WO2013055246A2

WO2013055246A2 - A method and a device for the measurement of changes in magnetic field

Info

Publication number: WO2013055246A2
Application number: PCT/PL2012/000104
Authority: WO
Inventors: Szymon PUSTELNY; Wojciech GAWLIK; Piotr WCISLO; Przemyslaw WLODARCZYK
Original assignee: Uniwersytet Jagiellonski
Priority date: 2011-10-14
Filing date: 2012-10-15
Publication date: 2013-04-18
Also published as: WO2013055246A3; PL396636A1; PL224509B1

Abstract

A method and a device for measuring magnetic fields by optical detection of precession of spins in a magneto-optically active medium consisting in analysis of optical state of amplitude- or frequency-modulated elliptically polarized light. A light source is used to excite transitions between the ground and excited states in the atoms of the magneto-optically active medium contained within a cell, said light being polarized using the first polarizer and directed onto a quarter waveplate having its optical axis placed at an angle of 1 to 10 degrees to the direction of light polarization, thus transforming the linear polarization of light into elliptical polarization of light; next, said light is directed into a cell containing the active medium and the light passing through the cell is received at the analyzer consisting of a polarizer with the axis rotated at an angle of 70 to 1 10 degrees compared to the axis of the first polarizer, and the light transmitted through the analyzer is recorded by means of a detector that generates an electric signal which is subjected to frequency analysis; the signal of the angle of rotation of the semi-major axis of the polarization plane at a particular harmonic of the modulation frequency is used to determine changes in the magnetic field.

Description

A METHOD AND A DEVICE FOR THE MEASUREMENT OF CHANGES IN

MAGNETIC FIELD

DESCRIPTION

The invention relates to a method and a device for the measurement of changes in magnetic field, in particular for the measurement of minute changes of stronger stationary and quasi-stationary magnetic fields over a broad range of intensities.

The broad range of magnetic fields as defined in this description is the range of magnetic fields from 10^"7 to 10^"4 T which can be detected using the method and the device according to the invention with the sensitivity up to 10^"14 - 10^"13 T/Hz^{1 2}. The method and the device according to the invention allow detecting changes in a range of magnetic fields spanning from static fields to oscillating fields of the frequency up to 1 kHz.

Devices making use of optical methods for the measurement of magnetic fields constitute a significant part of all known magnetometer types. Such magnetometers detect changes in certain properties of light propagated through a medium that result from application of external magnetic fields. A typical example of such devices is magnetometers based on the Faraday effect. The Faraday effect consists in the rotation of the plane of polarization of linearly polarized light upon its propagation through a medium placed in a longitudinal external magnetic field. Faraday rotation is linearly dependent on the applied magnetic field as well as related to the length and the material of the medium. The quantity that characterizes the ability of a material to rotate the plane of polarization (the material constant) is the Verdet constant; depending on the material, the values of the Verdet constant range from 0 to 40 rad/(T m).

A separate group of optical magnetometers consists of devices that make use of nonlinear optical effects. In such effects, intense light propagating through a medium modifies the properties of the material and, in turn, the modified properties affect the propagation of light. The nonlinear media that are most commonly used in the context of applications for the measurement of magnetic fields are gases. The use of gases allows detection of nonlinear phenomena at low intensity (~10 W/m² of CW light) monochromatic light beams resonant with the gaseous medium. For nonlinear effects dependent on the magnetic field, the width of recorded optical signals is directly related to the sensitivity of magnetic field measurements. Magnetometers based on nonlinear optical effects are able to achieve the sensitivity of 10^"16 - 10^"14 T/Hz ² with fundamental sensitivity limits of 10^"18 - 10^"15 T/Hz^1/2 (depending on particular arrangement).

All types of optical magnetometers based on nonlinear optical effects make use of the dependency of energy of magnetic sublevels of atoms or molecules on the magnetic field (for the sake of clarity of this description, the term "atoms" will henceforth be used to describe the microscopic elements of medium, i.e. both atoms and molecules). For alkali metal atoms, which are most frequently used in such measurements, the relationship between the energy of a particular magnetic sublevel

^MF of a particular ground-state hyperfine level ^F and the magnetic field is defined by the following formula

HF I rf¾_F

j l + x + %^■

2(2F + 1) 21 - 1

(1) where:

£y - energy of the "center of mass";

% - energy difference between two ground-state hyperfine sublevels;

- nuclear spin;

P - total angular momentum in particular hyperfine state; x =— _

^AHF where ^{0J L ~} &^{f Ps} & is the Larmor frequency, s is the Bohr magneton, ^B is the magnetic field induction, 9F is the Lande factor for the hyperfine level ^F and ft is the Planck constant divided by 2π.

The splitting between ground state magnetic sublevels may lead to a change in the magnetic properties of the gas, which in turn may influence the parameters of light propagating in the medium. In particular, changes may occur with regard to the intensity of the propagating light or the light's polarization direction. The relatively low dynamic range of magnetic-field measurement of traditional optical magnetometers (10^"1° - 10^"8 T) is a limitation the devices. Thus, the use of these methods implies the need to shield external magnetic fields, in particular the Earth's magnetic field, or to compensate for these fields using calibrated magnetic field coils. The first approach allows only for the measurement of very weak magnetic fields, while the other leads to significant reduction of method's sensitivity. Another limitation of the traditional optical magnetometers is the need to calibrate the recorded signal, e.g., recalculate the change in detected light polarization direction into magnetic field. Such solutions pose certain problems as the measured signals depend also on other experimental parameters and any fluctuations of non-magnetic parameters in the magnetometer may be interpreted as changes in the magnetic field. It implies a need for precisely control of all physical parameters in the system, in particular, light intensity, tuning, atomic concentration, etc.

