WO2020201372A1

WO2020201372A1 - Apparatus for measuring magnetic field and associated methods

Info

Publication number: WO2020201372A1
Application number: PCT/EP2020/059289
Authority: WO
Inventors: Stuart INGLEBY; Erling Riis; Paul F GRIFFIN; Aidan S ARNOLD
Original assignee: University Of Strathclyde
Priority date: 2019-04-03
Filing date: 2020-04-01
Publication date: 2020-10-08
Also published as: GB2582793A; GB201904690D0

Abstract

Disclosed herein is an apparatus for measuring a magnetic field gradient, the apparatus comprising: a first module and a second module, each module being configured to hold an atomic sample; a first magnetic field generator configured to apply a first alternating magnetic field to the atomic sample of the first module; a second magnetic field generator configured to apply a second alternating magnetic field to the atomic sample of the second module; a radiation source configured to transmit a beam of radiation through the atomic sample of the first and second modules, the beam of radiation configured to be resonant with a transition of the atomic sample; and a detection system configured to separate a first component from a second component of the beam of radiation transmitted through the atomic sample of the first and second modules to facilitate identification of a property of the beam of radiation indicative of the magnetic field gradient experienced by the atomic sample of the first and second modules. Also disclosed herein is a corresponding method of operation and computer program product.

Description

Apparatus for Measuring Magnetic Field and Associated Methods

FIELD

Described examples relate to apparatus and associated methods for measuring a magnetic field gradient.

BACKGROUND

In stable homogenous magnetic fields, atomic magnetometers can achieve highly accurate DC measurements, with intrinsic sensitivities below 1 fT.Hz ^1/2. However, in the presence of magnetic field noise and gradients, this performance is difficult to achieve. Certain atomic magnetometers may be unable to operate in unshielded environments, which may limit their ability to be deployed in a wide range of applications.

SUMMARY

In described examples, there are apparatus and associated methods for determining a magnetic field gradient. These apparatus and associated methods may overcome one or more problems identified in the background section.

According to a first aspect of the present disclosure is an apparatus for measuring a magnetic field gradient, the apparatus comprising: a first module and a second module, each module being configured to hold an atomic sample; a first magnetic field generator configured to apply a first alternating magnetic field to the atomic sample of the first module; a second magnetic field generator configured to apply a second alternating magnetic field to the atomic sample of the second module; a radiation source configured to transmit a beam of radiation through the atomic sample of the first and second modules, the beam of radiation configured to be resonant with a transition of the atomic sample; and a detection system configured to separate a first component from a second component of the beam of radiation transmitted through the atomic sample of the first and second modules to facilitate identification of a property of the beam of radiation indicative of the magnetic field gradient experienced by the atomic sample of the first and second modules. In use, the apparatus may be used to measure the gradient (i.e., the difference in magnitude) in the magnetic field in the region of the first and second modules. The difference in the magnitude of the magnetic field experienced by the atomic sample in the first and second modules may affect the property of the beam of radiation such that the magnetic field gradient may be determined by analysing the first and second components. The apparatus may be capable of distinguishing the magnetic field gradient from an ambient magnetic field. Accordingly, the apparatus may be used in an unshielded mode of operation. In other similar words, magnetic shielding may not be required in order to measure a magnetic field gradient. The apparatus may therefore be relatively compact compared with shielded arrangements and may be used in various applications such as unshielded magnetocardiography, archaeological surveying and maritime security applications. The ability to distinguish a magnetic field gradient from an ambient magnetic field, may allow use of the apparatus in the presence of magnetic field noise. Unshielded magnetic field noise may be broadband with amplitude in the nT (nano-Tesla) range. The apparatus may be capable of at least one of: achieving fT (femto-Tesla) range sensitivity to local magnetic field gradients; and rejecting common-mode environmental noise. By separating the first component from the second component of the beam of radiation transmitted through the atomic sample of the first and second modules, identification of the property of the beam of radiation indicative of the magnetic field gradient experienced by the atomic sample of the first and second modules may be facilitated.

Some optional features of the aspect or embodiment are set out below.

The detection system may be configured to subtract a signal representative of the first component from a signal representative of the second component, e.g. to form a resultant subtracted signal. The detection system may be configured to demodulate the resultant subtracted signal to determine the magnetic field gradient.

The detection system may be configured to obtain an in-phase or quadrature component of the resultant subtracted signal to determine the magnetic field gradient. The detection system may be configured to use a phase relationship between the first and second alternating magnetic fields to facilitate identification of the property of the beam of radiation indicative of the magnetic field gradient experienced by the atomic sample of the first and second modules. The detection system may be configured to facilitate identification of the property of the beam of radiation at a plurality of phase relationships between the first and second alternating magnetic fields, the plurality of phase relationships being usable to determine the magnetic field gradient. The detection system may be configurable to determine the magnetic field gradient where the phase relationship between the first and second alternating magnetic fields is out of phase. The detection system may be configurable such that the first and second alternating magnetic fields are out of phase by pi (TT) radians. The detection system may be configurable to determine an ambient magnetic field experienced by the atomic sample of the first and second modules where the phase relationship between the first and second alternating magnetic fields is in phase.

