Atomic magnetometer

Abstract

A method of measuring an external magnetic field using an atomic magnetometer comprises: using a polarized pump beam 1 to spin-polarise the atomic vapour; magnetising the polarized atomic vapour by a

Description

FIELD OF THE INVENTION The invention relates to a magnetometer, and particularly to an atomic magnetometer. BACKGROUND High-sensitivity operation of a radio frequency atomic magnetometer requires the precise application of a stable DC bias magnetic field. Operation in unshielded environment is difficult due to low-frequency ambient magnetic noise, which introduces fluctuations in the bias magnetic fields and affects the sensitivity of the magnetometer. Conventionally, this is addressed by measuring the actual value of the bias magnetic field with one or more fluxgate magnetometers in proximity of the atomic sensor, so to derive an approximate value of the field on the sensor. This value is then used to stabilize the bias field via a feedback system. This approach has two disadvantages: (1) reduced sensitivity of the fluxgate magnetometer with respect to the atomic sensor; and (2) measurements of the ambient field are not truly in-situ as it is impossible to overlap the fluxgate magnetometer with the atomic sensor. A magnetically-quiet environment is essential for a magnetometer to operate at extreme sensitivity. The response of the atoms is susceptible to changes in the surrounding magnetic field noise, with the amplitudes of the magnetic field signals to be detected typically several orders of magnitude smaller than the ambient magnetic field noise. A magnetically-quiet environment can be realised by either passive magnetic shielding or active magnetic field compensation systems. The former is done by shielding the experimental region with soft iron or large magnetic permeability materials, or with thick conducting material or superconducting layers. However, the shield reduces the field of applicability of the magnetometer, and limits the potential for measurements of large-sized samples. The ability to achieve a satisfactory ambient magnetic field noise reduction without any passive shielding is of interest in many situations, for instance, where easy access is required, or when large and magnetically clean volumes are needed, which would make the magnetic shield bulky and very expensive. Methods of unshielded operation have been proposed wherein an active compensation systems is used to this purpose. The currents in a set of magnetic field coils around the sensor are actively controlled in response to changes in the background magnetic field. One way to monitor the bias magnetic field is to place a miniature DC magnetic field sensor (such as a fluxgate magnetometer) in close proximity of the atomic sensing unit of the atomic magnetometer, along the bias field direction next to the cell. Alternatively, one can take the average of the output of a set of fluxgate sensors around the sensing unit to monitor the value of the magnetic field at the position of the magnetometer. SUMMARY In a first aspect there is described a method of measuring an external magnetic field using an atomic magnetometer comprising an atomic vapour cell containing an atomic vapour. The method comprises: using a polarized pump beam to spin-polarise the atomic vapour; magnetising the polarized atomic vapour in the atomic magnetometer by applying the first bias magnetic field to the atomic vapour cell containing the atomic vapour; using an oscillating excitation magnetic field in the atomic vapour to cause the atomic spins to precess about the first bias magnetic field, wherein using the oscillating excitation magnetic field comprises either i) applying the oscillating excitation magnetic field to the atomic vapour cell perpendicular to the first bias magnetic field, or ii) modulating the polarized pump beam ; and measuring the external magnetic field by measuring one or more properties of a probe beam passing through the atomic vapour. The method further comprises: compensating the atomic magnetometer for stray magnetic fields by: determining a phase-frequency response of the atomic magnetometer, wherein the phase-frequency response defines a variation, with a frequency of the oscillating excitation magnetic field, of a phase of a sensing signal of the atomic magnetometer derived from the probe beam and responsive to the external field, and applying a second bias magnetic field to the atomic vapour cell dependent on the determined phase-frequency response. This may provide any of a number of advantages. The atomic magnetometer allows for highly sensitive measurements of external oscillating magnetic fields, with no requirement for passive shielding. Accordingly, the atomic magnetometer may be used in a wide variety of applications. This also allows for miniaturisation of the atomic magnetometer compared to conventional shielded atomic magnetometers. Additionally, since fluxgate sensors are not required, the external magnetic field may be measured in-situ at the position of the magnetometer (rather than by averaging the magnetic field values measured by fluxgate sensors located around the magnetometer). Furthermore, the theoretical phase-frequency response is not affected by the intensity of the oscillating excitation magnetic field or the longitudinal relaxation time of atoms, and this reduces the risk of broadening caused by strong excitation magnetic fields. The oscillating excitation magnetic field may have an amplitude B’, where the actual Aty = ^1 + (^TT / 2)2 linewidth Aw of the magnetic resonance curve is T * , where Ti and T2 are the longitudinal and transverse spin relaxation lifetime respectively, which shows the combined contributions of transverse field amplitude and relaxation time. A strong oscillating excitation magnetic field may have an amplitude B! >The oscillating excitation magnetic field may be used continuously whilst the magnetometer is operating. The oscillating excitation magnetic field may have a frequency wex at, or close to, the Larmor frequency wl. In particular, the oscillating excitation magnetic field may have a frequency wex = wL ± 3Aw. More particularly, the oscillating excitation magnetic field may have a frequency wex = a)L + 2Aw . Even more particularly, the oscillating excitation magnetic field may have a frequency wex = wL + Aw. The oscillating excitation magnetic field may be applied as an oscillating excitation magnetic field, orthogonal to the first bias magnetic field. Alternatively, the pump beam may be modulated to produce a magnetic field that perturbs the magnetisation direction away from the magnetic field direction, so that precession of the spins about the magnetic field direction can take place. The pump beam may be frequency-modulated or amplitude-modulated. The pump beam may be modulated at a frequency wex at or close to the Larmor frequency. In particular, the pump beam may be modulated at a frequency wex = wL ± 3Aw. More particularly, the oscillating excitation magnetic field may be modulated at a frequency a)ex = a)L + 2Aa> . Even more particularly, the oscillating excitation magnetic field may be modulated at a frequency wex = <ml + Ato. The theoretical phase-frequency response may be an inverse trigonometric function of the frequency wex of the oscillating excitation magnetic field, and may have a value of zero at magnetic resonance (i.e. when the frequency of the oscillating excitation field wex matches the Larmor frequency wL). The Larmor frequency col is defined as shown in Equation (1) below: Ml = rl^l (1) where col is the Larmor frequency, y is the gyromagnetic ratio of the atoms in the atomic vapour, and \B\ is the magnitude of the total magnetic field B experienced by the atoms in the atomic vapour. The total magnetic field B experienced by the atoms in the atomic vapour cell is given by Equation (2): ® ^external T ^bias T ^stray (2) where Bextemai is the external magnetic field to be measured, Bbias is the bias magnetic field, and Bstray is the total stray magnetic field (i.e. the magnetic field due to sources other than the external magnetic field to be measured and the bias magnetic field). Since the value of wl may be affected by stray magnetic fields in addition to the external magnetic field to be measured and the bias magnetic field, the bias magnetic field may be adjusted to compensate for fluctuations in wL due to the stray magnetic fields, allowing the value of Bextemai to be measured more accurately. That is, a second bias magnetic field may be applied based on the determined phase-frequency response. The optical properties of the atomic vapour also depend on the total magnetic field B. Accordingly, by passing a probe beam through the atomic vapour and measuring one or more properties of the transmitted probe beam, the total magnetic field B (and hence the value of Bextemai) may be determined. The one or more properties of the transmitted probe beam may comprise one or more of: a transmittance of the probe beam, an AC component of the transmitted probe beam, a DC component of the transmitted probe beam, a polarisation angle of the transmitted probe beam, one or more polarisation components of the transmitted probe beam, and a ratio of two orthogonal polarisation components of the transmitted probe beam. The theoretical phase-frequency response measured in the x-direction of the magnetometer may be expressed as: = arctan(---——) ^ex - Where the oscillating excitation magnetic field B’ along the y-axis of the magnetometer is expressed as B = t)y, where B’ is the amplitude of the oscillating excitation magnetic field oscillating at wex, t is time, and y is the unit vector in the y-direction of the magnetometer, the bias magnetic field Bbtas is applied in the z-direction of the magnetometer and wl is the Larmor frequency corresponding to the bias magnetic field Bbias. The atomic magnetometer may comprise one or more photodetectors configured to derive the sensing signal from the probe beam. For example, the atomic magnetometer may comprise one or more photodetectors configured to measure two orthogonal polarisation components of the probe beam. The photodetectors may be further configured to measure the one or more properties of the probe beam. The external magnetic field may be an oscillating magnetic field. In particular, the external magnetic field may be a radio-frequency magnetic field, i.e. a magnetic field oscillating at a frequency between 300 Hz and 3,000 gigaHz. The atomic magnetometer may be a Hanle magnetometer. In particular, the atomic magnetometer may be a Hanle magnetometer operating in the SERF (spin exchange relaxation-free) regime. Advantageously, this may provide a highly sensitive measurement of the external magnetic field. Alternatively, the atomic magnetometer may be a Bell-Bloom magnetometer. The atomic magnetometer may be configured to stabilise one component of the bias magnetic field (e.g. to compensate for stray fields in a direction parallel to the probe beam). Alternatively, the atomic magnetometer may be configured to stabilise multiple orthogonal components of the bias magnetic field. The channel used to stabilize the bias magnetic field may demodulate the magnetometer response signal with a large bandwidth to capture the noise and generate the phase-frequency response, which allows the atomic magnetometer to use separate demodulation channels of different bandwidths to filter the noise and realise magnetic field measurement. In particular, the channel used to stabilise the bias magnetic field may demodulate the magnetometer response signal with a bandwidth of from 105 Hz to 1010 Hz. The channel used to measure the external magnetic field may demodulate the magnetometer response signal with a bandwidth of from 1Hz to 104 Hz. However, any bandwidth which is larger than that of the measurement channel may be used. In some implementations, i) measuring the external magnetic field comprises: measuring the external magnetic field at intervals of a first timescale xi, and applying the second bias magnetic field to the atomic vapour cell comprises determining a value of the second bias magnetic field at intervals of a second timescale X2, wherein X2 <xi; and / or ii) measuring the external magnetic field comprises: measuring the external magnetic field with a first bandwidth bi, and applying the second bias magnetic field to the atomic vapour cell comprises determining a value of the second bias magnetic field with a second bandwidth b2, wherein bi <b2. Advantageously, this enables the atomic magnetometer signal to be analysed at different bandwidths to produce the measurement of the external magnetic field and the signal used to suppress the ambient magnetic field fluctuations. The bandwidth can be derived from the corresponding time constant, e.g. based on the response of the relevant measurement which may have, e.g., a Lorentzian response or a Gaussian response, or some other response. The bandwidth bi may be the 3dB bandwidth or the NEP bandwidth for a low-pass filter with the time constant xi. The bandwidth b2 may be the 3dB bandwidth or the NEP bandwidth for a low-pass filter with the time constant X2. The bandwidths bi and b2 may be defined in the same way. In implementations, b2 may be at least 101, 102, 103, 104, 105, 106 or 107 times greater than bi. The second timescale X2 may be in the range of from 1 ns to 1,6ps Alternatively or additionally, the first timescale xi may be in the range of from 1ms to 100ms. Advantageously, low-frequency ambient magnetic field fluctuations may thus be suppressed, enabling the atomic magnetometer to be used to measure external magnetic fields oscillating at higher frequencies with greater sensitivity. Measuring the external magnetic field by measuring one or more properties of a probe beam passing through the atomic vapour may comprise determining the magnitude and direction of the external magnetic field based on the phase-frequency response. In particular, determining the magnitude and direction of the external magnetic field based on the phase-frequency response may comprise determining a ratio of two transverse (orthogonal) polarisation components of the probe beam to determine the phase of the sensing signal of the atomic magnetometer. The common coefficients of the in-phase and out-of-phase transverse components of the atomic spin polarisation vector precession signal cancel out in the ratio, so the phase-frequency response is insensitive to the common coefficient fluctuations of the two transverse components, and the phase values do not need to be normalized. The phase-frequency response is therefore more stable than the two transverse components and the amplitudefrequency signal and can be directly used for the closed loop control of the bias magnetic field. In some implementations, determining the second bias magnetic field may comprise determining a magnitude and direction of the second bias magnetic field calculated to reduce a magnitude of the phase-frequency response. That is, the magnitude and direction of the second bias magnetic field may be calculated to move the atomic magnetometer closer to the magnetic resonance, and thereby compensate for stray magnetic fields and enhance the sensitivity of the atomic magnetometer (assuming a constant phase offset of the phase-frequency response). A magnitude of the phase-frequency response of the magnetometer may thus be maintained at (or close to) zero by adjusting the bias magnetic field to stabilise the bias magnetic field, so to obtain magnetic resonance at a specified operating frequency without magnetic shielding. In some implementations, obtaining the phase-frequency response may comprise performing spectrum analysis on a signal derived from the probe beam. In some implementations, obtaining the phase-frequency response may comprise: receiving, using a lock-in amplifier, a signal derived from the probe beam, and demodulating the signal derived from the probe beam using the oscillating excitation magnetic field as a reference. The lock-in amplifier may be a dual-channel amplifier, and determining a second bias magnetic field may comprise: inputting the signal derived from the probe beam to a first channel of the amplifier, and measuring the external magnetic field may comprise inputting the signal derived from the probe beam to a second channel of the amplifier. In some implementations, the method may further comprise: emitting, by the atomic magnetometer, an oscillating probe magnetic field, and measuring the external magnetic field may comprise measuring an external magnetic field induced by the oscillating probe magnetic field. Advantageously, this enables the method to be used to detect the presence of metals. The atomic vapour may be an alkali metal vapour - that is, the atomic vapour may comprise atoms of an alkali metal. In some implementations, the atomic vapour comprises rubidium-87 vapour. Advantageously, this may increase the dynamic range of the atomic magnetometer. In some implementations, the atomic vapour comprises rubidium-85 vapour. Advantageously, this may increase the signal-to-noise ratio of the atomic magnetometer. In some implementations, the atomic vapour comprises caesium-133 vapour. Advantageously, this may provide a higher vapour pressure in the atomic vapour cell at a given atomic vapour cell temperature, and therefore enhance the performance of the atomic magnetometer at lower temperatures. In some implementations, the atomic vapour comprises potassium-39 vapour. Advantageously, this may increase the sensitivity of the atomic magnetometer. However, any suitable alkali metal may be used in the alkali metal vapour. The atomic vapour cell may further comprise a buffer gas. Advantageously, collisions between the alkali metal atoms and the buffer gas atoms may reduce the diffusion speed of the alkali metal atoms, reducing the probability that the alkali metal atoms will collide with the walls of the atomic vapour cell and thereby reduce the spin-coherence of the atomic vapour. The buffer gas may be nitrogen (N2) or helium-4 (He). Where the buffer gas is nitrogen, the buffer gas may also act as a quenching gas for the atomic vapour cell. Advantageously, the buffer gas may prevent radiation trapping of spontaneous emission. Alternatively or additionally, the internal surfaces of the atomic vapour cell may be provided with an anti-relaxation coating (for example, paraffin). In some implementations, the first bias magnetic field and the second bias magnetic field may be applied along the same axis. In particular, the first and second bias magnetic field may each be applied parallel to the axis of the probe beam. The pump beam may be an electromagnetic probe beam. In particular, the pump beam may be a laser (more particularly, a continuous-wave laser), and the probe beam may be circularly polarised. The continuous-wave laser may be implemented using a diode laser. The probe beam may be an electromagnetic probe beam. In particular, the probe beam may be a laser (more particularly, a continuous-wave laser), and the