Methods and systems for generating atomic spin orientation

Abstract

The present invention discloses a method for generating atomic spin orientation in an atomic ensemble. The method includes providing a steady magnetic field (5) to the atomic ensemble to cause Zeeman splitting within a first manifold and a second manifold of the ground state of the atomic energy levels of the atomic ensemble. The method includes pumping the atomic ensemble with an electromagnetic light radiation beam that is detuned due to transitions involving the first manifold, such that a majority of the atomic population of the first manifold in the atomic ensemble is transferred from the first manifold to magnetic Zeeman sublevels of the second manifold. A system for generating atomic spin orientation in an atomic ensemble is also disclosed.

Description

Technical Field

[0001] The present invention relates to methods and systems for generating atomic spin orientation. Background Art

[0002] The generation of spin polarization is an important step in the research and application of a variety of systems, from solid-state samples [1] to cold atomic ensembles [2, 3]. In the field of atomic physics, the standard method (optical pumping) relies on the transfer of angular momentum from polarized light to the atomic system [4]. Although typical schemes involve the interaction of an atomic sample with a circularly polarized laser beam propagating along a static magnetic field, other configurations have been demonstrated, including different polarizations [5 - 7] and numbers of lasers [8]. Optical pumping also encompasses the transfer of optical angular momentum to target atoms via spin-exchange collisions (SEC) [9, 10]. Another class of spin polarization processes combines optical pumping with non-linear spin dynamics [11, 12]. One particular implementation, the so-called alignment-to-orientation conversion, involves the evolution of population imbalance in mutually orthogonal magnetic and electric fields [13 - 15]. In this way, tensor polarization (alignment), where the spins are aligned along a preferred axis rather than a preferred direction, can be transformed into vector polarization (orientation), where the spins are biased in one direction

[16] . Summary of the Invention

[0003] Aspects of the present invention seek to provide an improved method and system for generating atomic spin orientation.

[0004] According to an aspect of the present invention, there is provided a method for generating atomic spin orientation in an atomic ensemble, comprising:

[0005] Providing a steady magnetic field to the atomic ensemble to cause Zeeman splitting within a first manifold and a second manifold of the ground state of the atomic energy levels of the atomic ensemble;

[0006] Pumping the atomic ensemble with an electromagnetic light radiation beam that is detuned due to transitions involving the first manifold, such that a majority of the atomic population of the first manifold in the atomic ensemble is transferred to the magnetic Zeeman sub-levels of the second manifold.

[0007] In some embodiments, the beam is detuned due to transitions involving the first manifold such that a majority of the atomic population of the first manifold in the atomic ensemble is transferred to the magnetic Zeeman sub-levels of the second manifold having the maximum or minimum magnetic quantum number.

[0008] In some embodiments, the optical radiation power of the beam exceeds a threshold power to cause an asymmetry in the distribution of the atomic population of the Zeeman sub-levels of the second manifold in order to generate atomic spin orientation.

[0009] In some embodiments, the threshold power is the power at which the dependence of the magneto-optical rotation signal of the atomic ensemble on the optical radiation beam power becomes non-linear. Those skilled in the art will understand that after the beam has passed through the atomic ensemble, preferably when the ensemble is subjected to an oscillating magnetic field, the magneto-optical rotation signal can be obtained from the detection of the beam. The signal can be related to the amplitude of the oscillation of the beam polarization. Those skilled in the art will understand that the magneto-optical signal originates from the coupling generated by the oscillating magnetic field between the Zeeman sub-levels in the atomic ensemble subjected to a steady magnetic field.

[0010] In some embodiments, the threshold power is 2 mW.

[0011] In some embodiments, the steady magnetic field is configured to generate a Larmor frequency not exceeding 30 kHz in the atomic ensemble.

[0012] In some embodiments, the steady magnetic field is configured to generate a Larmor frequency not exceeding 20 kHz in the atomic ensemble.

[0013] In some embodiments, the frequency of the beam is the frequency that maximizes the magneto-optical rotation signal from the second manifold.

[0014] In some embodiments, the beam is negatively detuned due to a transition involving the first manifold.

[0015] In some embodiments, the beam has linear polarization. In other embodiments, the beam has circular polarization. Preferably, the circularly polarized beam is parallel to (or substantially parallel to) the steady magnetic field.

[0016] In some embodiments, the steady magnetic field is configured to generate a Larmor frequency greater than 20 kHz in the atomic ensemble.