The apparatus may comprise a polarising beam splitter. The polarising beam splitter may be configured to separate the first component from the second component of the beam of radiation. The first component may have a different polarisation state to the second component.

The property may be a rotation angle of a polarisation axis of the beam of radiation. The detection system may be configured to detect a change in the rotation angle based on a difference between the first and second components.

The apparatus may be configured such that a polarisation axis of the beam of radiation is aligned parallel to a magnetic field line of an ambient magnetic field. The beam of radiation may be linearly polarised for transmission through the atomic sample of the first and second modules.

The apparatus may be configured such that at least one of the first and second modules are rotatable about an optical axis of the beam of radiation that propagates through the first and second modules. The radiation source may be wavelength stabilised relative to the transition.

The first and second magnetic field generators may be configured to produce the first and second alternating magnetic fields at a frequency sufficiently close to a Larmor frequency of the atomic sample such that a resonance condition is satisfied, which may facilitate identification of the property of the beam of radiation. The detection apparatus may be configured to use data obtainable from the first and second components of the beam of radiation to determine if the resonance condition is satisfied. The detection apparatus may be configured such that, if the resonance condition is not satisfied, the detection apparatus may be configured to modify the frequency until the resonance condition is satisfied.

The detection apparatus may be configured to distinguish the magnetic field gradient from an ambient magnetic field, which may facilitate use of the detection apparatus in an unshielded mode of operation.

According to a second aspect of the present disclosure is a method for measuring a magnetic field gradient, the method comprising: applying a first alternating magnetic field to an atomic sample of a first module; applying a second alternating magnetic field to an atomic sample of a second module; transmitting a beam of radiation through the atomic sample of the first and second modules, the beam of radiation configured to be resonant with a transition of the atomic sample; and separating a first component from a second component of the beam of radiation transmitted through the atomic sample of the first and second modules to facilitate identification of a property of the beam of radiation indicative of the magnetic field gradient experienced by the atomic sample of the first and second modules.

The method may comprise subtracting a signal representative of the first component from a signal representative of the second component and demodulating the resultant subtracted signal to determine the magnetic field gradient. The method may comprise obtaining an in-phase or quadrature component of the subtracted signal, e.g. to determine the magnetic field gradient. The method may comprise using a phase relationship between the first and second alternating magnetic fields to facilitate identification of the property of the beam of radiation indicative of the magnetic field gradient experienced by the atomic sample of the first and second modules. The method may comprise facilitating identification of the property of the beam of radiation at a plurality of phase relationships between the first and second alternating magnetic fields, the plurality of phase relationships being usable to determine the magnetic field gradient. The method may comprise determining the magnetic field gradient where the phase relationship between the first and second alternating magnetic fields is out of phase. The method may comprise providing the first alternating magnetic field out of phase with the second alternating magnetic field, e.g. by pi (TT) radians. The method may comprise determining an ambient magnetic field experienced by the atomic sample of the first and second modules where the phase relationship between the first and second alternating magnetic fields is in phase.

The method may comprise separating the first component from the second component of the beam of radiation such that the first component has a different polarisation state to the second component. The property may be a rotation angle of a polarisation axis of the beam of radiation. The method may comprise detecting a change in the rotation angle based on a difference between the first and second components. The method may comprise aligning a polarisation axis of the beam of radiation to be parallel to a magnetic field line of an ambient magnetic field. The method may comprise linearly polarising the beam of radiation, e.g. for transmission through the atomic sample of the first and second modules. The method may comprise stabilising a radiation source, e.g. such that its wavelength is stabilised relative to the transition. The method may comprise producing the first and second alternating magnetic fields at a frequency sufficiently close to a Larmor frequency of the atomic sample such that a resonance condition is satisfied to facilitate identification of the property of the beam of radiation. The method may comprise using data obtainable from the first and second components of the beam of radiation to determine if the resonance condition is satisfied. The method may comprise, if the resonance condition is not satisfied, modifying the frequency until the resonance condition is satisfied.

The method may comprising distinguishing the magnetic field gradient from an ambient magnetic field, e.g. to facilitate use of a detection apparatus comprising the first and second modules in an unshielded mode of operation.

According to a third aspect of the present disclosure is a computer program product configured such that, when run on a suitable processing apparatus, causes the processing apparatus to at least partially implement the method of the second aspect.

According to a fourth aspect of the present disclosure is a carrier medium comprising the computer program product of the third aspect.

It should be understood that the features defined above in accordance with any aspect, example or embodiment or below in relation to any specific embodiment described herein may be utilised, either alone or in combination with any other defined feature, in any other aspect, example or embodiment described herein. Furthermore, the present invention is intended to cover apparatus configured to perform any feature described herein in relation to a method and/or a method of using or producing or manufacturing any apparatus feature described herein.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments will now be described by way of example only and with reference to the following drawings, of which:

Figure 1 is a schematic representation of an apparatus for determining a magnetic field gradient;

Figure 2 is a further schematic representation of the apparatus of Figure 1 ;

Figure 3 is a simplified physical representation of a property of a beam of radiation in the apparatus of Figure 1 ; and

Figure 4 is a flow diagram representing steps for determining a magnetic field gradient.