probe beam may be linearly polarised. The continuous-wave laser may be implemented using a diode laser. The pump beam and the probe beam may be orthogonally interacted in the atomic vapour cell (that is, the axis of the pump beam may be orthogonal to the axis of the probe beam). Alternatively, the pump beam and probe beam may be interacted at an angle other than 90°. In some implementations, the probe beam and pump beam may be continuously applied to the atomic vapour cell. Alternatively, the application of the probe beam and the pump beam to the atomic vapour cell may be alternating, such that the probe beam and pump beam are not applied to the atomic vapour cell at the same time. In some implementations, a single probe beam is used. In other implementations, two probe beams are used. Advantageously, this increases the efficiency and the sensitivity of the atomic magnetometer. The two probe beams may be orthogonal to one another, and also both orthogonal to the pump beam. The frequency of the pump beam may be selected to cause a first atomic transition of the atoms in the atomic vapour. In particular, the first atomic transition may be the D1 line of the atoms. The frequency of the probe beam may be selected to cause a second atomic transition of the atoms in the atomic vapour, or, alternatively, may be detuned from the frequency of the second atomic transition. In particular, the second atomic transition may be the D2 line of the atoms. The frequency of the probe beam may be detuned from the frequency of the second atomic transition, to reduce the loss of light power. The frequency of the probe beam may be blue-detuned from the frequency of the second atomic transition (that is, the probe beam may have a frequency greater than that of the second atomic transition), to improve the convenience of locking the laser frequency. In another aspect there is provided a magnetometer comprising an atomic vapour cell containing an atomic vapour. The magnetometer is configured to: use a polarized pump beam to spin-polarise the atomic vapour; magnetise the polarized atomic vapour in the atomic magnetometer by applying the first bias magnetic field to the atomic vapour cell containing the atomic vapour; use, to cause the atomic spins to precess about the first bias magnetic field, an oscillating excitation magnetic field in the atomic vapour, wherein using the oscillating excitation magnetic field comprises either i) applying the oscillating excitation magnetic field to the atomic vapour cell perpendicular to the first bias magnetic field, or ii) modulating the polarized pump beam; measure the external magnetic field by measuring one or more properties of a probe beam passing through the atomic vapour. The magnetometer is further configured to: compensate the atomic magnetometer for stray magnetic fields by: determining a phase-frequency response of the atomic magnetometer, wherein the phase frequency response defines a variation, with a frequency of the oscillating excitation magnetic field, of a phase of a sensing signal of the atomic magnetometer derived from the probe beam and responsive to the external field, and applying a second bias magnetic field to the atomic vapour cell dependent on the determined phase-frequency response. This may provide any of a number of advantages. The atomic magnetometer allows for highly sensitive measurements of external oscillating magnetic fields, with no requirement for passive shielding. Accordingly, the atomic magnetometer may be used in a wide variety of applications. This also allows for miniaturisation of the atomic magnetometer compared to conventional shielded atomic magnetometers. Additionally, since fluxgate sensors are not required, the external magnetic field may be measured in-situ at the position of the magnetometer (rather than by averaging the magnetic field values measured by fluxgate sensors located around the magnetometer). Furthermore, the theoretical phase-frequency response is not affected by the intensity of the oscillating excitation magnetic field or the longitudinal relaxation time of atoms, and this reduces the risk of broadening caused by strong excitation magnetic fields. The oscillating excitation magnetic field may have an amplitude B’, where the actual A® = ^1 +(^72)2^ linewidth Aw of the magnetic resonance curve is 2 2 , where Ti and T2 are the longitudinal and transverse spin relaxation lifetime respectively, which shows the combined contributions of transverse field amplitude and relaxation time. A strong oscillating excitation magnetic field may have an amplitude B' >^7^- / ^1^2- The oscillating excitation magnetic field may be used continuously whilst the magnetometer is operating. The oscillating excitation magnetic field may have a frequency wex at, or close to, the Larmor frequency wl. In particular, the oscillating excitation magnetic field may have a frequency a)ex = a)L + 3 Aoi. More particularly, the oscillating excitation magnetic field may have a frequency a)ex = a)L + 2Ato . Even more particularly, the oscillating excitation magnetic field may have a frequency a)ex = a)L+ The oscillating excitation magnetic field may be applied as an oscillating excitation magnetic field, orthogonal to the first bias magnetic field. Alternatively, the pump beam may be modulated to produce a magnetic field that perturbs the magnetisation direction away from the magnetic field direction, so that precession of the spins about the magnetic field direction can take place. The pump beam may be frequency-modulated or amplitude-modulated. The pump beam may be modulated at a frequency wex at or close to the Larmor frequency. In particular, the pump beam may be modulated at a frequency a)ex = a)L± 3 Aw. More particularly, the pump beam may be modulated at a frequency a)ex = ml + 2Aw. Even more particularly, the pump beam may be modulated at a frequency ajex = ± Aw. The theoretical phase-frequency response may be an inverse trigonometric function of the frequency wex of the oscillating excitation magnetic field, and may have a value of zero at magnetic resonance (i.e. when the frequency of the oscillating excitation field coex matches the Larmor frequency wQ. The Larmor frequency col is defined as shown in Equation (1) below: = rl^l (1) where col is the Larmor frequency, y is the gyromagnetic ratio of the atoms in the atomic vapour, and \B\ is the magnitude of the total magnetic field B experienced by the atoms in the atomic vapour. The total magnetic field B experienced by the atoms in the atomic vapour cell is given by Equation (2): B external T ^bias T ^stray (2) where Bextemai is the external magnetic field to be measured, Bbias is the bias magnetic field, and Bstray is the total stray magnetic field (i.e. the magnetic field due to sources other than the external magnetic field to be measured and the bias magnetic field). Since the value of col may be affected by stray magnetic fields in addition to the external magnetic field to be measured and the bias magnetic field, the bias magnetic field may be adjusted to compensate for fluctuations in wl due to the stray magnetic fields, allowing the value of Bextemai to be measured more accurately. That is, a second bias magnetic field may be applied based on the determined phase-frequency response. The optical properties of the atomic vapour also depend on the total magnetic field B. Accordingly, by passing a probe beam through the atomic vapour and measuring one or more properties of the transmitted probe beam, the total magnetic field B (and hence the value of Bextemai) may be determined. The one or more properties of the transmitted probe beam may comprise one or more of: a transmittance of the probe beam, an AC component of the transmitted probe beam, a DC component of the transmitted probe beam, a polarisation angle of the transmitted probe beam, one or more polarisation components of the transmitted probe beam, and a ratio of two orthogonal polarisation components of the transmitted probe beam. The theoretical phase-frequency response response measured in the x-direction of the magnetometer may be expressed as: e(?) T = arctan(-----—) ^ex where the oscillating excitation magnetic field B! along the y-axis of the magnetometer is expressed as B = B'cos(a)ex L)y, where B’ is the amplitude of the oscillating excitation magnetic field oscillating at wex, t is time, and y is the unit vector in the y-direction of the magnetometer, the bias magnetic field Bbias is applied in the z-direction of the magnetometer and wl is the Larmor frequency corresponding to the bias magnetic field Bbias. The atomic magnetometer may comprise one or more photodetectors configured to derive the sensing signal from the probe beam. For example, the atomic magnetometer may comprise one or more photodetectors configured to measure two orthogonal polarisation components of the probe beam. The photodetectors may be further configured to measure the one or more properties of the probe beam. The external magnetic field may be an oscillating magnetic field. In particular, the external magnetic field may be a radio-frequency magnetic field, i.e. a magnetic field oscillating at a frequency between 300 Hz and 3,000 gigaHz. The atomic magnetometer may be a Hanle magnetometer. In particular, the atomic magnetometer may be a Hanle magnetometer operating in the SERF (spin exchange relaxation-free) regime. Advantageously, this may provide a highly sensitive measurement of the external magnetic field. Alternatively, the atomic magnetometer may be a Bell-Bloom magnetometer. The