[0017] According to an aspect of the present invention, a method for detecting an oscillating magnetic field is provided, which includes the above method in which the beam has linear polarization, including detecting the beam after the beam has passed through the atomic ensemble in order to detect the oscillating magnetic field.

[0018] According to an aspect of the present invention, a method for detecting an oscillating magnetic field is provided, which includes the above method in which the beam has circular polarization, where the beam is a magnetometer pump beam, and the method includes probing the atomic ensemble with a magnetometer probe beam having linear polarization and degenerate in frequency with the magnetometer pump beam, and the method includes detecting the magnetometer probe beam after the magnetometer probe beam has passed through the atomic ensemble in order to detect the oscillating magnetic field.

[0019] In some embodiments, the method includes providing an oscillating primary magnetic field to cause a conductive or magnetically permeable object to generate a secondary magnetic field.

[0020] For any of the above aspects, the polarization of the linearly polarized beam is preferably parallel or substantially parallel to the static magnetic field. The linearly polarized beam can be transverse and preferably orthogonal to the direction of the static magnetic field, and can be transverse and preferably orthogonal to the oscillating magnetic field for detection.

[0021] According to an aspect of the present invention, there is provided a system for generating atomic spin orientation in an atomic ensemble, comprising:

[0022] An atomic ensemble having atomic energy levels including a ground state, the ground state including a first manifold and a second manifold;

[0023] A radiation source configured to pump the atomic ensemble with an electromagnetic light radiation beam that is detuned due to a transition involving the first manifold, such that most of the atomic population of the first manifold in the atomic ensemble is transferred to the magnetic Zeeman sublevels of the second manifold.

[0024] In some embodiments, the system is configured to provide a beam having an optical radiation power exceeding a threshold power to cause an asymmetry in the distribution of the atomic population of the Zeeman sublevels of the second manifold in order to generate atomic spin orientation.

[0025] In some embodiments, the beam has linear polarization.

[0026] In some embodiments, the beam is a pump beam having circular polarization.

[0027] In some embodiments, the system includes a radiation source configured to probe the atomic ensemble with a linearly polarized probe beam that is substantially degenerate in frequency with the circularly polarized pump beam. This radiation source can be the same radiation source as the radiation source used for pumping.

[0028] In some embodiments, the radiation source is configured to emit a single beam, and the system includes a beam splitter configured to split the single beam into a pump beam and a probe beam.

[0029] In some embodiments, the system includes a detector configured to detect the linearly polarized beam in order to detect the oscillating magnetic field.

[0030] In some embodiments, the atomic ensemble is rubidium, and the radiation source is configured to emit a beam having an optical radiation power not exceeding 4 mW.

[0031] In some embodiments, the radiation source is a vertical cavity surface emitting laser diode.

[0032] In some embodiments, the system includes a magnetic field source configured to provide a static magnetic field to the atomic ensemble to cause Zeeman splitting within the first and second manifolds of the ground state of the atomic energy levels of the atomic ensemble.

[0033] In some embodiments, the system is an atomic magnetometer. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Embodiments of the present invention are described below with reference to the drawings by way of example only.

[0035] Figure 1 A schematic configuration showing a single linearly polarized beam that generates a population imbalance (polarization) within the atomic ground state by transferring population between ground state manifolds. A static bias magnetic field creates an energy splitting within the ground state manifold. A resonant oscillating magnetic field creates coherence between the ground state manifolds, causing the atomic polarization to precess. This rotation of the atomic polarization is mapped onto the linearly polarized beam and detected by a simple polarimeter consisting of a balanced photodiode and a polarization beam splitter.

[0036] Figure 2 Showing where a single beam is split into two beams with degenerate optical frequencies. The linearly polarized beam acts in the same manner as described in Figure 1 . The circularly polarized beam is used to enhance the population transfer between the ground state manifolds.

[0037] Figure 3 A schematic diagram showing the generation of an orientation in a second manifold of an atomic ensemble.

[0038] Figure 4 (a) A schematic diagram depicting a linearly polarized laser beam that transfers population between the F = 3 and F = 4 cesium ground state manifolds and generates a population imbalance (atomic spin) therein.

[0039] Figure 4 (b) A schematic diagram depicting a weak radio frequency field B rf that creates coherence between adjacent F = 4 Zeeman sublevels, causing the atomic spin polarization to precess about B off marked with a black arrow. The spin precession is monitored by a linearly polarized probe beam.