Optical radio-frequency (rf) double resonance method may be a solution that allows for partial or complete elimination of these limitations. In the method, atoms placed in strong magnetic fields are illuminated with polarized light additionally interacting with electromagnetic field of a frequency of several hundred kHz. Intense light puts the atoms in a state, in which absorption of the light beam is significantly reduced. The rf field role is to modify the light generated state, which is achieved when the electromagnetic field couples the successive magnetic sublevels, i.e., when equation

Ehn_F + i) - Eini_f) = oj_Tf (2), is fulfilled. Here, ^&Jrf is the radio frequency of the electromagnetic field.

Despite the fact that the double resonance method allows the measurement of wide range of magnetic fields, it requires application of a system of magnetic-field coils that emits rf field. With this respect, all-optical methods not requiring the coils are more appealing in number of applications. The all-optical methods enabling for stronger magnetic-field measurements make use of the Raman resonance, in which two light beams of slightly different frequencies are used for indirect coupling of two energy sublevels of the same ground state (for instance, two magnetic sublevels of the hyperfine level F ). The coupling occurs if the frequency difference between two light beams matches the energy splitting between the sublevels. In such a case, the optical properties of the medium are modified, e.g. reducing absorption or modifying dispersion.

In general, Raman resonances may be induced by independent light beams emitted from two lasers operating at precisely controlled optical frequencies. Precise stabilization of laser light frequencies although possible is technically challenging. Thus, a better solution than application of two light beams is to used a single frequency-, amplitude-, or polarization-modulated light. Modulation of light leads to modification of its spectrum, in particular, appearance of additional frequencies known as sidebands. The number and amplitude of individual sidebands is determined by the modulation shape, while the distance between the sidebands depends on the frequency of modulation. Thus, appropriate selection on light modulation frequency allows coupling of individual levels, e.g. ground state levels. In particular, Raman resonance is observed when the splitting of energy is equal to or is a multiple of the modulation frequency.

One of the magnetometric methods exploiting modulated light makes use of the nonlinear Faraday effect. This method is based on detection of amplitude of polarization rotation of linearly polarized light traversing a medium subjected to the magnetic field. When the modulation frequency coincides with twice the splitting of two adjacent magnetic sublevels, the rotation resonance is observed. For an active medium consisting of alkali metal vapors, the resonance conditions may be easily determined from Eq. (1). In case of fields comparable to the magnetic field of the Earth, equation (1) may be expanded into a power series up to and including the second-order term (for such fields, the contribution of higher order terms is negligible), finally leading to the magneto-optical rotation resonance for

An important advantage of all modulation methods is that they do not require calibration of signal versus magnetic field; the position of the resonance is determined by the magnetic field and only the amplitude of the resonance, and thus the sensitivity of the measurement of the magnetic field, depends on the experimental conditions, including the concentration of atoms in the sample and the intensity of light.

The techniques of detection of magnetic field using modulated light are discussed in details in the following publications:

- V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson-Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, and J. Zachorowski "Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range" (Physical Review A 73, 053405 (2006)),

- W. Gawlik, L. Krzemien, S. Pustelny, D. Sangla, J. Zachorowski, M. Graf, A. Sushkov, and D. Budker "Nonlinear Magneto-Optical Rotation with Amplitude- Modulated Light" (Applied Physics Letters 88, 131 108 (2006)),

- S. Pustelny, A. Wojciechowski, M. Kotyrba, K. Sycz, J. Zachorowski, W. Gawlik, A. Cingoz, N. Leefer, J. M. Higbie, E. Corsini, A. O. Sushkov, M. P. Ledbetter, S. M. Rochester, D. F. Jackson Kimball, and D. Budker "Self-oscillating magnetometer based on nonlinear magneto-optical rotation with amplitude modulated light" (Proceedings of SPIE 6605, 660504 (2007)),

- S. Pustelny, A. Wojciechowski, M. Gring, M. Kotyrba, J. Zachorowski, W. Gawlik "Magnetometry Based on Nonlinear Magneto-Optical Rotation with Amplitude- Modulated Light" (Journal of Applied Physics 103, 063108 (2008)),

- D. Budker and M. Romalis "Optical magnetometry" (Nature Physics 3, 227 (2007)).

US patent application no. 201 1/0193555 presents a method for the differential magnetic measurements using laser light and two or more glass cells containing magneto-optically active medium. As opposed to typical magnetometric measurements, this method makes use of optical subtraction of fields, i.e. the same light beam passes through two or more vapors cells prepared with orthogonally circularly polarized light beams (right and left-handed circular polarization). If the field in two cells is equal the rotation should compensate and no net rotation should be observed. In the other case non-zero rotation would be observed. In this arrangement detection is achieved by means of a balanced polarimeter. Additionally, the method requires calibration. The method is suitable for use only for the measurement of weak magnetic fields, i.e. fields below ~10^"6 T for lower sensitivity and ~10^"10 T for enhanced sensitivity.

US patent no. 5,7038,450 presents a magnetometric technique using the spin- exchange relaxation free magnetometry. The technique exploits a large number of atoms for field measurements with simultaneous elimination of one of the major atom relaxation mechanisms (allowing to obtain narrow signals). This allows to obtain high signal-to-noise ratios which, combined with narrow optical signals, allows to achieve a very high sensitivity of the magnetic field measurements. The measurements make use of alkali metal vapors at temperatures higher than 150°C. The method requires additional introduction of a buffer gas (e.g. helium and nitrogen) under high pressures to the glass cell containing the atom vapors. Due to the capacity to measure only weak fields with intensities below 10^"8 T, the method requires the magnetic system being shielded from the external environment; in addition, calibration of the optical signal is required so that the field measurements may be made.

US patent no. 7,573,264 presents the use of an optical magnetometer for the measurement of nuclear magnetic resonance signals. This method makes use of atomic vapors at temperatures close to or slightly higher than the room temperature. The vapor is contained in specially designed cells with paraffin or with buffer gas introduced into the cell under the pressure of several dozen torr. The measurements make use of frequency-modulated light. The gradiometer system used in the method requires no calibration. In this method the light is polarized in an ideally linear fashion, the light beam passes through the sample twice but does not follow the same path across the medium. The detection of the signal is achieved by means of a balanced polarimeter. Due to the methodology of the measurement, the method allows to detect the signal only at the first harmonic of the modulation frequency. The solution was presented as suitable for the measurement of weak magnetic fields, i.e. fields of about 10^"6 T, although the method is based on a technique that allows the measurement of fields of up to 10^"4 T.