atomic magnetometer may be configured to stabilise one component of the bias magnetic field (e.g. to compensate for stray fields in a direction parallel to the probe beam). Alternatively, the atomic magnetometer may be configured to stabilise multiple orthogonal components of the bias magnetic field. The channel used to stabilize the bias magnetic field may demodulate the magnetometer response signal with a large bandwidth to capture the noise and generate the phase-frequency response, which allows the atomic magnetometer to use separate demodulation channels of different bandwidths to filter the noise and realise magnetic field measurement. In particular, the channel used to stabilise the bias magnetic field may demodulate the magnetometer response signal with a bandwidth of from 105 Hz to 1010 Hz. The channel used to measure the external magnetic field may demodulate the magnetometer response signal with a bandwidth of from 1Hz to 104 Hz. However, any bandwidth which is larger than that of the measurement channel may be used. In some implementations, i) measuring the external magnetic field comprises: measuring the external magnetic field at intervals of a first timescale Xi, and applying the second bias magnetic field to the atomic vapour cell comprises determining a value of the second bias magnetic field at intervals of a second timescale X2, wherein X2 <Xi; and / or ii) measuring the external magnetic field comprises: measuring the external magnetic field with a first bandwidth bi, and applying the second bias magnetic field to the atomic vapour cell comprises determining a value of the second bias magnetic field with a second bandwidth b2, wherein bi <b2. Advantageously, this enables the atomic magnetometer signal to be analysed at different bandwidths to produce the measurement of the external magnetic field and the signal used to suppress the ambient magnetic field fluctuations. The bandwidth can be derived from the corresponding time constant, e.g. based on the response of the relevant measurement which may have, e.g., a Lorentzian response or a Gaussian response, or some other response. The bandwidth bi may be the 3dB bandwidth or the NEP bandwidth for a low-pass filter with the time constant xi. The bandwidth b2 may be the 3dB bandwidth or the NEP bandwidth for a low-pass filter with the time constant X2. The bandwidths bi and b2 may be defined in the same way. In implementations, b2 may be at least 101, 102, 103, 104, 105, 106 or 107 times greater than bi. The second timescale X2 may be in the range of from 1 ns to 1,6ps. Alternatively or additionally, the first timescale xi may be in the range of from 1ms to 100ms. Advantageously, low-frequency ambient magnetic field fluctuations may thus be suppressed, enabling the atomic magnetometer to be used to measure external magnetic fields oscillating at higher frequencies with greater sensitivity. Measuring the external magnetic field by measuring one or more properties of a probe beam passing through the atomic vapour may comprise determining the magnitude and direction of the external magnetic field based on the phase-frequency response. In particular, determining the magnitude and direction of the external magnetic field based on the phase-frequency response may comprise determining a ratio of two transverse (orthogonal) polarisation components of the probe beam to determine the phase of the sensing signal of the atomic magnetometer. The common coefficients of the in-phase and out-of-phase transverse components of the atomic spin polarisation vector precession signal cancel out, so the phase-frequency response is insensitive to the common coefficient fluctuations of the two transverse components, and the phase values do not need to be normalized. The phase-frequency response is therefore more stable than the two transverse components and the amplitude-frequency signal and can be directly used for the closed loop control of the bias magnetic field. In some implementations, determining the second bias magnetic field may comprise determining a magnitude and direction of the second bias magnetic field calculated to reduce a magnitude of the phase-frequency response. That is, the magnitude and direction of the second bias magnetic field may be calculated to move the atomic magnetometer closer to the magnetic resonance, and thereby compensate for stray magnetic fields and enhance the sensitivity of the atomic magnetometer (assuming a constant phase offset of the phase-frequency response). A magnitude of the phase-frequency response of the magnetometer may thus be maintained at (or close to) zero by adjusting the bias magnetic field to stabilise the bias magnetic field, so to obtain magnetic resonance at a specified operating frequency without magnetic shielding. In some implementations, obtaining the phase-frequency response may comprise performing spectrum analysis on a signal derived from the probe beam. In some implementations, obtaining the phase-frequency response may comprise: receiving, using a lock-in amplifier, a signal derived from the probe beam, and demodulating the signal derived from the probe beam using the oscillating excitation magnetic field as a reference. The lock-in amplifier may be a dual-channel amplifier, and determining a second bias magnetic field may comprise: inputting the signal derived from the probe beam to a first channel of the amplifier, and measuring the external magnetic field may comprise inputting the signal derived from the probe beam to a second channel of the amplifier. In some implementations, the method may further comprise: emitting, by the atomic magnetometer, an oscillating probe magnetic field, and measuring the external magnetic field may comprise measuring an external magnetic field induced by the oscillating probe magnetic field. Advantageously, this enables the method to be used to detect the presence of metals. The atomic vapour may be an alkali metal vapour - that is, the atomic vapour may comprise atoms of an alkali metal. In some implementations, the atomic vapour comprises rubidium-87 vapour. Advantageously, this may increase the dynamic range of the atomic magnetometer. In some implementations, the atomic vapour comprises rubidium-85 vapour. Advantageously, this may increase the signal-to-noise ratio of the atomic magnetometer. In some implementations, the atomic vapour comprises caesium-133 vapour. Advantageously, this may provide a higher vapour pressure in the atomic vapour cell at a given atomic vapour cell temperature, and therefore enhance the performance of the atomic magnetometer at lower temperatures. In some implementations, the atomic vapour comprises potassium-39 vapour. Advantageously, this may increase the sensitivity of the atomic magnetometer. However, any suitable alkali metal may be used in the alkali metal vapour. The atomic vapour cell may further comprise a buffer gas. Advantageously, collisions between the alkali metal atoms and the buffer gas atoms may reduce the diffusion speed of the alkali metal atoms, reducing the probability that the alkali metal atoms will collide with the walls of the atomic vapour cell and thereby reduce the spin-coherence of the atomic vapour. The buffer gas may be nitrogen (N2) or helium-4 (He). Where the buffer gas is nitrogen, the buffer gas may also act as a quenching gas for the atomic vapour cell. Advantageously, the buffer gas may prevent radiation trapping of spontaneous emission. Alternatively or additionally, the internal surfaces of the atomic vapour cell may be provided with an anti-relaxation coating (for example, paraffin). In some implementations, the first bias magnetic field and the second bias magnetic field may be applied along the same axis. In particular, the first and second bias magnetic field may each be applied parallel to the axis of the probe beam. The pump beam may be an electromagnetic probe beam. In particular, the pump beam may be a laser (more particularly, a continuous-wave laser), and the probe beam may be circularly polarised. The continuous-wave laser may be implemented using a diode laser. The probe beam may be an electromagnetic probe beam. In particular, the probe beam may be a laser (more particularly, a continuous-wave laser), and the probe beam may be linearly polarised. The continuous-wave laser may be implemented using a diode laser. The pump beam and the probe beam may be orthogonally interacted in the atomic vapour cell (that is, the axis of the pump beam may be orthogonal to the axis of the probe beam). Alternatively, the pump beam and probe beam may be interacted at an angle other than 90°. In some implementations, the probe beam and pump beam may be continuously applied to the atomic vapour cell. Alternatively, the application of the probe beam and the pump beam to the atomic vapour cell may be alternating, such that the probe beam and pump beam are not applied to the atomic vapour cell at the same time. In some implementations, a single probe beam is used. In other implementations, two probe beams are used. Advantageously, this increases the efficiency and the sensitivity of the atomic magnetometer. The two probe beams may be orthogonal to one another, and also both orthogonal to the pump beam. The frequency of the pump beam may be selected to cause a first atomic transition of the atoms in the atomic vapour. In particular, the first atomic transition may be the D1 line of the atoms. The frequency of the probe beam may be selected to cause a second atomic transition of the atoms in the atomic vapour, or, alternatively, may