DETAILED DESCRIPTION OF THE DRAWINGS

Figure 1 shows a simplified schematic representation of an apparatus 10 for measuring a magnetic field gradient DB (i.e., the difference between a magnetic field B1 in a first region and a magnetic field B2 in a second region). The apparatus 10 comprises a first module 12 and a second module 14. Each module 12, 14 is configured to hold an atomic sample such as an alkali metal vapour (e.g., rubidium, caesium, or the like). Each module 12, 14 may hold the same atomic sample, or a separate atomic sample. The first and second modules 12, 14 are spaced apart by a distance that may depend on the application concerned. For example, the modules 12, 14 may be spaced apart with a baseline in the range 5 to 10 cm, 10 cm to 1 m, or otherwise. A small baseline (e.g. 5 to 10 cm, or the like) between the modules 12, 14 may reduce the effect of acoustic noise and/or vibrations on measurements, thereby reducing sensitivity to noise.

A first magnetic field generator 16 (e.g., a Flelmholtz coil, or the like) is associated with the first module 12 and configured to apply a first alternating magnetic field to the atomic sample of the first module 12. Similarly, a second magnetic field generator 18 (e.g., a Helmholtz coil, or the like) is associated with the second module 14 and configured to apply a second alternating magnetic field to the atomic sample of the second module 14.

A radiation source 20 such as a laser is configured to transmit a beam of radiation 22 through the atomic sample of the first and second modules 12, 14. The beam of radiation 22 is configured to be resonant with a transition (e.g., a hyperfine transition) of the atomic sample. As such, the radiation source 20 is configured such that the beam of radiation 22 comprises a wavelength sufficiently close to a corresponding wavelength associated with the energy level difference of the transition so that resonance may occur. The radiation source 20 may comprise a vertical cavity surface emitting laser (VCSEL), external cavity diode laser (ECDL) or other laser. The radiation source 20 may be controlled such that its operating wavelength is stabilised relative to the transition. Techniques such as electrical current control, cavity length control and/or temperature control, or the like may be used to stabilise the operating wavelength of the radiation source 20.

A polariser 24 such as a polarising film, polarising beam splitter, or the like is provided in the path of the beam of radiation 22 so that the beam of radiation 22 has a linear polarisation state upon entry to the atomic sample of the first module 12. This linear polarisation state may be substantially or completely maintained upon being transmitted through the atomic sample of the first and second modules 12, 14 although this property may vary (e.g., rotation of the polarisation axis, or the like) after propagation through the first and second modules 12, 14 due to other effects, as described in further detail herein. The radiation source 20 may produce a beam of radiation B with a linear polarisation state such that a polariser 24 may not necessarily be required.

A collimator 26 such as a collimating lens is provided in the path of the beam of radiation 22 so that the beam of radiation 22 transmitted through the first and second portions 12, 14 has a similar interaction volume with the atomic sample for each of the first and second modules 12, 14. Thus, the atomic sample of the first module 12 may be expected to have a similar effect on a property of the beam of radiation 12 as that of the atomic sample of the second module 14 where the conditions (e.g., atomic vapour pressure, temperature, local magnetic field, etc) are similar in each module 12, 14. The radiation source 20 may produce a collimated beam of radiation 22 such that a collimator 26 may not necessarily be required.

The apparatus 10 further comprises a detection system 28 configured to separate a first component 30 from a second component 32 of the beam of radiation 22 transmitted through the atomic sample of the first and second modules 12, 14 to facilitate identification of a property of the beam of radiation 22 indicative of the magnetic field gradient DB experienced by the atomic sample of the first and second modules 12, 14.

In this embodiment, the detection system 28 comprises a polarising beam splitter 34 arranged at 45 degrees relative to the polarisation axis of the beam of radiation 22. Thus, for a linearly polarised beam of radiation 22, the first and second components 30, 32 have linear polarisation states that are orthogonal to each other.

The detection system 28 further comprises two detectors 36, 37 such as a photodiode associated with the first and second components 30, 32, respectively. The intensity of the first and second components 30, 32 of the beam of radiation may be registered by the detectors 36, 37. The detectors 36, 37 associated with the first and second components 30, 32 respectively produce data signals S1 , S2 that correspond to the intensity registered by detectors 36, 37. These data signals S1 , S2 are subtracted from each other using a subtraction module 38 such as a differential amplifier.

The resultant subtracted signal (i.e., S1 minus S2, or vice versa) is converted into a digital signal with a processing apparatus 40, which may or may not be part of the detection system 28. The processing apparatus 40 may comprise an analogue-to- digital converter (not shown), for example, to facilitate the subsequent digital processing of the resultant signal from the subtraction module 38. The processing apparatus 40 may comprise one or more digital-to-analogue converters (not shown), for example, to provide a signal for operating the first and second magnetic field generators 16, 18, and/or to provide a signal for controlling and/or stabilising the radiation source 20. Thus, the processing apparatus 40 may be operative to control the first and second alternating magnetic fields applied to the atomic sample of the first and second modules 12, 14, respectively. The amplitude, frequency and/or relative phase of the first and second alternating magnetic fields may be controlled with the processing apparatus 40.