The objective of this invention is to develop a method and a device for the measurement of changes in the magnetic field that would allow for measurements of magnetic fields in a broad dynamic range (from 10^"6 to 10^~4 T) with a high sensitivity of up to 10^"14 - 10^"13 T/Hz^1/2. The technique enables for measurement of magnetic fields spanning from static fields to oscillating fields with oscillation frequency of 1 kHz.

The invention relates to a method of magnetic-field measurements using magneto-optically active medium (atomic vapor) and consists in detection of the amplitude of modulation of rotation of the semi-major axis of elliptically polarized light versus modulation frequency. In the method: a linearly polarized light tuned in resonance with a specific transition between atomic ground and excited states is linearly polarized with a first polarizer; the polarization state is affected by a quarter- waveplate of an optical axis rotated at 1 to 10 degrees with respect to initial polarization, which allows transforming the linear polarization of light into elliptical polarization; light is directed into a cell containing magneto-optically active medium; after passing through the cell the polarization state of light is analyzed by a polarizer of an optical axis rotated at an angle of 70 to 110 degrees compared to the axis of the first polarizer; light transmitted through the analyzer is recorded by means of a detector that generates an electric signal which is subjected to frequency analysis; the recorded signal is de-modulated at a particular harmonic of the modulation frequency and is used to determine changes in the magnetic field.

Preferably, the light is directed from the light source onto the polarizer using a polarization retaining single-mode optical fiber.

Preferably, the cell containing the active medium contains additional gases under pressure of several to several hundred torr.

Preferably, the walls of the cell containing the active medium are coated with a protective layer, particularly with paraffin.

Preferably, alkali metal atoms are used as the active medium.

Preferably, the cell containing the active medium is heated to a temperature from the range of 5 to 60° C.

Preferably, the heating of the cell is achieved by means of resistive heater consisting of pairs of doubly twisted bifilar high-resistance wires through with alternating current of the frequency of several to several dozen kHz and the amplitude of several hundred mA being passed through said wires.

Preferably, the cell is heated in a stream of hot air. Preferably, the cell is heated by hot liquid, for example by heating shields with circulating water of elevated temperature placed on the cell.

Preferably, the light that had passed through the cell is reflected in opposite direction using a mirror or retroreflector; after the second passage, the light illuminate the quarter waveplate and the first polarizer acting as an analyzer, the component perpendicular to the axis of the first polarizer is received at the detector.

Preferably, a photodiode is used as a detector

Preferably, a laser diode allowing for resonance tuning of the light wavelength to one of the transitions in atoms of the element constituting the active medium is used as the light source.

Preferably, the light generated by the light source is modulated using a modulator external to the light source.

Preferably, an acousto-optic modulator, or an electro-optic modulator, in particular a fiber optic modulator, is used as the light amplitude modulator.

Preferably, a single beam system is used in which anisotropy is generated and detected using a single modulated beam of polarized light.

Preferably, a dual beam system is used in which anisotropy is generated by one beam of elliptically polarized light and detected by another beam of linearly polarized light.

Preferably, changes in the magnetic field are determined from the signal of the angle of rotation of the plane of polarization at the first harmonic of the modulation frequency.

Preferably, changes in the magnetic field are determined from the signal of the angle of rotation of the plane of polarization at the second harmonic of the modulation frequency

Preferably, the electric detector output signal is demodulated at the modulation frequency (^im d) using a phase-sensitive detector and the resonance modulation frequency is determined by iterative changes of the modulation frequency (ω^^ηο-ί) for the light generated by the light source.

Preferably, the detector output signal is filtered to obtain a narrowed frequency bandwidth in which a signal close to the modulation frequency is being recorded; said signal is delivered to the system of the phase shifter and amplifier, the output signal of which is delivered to the light source as the modulation signal. Preferably, the detector output signal is filtered to obtain a narrowed frequency bandwidth in which a signal close to the double of the modulation frequency is being recorded; said signal is delivered to the system of the phase shifter and amplifier, the output signal of which is delivered to the light source as the modulation signal.

Preferably, the measurement of signal frequency using a frequency counter provides information on the magnetic field.

Preferably, two magnetometers are used, one being located closer to the source of the magnetic field than the other. The changes in the magnetic field generated by the source are determined from the difference in the magnetic fields recorded at both magnetometers.

The invention also relates to a device for the measurement of changes in the magnetic field within an active medium filled with atom vapor consisting in detection of the amplitude of modulation of rotation of the semi-major axis of the polarization plane of elliptical polarization of light, wherein said device comprises a light source designed to emit light at a wavelength tuned to the energy of transition between the ground state and the excited state of the atoms of the active medium contained within a cell, with light path passing from the light source through the first polarizer followed by a quarter wave phase plate having its optical axis placed at an angle of 1 to 10 degrees to the direction of light polarization and designed to transform the linear polarization of light into elliptical polarization of light, into a cell containing the active medium, wherein said device also comprises an analyzer consisting of a polarizer with the axis rotated at an angle of 70 to 110 degrees compared to the axis of the first polarizer, designed to receive the light passing through the cell and of a detector designed to record the intensity of light transmitted through the analyzer and to generate an electric signal delivered to an electronic system designed for frequency analysis and determination of changes in the magnetic field on the basis of the signal of the angle of rotation of the semi-major axis of the polarization plane at a particular harmonic of the modulation frequency isolated using a phase sensitive detector.

Preferably, the device includes a polarization retaining single-mode optical fiber for directing the light from the light source onto the polarizer.

Preferably, the cell containing the active medium contains additional gases under pressure of several to several hundred torr. Preferably, the walls of the cell containing the active medium are coated with a protective layer, particularly with paraffin.

Preferably, the active medium contains alkali metal atoms.