be detuned from the frequency of the second atomic transition. In particular, the second atomic transition may be the D2 line of the atoms. The frequency of the probe beam may be blue-detuned from the frequency of the second atomic transition (that is, the probe beam may have a frequency greater than that of the second atomic transition), to improve the convenience of locking the laser frequency. BRIEF DESCRIPTION OF THE DRAWINGS These and other aspects of the invention will now be further described, by way of example only, with reference to the accompanying figures in which: Figure 1 is a schematic diagram of an atomic magnetometer. Figure 2 is a schematic diagram of an atomic magnetometer. Figure 3 shows a method of operating an atomic magnetometer. DETAILED DESCRIPTION In general terms, the invention relates to a method for stabilizing the bias magnetic field in a radio-frequency atomic magnetometer based on atomic magnetic resonance phase frequency analysis, implemented by: the application of a bias magnetic field and the use of an oscillating excitation magnetic field perpendicular to the bias magnetic field, whose resonance frequency is determined by the bias magnetic field. The response signal of the atomic magnetometer may be subjected to spectrum analysis or demodulated by a lock-in amplifier at the frequency of the oscillating excitation magnetic field to obtain the phase-frequency response of the magnetometer. As discussed above, the operation frequency range of the atomic magnetometer is set by the total magnetic field B experienced by the atomic vapour cell, which can be expressed as shown in Equation (1) below: = rl#l (1) where wl is the Larmor frequency, y is the gyromagnetic ratio of the atoms in the atomic vapour, and \B\ is the magnitude of the total magnetic field B. The operation frequency fL in Hz is related to the Larmor frequency wl in rad s-1 as shown in Equation (3) below: 'L “ 2n (3) The Larmor frequency col is the frequency corresponding to magnetic resonance of the atomic magnetometer. In other words, the atomic magnetometer will be most sensitive to external magnetic fields oscillating at frequencies close to fL. The bias magnetic field is selected to provide a magnitude of the total magnetic field B such that fi is close to the frequency or frequencies of external magnetic field fextemai which to be measured. In particular, the bias magnetic field may be selected such that fexternai = A ± 3A / , where Lf = — (and, more generally, ui = 2TTf). More particularly, the bias magnetic 2n field may be selected such that fexternai = fL± 2hf . Even more particularly, the bias magnetic field may be selected such that fextemai = fL± &f. Figure 1 shows an atomic magnetometer 100 according to an embodiment of the invention. The atomic magnetometer 100 comprises an atomic vapour cell 106 comprising an atomic vapour. The atomic vapour may comprise any suitable atoms. For example, the atomic vapour may be an alkali metal vapour - that is, the atomic vapour may comprise atoms of an alkali metal. The alkali metal may be rubidium-85, rubidium-87, caesium-133, or potassium-39, or any other suitable alkali metal. The atomic vapour cell may further comprise a buffer gas to assist in maintaining the spin-coherence of the polarised atomic vapour, such as nitrogen (N2). Alternatively or additionally, the inner surfaces of the atomic vapour cell 106 may be provided with an anti-relaxation coating to assist in maintaining the spin-coherence of the polarised atomic vapour. The atomic magnetometer 100 further comprises a heating device 107 configured to heat the atomic vapour cell 106. The heating device 107 may be a non-magnetic electric heating device to avoid generating additional stray magnetic fields. Alternatively, the atomic magnetometer 100 may be configured to compensate for the effect of the stray magnetic fields generated by the heating device 107, or to filter magnetic fields at the frequencies generated by the heating device 107. The atomic magnetometer 100 may further comprise heat insulation to reduce thermal convection and heat conduction so to maintain a stable temperature in the atomic vapour cell 106. The atomic magnetometer 100 further comprises a pump beam generator 101 configured to generate a polarized pump beam 1011. The pump beam 1011 may be circularly polarised. The pump beam generator 101 may comprise a laser, which may be a continuous-wave laser. The atomic magnetometer 100 further comprises a probe beam generator 109 configured to generate a polarized probe beam 1091. The probe beam 1091 may be linearly polarised. The probe beam generator 109 may comprise a laser, which may be a continuous-wave laser. In the embodiment of Fig. 1, the probe beam 1091 is directed along the x axis of the atomic magnetometer 100, but in variants of the embodiment the probe beam 1091 may be applied along any axis perpendicular to the axis of the bias magnetic field. The atomic magnetometer 100 further comprises a bias magnetic field generator 105a configured to apply a bias magnetic field to the atomic vapour cell along the axis of the pump beam 1011. In the embodiment of Fig. 1, the bias magnetic field is applied to the atomic vapour cell 106 along the z axis of the atomic magnetometer 100, but in variants of the embodiment the bias magnetic field may be applied along any axis. The atomic magnetometer also comprises an oscillating excitation field generator 105b configured to generate an oscillating excitation magnetic field orthogonal to the bias magnetic field, the oscillating excitation magnetic field oscillating at the operating frequency corresponding to the frequency of the external magnetic field to be measured. In the embodiment of Fig. 1, the oscillating excitation magnetic field is applied to the atomic vapour cell 106 along the y axis, but in variants of the embodiment the oscillating excitation magnetic field may be applied along any axis perpendicular to the axis of the bias magnetic field. The atomic magnetometer 100 further comprises a detector 113. The detector 113 is configured to measure one or more properties of the probe beam 1092. Based on the one or more properties, the detector 113 is configured to obtain a sensing signal 1131, and provide the sensing signal 1131 as an input to the phase-frequency response determination unit 114. The atomic magnetometer 100 further comprises a phase-frequency response determination unit 114. The phase-frequency determination unit 114 is configured to determine a phase-frequency response 1141 of the atomic magnetometer 100, wherein the phase-frequency response 1141 defines a variation, with a frequency of the oscillating excitation magnetic field, of a phase of the sensing signal 1131 of the atomic magnetometer 100 derived from the transmitted probe beam 1092 and responsive to the external magnetic field. The phase-frequency response determination unit 114 may be configured to determine the phase-frequency response 1141 by determining a ratio of two orthogonal polarisation components of the transmitted probe beam 1092. The phase-frequency response determination unit 114 is configured to provide the determined phase-frequency response 1141 to the bias magnetic field controller 115. In some implementations of the embodiment of Fig. 1, the phase-frequency response determination unit 114 may comprise a lock-in amplifier configured to receive the sensing signal derived from the probe beam, and demodulate the sensing signal derived from the probe beam using the oscillating excitation magnetic field as a reference. More particularly, the lock-in amplifier may be a dual-channel amplifier. Alternatively or additionally, the phase-frequency response determination unit 114 may comprise a spectrum analyser configured to perform spectrum analysis of the sensing signal 1131 derived from the probe beam. The atomic magnetometer 100 further comprises a bias magnetic field controller 115. The bias magnetic field controller 115 is configured to control, by outputting control signal 1151, the magnitude and direction of the bias magnetic field applied by the bias field generator 105a based on the output 1141 of the phase-frequency response determination unit 114. The atomic magnetometer 100 further comprises an external magnetic field measurement unit 116. The external magnetic field measurement unit 116 is configured to receive the sensing signal 1131 from the detector 113 and, based on the one or more measured properties of the transmitted probe beam 1092, determine a magnitude 1161 of an external magnetic field to which the atomic magnetometer 100 is subject. Before being used to measure an external magnetic field, the atomic magnetometer 100 may be calibrated to optimise its accuracy and / or sensitivity. For example, the magnitude of a magnetic field applied along the x and y axes may be varied and the resulting Larmor frequency measured, in order to determine an applied magnetic field along the x and y axes minimises the Larmor frequency (i.e. compensates for stray fields along the x and y axes). The temperature of the atomic vapour cell may be adjusted in order to vary the density of the atomic vapour and optimise the intensity of the measured probe beam signal. The properties of the pumping laser (for example, the intensity and wavelength) may be adjusted to ensure that the variation in the intensity of the probe beam is detectable by photodetector 113, and may be further adjusted to optimise the intensity of the measured probe signal. In use, the pump beam 1011 