The resultant subtracted signal may provide information regarding the property of the beam of radiation 22 indicative of the magnetic field gradient DB experienced by the atomic sample of the first and second modules 12, 14. If the frequency, w, of the first and second alternating magnetic fields is sufficiently close to a Larmor frequency of the atomic sample such that a resonance condition is satisfied, the property of the beam of radiation 20 indicative of the magnetic field gradient DB may be identified. The processing apparatus 40 may, using the frequency w as a reference signal, demodulate the resultant subtracted signal to determine the magnetic field gradient DB.

As mentioned previously, the beam of radiation 22 is linearly polarised for propagation through the atomic sample of the first and second modules 12, 14. In this example, the beam of radiation 22 is arranged such that that the polarisation axis of the linearly polarised beam of radiation 22 is parallel to the direction of an ambient magnetic field Bo, which may be the average of the magnetic fields B1 , B2 depicted in Figure 1.

To facilitate alignment of the polarisation axis with the ambient magnetic field B₀, one or more parts of the apparatus 10 may be rotatable with respect to one or more other parts of the apparatus 10. As shown by the example of Figure 2, a first mount 42 comprising several parts of the apparatus 10 is rotatable with respect to a second mount 44 comprising several other parts of the apparatus 10 about an optical axis of the beam of radiation 22 defined between the first and second modules 12, 14 (see the dashed line in Figure 1 ). In this particular example, the first mount 42 comprises the radiation source 20, polariser 24, collimator 26, first module 12 and the first magnetic field generator 16. The second mount 44 comprises the second module 14, second magnetic field generator 18, polarising beam splitter 34, the two detectors 36, 37 and the subtraction module 38.

The polarisation state of the beam of radiation may be affected by the spin precession of the atoms in the atomic sample. In particular, the polarisation axis of the linearly polarised beam of radiation 22 may be rotated, via a Faraday rotation effect, if the wavelength of beam of radiation 22 is substantially resonant with a transition and the frequency w of the first and second alternating magnetic field is sufficiently close to the Larmor frequency due to the ambient magnetic field B₀. This rotation of the polarisation axis is modulated at the frequency w, and hence the two detectors 36, 37 may identify a variation in intensity (by virtue of the difference between S1 and S2) if the resonance condition is satisfied.

Therefore, subtraction of the signals S1 , S2 corresponding to the first and second components 30, 32 may be used to determine the relationship between the magnetic field gradient DB and the angle of rotation of the polarisation axis caused by the Faraday rotation effect. For example, a magnetic field of a certain magnitude may be expected to cause a rotation in the polarisation axis of the beam of radiation 22 propagating through one of the first and second modules 12, 14. If there is a gradient in the magnetic field experienced by the first and second modules 12, 14, a different rotation in the polarisation axis of the beam of radiation may occur for the beam of radiation propagating through the other of the first and second modules 12. 14. This difference in the rotation of the polarisation axis experienced by the beam of radiation 22 may be comprised in or represent the property of the beam of radiation 22 indicative of the magnetic field gradient experienced by the atomic sample of the first and second modules 12, 14.

Figure 3 is a table schematically depicting a simplified physical representation of the Faraday rotation effect introduced at each of the first and second modules 12, 14 and how the relative phase between the first and second alternating magnetic fields can be used to determine the magnetic field gradient DB. The direction of the arrows depicted in the table represents an angle of rotation of the polarisation axis at a given time caused by spin precession arising from the ambient magnetic field. Flowever, the depicted angle of rotation may be exaggerated to illustrate the effect more clearly. This angle of rotation may vary according to the application of the first and second alternating magnetic fields.

In a scenario depicted by the second row in the table, there is no magnetic field gradient such that DB = B1 - B2 = 0 (i.e., the local magnetic fields B1 and B2 are the same) and the first and second alternating magnetic fields are applied in phase (i.e., Df = fi - f₂ = 0 where fi_,2 is the phase of the first and second alternating magnetic field, respectively) such that the magnetic field varies in the same way and at the same time for each of the first and second modules 12, 14. The rotation of the polarisation axis due to the local magnetic field B1 introduced by the atomic sample of the first module 12 is depicted by the relevant arrow in the table, which is depicted at an angle to the vertical. The angle of rotation oscillates in time at the same frequency w as that of the first alternating magnetic field. Similarly, the rotation of the polarisation axis due to the local magnetic field B2 introduced by the atomic sample of the second module 14 is depicted by the relevant arrow in the table, which is at the same angle to the vertical as the arrow depicted in relation to the first module 12. The net effect of this rotation (i.e. “net rotation”) introduced by the first and second modules 12, 14 is depicted by the relevant arrow in the table. Since the rotation produced by the first and second modules 12, 14 is in phase, the net rotation introduced by the first module 12 is effectively doubled by the second module 14. As the first and second alternating magnetic fields vary in time, the signal observed by the detectors 36, 37 also vary in time and produce corresponding signals S1 , S2, which when subtracted, allow the ambient magnetic field B₀ to be determined (i.e., after demodulation of the subtracted signal) since the net rotation (and hence the subtracted signal) is proportional to the ambient magnetic field B₀.