Preferably, the device consists also of a heater system used to heat the temperature of the cell containing the active medium to a temperature from the range of 15 to 60°C.

Preferably the heater system is a resistive heater consisting of pairs of doubly twisted bifilar high-resistance wires through with alternating current of the frequency of several to several dozen kHz.

Preferably, the heater system generates a stream of hot air directed onto the cell.

Preferably, the heater system comprises heating shields with circulating water of elevated temperature placed on the cell.

Preferably, the device comprises also a mirror designed to direct light having passed through the cell in the opposite direction, so that after the light once again passes through the cell, the quarter wave plate, the first polarizer acting as an analyzer, and the detector is used to receive the light component perpendicular to the axis of the first polarizer.

Preferably, the detector is a photodiode.

Preferably, the light source is a laser diode allowing for resonance tuning of the light wavelength to one of the transitions in atoms of the element constituting the active medium.

Preferably, the device comprises a modulator external to the light source and designed to modulate light generated by the light source.

Preferably, the modulator is an acousto-optic modulator, or an electro-optic modulator, in particular a fiber optic modulator.

Preferably, the device makes use of a single beam system is used in which anisotropy is generated and detected using a single modulated beam of polarized light.

Preferably, the device makes use of dual beam system is used in which anisotropy is generated by one beam of elliptically polarized light and detected by another beam of non-polarized light. Preferably, the filtering system is designed to limit the bandwidth of the recorded electronic signal.

Preferably, the electric detector output signal is demodulated at the first harmonic of the modulation frequency (<^¾j^?nod) using a phase-sensitive detector.

Preferably, the electric detector output signal is demodulated at the second harmonic of the modulation frequency (^i™^) using a phase-sensitive detector.

Preferably, the device comprises a computer-based system connected with the phase-sensitive detector enabling determination of the signal parameters at the frequency generated by an external oscillator, which is also used for modulation of light.

Preferably, the device comprises a filtering system designed to filter the electric output signal of the photodetector in order to narrow down the bandwidth of the recorded signal to a frequency close to the light modulation frequency.

Preferably, the device comprises a filtering system designed to filter the electric output signal of the detector in order to narrow down the bandwidth of the recorded signal to a frequency close to the double of the light modulation frequency.

Preferably, the device comprises a phase shifter and amplifier, the output signal of which is delivered as a modulation signal to the light source.

Preferably, the output signal of the phase shifter and amplifier is delivered to the light source via a frequency divider.

Moreover, the device relates to a system consisting of at least two devices according to the invention wherein one device is located closer to the magnetic field source than the other one, complete with a computation system for determination of the difference between the magnetic fields recorded by both devices and using this difference as the basis for determination of changes in the magnetic field generated at the source.

The subject of the solution is presented in its example embodiments in the enclosed figures, wherein:

Fig. 1 presents a block diagram of a measurement system according to the first embodiment of the invention;

Fig. 2 presents a block diagram of a measurement system according to the second embodiment of the invention; Figs. 3A-3C present polarization of light used in the system;

Fig. 4 presents the first embodiment of the magnetic field detection system;

Fig. 5 presents the outline of the iterative algorithm;

Fig. 6 presents the second embodiment of the magnetic field detection system;

Fig. 7 presents the detector system in the gradiometer mode;

Fig. 8 presents the diagram of the magnetometric sensor head;

Fig. 9 presents the signal recorded as a function of frequency modulation; Fig. 10 presents the magnetometric signal recorded using the method according to the invention.

The method for the measurement of the magnetic field according to the invention is a modification of the method making use of the nonlinear Faraday effect, The first significant change in comparison to prior methods consists in the use of

¾ - - _{Q a} elliptically polarized light of relatively low degree of ellipticity [(li + U) ], where > t± are the respective light intensities along each of the semi-axes of the polarization ellipse. The light is modulated in the intensity and/or the frequency, which results in the appearance of sidebands in the light spectrum. The light couples magnetic sublevels ^m of the particular hyperfine state F that differ in the magnetic quantum number by 2. This interaction disturbs the thermodynamic equilibrium in the medium and allows for development of its optical anisotropy. The axis of anisotropy rotates in the external magnetic field with the frequency equal to twice the Larmor frequency, which results in modulation the same frequency of modulation of the direction of the semi-major axis of elliptical polarization of light, as well as light ellipticity. Synchronization of polarization rotation with the frequency of light modulation (by appropriate selection of modulation frequency), i.e. satisfying the condition defined by Eq. (3), leads to generation of a strong optical signal. The detection of this signal and the measurement of modulation frequency provide information on the value of the magnetic field that encompasses the tested atoms.

Fig 1. presents a block diagram of a measurement system used to measure the magnetic field according to the first embodiment of the invention.

The solution according to invention comprises a light source 101 emitting radiation precisely tuned to a specific transition between the ground state and the excited state in the atoms of the medium. It is desirably that the emitted radiation has a narrow spectrum. In this context, the use of low power laser diodes, i.e. lasers with the power range of 10 pW - 10 mW, is an ideal solution. Such lasers allow accurately selecting and controlling the wavelength of the emitted light. Widely available laser diodes that allow for resonance tuning of the light wavelength to one of the transitions in alkali metal atoms (rubidium, cesium, potassium, etc.) being the most common active magneto-optic media, may be used. In addition, the laser diodes present the possibility to modulate the wavelength and/or the intensity of radiation, e.g. by modulation of the current flowing through a semiconductor connection within the range of up to several GHz. Another important advantage of laser diodes is their capability of being directly integrated with optic fibers allowing the beam being directed along any possible pathway.

Modulation of light can also be achieved by means of external modulators 102. An acousto-optic modulator, or an electro-optic modulator, in particular a fiber optic modulator, may be used. Such devices allow modulating the amplitude or the wavelength within the range spanning from 0 to several MHz for acousto-optic modulators and from 0 to several GHz for electro-optic modulators.

In the solution according to the invention, the measurements of magnetic fields of up to 10^"4 T require modulation methods allowing to obtain modulation frequencies not larger than 2 MHz.