interacts with the atoms of the atomic vapour in the atomic vapour cell 106 to spin-polarize the atomic vapour. The bias magnetic field generator 105a generates a first bias magnetic field along the z-axis (parallel to axis of pump beam 1011) which is applied to the spin-polarized atomic vapour. The magnitude of the first bias magnetic field is selected to provide a Larmor frequency col corresponding to the desired operating frequency of the atomic magnetometer 100 (i.e. the frequency of external magnetic fields to be measured), according to Equation (1). In the embodiment of Fig. 1, the pump beam 1011 is used to spin-polarize the atomic vapour before the first bias magnetic field is applied. However, in variants of the embodiment, the order of these steps may be reversed, or the pump beam 1011 may be interacted with the atomic vapour and the first bias magnetic field generated simultaneously. The oscillating excitation field generator 105b is then used to apply an oscillating excitation magnetic field, orthogonal to the first bias magnetic field and oscillating at the Larmor frequency, to the atomic vapour cell 106. The application of the oscillating excitation magnetic field perturbs the magnetisation direction away from the magnetic field direction, so that precession of the spins about the magnetic field direction can take place. Thereby, applying the oscillating excitation magnetic field causes the spins of the atoms in the atomic vapour to precess about the axis of the total magnetic field. In the embodiment of Fig. 1, the oscillating excitation field generator 105b is used to apply an oscillating excitation magnetic field, orthogonal to the first bias magnetic field. However, in variants of the embodiment, the oscillating excitation field generator 105b may modulate the pump beam to produce a magnetic field that perturbs the magnetisation direction away from the magnetic field direction, so that precession of the spins about the magnetic field direction can take place. The pump beam may be frequency-modulated or amplitude-modulated. The pump beam may be modulated at a frequency wex at or close to the Larmor frequency. . In particular, the oscillating excitation magnetic field may have a frequency coex = ml± 3 Aco. More particularly, the oscillating excitation magnetic field may have a frequency coex = coL± 2Aco. Even more particularly, the oscillating excitation magnetic field may have a frequency a)ex = a)L + A&j. In use, the atomic magnetometer 100 may be subject to both the external magnetic field to be measured and stray magnetic fields (in addition to the bias magnetic field and the oscillating excitation magnetic field). Accordingly, the total magnetic field experienced by the atoms of the atomic vapour may vary. The changing total magnetic field affects the optical properties of the atomic vapour (for example, by changing the value of the Larmor frequency, and therefore changing the phase-frequency response of the atomic magnetometer 100). Thus, by measuring one or more properties of the probe beam 1092 which is transmitted through the atomic vapour cell 106, the atomic magnetometer 100 can be used to measure the external magnetic field and any stray magnetic fields. The probe beam 1091 is received by the atomic vapour cell 106 and interacts with the atoms of the atomic vapour to produce transmitted probe beam 1092. One or more properties of the transmitted probe beam 1092 are measured by the detector 113. Based on the one or more properties, the detector 113 obtains a sensing signal 1131, which is received as an input by the phase-frequency response determination unit 114. Based on the sensing signal 1131, the phase-frequency response determination unit 114 determines a phase-frequency response 1141 of the atomic magnetometer 100. The determined phase-frequency response 1141 is received by the bias magnetic field controller 115. Based on the phase-frequency response 1141, the bias magnetic field controller 115 determines a magnitude and a direction of a second bias magnetic field to be applied to the atomic vapour cell 106 via the bias magnetic field generator 105a, and transmit a control signal 1151 to the bias magnetic field generator 105a. In particular, the bias magnetic field controller 115 may determine a magnitude and a direction of a second bias magnetic field to reduce a magnitude of the phase-frequency response 1141, and thereby move the atomic magnetometer 100 closer to magnetic resonance. The pump beam 1011 and probe beam 1091 are orthogonally interacted in the atomic vapour cell 106 in the embodiment of Fig. 1, but in variants of the embodiment the pump beam 1011 and probe beam 1091 may be interacted in the atomic vapour at an angle other than 90°. In some implementations, the probe beam 1011 and pump beam 1091 are continuously applied to the atomic vapour cell 106. Alternatively, the application of the probe beam 1011 and the pump beam 1091 to the atomic vapour cell 106 may be alternating, such that the probe beam 1011 and pump beam 1091 are not applied to the atomic vapour cell 106 at the same time. The bias magnetic field controller 115 is further configured to transmit control signal 1151 to control the bias magnetic field generator 105a to apply the second bias magnetic field to atomic vapour cell 106, and thereby stabilise the total bias magnetic field experienced by the atomic vapour cell 106. In some implementations of the atomic magnetometer of Figure 1, the bias magnetic field controller 115 and bias magnetic field generator 105a may cooperate to stabilise one orthogonal component of the bias magnetic field (for example, a component parallel to one of the coils of a coil set used to generate the bias magnetic field). In other implementations, the bias magnetic field controller 115 and bias magnetic field generator 105a may cooperate to stabilise two or more orthogonal components of the bias magnetic field. The atomic magnetometer 100 further comprises an external magnetic field measurement unit 116. External magnetic field measurement unit 116 is configured to receive the sensing signal 1131 and, based on one or more measured properties of the transmitted probe beam 1092, determine a magnitude and a direction of the external magnetic field 1161. Alternatively or additionally, the external magnetic field measurement unit 116 may be configured to receive the calculated phase-frequency response from the phase-frequency response determination unit 114, and to obtain a magnitude and a direction of the external magnetic field 1161 based on the phasefrequency response. In the embodiment of Fig 1, the external magnetic field measurement unit 116 is configured to determine the external magnetic field 1161 at intervals of a first timescale Xi. The bias magnetic field controller 115 is configured to determine the second bias magnetic field at intervals of a second timescale X2, where X2 <Xi. The second timescale X2 may be in the range of from 1 ns to 1,6ps. Alternatively or additionally, the first timescale xi may be in the range of from 1ms to 100ms. The corresponding bandwidth can be derived from the time constant, e.g. based on the response of the relevant measurement which may have, e.g., a Lorentzian response or a Gaussian response, or some other response. The bandwidth bi may be the 3dB bandwidth or the NEP bandwidth for a low-pass filter with the time constant xi. The bandwidth bz may be the 3dB bandwidth or the NEP bandwidth for a low-pass filter with the time constant xz. The bandwidths bi and bz may be defined in the same way. In implementations of the embodiment of Fig. 1, bz may beat least 101, 102, 103, 104, 105, 106 or 107 times greater than bi. The atomic magnetometer 100 may further comprise a means for generating a probe magnetic field. The external magnetic field measurement unit 116 may then be used to measure the external magnetic field induced in metallic objects by the probe magnetic field, and thereby detect metallic objects. Figure 2 shows one particular implementation of the magnetometer of Figure 1. The atomic magnetometer of Figure 2 is a radio-frequency atomic magnetometer, the atomic magnetometer comprising a lock-in amplifier 14. The internal part of the atomic magnetometer comprises an alkali metal vapour cell 6 and its outer part comprises a non-magnetic electric heating device 7, heat insulation chamber 8 and coil set 5. The non-magnetic electric heating device 7 is used to heat the alkali metal vapour cell 6, and the heat insulation chamber 8 is used to reduce thermal convection and heat conduction so to maintain a stable cell temperature. The set of coils 5 (x coil, y coil, and z coil) is used to generate magnetic fields in three orthogonal directions. Along the z direction are a pumping laser 1, a beam expander 2, a first polariser 3 and a quarterwave plate 4 to generate circularly polarised light to polarize the alkali metal vapour. The pumping laser 1 is a continuous-wave (CW) laser. The probe light path in the x direction, including a probe laser 9, a second polariser 10, a half-wave plate 11, a polarising beam splitter prism 12, a mirror 17 and a balanced photodetector 13 to detect the rotation of the polarisation plane of the linearly polarised probe light caused by the precession of the polarisation vector. The probe laser is a continuous-wave (CW) laser. Advantageously, the pumping light (circularly polarised) and the probe light (linearly polarised) are orthogonally interacted at the centre of the alkali metal vapour cell 6. In variants of the embodiment, the