[0040] Figure 5 Showing the dependence of the rf signal amplitude R on the probe beam detuned due to the 6 2 S 1 / 2 F = 3 → 6 2 P 3 / 2 F' = 2 transition. The F = 3 and F = 4 resonances are marked with red and black arrows respectively. The measurements were made with a laser beam power of 5.9 mW.

[0041] Figure 6 Showing the use of 6 2 S 1 / 2 F = 3 → 6 2 P 3 / 2RF spectroscopy signals recorded at a laser beam frequency tuned near the F' = 2 transition (detuning -100 MHz). The F = 3 and F = 4 resonances are marked with red and black arrows respectively. The transition from alignment (a) to orientation (b) is visible in the spectral profile generated by the F = 4 coherence. Measurements were performed with laser beam powers of (a) 200 μW and (b) 9.1 mW.

[0042] Figure 7 (a) Shows the magneto-optical rotation signals recorded with only a linearly polarized beam (black solid line) and with the orthogonally polarized components (red dash and blue dotted line) in the presence of a circularly polarized pump beam. The linearly polarized beam power was 12.4 mW and the pump power was 17 μW.

[0043] Figure 7 (b) Shows the dependence of the signal amplitude on the laser beam power for only the linearly polarized beam (black triangles) and the linearly polarized beam combined with a circularly polarized beam parallel to B off (red dots and blue diamonds represent measurements with either of the two orthogonal circular polarizations for the pump beam).

[0044] Figure 8 Shows the dependence of the orthogonal components of the RF signal amplitude (a) and phase (b) on the offset magnetic field strength (Larmor frequency). The frequency of the RF spectrum is expressed in terms of the detuning from the center of the RF spectrum. Measurements were performed with a laser beam power of 4.6 mW.

[0045] Figures 9 to 11 Illustrates how the signal of the magnetometer, also known as the magneto-optical rotation signal, is generated in three stages.

[0046] Figure 12 Shows an example of an RF spectrum.

[0047] Figure 13 Is a graph showing the magnetometer amplitude versus the pump beam power of the circularly polarized beam. Detailed Description

[0048] As described below, embodiments of the present invention are capable of achieving atomic spin orientation in a room-temperature alkali metal vapor in an efficient manner in some embodiments with a linearly polarized beam.

[0049] Conventionally, atomic spin orientation is achieved by transferring angular momentum from polarized light to the atomic system.

[0050] The measurement configuration discussed below implements a simple and robust radio-frequency atomic magnetometer based on a single low-power laser diode, which approaches the performance of a multi-laser pump-probe system.

[0051] Some embodiments of the invention described below provide an alignment generation mechanism, e.g., in room-temperature cesium vapor, which combines three elements: optical pumping, non-linear spin dynamics, and spin-exchange collisions. A transition between an aligned atomic sample and an oriented atomic sample is presented by a change in the spin-exchange relaxation rate. Observation is performed by monitoring the atomic radio-frequency spectrum.

[0052] Figure 1 A radio-frequency atomic magnetometer is shown, which may be tunable in some embodiments. The magnetometer is for use with a primary magnetic field source (not shown) configured to provide an oscillating primary magnetic field. The primary magnetic field source is an rf coil in this embodiment; however, other variable magnetic field sources may be used in other embodiments. The rf coil is configured to provide a primary magnetic field generally orthogonal to the surface of the sample to be studied. In this embodiment, the surface is the surface under study, which is the principal surface of the sample.

[0053] In this embodiment, the rf coil is a 1000-turn coil with 0.02 mm diameter copper wire, 10 mm height, 2 mm inner diameter, and 4 mm outer diameter. However, those skilled in the art will appreciate that the dimensions may vary depending on the application.

[0054] The rf coil is configured such that it can be placed adjacent to the sample, but entirely on one side of it and in a non-overlapping relationship therewith, and can be operated to generate an oscillating primary magnetic field to cause the sample to generate a secondary magnetic field 4 oscillating at the same frequency as the primary magnetic field. The secondary magnetic field indicates the material response of the sample.

[0055] The sample should be conductive (but not necessarily highly conductive) and / or should have a magnetic permeability such that it can be magnetized.

[0056] The atomic magnetometer is configured to detect the secondary magnetic field, e.g., to perform material defect imaging.