Modulated light is directed into the polarization maintaining single-mode optical fiber 103. This allows the beam being directed in space along any possible pathway while minimizing the impact of mechanical interferences on the intensity and polarization of the light propagating through the fiber optics cable - the parameters of the light leaving the fiber optics cable (intensity, polarization) are stable over time.

After leaving the optical fiber, the light is polarized by a high-quality crystal polarizer 104. The goal of the polarizer is to ensure a high degree of polarization of light (polarizers in use are characterized by extinction of 10^"5 or lower), which is of consequence for the quality of the obtained magneto-optical signals, and thus on the sensitivity of measurements of the magnetic field.

Having passed the polarizer, the light propagates through the phase plate 105 of type λ/4 (a quarter waveplate), which delays the phase of oscillations of the electric field component of light along the slow axis of the plate by the value of ττ/2 in relation to the component oscillating along the fast axis of the plate. The optical axis of the plate is placed at an angle of 1 to 10 degrees relative to the plane of polarization, thus transforming linear polarization of light into elliptical polarization of light characterized by a low degree of ellipticity, as shown in Fig. 3A-3B.

Next, the light propagates through the gas-containing vapor cell 106 (for example, alkali metal atom vapors). The measurements make use of cells with paraffin wall coatings, i.e. cells inner walls are covered with a special protective layer and/or various gases (noble gases, molecular nitrogen, etc.) under pressure of several to several hundred torr (the pressure of the magneto-optically active gas is at the level of 10^"6 torr) are additionally introduced into the cell. The objective of these procedures is to elongate the time during which the gas reveals optical anisotropy (elongation of the lifetime of atoms in the ground state). The use of a buffer gas enables prolongation of the time by a factor of 1000, while in paraffin-coated cells it may be even elongated 10,000 times compared to cases when both procedures are not applied. The temperature of the cell may also be increased using the 107 up to several tens of degrees Celsius, i.e. from 15°C to 60°C (as an example, a cell at the temperature of ca. 55°C was used in the prototype), allowing to obtain a higher density of atoms in the sample, and thus a higher sensitivity of the measurements of the magnetic field. The cell 106 may be heated by a resistive heater consisting of pairs of doubly twisted bifilar high-resistance wires through with alternating current of the frequency of several kHz. The heater itself is located at the distance of several dozen millimeters from the cell. Other methods may also be used for heating the cell, for example methods making use of heated air or liquid. In such cases, the stream of heated air is directed at the cell containing the gas so that it is heated laterally. The air stream is directed at the cell so that circulation of air in the beam propagation area is prevented and does not cause additional fluctuations in the power and the polarization of light. Alternatively, the cell may be heated by heater shields placed on the cell and filled with circulating water of elevated temperature. The shields are so designed that they do not block the access of the light beam to the cell (access ports).

In the first embodiment of the invention, the light passing through the cell falls onto the analyzer 108 consisting of a polarizer having its axis rotated at an angle in the range of 70 to 1 10 degrees, preferably at a right angle, to the axis of the first polarizer 104. Due to modulation of the intensity and periodical changes in the direction of the semi-major axis of the elliptical polarization of light, the light subject to modulation is the light transmitted by analyzer 108; the intensity of this light, , can be calculated based on the Malus law.

!_t( t = l_p (t) s in²[j4s.-n(2&)x,t) + ex] (4)

where:

/pit) _ time-dependent intensity of incident light;

A - amplitude of oscillation of the plane of polarization rotation angle;

: - angle of deviation of the analyzer axis from the angle of 90°.

For small angles, i.e. angles up to several degrees (as is the case of the protecting method), Eq. (4) may be approximated as

I_t w i_p (t)[Asin(2c _L t) + a]² (5)

The light transmitted by the analyzer is recorded by the detector 109, which can consist of a photodiode. Thus obtained electric signal is amplified and filtered.

Fig. 2 presents a block diagram of the measurement system according to the second embodiment, where elements 201 , 202, 203, 204, 205, 206, 207, 209 are analogous to elements 101 , 102, 103, 104, 105, 106, 107, 109 in Fig. 1.

In the second embodiment, mirror 210 is placed behind cell 206. Mirror 210 directs the light back to the vapor cell 210, allowing for repeated interaction between the light and the medium. This results in effective elongation of the optical path, and thus in increase of the sensitivity of magnetic-field measurements.

Having again passed through cell 206, the light falls onto a quarter waveplate 205, which transforms the elliptical polarization into linear polarization (or into elliptical polarization with a low degree of ellipticity) having the polarization/major axis rotated by twice the angle between initial polarization and the quarter waveplate axis (symmetrical reflection of polarization relative to the slow axis of the quarter wave plate), as shown in Fig. 3C. Next, the light is directed onto the first polarizer 204, this time acting as the analyzer. The component perpendicular to the axis of the polarizer is directed into the perpendicular channel of the crystal (not in the direction of the optical fiber), and its intensity is given by a formula analogous to Eq. (5), i.e.

¾ Ip (t Asin(2 _L t) - φ]² _ (β)

where:

Ψ - the angle between the optical axis of the quarter wave plate and the initial polarization.

Next, the light transmitted by the analyzer 204 into perpendicular channel is recorded by the detector 209, which is a photodiode. Measured electric signal is amplified and filtered.

Fig. 3A presents linear polarization of light after passing through the polarizers 104 (204) and before passing through quarter waveplate 105 (205). Fig. 3B presents elliptical polarization of light after passing through quarter waveplate 105 (205). Fig. 3C presents the polarization of light after second transition through the quarter waveplate 205 according to the second embodiment of the invention presented in Fig. 2.

Both the first and the second embodiment of the system may be realized in either a single-beam or a two-beam arrangement. In the single-beam arrangement, the same modulated beam is responsible for both generation and detection of anisotropy. This means that the intensity of light in Eqs. (4)-(6) is additionally modulated. For sinusoidal modulation, is given by

a cos co_moa t)

(7)

where:

- mean intensity of light;

a - modulation depth.

