the tuneable resonator in dependence from the frequency relation signal so as to reduce frequency deviation.

Abstract: An atomic clock including a mechanism applying both a static magnetic field and two oscillating magnetic fields, all mutually perpendicular, in a magnetic shield. The amplitudes and frequencies of the oscillating magnetic fields may be chosen so as to annihilate energy variations between sub-transition levels of excited atoms and to reinforce a clock output signal, and with low sensitivity to defects in regulation.

Abstract: An atomic clock at optical frequency based on atomic beam and a method for generating the atomic clock comprises: The atomic beam (8) is ejected from a pile mouth after heating an atomic pile (1) in a vacuum chamber (2); A laser (4) corresponding to frequency of a clock transition transfers the atomic beam (8) from a ground state of the clock transition to an excited state of the clock transition in a adiabatic passing mode; After interaction with the laser corresponding to the frequency of a clock transition, the atomic beam (8) passes a signal detection region with a detection laser (5), and after the interaction with the detection laser (5), each of the atoms gives off a photon of spontaneous emission; An emitted fluorescence photon signal from atoms which is excited by the detection laser (5) is explored; A clock laser (4) for exploring transition frequency of an atomic clock is modulated.

Abstract: A system and technique for providing to flexible, programmable frequency estimators and spectrum analyzers that can operate over extremely large bandwidths and yet provide high spectral resolution are described. The acquisition time and hardware complexity of one technique scale as O(N), where N denotes the number of frequency bins acquired. Embodiments are disclosed in which architectures are implemented using exponentially-tapered transmission lines and filter cascades.

Abstract: An atomic oscillator includes: a gas cell in which a gaseous metal atom is sealed; heating units heating the gas cell to a predetermined temperature and being a first heater and a second heater; a light source of exciting light exciting the metal atom in the gas cell; a light detecting unit detecting the exciting light which has passed through the gas cell; a substrate including at least a temperature controlling circuit for the heating units; a first heater wiring coupling the first heater and the substrate; a second heater wiring coupling the second heater and the substrate; and a third heater wiring coupling the first heater and the second heater. In the atomic oscillator, the gas cell includes a cylindrical portion; and windows which respectively seal openings at both ends of the cylindrical portion and constitute an incident surface and an emitting surface on an optical path of the exciting light.

Abstract: The invention relates to a method of operating a spin-transfer torque structure to generate voltage oscillations, said structure comprising a first layer of magnetic material having a fixed magnetization vector, a spacer of non magnetic material and a second layer of magnetic material having a free magnetization vector. The method includes the application of a current (jop) through said structure and a magnetic field (Hext) in the plane of the second layer. It makes use of a region of bistability and hysteretic behaviour to trigger and stop the voltage oscillations.

Abstract: An atomic ion clock with a first ion trap and a second ion trap, where the second ion trap is of higher order than the first ion trap. In one embodiment, ions may be shuttled back and forth from one ion trap to the other by application of voltage ramps to the electrodes in the ion traps, where microwave interrogation takes place when the ions are in the second ion trap, and fluorescence is induced and measured when the ions are in the first ion trap. In one embodiment, the RF voltages applied to the second ion trap to contain the ions are at a higher frequency than that applied to the first ion trap. Other embodiments are described and claimed.

Abstract: The present invention is a Chip Scale Atomic Clock (CSAC)-enabled Time and Frequency Standard (CTFS) architecture. The CTFS architecture includes a microcontroller, a Time Compensated Crystal Oscillator (TCCO) circuit which is connected to the microcontroller, and a Chip Scale Atomic Clock (CSAC) which is connected to the microcontroller. The microcontroller is configured for selectively causing the CTFS to provide a TCCO circuit-based output frequency when the CTFS has not locked to a predetermined atomic resonance, and is further configured for causing the CTFS to provide a CSAC-based output frequency when the CTFS has locked to a predetermined atomic resonance.