[0057] In this embodiment, the atomic magnetometer includes a detection unit 3, which in this embodiment is a 1 cm paraffin-coated glass cell at the ambient temperature of the atomic ensemble. 3 In this embodiment, the atomic ensemble is cesium atomic vapor (where the atomic density n Cs = 3.3 x 10 10 cm -3 )

[0058] The magnetometer includes a bias magnetic field source (not shown) configured to provide a bias magnetic field 5 at the detection unit 3 and thus provide the bias magnetic field to the atomic ensemble in the direction of the bias magnetic field. The terms 'bias' and 'offset' are used interchangeably in the context of this magnetic field. The bias magnetic field is a steady or static magnetic field; it can vary, but it is stable and non-oscillating. The bias magnetic field is configured to cause Zeeman splitting within a first manifold and a second manifold of the ground state of the atomic energy levels of the atomic ensemble. The intensity of the bias field defines the Larmor frequency.

[0059] In this embodiment, the offset magnetic field is actively stabilized by three pairs of nested orthogonal square Helmholtz coils. These coils provide the bias magnetic field source, but other bias magnetic field sources may be used in other embodiments.

[0060] The magnetometer includes a radiation source 1, which is a laser in this embodiment, configured to pump the atoms of the atomic sample in the detection unit 3 with an electromagnetic optical radiation beam 2 that is transverse and in this embodiment orthogonal to the bias magnetic field.

[0061] The electromagnetic optical radiation beam 2 is configured to pump the atomic sample to create an orientation in the atomic ensemble.

[0062] The electromagnetic optical radiation beam 2 also acts as a probe beam to probe the detection unit 3 to probe the atomic ensemble, in particular to probe the precession of atomic coherence within the atomic ensemble.

[0063] The evolution of the collective atomic spin of the atomic ensemble is mapped onto the polarization state of the electromagnetic optical radiation beam 2.

[0064] The atomic magnetometer includes a detector. In this embodiment, the detector includes a balanced polarimeter 6 configured to receive and detect the beam after the electromagnetic optical radiation beam 2 passes through the atomic ensemble in the detection unit 3 in order to detect an oscillating magnetic field near the atomic ensemble. The polarimeter 6 includes: a polarization beam splitter 9; a half-wave plate 10 configured such that the electromagnetic optical radiation beam 2 passes through the half-wave plate 10 on its path to the beam splitter 9; a photodiode configured to receive the two outputs of the beam splitter 9, one of which is routed from the beam splitter 9 to the photodiode 7 via a mirror 8.

[0065] The laser transmitted through the unit 3 is analyzed by the polarimeter.

[0066] The detector is configured to output a detection signal in response to the detection of the electromagnetic optical radiation beam 2. This detection signal is typically a voltage or current signal representing the polarization and / or amplitude of the detected electromagnetic optical radiation beam 2. In this embodiment, the output of the detector is the output of a balanced photodetector that provides a voltage signal representing the polarization of the electromagnetic optical radiation beam 2. The amplitude and phase of the signal can be used, for example, by a computer to detect the secondary magnetic field 4 and thus detect the material response of the sample, and in some cases perform material defect imaging.

[0067] Those skilled in the art will understand that the signal of the magnetometer generated in the three stages is also referred to as the magneto - optical rotation signal. Figures 9 to 11 This is shown for a conventional pump - and - probe beam system. However, as explained herein, in the embodiments discussed, a single beam serves both of these roles.

[0068] First, referring to Figure 9 , we generate atomic population polarization in the atomic ensemble by coupling to the pump beam (or in other words, the spin component along the bias magnetic field, which is marked with a black arrow in Figure 9 ). Although the pump beam is shown in Figure 9 as a circularly polarized beam parallel to the bias field, which is the case in many conventional systems, in the embodiments of Figure 1 , it is the same beam as the probe beam.

[0069] Referring to Figure 10 , an oscillating magnetic field (such as a secondary field) generates atomic coherence, or in other words, tilts the atomic spins, which causes their precession around the bias field. The spin component perpendicular to the bias field (i.e., the atomic coherence) precesses at the Larmor frequency defined by the strength of the bias magnetic field.

[0070] Referring to Figure 11 , the oscillation of the atomic spins is monitored by a linearly polarized probe beam.

[0071] The spin precession is mapped onto the beam polarization, i.e., the oscillation of the spins generates an oscillation of the beam polarization (Faraday effect). The photodetector records the amplitude of the oscillation at a specific drive frequency. Scanning the drive frequency provides us with an rf spectrum, otherwise referred to as the magneto - optical rotation signal, an example of which is shown in Figure 12 . The F = 3 and F = 4 spins oscillate at different frequencies (the Larmor frequencies of the F = 3 and F = 4 spins are different). The amplitude and phase of the F = 4 resonance profile generate amplitude and phase images in non - destructive testing.