For such modulation, simple trigonometric transformations of Eq. (5) lead to h ^¾ y C* - a CQs io_moa t}[Asin( _modt^') + a]' =

= l_QA₃ cos 3a>_mod + I_QA₂ COS Zm^t + ¾ A_T cos ω^ί + ½ A_Q, (8) where:

^ 1,2,3.4 - numerical factors dependent on the depth of modulation ^a , deviation angle ^a and the amplitude of the magneto-optic signal ^A .

Fig. 4 presents the first embodiment of a passive regime magnetic-field detection scheme; The modulated light is generated by a light source 401 or by a CW light source 101 (201 ) modulated by the modulator 102 (202) and then transmitted through optical fiber 402 to the magnetometric sensor head 403 featuring a detector system consisting of the elements 104-109 (204-210), where it is measured and the electric signal is amplified in the system 404. As shown by Eq. (8), recorded signals have four Fourier spectral components (four frequencies). The magnetic field is measured by the analysis of the signal (amplitude of rotation of the polarization plane or intensity of light) at a particular harmonic of the light modulation frequency. Typical measurement consists in demodulation of the recorded signal at the modulation frequency ^ mod using a phase-sensitive detector 406. The measurement of the magnetic field is carried out using an iterative algorithm performed by computer 407. The steps of the algorithm are presented in Fig. 5. The aim of the algorithm is to optimize the amplitude of the recorded signal (for the first harmonic, amplitude is being maximized). During the step 501 , one measures the amplitude and phase of the signal. If step 502 shows that the resonance condition is satisfied, the frequency of modulation provides information on the intensity of the magnetic field, in which the gas is placed. Every change in the magnetic field leads to the resonance condition not being satisfied and the signal amplitude being reduced. In such case, in the step 503 of the iterative algorithm, the computer 407 modifies the modulation frequency to find new conditions that satisfies resonance conditions. This procedure allows tracking the changes in the magnetic field. Modulation frequencies are recorded in step 504. The external oscillator 405 generates an electric signal delivered to the modulator in order to control the modulation of light.

The measurements of the magnetic field may also be made on the basis of the analysis of the field component at second harmonic of the modulation frequency. Although such signal is by definition of lower amplitude than the signal at the first harmonic, the signal to noise ratio at the second harmonic may be better and thus the measurement sensitivity may be higher. This is in case when the technical noise in phase with light modulation strongly contributes to the observed signals. The measurement of the field at the second harmonic is carried in an analogous manner to that for the first harmonic, i.e. using the iterative algorithm presented in Fig. 5.

Fig. 6 presents the second embodiment of the magnetic field detection system in the so-called gradiometer mode. Elements 601-604 are analogous to elements 401-404 of the first embodiment of the detection system presented in Fig. 4. In the system according to the second embodiment, filtered, amplified, and phase shifted (system 605) output signal is feed into the light source + modulation system 601. In such case, any change in the magnetic field, which manifests as a change of the frequency of recorded magneto-optical signal is instantly feed into the modulator system and the resonance condition is automatically fulfilled. In such system, the measurement of the magnetic field is achieved by means of the measurement of the frequency of modulation of light using the frequency meter 606.

Similarly as before, the system can work at both the first and the second harmonic of the modulation frequency. However, the latter approach requires the use of the divider system 607 that would divide the frequency of the signal between delivering it to the modulation system.

An alternative to the single beam system is a two-beam arrangement that includes a modulated beam that generates anisotropy and non-modulated light beam to probe the anisotropy. In such case, the pumping beam is delivered to the magnetometric head 403(603), where it interacts with the atoms (optical pumping). In contrast to the former case, the pump light may be either linearly or elliptically polarized. Having passed through the gas in the cell 106 (206), the pumping beam is blocked. The unmodulated probing beam passes along the entire above path (excluding the modulator), and the intensity of light transmitted through the polarizer is recorded. Based on Eq. (5), one may show that the intensity is given by

l_t w Ι_α[ΑΞΪΐΐ(ω -mog t) + a]³ = l₀B- cos 4ej|,t 4- B_t cos 2ω ^ ί f- ₀ 5_B where:

s 2,i.o - numerical coefficients (of the amplitude) dependent on the deviation angle and the amplitude of the magneto-optical signal . The recorded signal has three Fourier series components being multiples of the double of Larmor frequency. In order to enhance the sensitivity of the measurements of weak magnetic fields, the magnetic system described above may operate in the so-called gradient mode as presented in Fig. 7 (analogous to Fig. 6 in the single beam arrangement). In this system, two identical sensors/magnetometers 701 and 702 are placed at a distance from each other. The sensor 701 is located closer to the source of a weak magnetic field and it measures magnetic field originating at the weak source and uncontrolled external sources. The other magnetometer 702, placed at a distance from the source of a weak magnetic field measures only the field originating from external fields (the amplitude of the magnetic field drops with distance). The difference in the magnetic fields recorded by both magnetometers provides information about the magnetic field generated by the weak source and is recorded by the computation system 703. In addition, this method allows for reduction of magnetic noise and significant increase in the sensitivity of the device.

Fig. 8 presents a diagram of the magnetometric sensor head developed according to the above method for a single beam reflection system. For the sake of simplicity, the light source and the modulator are not shown in the figure. The head body 800 features a fiber optics cable holder 803, polarizer/analyzer 804, quarter wave plate 805, cell containing gas 806, mirror 810 and detector 809 mounted within the head.