Abstract: Local magnetic field strength in a trapped ion atomic clock is measured in real time, with high accuracy and without degrading clock performance, and the measurement is used to compensate for ambient magnetic field perturbations. First and second isotopes of an element are co-located within the linear ion trap. The first isotope has a resonant microwave transition between two hyperfine energy states, and the second isotope has a resonant Zeeman transition. Optical sources emit ultraviolet light that optically pump both isotopes. A microwave radiation source simultaneously emits microwave fields resonant with the first isotope's clock transition and the second isotope's Zeeman transition, and an optical detector measures the fluorescence from optically pumping both isotopes.

Abstract: A polarization gain medium such as an emitting laser diode provides the optical pumping. An atomic vapor cell is positioned in the laser cavity providing spontaneous push-pull optical pumping inside the laser cavity. This causes the laser beam to be modulated at hyperfine-resonance frequency. A clock signal is obtained from electrical modulation across the laser diode.

Abstract: A physical section of an atomic oscillator includes at least: a gas cell including a cylindrical portion and first and second windows respectively hermetically-closing openings of both sides of the cylindrical portion to form a cavity in which gaseous metal atoms are sealed; a light reflection unit disposed on the first window; a first heating unit disposed to be closely attached to the second window and heating the gas cell at a predetermined temperature; a light source disposed so as to allow a light emitting part thereof to face the light reflecting unit, emitting excitation light exciting the metal atoms in the gas cell, and provided on a side, which is a reverse side to a side to which the gas cell is provided, of the first heating unit; a light detection unit detecting the excitation light reflected by the light reflection unit and provided also on a side, which is a reverse side to a side to which the gas cell is provided, of the first heating unit; and a Peltier element interposed between the light so

Abstract: An apparatus in one example comprises a die structure that comprises a middle layer, a first outside layer, and a second outside layer. The middle layer comprises a cavity that holds an alkali metal, and one of the first outside layer and the second outside layer comprises a channel that leads to the cavity. The middle layer, the first outside layer, and the second outside layer comprise dies from one or more wafer substrates.

Abstract: A physic package for an atomic clock comprising: a block made of optical glass, a glass ceramic material or another suitable material that includes a plurality of faces on its exterior and a plurality of angled borings that serve as a vacuum chamber cavity, light paths and measurement bores; mirrors fixedly attached using a vacuum tight seal to the exterior of the block at certain locations where two light paths intersect; optically clear windows fixedly attached using a vacuum tight seal to the block's exterior over openings of the measurement bores and at one location where two light paths intersect; and fill tubes fixedly attached using a vacuum tight seal to the exterior of the block over the ends of the vacuum chamber cavity. This physics package design makes possible atomic clocks having reduced size and power consumption and capable of maintaining an ultra-high vacuum without active pumping.

Abstract: One embodiment of the invention includes an atomic clock system including an alkali beam cell and an interrogation system configured to generate an optical pump beam and at least one optical probe beam that illuminate a detection chamber of the beam cell to pump evaporated alkali metal atoms. An optical detection system can provide a microwave signal to the detection chamber and can measure an intensity of the optical pump beam to determine a transition frequency corresponding to optimum photon absorption of the evaporated alkali metal atoms. A photodetection system can measure an intensity of the at least one optical probe beam and to generate an intensity signal that is provided to the optical detection system to substantially cancel Doppler broadening of the transition frequency resulting from non-orthogonal planar movement of the evaporated alkali metal atoms relative to the optical pump beam and the at least one optical probe beam.

Abstract: An atomic oscillator that controls an oscillation frequency by using an optical absorption property derived from a quantum interference effect occurring when two kinds of resonance light are made incident as coherent light having different wavelengths from each other, includes an optical system that includes: a gas cell sealing metal atoms in a gas state therein; a coherent light source for supplying the resonance light to the metal atoms being in the gas cell; and a light detector for detecting light transmitted through the gas cell. In the atomic oscillator, a first refraction unit is formed at a light incident side, on which coherent light is made incident, of the gas cell.