In a scenario depicted by the third row in the table, there is no magnetic field gradient such that DB = 0 and the first and second alternating magnetic fields are applied out of phase (i.e., Df = fi - f₂ = p). Since the angle of rotation introduced by the first module 12 is out of phase with the angle of rotation introduced by the second module 14, the net rotation is effectively cancelled.

In a scenario depicted by the fourth row in the table, there is a magnetic field gradient such that DB ¹ 0 (i.e. there is a difference between B1 and B2) and the first and second alternating magnetic fields are applied in phase (i.e., Df = 0). Due to the difference in the ambient magnetic field experienced at the first and second modules 12, 14, the angle of rotation introduced by the first and second modules 12, 14 differs slightly, as depicted by the relevant arrows in the table. The net rotation (and the signal observed by the detectors 36, 37) may be similar to that observed in the case of DB = 0 and Df = 0 (i.e., the second row of the table). Since DB is expected to be much smaller than the ambient magnetic field, the signals produced by the detectors 36, 37 can be used to determine the ambient magnetic field Bo. In a scenario depicted by the fifth row in the table, there is a magnetic field gradient such that DB ¹ 0 (i.e. there is a difference between B1 and B2) and the first and second alternating magnetic fields are applied out of phase (i.e., Df = tt). Due to the difference in the ambient magnetic field experienced at the first and second modules 12, 14, the angle of rotation introduced by the first and second modules 12, 14 differs slightly, as depicted by the relevant arrows in the table. The net rotation (and the signal observed by the detectors 36, 37) may be similar to that observed in the case of DB = 0 and Df = p (i.e., the third row of the table). However, in contrast to the net rotation in the case depicted by the third row where there is no net effect due to DB = 0, the magnetic field gradient DB ¹ 0 causes a net rotation effect that is observable and can be used to distinguish the magnetic field gradient DB from the ambient magnetic field Bo. As the first and second alternating magnetic fields vary in time, the signal observed by the detectors 36, 37 also vary in time and produce corresponding signals S1 , S2, which when subtracted, allow the magnetic field gradient DB to be determined (i.e., after demodulation to obtain an in-phase or quadrature component of the subtracted signal) since the net rotation (and hence the subtracted signal) is proportional to the magnetic field gradient DB.

Accordingly, the apparatus 10 is configured to use a phase relationship between the first and second alternating magnetic fields to facilitate identification of the property of the beam of radiation 22 indicative of the magnetic field gradient DB experienced by the atomic sample of the first and second modules 12, 14. In the above example, two phase relationships were used to identify the ambient magnetic field B₀ and the magnetic field gradient DB. However, different phase relationships may be used to identify one or both of the ambient magnetic field B₀ and the magnetic field gradient DB. A plurality of phase relationships (e.g., in addition to or alternatively to Df = tt) may be used to determine the ambient magnetic field B₀ and/or the magnetic field gradient DB. For example, multiple measurements may be made and correlated with each other to determine the ambient magnetic field B₀ and/or magnetic field gradient DB within a reasonable degree of accuracy.

Since the apparatus 10 can be configured to distinguish the magnetic field gradient DB from an ambient magnetic field B₀, the apparatus 10 may be used in an unshielded mode of operation. In other similar words, magnetic shielding may not be required in order to measure a magnetic field gradient. The apparatus 10 may therefore be relatively compact compared with shielded arrangements and may be used in various applications. The ability to distinguish a magnetic field gradient DB from an ambient magnetic field B₀, may allow use of the apparatus 10 in the presence of magnetic field noise. Unshielded magnetic field noise is broadband with amplitude in the nT (nano- Tesla) range. The apparatus 10 may be capable of at least one of: achieving fT (femto-Tesla) range sensitivity to local magnetic field gradients; and rejecting common mode environmental noise due to effectively optically subtracting the Faraday rotation introduced by the atomic sample of the first and second modules 12, 14.

As mentioned previously, the ability to determine a magnetic field gradient DB with the level of sensitivity achievable with the apparatus 10 may have applications in one or more of: unshielded magnetocardiography (which may require sensitivity around 1 pT/Hz^1/2 - this sensitivity being difficult to achieve with unshielded magnetometers); archaeological surveying of buried structures (which may produce a distinctive magnetic field gradient); and maritime security applications (e.g. identification of submerged vessels and other objects which may create a local magnetic field gradient such as in the pT-nT field range).

A method for measuring a magnetic field gradient DB using the apparatus 10 is now described with reference to Figures 1 to 4. An atomic sample is provided or introduced in the first and second modules 12, 14. This atomic sample may be an atomic vapour sample such as a saturated vapour at ambient or elevated temperature.