An example embodiment of the device features an Eagleyard Photonics photodiode (EYP-RWL-0790-00100-1500-SOT02-0000) and a laser controller developed at the Department of Photonics of the Institute of Physics of the Jagiellonian University used for stabilization of the operation temperature and laser current. The measurements were carried out using the light wavelength of 795 nm, tuned to the F=2-F -1 transition of rubidium-87. The intensity of light was modulated using an Isowave acousto-optic modulator 1205-C, optimized for first order diffraction. The intensity of light subject to first order diffraction was modulated by changing amplitude of an acoustic wave in the modulator. The modulated light was then introduced into a Nuffern polarization-retaining fiber optics cable (Thorlabs F220FC-B fiber optics coupler). Polarization of light and the light path within the magnetometric head were achieved using optical elements from Foctek, Inc: a Glan- Laser crystal polarizer (GLP 6708), a quarter waveplate for a wavelength of 795 nm (WPL212Q) and a dielectric mirror with broadband reflective coating (750 nm - 900 nm). The magneto-optically active medium consisted of vapors of isotopically enriched ⁸⁷Rb, placed in a cylindrical glass cell of 10 mm length and a diameter of 10 mm. The walls of the cell were coated by a special paraffin layer to maintain the anisotropy in the system. The intensity of light was recorded using a photodiode (SFH203) with operation amplifier. The signal was detected by a Stanford Research SR830 phase-sensitive detector. The entire experiment was controlled using a PC.

Fig. 9 presents the magnetometric signal recorded as a function of frequency modulation for the magnetic field of 3 μΤ; Presented plots clearly shows that the signal peaks when the resonance condition (Eq. (3)) is satisfied. The graph compares the in-phase and quadrature phase signals recorded at the first and second harmonic of the modulation frequency.

Fig. 10 presents the magnetometric signal recorded using the method according to the invention. 50-ms pulses of 100 pT magnetic field are generated with a 5 Hz repetition rate. The signal was recorded in a single beam system using a single head. In the presented example, a signal noise level of 10^"11 T is observed at integration constant of 30 ms (elongation of this time to 1 s leads to a nearly six-fold increase in sensitivity, down to the level of ~2·10^"12 T/Hz^1/2). This sensitivity may be further enhanced by using a gradiometer mode (fluctuations of the external magnetic field contributes to the noise of the observed signals).

Claims

1 . A method for the measurement of changes in magnetic field using magneto- optically active medium being atomic vapor and consists in detection of the amplitude of modulation of rotation of the semi-major axis of elliptically polarized light versus modulation frequency, where a light source (101 , 102, 201 , 202) resonant with a particular transition of gas-phase atoms contained in specially prepared glass cell (106, 206) is elliptically polarized using a polarizer (104, 204) and a quarter waveplate (105, 205) of an optical axis by an angle of 1 to 10 degrees with respect to the polarizer axis and directed into a cell (106, 206) containing the magneto-optically active medium being later analyzed by an analyzer (108, 204) consisting of a polarizer with the axis rotated at an angle of 70 to 1 10 degrees compared to the axis of the first polarizer (104, 204) and recorded by a detector (109, 209) that generates an electric signal which is subjected to frequency analysis and the signal detected at a particular harmonic of the modulation frequency is used to determine changes in the magnetic field.

2. A method according to claim 1 , wherein the light is directed from the light source (101 , 102, 201 , 202) onto the polarizer (104) using a polarization maintaining single-mode optical fiber (103).

3. A method according to claim 1 , wherein a buffer gas under pressure of several to several hundred torr is introduced to the cell (106) containing the magneto-optically active medium.

4. A method according to claim 1 , wherein the walls of the cell (106) containing the magneto-optically active medium are coated with a protective layer, particularly with paraffin.

5. A method according to claim 1 , wherein alkali metal atoms are used as the magneto-optically active medium.

6. A method according to claim 1 , wherein the cell (106) containing the magneto- optically active medium is heated to a temperature from the range of 15 to 60°C.

7. A method according to claim 6, wherein the heating of the cell (106) is achieved by means of resistive heater (107) consisting of pairs of doubly twisted bifilar high-resistance wires through with alternating current of the frequency of several to several dozen kHz and the amplitude of several hundred mA being passed through the wires.

8. A method according to claim 6, wherein the cell (106) is heated by hot air.

9. A method according to claim 6, wherein the cell (106) is heated by hot liquid.

10. A method according to claim 6, wherein the light that had passed through the cell (206) is reflected in opposite direction using a mirror or retroreflector (210) and after the second passage, the light illuminate the quarter waveplate (205) and the first polarizer (204) acting as an analyzer and the component perpendicular to the axis of the first polarizer (204) is received at the detector (209).

1 1. A method according to claim 1 , wherein a photodiode is used as the detector (109, 209).

12. A method according to claim 1 , wherein a diode laser is used as the light source (101 , 201 ).

13. A method according to claim 1 , wherein light generated by the light source (101 , 201 ) is modulated by a modulator (102, 202) external to the light source (101 , 201).

14. A method according to claim 13, wherein an acousto-optic modulator, or an electro-optic modulator, in particular a fiber optic modulator, is used as the modulator (102, 202).

15. A method according to claim 1 , wherein a single beam system is used in which anisotropy is generated and detected using a single modulated beam of polarized light.

16. A method according to claim 1 , wherein two light beams are used, where modulated beam is used for generation of the optical anisotropy and unmodulated light beam is used for detection of the anisotropy.

17. A method according to claim 1 , wherein changes in the magnetic field are determined from the optical signal detected at the first harmonic of the modulation frequency (&>_tmoe.) .

18. A method according to claim 1 , wherein changes in the magnetic field are determined from the signal detected at the second harmonic of the modulation frequency (*¾mod) _

19. A method according to claim 1 , wherein the electric detector (109, 209) output signal is demodulated at the modulation frequency (^wi^morf) using a phase-sensitive detector (406) and the resonance modulation frequency is determined by iterative changes of the modulation frequency (^-mocf) f_or the light generated by the light source (101 , 102, 201 , 202).

20. A method according to claim 1 , wherein the detector (109, 209) output signal is filtered to obtain a narrowed frequency bandwidth in which a signal close to the modulation frequency is being recorded and said signal is delivered to the system (605) of the phase shifter and amplifier, the output signal of which is delivered to the light source (101 , 102, 201 , 202) as the modulation signal.

21. A method according to claim 1 , wherein the detector (109, 209) output signal is filtered to obtain a narrowed frequency bandwidth in which a signal close to the double of the modulation frequency is being recorded and said signal is delivered to the system (605) of the phase shifter and amplifier, the output signal of which is delivered to the light source (101 , 102, 201 , 202) as the modulation signal.