Abstract: An atomic clock having a physics package that includes a vacuum chamber cavity that holds atoms of Rb-87 under high vacuum conditions, an optical bench having a single laser light source, a local oscillator, a plurality of magnetic field coils, an antenna, at least one photo-detector and integrated control electronics. The single laser light source has a fold-retro-reflected design to create three retro-reflected optical beams that cross at 90° angles relative to one another in the vacuum chamber cavity. This design allows the single laser light source to make the required six trapping beams needed to trap and cool the atoms of Rb-87. The foregoing design makes possible atomic clocks having reduced size and power consumption and capable of maintaining an ultra-high vacuum without active pumping.

Abstract: An atomic frequency acquisition apparatus includes: a cell enclosing atomic gas therein; a laser light source that oscillates a laser light that enters the cell and excites the atomic gas; and a photodetecting section that detects the laser light that has passed through the cell, wherein the cell has at least a laser light reflection section inside thereof.

Abstract: An optical system of an atomic oscillator that regulates an oscillation frequency by using an optical absorption property by one of a double resonance method utilizing light and micro waves and a coherent population trapping (CPT) method utilizing a quantum interference effect produced by two kinds of resonance light, includes: a light source emitting the resonance light; a gas cell disposed at an emitting side of the light source, sealing a gaseous metal atom therein and transmitting the resonance light through a metal atom gas; a light detecting unit detecting the transmitted light that is transmitted through the metal atom gas; and a fluorescence blocking unit blocking at least a part of fluorescence, which is emitted from the metal atom gas to the light detecting unit, and disposed between the metal atom gas and the light detecting unit.

Abstract: An atomic oscillator includes: a gaseous alkali metal atom; a light source to generate a resonant light pair for generating an electromagnetically induced transparency phenomenon in the alkali metal atom; a high frequency generation unit that supplies a high frequency signal to the light source and generates the resonant light pair; a center frequency variable unit that supplies a direct current signal to the light source and varies a center frequency of the resonant light pair; a light detection unit that detects the resonant light pair transmitted through the alkali metal atom and outputs a detection signal corresponding to intensity of the transmitted resonant light pair; an absorption detection unit that detects a minimum value of the detection signal when the center frequency of the resonant light pair is varied; and a signal processing unit that controls supply or stop of the high frequency signal outputted from the high frequency generation unit, wherein the signal processing unit compares the minimum

Abstract: The present invention provides a system and method for achieving a calibration-free primary atomic clock standard operating at the 0-0 transition free-atom frequency, thus creating a primary frequency standard, with attributes that include scalable to chip-scale dimensions and power consumption.

Abstract: One embodiment of the invention includes an alkali beam cell system that comprises a reversible alkali beam cell. The reversible alkali beam cell includes a first chamber configured as a reservoir chamber that is configured to evaporate an alkali metal during a first time period and as a detection chamber that is configured to collect the evaporated alkali metal during a second time period. The reversible alkali beam cell also includes a second chamber configured as the detection chamber during the first time period and as the reservoir chamber during the second time period. The reversible alkali beam cell further includes an aperture interconnecting the first and second chambers and through which the alkali metal is allowed to diffuse.

Abstract: One embodiment of the invention includes an atomic clock system including an alkali beam cell and an interrogation system configured to generate an optical pump beam and at least one optical probe beam that illuminate a detection chamber of the beam cell to pump evaporated alkali metal atoms. An optical detection system can provide a microwave signal to the detection chamber and can measure an intensity of the optical pump beam to determine a transition frequency corresponding to optimum photon absorption of the evaporated alkali metal atoms. A photodetection system can measure an intensity of the at least one optical probe beam and to generate an intensity signal that is provided to the optical detection system to substantially cancel Doppler broadening of the transition frequency resulting from non-orthogonal planar movement of the evaporated alkali metal atoms relative to the optical pump beam and the at least one optical probe beam.

Abstract: A microfabricated ion frequency standard (i.e. an ion clock) is disclosed with a permanently-sealed vacuum package containing a source of ytterbium (Yb) ions and an octupole ion trap. The source of Yb ions is a micro-hotplate which generates Yb atoms which are then ionized by a ultraviolet light-emitting diode or a field-emission electron source. The octupole ion trap, which confines the Yb ions, is formed from suspended electrodes on a number of stacked-up substrates. A microwave source excites a ground-state transition frequency of the Yb ions, with a frequency-doubled vertical-external-cavity laser (VECSEL) then exciting the Yb ions up to an excited state to produce fluorescent light which is used to tune the microwave source to the ground-state transition frequency, with the microwave source providing a precise frequency output for the ion clock.