The radiation source 20 produces the beam of radiation 22 that is resonant with a ground state hyperfine transition of the atomic sample. The wavelength of the beam of radiation may be stabilised relative to the atomic transition (e.g., through control of the radiation source by the processing apparatus 40, or the like). The beam of radiation 22 is linearly polarised (e.g., further linearly polarised) by the polariser 24 and collimated (e.g., further collimated) by the collimator 26. The beam of radiation 22 is arranged to propagate through the atomic sample of the first and second modules 12, 14 with its polarisation axis aligned parallel to the ambient magnetic field B₀.

The first and second alternating (e.g., radio frequency (RF)) magnetic fields are generated by the first and second magnetic field generators 16, 18 respectively based on signals supplied by a digital-to-analogue converter associated with the processing apparatus 40. As explained above, the polarisation axis of the beam of radiation 22 is rotated by the atomic sample of the first and second modules 12, 14 depending on the local magnetic field experienced by the first and second modules 12, 14 as well as the first and second alternating magnetic fields (the angle of rotation being modulated by the frequency of the applied first and second magnetic fields).

The angle of rotation of the polarisation axis can be determined by separating a first polarisation component (i.e., the first component 30) from the second polarisation component (i.e., the second component 32) of the beam of radiation 22 transmitted through the atomic sample of the first and second modules 12, 14.

As an initial step S100, the first and second alternating magnetic fields are applied with the same amplitude, frequency and phase (i.e. such that Df = 0). The amplitude of the alternating magnetic fields is much smaller than the magnitude of the ambient magnetic field B₀. As a subsequent step S102, the corresponding data signals S1 , S2 generated by the detectors 36, 37, respectively are subtracted from each other. As a subsequent step S104, the resultant subtracted signal is digitised and demodulated. As a subsequent step S106, the frequency w of the first and second alternating magnetic fields may be modified to satisfy a resonance condition where the frequency w matches the atomic Larmor frequency due to the ambient magnetic field using the demodulated data from step S104. In this manner, the frequency w may be modified until the resonance condition is satisfied, as observed via the subtracted and demodulated signal.

In an alternative method, the frequency w that satisfies the resonance condition for the atomic sample of the first module 12 (where there is a local magnetic field B1 ) may be identified by only applying the first alternating magnetic field (the second alternating magnetic field is not applied). Similarly, the frequency w that satisfies the resonance condition for the atomic sample of the second module 14 (where there is a local magnetic field B2) may be identified by only applying the second alternating magnetic field (the first alternating magnetic field is not applied). The average of the two frequencies identified by this method may be calculated to determine the average frequency w₃ so that in a subsequent step, this average frequency w₃ can be applied to the atomic sample of both the first and second modules 12, 14. In an alternative method, the ambient magnetic field B₀ may be identified by a different apparatus. The frequency w that satisfies the resonance condition may have already been determined. Steps S100 to S106 (or their alternatives) may be considered to be optional steps.

As a subsequent step S108, the steps of S100 to S104 are performed (or repeated) but with the phase relationship between the first and second alternating magnetic fields modified such that Df ¹ 0, and preferably Df = tt. The in-phase or quadrature component of the signal, which is obtained by demodulation, is proportional to the magnetic field gradient DB. Therefore, the magnetic field gradient DB can be determined. One or more of the steps S100 to S108 may be repeated, for example, at different phase Df values. Additionally, certain parts of the steps S100 to S108 may be omitted, for example, if a value is already known.

Aspects or embodiments described herein may be combined or modified as appropriate. Features described in relation to one aspect or embodiment, even if not explicitly described in relation to another aspect or embodiment, may be applicable or used in that other aspect or embodiment.

Although the subtraction module 38 and processing apparatus 40 are depicted as separate components, the subtraction module 38 and processing apparatus 40 may alternatively be provided as part of the same component. Further, one or more functions may be provided by one or both of the subtraction module 38 and processing apparatus 40. One or more of the functions described in relation to the subtraction module 38 and the processing apparatus 40 may be performed by the same processing apparatus, or may be performed on separate components or processing apparatus. One or more processing apparatus may be provided to perform one or more functions described herein.

A processing apparatus may comprise one or more processors or functional blocks configured to perform one or more operations or at least partially implement one or more methods described herein. A processing apparatus may comprise a digital signal processor (DSP), field programmable gate array (FPGA), application specific integrated circuit (ASIC) or other processing apparatus, for performing one or more steps or operations described herein. A computer program may be configured to provide any of the above described methods. The computer program may be provided on a computer readable medium. The computer program may be a computer program product. The product may comprise a non-transitory computer usable storage medium. The computer program product may have computer-readable program code embodied in the medium configured to perform the method. The computer program product may be configured to cause at least one processor to perform some or all of a method described herein.