22. A method according to claim 1 , wherein the measurement of signal frequency using a frequency counters (606) provides information on the magnetic field.

23. A method according to claim 1 , wherein two magnetometers are used, one being located closer to the source of the magnetic field than the other and the changes in the magnetic field generated by the source are determined from the difference in the magnetic fields recorded with both magnetometers.

24. A device for the measurement of changes in the magnetic field within an active medium filled with atom vapor consisting in detection of the amplitude of modulation of rotation of the semi-major axis of the polarization plane of elliptical polarization of light, wherein said device comprises a light source (101 , 102, 201 , 202) designed to emit light at a wavelength tuned to the energy of transition between the ground state and the excited state of the atoms of the active medium contained within a cell (106, 206), with light path passing from the light source (101 , 102, 201 , 202) through the first polarizer (104, 204) followed by a quarter waveplate (105, 106) having its optical axis placed at an angle of 1 to 10 degrees to the direction of light polarization and designed to transform the linear polarization of light into elliptical polarization of light, into a cell (106, 206) containing the active medium, wherein said device also comprises an analyzer (108, 204) consisting of a polarizer with the axis rotated at an angle of 70 to 1 10 degrees compared to the axis of the first polarizer (104, 204), designed to receive the light passing through the cell (106, 206) and of a detector (109, 209) designed to record the intensity of light transmitted through the analyzer (108, 208) and to generate an electric signal delivered to an electronic system (405- 407, 605-607) designed for frequency analysis and determination of changes in the magnetic field on the basis of the signal of the angle of rotation of the semi-major axis of the polarization plane at a particular harmonic of the modulation frequency isolated using a phase sensitive detector (404).

25. A device according to claim 24, wherein the device includes a polarization maintaining single-mode optical fiber (103) for directing the light from the light source (101 , 102, 201 , 202) onto the polarizer (104).

26. A device according to claim 24, wherein the cell (106) containing the magneto- optically active medium contains a buffer gas under pressure of several to several hundred torr is used.

27. A device according to claim 24, wherein the walls of the cell (106) containing the magneto-optically active medium are coated with a protective layer, particularly with paraffin.

28. A device according to claim 24, wherein the magneto-optically active medium contains alkali metal atoms.

29. A device according to claim 24, wherein the device consists of a heater system (107) used to heat the temperature of the cell (106) containing the active medium to a temperature from the range of 15 to 60°C.

30. A device according to claim 29, wherein the heater system (107) is a resistive heater consisting of pairs of doubly twisted bifilar high-resistance wires through with alternating current of the frequency of several to several dozen kHz.

31. A device according to claim 29, wherein the heater system (107) generates a stream of hot air directed onto the cell (106).

32. A device according to claim 29, wherein the heater system (107) comprises heating shields with circulating water of elevated temperature placed on the cell (106).

33. A device according to claim 24, wherein the device comprises a mirror or retroreflector (210) designed to redirect light toward the cell (206) and after the second pass through the cell (206) and the quarter waveplate (205), the polarizer (204) acts as an analyzer that directs the polarization component of light perpendicular to the analyzer (204) axis into the other channel of the polarizer and is recorded with the detector (209).

34. A device according to claim 24, wherein the detector (109, 209) is a photodiode.

35. A device according to claim 24, wherein the light source (101 , 201) a laser diode allowing for resonance tuning of the light wavelength to one of the transitions in atoms of the element constituting the magneto-optically active medium.

36. A device according to claim 24, wherein said device comprises a modulator (102, 202) external to the light source (101 , 201) and designed to modulate the light generated by the light source (101 , 201 ).

37. A device according to claim 36, wherein an acousto-optic modulator, or an electro-optic modulator, in particular a fiber optic modulator, is used as the modulator (102, 202).

38. A device according to claim 24, wherein the device makes use of a single- beam arrangement in which anisotropy is generated and probed using the same modulated beam.

39. A device according to claim 24, wherein the device makes use two light beams, where modulated beam is used for generation of the optical anisotropy and unmodulated light beam is used for detection of the anisotropy.

40. A device according to claim 24, wherein a filtering system (404, 604) is designed to limit the bandwidth of the recorded electronic signal.

41. A device according to claim 24, wherein the output signal is demodulated at the first harmonic of the modulation frequency (<^■<-> χ ηιο ά) using a phase-sensitive detector (406).

42. A device according to claim 24, wherein the output signal is demodulated at the second harmonic of the modulation frequency (^ρηοά using a phase-sensitive detector (406).

43. A device according to claim 24, wherein the device comprises a computation system (407) to which the output signal of the phase-sensitive detector (406) is delivered and which is being designed to determine the magnetic field by analyzing properties of the recorded signal and optimizing the modulation frequency (^mocE) by iterative changes of the modulation frequency of the signal provided by the external oscillator (405) and used for modulation of light generated by the light source (101 , 102, 201 , 202).

44. A device according to claim 24, wherein the device comprises a filtering system (404, 604) designed to filter the electric output signal of the detector (109, 209) in order to narrow down the bandwidth of the recorded signal to a frequency close to the light modulation frequency.

45. A device according to claim 24, wherein the device comprises a filtering system (404, 604) designed to filter the electric output signal of the detector (109, 209) in order to narrow down the bandwidth of the recorded signal to a frequency close to twice the light modulation frequency.

46. A device according to claim 24, wherein said device comprises a phase shifter and amplifier (606), the output signal of which is delivered as a modulation signal to the light source (101 , 102, 201 , 202).

47. A device according to claim 46, wherein the output signal from the phase shifter and amplifier (606) is delivered to the light source (101 , 102, 201 , 202) via a frequency divider (607).

48. A system comprised of at least two devices according to claim 24, wherein one device (701) is located closer to the magnetic field source than the other one (702), complete with a computation system (703) for determination of the difference between the magnetic fields recorded by both devices and using this difference as the basis for determination of changes in the magnetic field generated at the source.