pumping light and the probe light may not be orthogonal to one another, and any suitable arrangement of the pumping light and probe light which allows the atomic vapour to be polarised by the pumping light and interrogated by the probe light may be used. A transverse excitation oscillation magnetic field is applied to the spins in the atomic vapour through the y coil and also used as a reference to demodulate the magnetometer response signal detected by the balanced photodetector 13. In use, the alkali metal vapour cell 6 in the heat insulation chamber 8 is heated to between 40°C and 200°C through the non-magnetic electric heating device 7 to vaporise the alkali metal, the pumping laser 1 is turned on, and the beam expander 2 makes the pumping light cover the entire alkali metal vapour cell 6, generate linearly polarised light with the help of the first polariser 3, and generate circularly polarised pumping light propagating along the z direction with the help of the quarter-wave plate 4. The alkali metal vapour cell 6 may be heated to near room temperature, i.e. 40±5°C. As discussed above regarding the atomic magnetometer of Figure 1, properties of the atomic magnetometer such as atomic vapour cell temperature, pumping laser frequency, pumping laser intensity, and bias magnetic field magnitude may be varied to optimise the accuracy and the sensitivity of the atomic magnetometer. For example, the temperature of the alkali metal vapour cell 6 may be varied to optimise the linewidth and amplitude of the signal. The pumping light frequency is adjusted to the D1 line of rubidium atoms. The probe laser 9 is turned on to obtain linearly polarised light propagating along the x direction through the second polariser 10. Advantageously, the probe light frequency is adjusted to be blue detuned with respect to the D2 line of rubidium 87 atoms to improve the convenience of locking the probe laser frequency, but in variants of the embodiment the probe laser frequency may not be blue-detuned with respect to the D2 line of rubidium atoms. The parameters of the probe laser 9 and pumping laser 1 are adjusted based on the temperature of the alkali vapour cell 6. High temperature increases the optical depth of the atoms, which causes strong absorption of light at the resonance frequency in the atomic vapour cell 6. The intensity and wavelength of the pumping light and the probe light are tuned to have sufficient light traversing the atomic vapour cell 6 while not degrading the quality of the magnetic resonance by strong light power broadening. In particular, the intensity and wavelength of the pumping light and the probe light are calibrated to ensure that the variation in the polarisation of the probe light is detectable by the balanced photodetector 13, and may be tuned further to optimise the sensitivity of the magnetometer. In the embodiment of Fig. 2, referring to standard experimental conditions of operation of atomic magnetometers, at an atomic vapour cell temperature of 86.5°C, the pumping light intensity is set to 0.18mW, the probe light intensity is set to 0.12mW, and the probe light frequency is set to be 1.42GHz blue detuned with respect to the D2 line of rubidium 87 atoms. More generally, the detuning of the probe laser 9 may be set according to the type of alkali metal used in the atomic vapour cell 6, the temperature of the atomic vapour cell 6, and the other parameters of the probe laser 9, so as to optimise the linewidth and amplitude of the signal. The half-wave plate 11 is adjusted so that the intensity of the transmitted light and the reflected light of the polarising beam splitter 12 are equal when atoms in the atomic vapour are not being excited, that is, the output signal of the balanced photodetector 13 is zero. More generally, the atomic magnetometer may comprise means for measuring two transverse polarisation components of the probe beam. A first bias magnetic field is applied in the z direction through the coil set 5. Referring to standard experimental conditions of operation of atomic magnetometers, at a designed atomic magnetic resonant frequency of 100 kHz, and to Equation 1 relating the Larmor frequency, the gyromagnetic ratio of the rubidium-87 atoms, and the bias magnetic field, the corresponding bias magnetic field is approximately 13333nT. The embodiment of Figure 2 is described with reference to Rb-87 atoms and an operating frequency of 100kHz, but any suitable alkali metal may be used in the alkali metal vapour cell (for example Rb-85, Cs, or K). In each case, the appropriate bias magnetic field for a given desired Larmor frequency may be obtained using the formula wl = yB, relating the desired Larmor frequency wl to the gyromagnetic ratio of the specific alkali metal and the total magnetic field B. The balanced photodetector 13 is connected to the signal input port 14a of the lock-in amplifier 14, and an oscillating excitation magnetic field is applied in the y direction at the designed operating frequency through the coil set 5. Referring to standard experimental conditions of operation of atomic magnetometers, the magnetic field amplitude is set to 90 nT, the input magnetometer signal is demodulated through the lock-in amplifier 14, and the phase component of the demodulated signal is input into the closed-loop feedback controller 15 via output port 14c. A first channel 14c of the lock-in amplifier 14 demodulates the input magnetometer signal to obtain the phasefrequency response using a time constant of from 1ns to 1.6ps and using the oscillating excitation magnetic field (input port 14b) as a reference. More generally, the oscillating excitation magnetic field may have an amplitude of 100±20 nT. In a variant of the embodiment, the output of the balanced photodetector 13 may be analysed by a spectrum analyser. As discussed above regarding Figure 1, the lock-in amplifier 14 uses the phasefrequency response derived from two transverse polarisation components of the probe laser 9 to determine a magnitude and a direction of the second bias magnetic field. The second bias magnetic field is applied to the atomic vapour cell 6 via the coil set 5. In the embodiment of Figure 2, the phase-frequency response is also used to calculate the external magnetic field - but in variants of the embodiment, the external magnetic field may be determined based on one or more other properties of the probe beam measured by the photodetector 113. The output of the closed-loop feedback controller 15 is connected to the coil set 5 to adjust the bias magnetic field in the z direction (that is, to apply a second bias magnetic field) to stabilize the bias magnetic field. A second channel 14d of different bandwidth of the lock-in amplifier 14 demodulates the magnetometer response signal with a time constant of from 1ms to 100ms and using the oscillating excitation magnetic field (input port 14b) as a reference to filter noise and provide readout of the external magnetic field sensed by the magnetometer. In the embodiment of Figure 2, the phase-frequency response is also used to calculate the external magnetic field - but in variants of the embodiment, the external magnetic field may be determined based on one or more other properties of the probe beam. Figure 3 shows a method of operating an atomic magnetometer. The atomic magnetometer comprises an atomic vapour cell containing an atomic vapour. The steps of Figure 3 do not have to be performed in the order shown. In step S101 of the method, a polarized pump beam is used to spin-polarise the atomic vapour. In step S102 of the method, a first bias magnetic field is applied to an atomic vapour cell to magnetise the polarized atomic vapour in the atomic magnetometer In step S103 of the method, an oscillating excitation magnetic field is used in the atomic vapour to cause the atomic spins to precess about the first bias magnetic field, wherein using the oscillating excitation magnetic field comprises either i) applying the oscillating excitation magnetic field to the atomic vapour cell perpendicular to the first bias magnetic field, or ii) modulating the polarized pump beam. In step S104 of the method, the external magnetic field is measured by measuring one or more properties of a probe beam passing through the atomic vapour. The method of Figure 3 further comprises compensating the atomic magnetometer for stray magnetic fields (step S105) by: determining (step S106) a phase-frequency response of the atomic magnetometer, wherein the phase-frequency response defines a variation, with a frequency of the oscillating excitation magnetic field, of a phase of a sensing signal of the atomic magnetometer derived from the probe beam and responsive to the external field, and applying (step S107) a second bias magnetic field to the atomic vapour cell dependent on the determined phase-frequency response. In other words, step S105 comprises tracking the change of Larmor frequency via the phase-frequency response, and applying a corresponding second bias magnetic field so as to maintain the atomic magnetometer on resonance. 5 The method of Figure 3 may be implemented using an atomic magnetometer according to Figure 1 or Figure 2, or using any other suitable atomic magnetometer. No doubt many other effective alternatives will occur to the skilled person. It will be understood that the invention is not limited to the above-described embodiments, and 10 that the invention encompasses modifications obvious to the skilled person and falling within the scope and spirit of the claims appended hereto.