Various methods and apparatus are described herein with reference to block diagrams or flowchart illustrations of computer-implemented methods, apparatus (systems and/or devices) and/or computer program products. It is understood that a block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented by computer program instructions that are performed by one or more computer circuits. These computer program instructions may be provided to a processor circuit of a general purpose computer circuit, special purpose computer circuit, and/or other programmable data processing circuit to produce a machine, such that the instructions, which execute via the processor of the computer and/or other programmable data processing apparatus, transform and control transistors, values stored in memory locations, and other hardware components within such circuitry to implement the functions/acts specified in the block diagrams and/or flowchart block or blocks, and thereby create means (functionality) and/or structure for implementing the functions/acts specified in the block diagrams and/or flowchart block(s).

Computer program instructions may also be stored in a computer-readable medium that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer- readable medium produce an article of manufacture including instructions which implement the functions/acts specified in the block diagrams and/or flowchart block or blocks.

A tangible, non-transitory computer-readable medium and/or carrier medium may include an electronic, magnetic, optical, electromagnetic, or semiconductor data storage system, apparatus, or device. More specific examples of the computer- readable medium would include the following: a portable computer diskette, a random access memory (RAM) circuit, a read-only memory (ROM) circuit, an erasable programmable read-only memory (EPROM or Flash memory) circuit, a portable compact disc read-only memory (CD-ROM), and a portable digital video disc read-only memory (DVD/Blu-ray). The carrier medium may be, comprise or be comprised in a non-tangible carrier medium such as an electromagnetic wave, electronic or magnetic signal, digital data and/or the like.

The computer program instructions may also be loaded onto a computer and/or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer and/or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions/acts specified in the block diagrams and/or flowchart block or blocks.

In addition, it will be well understood by persons of ordinary skill in the art that whilst some embodiments may implement certain functionality by means of a computer program having computer-readable instructions that are executable to perform the method of the embodiments, the computer program functionality could be implemented in hardware (for example by means of a CPU or by one or more ASICs (application specific integrated circuits), FPGAs (field programmable gate arrays) or GPUs (graphic processing units)) or by a mix of hardware and software.

Accordingly, the present disclosure may be embodied in hardware and/or in software (including firmware, resident software, micro-code, etc.) that runs on a processor or processing apparatus, which may collectively be referred to as "circuitry," "a module" or variants thereof.

It should also be noted that in some alternate implementations, the functions/acts noted in the blocks may occur out of the order noted in the flowcharts. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Moreover, the functionality of a given block of the flowcharts and/or block diagrams may be separated into multiple blocks and/or the functionality of two or more blocks of the flowcharts and/or block diagrams may be at least partially integrated. Finally, other blocks may be added/inserted between the blocks that are illustrated.

The applicant discloses in isolation each individual feature described herein and any combination of two or more such features, to the extent that such features or combinations are capable of being carried out based on the specification as a whole in the light of the common general knowledge of a person skilled in the art, irrespective of whether such features or combinations of features solve any problems disclosed herein, and without limitation to the scope of the claims. The applicant indicates that aspects of the invention may consist of any such individual feature or combination of features. In view of the foregoing description it will be evident to a person skilled in the art that various modifications may be made within the scope of the invention.

Claims

1. Apparatus for measuring a magnetic field gradient, the apparatus comprising: a first module and a second module, each module being configured to hold an atomic sample;

a first magnetic field generator configured to apply a first alternating magnetic field to the atomic sample of the first module;

a second magnetic field generator configured to apply a second alternating magnetic field to the atomic sample of the second module;

a radiation source configured to transmit a beam of radiation through the atomic sample of the first and second modules, the beam of radiation configured to be resonant with a transition of the atomic sample; and

a detection system configured to separate a first component from a second component of the beam of radiation transmitted through the atomic sample of the first and second modules to facilitate identification of a property of the beam of radiation indicative of the magnetic field gradient experienced by the atomic sample of the first and second modules.

2. The apparatus of claim 1 , wherein the detection system is configured to subtract a signal representative of the first component from a signal representative of the second component and demodulate the resultant subtracted signal to determine the magnetic field gradient.

3. The apparatus of claim 2, wherein the detection system is configured to obtain an in-phase or quadrature component of the subtracted signal to determine the magnetic field gradient.

4. The apparatus of claim 1 , 2 or 3, wherein the detection system is configured to use a phase relationship between the first and second alternating magnetic fields to facilitate identification of the property of the beam of radiation indicative of the magnetic field gradient experienced by the atomic sample of the first and second modules.

5. The apparatus of claim 4, wherein the detection system is configured to facilitate identification of the property of the beam of radiation at a plurality of phase relationships between the first and second alternating magnetic fields, the plurality of phase relationships being usable to determine the magnetic field gradient.

6. The apparatus of claim 4 or 5, wherein the detection system is configurable to determine the magnetic field gradient where the phase relationship between the first and second alternating magnetic fields is out of phase.

7. The apparatus of claim 6, wherein the detection system is configurable such that the first and second alternating magnetic fields are out of phase by pi (TT) radians.

8. The apparatus of any one of claims 4 to 7, wherein the detection system is configurable to determine an ambient magnetic field experienced by the atomic sample of the first and second modules where the phase relationship between the first and second alternating magnetic fields is in phase.