Abstract: A solid state atomic clock may utilize quantum states capable of exhibiting a hyperfine resonance in order to generate a frequency standard. A device capable of coupling a free running oscillator to the hyperfine resonance frequency in order to generated output signal is described herein. In some aspect of the invention, the atomic clock may be fabricated on a silicon substrate and it may be integrated, in chip scale, as part of an electronic integrated circuit. The principal of operation, the method of making and system which utilized a solid state atomic clock are also disclosed.

Abstract: A chip scale atomic clock is disclosed that provides a low power atomic time/frequency reference that employs direct RF-interrogation on an end-state transition.

Abstract: The present invention relates to a method and system to suppress or eliminate light shift in an optical pumping system, such as an atomic clock. The method uses modulation of a radiation source, such as a radio frequency or microwave source, to simultaneously lock the frequency of the radiation source to an atomic resonance and lock the frequency of the optical pumping source in order to suppress or eliminate light shift. In one embodiment, the method of the present invention directly utilizes the out-of-phase channel of a lock-in amplifier to additionally lock an optical pumping source to a zero-light-shift frequency, where the in-phase channel is used to lock the frequency of the radiation source to an atomic resonance.

Abstract: A micro-structured optics apparatus includes a concave microlens to expand a beam of light, a reflector to provide a first reflection of at least a portion of the beam of light and a micro-Fresnel lens to collimate the at least a portion of the beam of light after the expansion.

Abstract: A quantum interference device includes: gaseous alkali metal atoms; and a light source for causing a resonant light pair having different frequencies that keep a frequency difference equivalent to an energy difference between two ground states of the alkali metal atoms, the quantum interference device causing the alkali metal atoms and the resonant light pair to interact each other to cause an electromagnetically induced transparency phenomenon (EIT), wherein there are a plurality of the resonant light pairs, and center frequencies of the respective resonant light pairs are different from one another.

Abstract: An atomic frequency acquisition apparatus includes: a cell enclosing atomic gas therein; a laser light source that oscillates a laser light that enters the cell and excites the atomic gas; and a photodetecting section that detects the laser light that has passed through the cell, wherein the cell has at least a laser light reflection section inside thereof.

Abstract: An atomic clock having a physics package that includes a vacuum chamber cavity that holds atoms of Rb-87 under high vacuum conditions, an optical bench having a single laser light source, a local oscillator, a plurality of magnetic field coils, an antenna, at least one photo-detector and integrated control electronics. The single laser light source has a fold-retro-reflected design to create three retro-reflected optical beams that cross at 90° angles relative to one another in the vacuum chamber cavity. This design allows the single laser light source to make the required six trapping beams needed to trap and cool the atoms of Rb-87. The foregoing design makes possible atomic clocks having reduced size and power consumption and capable of maintaining an ultra-high vacuum without active pumping.

Abstract: The present invention provides a system and method for achieving a calibration-free primary atomic clock standard operating at the 0-0 transition free-atom frequency, thus creating a primary frequency standard, with attributes that include scalable to chip-scale dimensions and power consumption.

Abstract: A method for optical pumping of particles and a device for implementing same. The particles (14) are changed from one long lifetime level to another long lifetime level via a short lifetime level by means of interaction with light radiation (16) emitted by a laser source. Prior to this interaction, the light radiation undergoes depolarization in a direction that is essentially perpendicular to the direction of propagation thereof, so as to reduce the entrapment of particles (14) in the black state.

Abstract: An oscillator includes at least one of: (i) a parallel array of resistors (420, 421, 422, 701, 801, 901, 902) or magnetoresistive contacts to a magnetoresistive film (120, 320); and (ii) a series array of resistors (620, 621, 702, 902) or magnetoresistive contacts to individualized areas of at least one magnetoresistive film.