Claims

1. A method of measuring an external magnetic field using an atomic magnetometer, the atomic magnetometer comprising an atomic vapour cell containing an atomic vapour, and the method comprising:using a polarized pump beam to spin-polarise the atomic vapour;magnetising the polarized atomic vapour in the atomic magnetometer by applying the first bias magnetic field to the atomic vapour cell containing the atomic vapour;using an oscillating excitation magnetic field in the atomic vapour to cause the atomic spins to precess about the first bias magnetic field, wherein using the oscillating excitation magnetic field comprises either i) applying the oscillating excitation magnetic field to the atomic vapour cell perpendicular to the first bias magnetic field, or ii) modulating the polarized pump beam; andmeasuring the external magnetic field by measuring one or more properties of a probe beam passing through the atomic vapour; the method further comprisingcompensating the atomic magnetometer for stray magnetic fields by:determining a phase-frequency response of the atomic magnetometer, wherein the phase-frequency response defines a variation, with a frequency of the oscillating excitation magnetic field, of a phase of a sensing signal of the atomic magnetometer derived from the probe beam and responsive to the external field, andapplying a second bias magnetic field to the atomic vapour cell dependent on the determined phase-frequency response.

2. The method according to claim 1, wherein:i) measuring the external magnetic field comprises: measuring the external magnetic field at intervals of a first timescale xi, and applying the second bias magnetic field to the atomic vapour cell comprises determining a value of the second bias magnetic field at intervals of a second timescale X2, wherein X2 <xi; and / orii) measuring the external magnetic field comprises: measuring the external magnetic field with a first bandwidth bi, and applying the second bias magnetic field to the atomic vapour cell comprises determining a value of the second bias magnetic field with a second bandwidth b2, wherein bi <b2.

3. The method according to claim 2, wherein the second timescale X2 is in the range of from 1ns to 1 .Ops.

4. The method according to claim 2 or claim 3, wherein the first timescale Xi is in the range of from 1ms to 100ms.

5. The method of any preceding claim, wherein the external magnetic field is an oscillating external magnetic field.

6. The method of any preceding claim, wherein measuring the external magnetic field by measuring one or more properties of a probe beam passing through the atomic vapour comprises determining a magnitude and a direction of the external magnetic field based on the phase-frequency response.

7. The method of claim 6, wherein determining the value of the external magnetic field based on the phase-frequency response comprises determining a ratio of two transverse polarisation components of the probe beam to determine the phase of the sensing signal of the atomic magnetometer.

8. The method according to any preceding claim, wherein determining the second bias magnetic field comprises determining a magnitude and a direction of the second bias magnetic field calculated to reduce a magnitude of the phase-frequency response.

9. The method according to any preceding claim, wherein obtaining the phasefrequency response comprises performing spectrum analysis on a signal derived from the probe beam.

10. The method according to any of claims 1-9, wherein obtaining the phasefrequency response comprises:receiving, using a lock-in amplifier, a signal derived from the probe beam, and de-modulating the signal derived from the probe beam using the oscillating excitation magnetic field as a reference.

11. The method according to claim 10, wherein the lock-in amplifier is a dualchannel amplifier, and determining a second bias magnetic field comprises:inputting the signal derived from the probe beam to a first channel of the amplifier, andmeasuring the external magnetic field comprises inputting the signal derived from the probe beam to a second channel of the amplifier.

12. The method according to any preceding claim, wherein the method further comprises:emitting, by the atomic magnetometer, an oscillating probe magnetic field, and measuring the external magnetic field comprises measuring an external magnetic field induced by the oscillating probe magnetic field.

13. The method according to any preceding claim, wherein the atomic vapour comprises rubidium-87 vapour.

14. The method according to any of claims 1-12, wherein the atomic vapour comprises rubidium-85 vapour.

15. The method according to any of claims 1-12, wherein the atomic vapour comprises caesium-133 vapour.

16. The method according to any one of claims 1-12, wherein the atomic vapour comprises potassium-39 vapour.

17. A magnetometer comprising an atomic vapour cell containing an atomic vapour, wherein the magnetometer is configured to:use a polarized pump beam to spin-polarise the atomic vapour;apply a first bias magnetic field to the atomic vapour cell to magnetise the polarized atomic vapour in the atomic vapour cell;use, to cause the atomic spins to precess about the first bias magnetic field, an oscillating excitation magnetic field in the atomic vapour, wherein using the oscillating excitation magnetic field comprises either i) applying the oscillating excitation magnetic field to the atomic vapour cell perpendicular to the first bias magnetic field, or ii) modulating the polarized pump beam;measure the external magnetic field by measuring one or more properties of a probe beam passing through the atomic vapour; wherein the magnetometer is further configured to:compensate the atomic magnetometer for stray magnetic fields by:5 determining a phase-frequency response of the atomic magnetometer, whereinthe phase-frequency response defines a variation, with a frequency of the oscillating excitation magnetic field, of a phase of a sensing signal of the atomic magnetometer derived from the probe beam and responsive to the external field, andapplying a second bias magnetic field to the atomic vapour cell dependent on 10 the determined phase-frequency response.

18. The magnetometer of claim 17, wherein the magnetometer is further configured to perform the steps of the method of any of claims 2-16.

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