9. The apparatus of any one of claims 1 to 8, comprising a polarising beam splitter configured to separate the first component from the second component of the beam of radiation, the first component having a different polarisation state to the second component.

10. The apparatus of any one of claims 1 to 9, wherein the property is a rotation angle of a polarisation axis of the beam of radiation.

1 1 . The apparatus of claim 10, wherein the detection system is configured to detect a change in the rotation angle based on a difference between the first and second components.

12. The apparatus of any one of claims 1 to 1 1 , wherein the apparatus is configured such that a polarisation axis of the beam of radiation is aligned parallel to a magnetic field line of an ambient magnetic field.

13. The apparatus of any one of claims 1 to 12, wherein the beam of radiation is linearly polarised for transmission through the atomic sample of the first and second modules.

14. The apparatus of any one of claims 1 to 13, wherein the apparatus is configured such that at least one of the first and second modules are rotatable about an optical axis of the beam of radiation that propagates through the first and second modules.

15. The apparatus of any one of claims 1 to 14, wherein the radiation source is wavelength stabilised relative to the transition.

16. The apparatus of any one of claims 1 to 15, wherein the first and second magnetic field generators are configured to produce the first and second alternating magnetic fields at a frequency sufficiently close to a Larmor frequency of the atomic sample such that a resonance condition is satisfied to facilitate identification of the property of the beam of radiation.

17. The apparatus of claim 16, wherein the detection apparatus is configured to use data obtainable from the first and second components of the beam of radiation to determine if the resonance condition is satisfied and if not satisfied, modify the frequency until the resonance condition is satisfied.

18. The apparatus of any one of claims 1 to 17, wherein the detection apparatus is configured to distinguish the magnetic field gradient from an ambient magnetic field to facilitate use of the detection apparatus in an unshielded mode of operation.

19. A method for measuring a magnetic field gradient, the method comprising: applying a first alternating magnetic field to an atomic sample of a first module; applying a second alternating magnetic field to an atomic sample of a second module;

transmitting a beam of radiation through the atomic sample of the first and second modules, the beam of radiation configured to be resonant with a transition of the atomic sample; and

separating a first component from a second component of the beam of radiation transmitted through the atomic sample of the first and second modules to facilitate identification of a property of the beam of radiation indicative of the magnetic field gradient experienced by the atomic sample of the first and second modules.

20. The method of claim 19, comprising subtracting a signal representative of the first component from a signal representative of the second component and demodulating the resultant subtracted signal to determine the magnetic field gradient.

21 . The method of claim 20, comprising obtaining an in-phase or quadrature component of the subtracted signal to determine the magnetic field gradient.

22. The method of claim 19, 20 or 21 , comprising using a phase relationship between the first and second alternating magnetic fields to facilitate identification of the property of the beam of radiation indicative of the magnetic field gradient experienced by the atomic sample of the first and second modules.

23. The method of claim 22, comprising facilitating identification of the property of the beam of radiation at a plurality of phase relationships between the first and second alternating magnetic fields, the plurality of phase relationships being usable to determine the magnetic field gradient.

24. The method of claim 22 or 23, comprising determining the magnetic field gradient where the phase relationship between the first and second alternating magnetic fields is out of phase.

25. The method of claim 24, comprising providing the first alternating magnetic field out of phase with the second alternating magnetic field by pi (TT) radians.

26. The method of any one of claims 22 to 25, comprising determining an ambient magnetic field experienced by the atomic sample of the first and second modules where the phase relationship between the first and second alternating magnetic fields is in phase.

27. The method of any one of claims 19 to 26, comprising separating the first component from the second component of the beam of radiation such that the first component has a different polarisation state to the second component.

28. The method of any one of claims 19 to 27, wherein the property is a rotation angle of a polarisation axis of the beam of radiation.

29. The method of claim 28, comprising detecting a change in the rotation angle based on a difference between the first and second components.

30. The method of any one of claims 19 to 29, comprising aligning a polarisation axis of the beam of radiation to be parallel to a magnetic field line of an ambient magnetic field.

31 . The method of any one of claims 19 to 30, comprising linearly polarising the beam of radiation for transmission through the atomic sample of the first and second modules.

32. The method of any one of claims 19 to 31 , comprising stabilising a radiation source such that its wavelength is stabilised relative to the transition.

33. The method of any one of claims 19 to 32, comprising producing the first and second alternating magnetic fields at a frequency sufficiently close to a Larmor frequency of the atomic sample such that a resonance condition is satisfied to facilitate identification of the property of the beam of radiation.

34. The method of claim 33, comprising using data obtainable from the first and second components of the beam of radiation to determine if the resonance condition is satisfied and if not satisfied, modifying the frequency until the resonance condition is satisfied.

35. The method of any one of claims 19 to 24, comprising distinguishing the magnetic field gradient from an ambient magnetic field to facilitate use of a detection apparatus comprising the first and second modules in an unshielded mode of operation.

36. A computer program product configured such that, when run on a suitable processing apparatus, causes the processing apparatus to at least partially implement the method of any one of claims 19 to 35.