[0072] As explained above, many conventional magnetometers use a circularly polarized pump beam at a frequency different from that of the linearly polarized probe beam. In contrast, in the embodiments of Figure 1 , the radiation source 1 is configured to emit a single linearly polarized electromagnetic optical radiation beam 2 that serves as both the pump beam and the probe beam. The polarization of the electromagnetic optical radiation beam 2 is generally parallel to the bias magnetic field; optimally, it is parallel polarization.

[0073] The present inventor has found that by detuning the beam due to transitions in the first manifold of the ground state of the atomic energy levels involving the atomic ensemble, it is possible to transfer a majority of the atomic population in the first manifold in the atomic ensemble from the first manifold to the magnetic Zeeman sublevels of the second manifold of the ground state. In addition, the present inventor has found that for a linearly polarized beam, by increasing the optical radiation power of the beam, the symmetry of the distribution in the second manifold is broken above a threshold power and an orientation is then obtained in the second manifold.

[0074] Population in atomic physics refers to the probability of occupancy of a specific energy level within an atomic ensemble. If we consider the population of the sublevel with the maximum magnetic number to be 0.5, it means that on average 50% of the atoms within a given ensemble occupy that energy level.

[0075] Thus, the electromagnetic optical radiation beam 2 is detuned due to transitions in the first manifold of the ground state of the atomic energy levels involving the atomic ensemble (in this embodiment, the first manifold is 6 2 S 1 / 2 F = 3, the second manifold is 6 2 S 1 / 2 F = 4, and the electromagnetic optical radiation beam 2 is detuned due to 6 2 S 1 / 2 F = 3 → 6 2 P 3 / 2 F' = 4 transitions), such that a majority of the atomic population in the first manifold in the atomic ensemble is transferred from the first manifold to the magnetic Zeeman sublevels of the second manifold of the ground state. To maximize this effect, in this embodiment, the frequency of the beam is the frequency that maximizes the magneto-optical rotation signal from the second manifold, and this can be done automatically in some embodiments, but those skilled in the art will understand that frequencies around this maximum that still have an observable signal can be used. Referring to Figure 5 , which consists of approximately 700 rf spectra recorded for different detunings of the probe beam (without pump) and shows the resonances for F = 3 and F = 4 marked with red and black arrows respectively. Also discussed below Figure 8 is recorded in the same way (as a set of rf spectra recorded for different Larmor frequencies). In this embodiment, the detuning can be in the range of approximately -416 MHz (for 3.3 mW) to approximately -290 MHz (for 10 mW).

[0076] In addition, in this embodiment, the optical radiation power of the electromagnetic optical radiation beam 2 exceeds the threshold power to cause an asymmetry in the distribution of the atomic population of the Zeeman sub-levels of the second manifold, so as to generate a spin orientation. In this embodiment, the threshold power is 2 mW, but for other embodiments, the threshold power may be different and will depend on the configuration of the atomic magnetometer, in particular on the atomic ensemble. A person skilled in the art can determine the appropriate threshold power to be used in any particular embodiment, as it can be the power at which the dependence of the optical radiation beam power on the magneto-optical rotation signal of the atomic ensemble becomes non-linear.

[0077] Figure 1 The embodiment has the following advantages: a linearly polarized rather than a circularly polarized beam can generate an orientation in the atomic ensemble, which means that the same beam can be used for polarization detection. This can reduce the number of required radiation sources. It can also result in lower power consumption and a smaller sensor size.

[0078] In this embodiment, the electromagnetic optical radiation beam 2 is negatively detuned due to the transitions involving the first manifold, such that most of the atomic population of the first manifold in the atomic ensemble is transferred from the first manifold to the magnetic Zeeman sub-levels of the second manifold having the maximum or minimum magnetic quantum number, which are the states with the highest momentum and are otherwise referred to as the stretched states of the second manifold. Negative detuning means that the frequency of the beam is reduced relative to the frequency of the transition.

[0079] Figure 3 A schematic diagram showing the generation of the orientation in the second manifold is provided. The orientation is characterized in that the population is pumped towards the Zeeman sub-levels with high or low magnetic quantum numbers, preferably towards the Zeeman sub-levels with the maximum or minimum quantum numbers.

[0080] On the Figure 3 left side, there is a schematic diagram of the energy levels of cesium.

[0081] Figure 3a The results of detuned pumping at a lower power below the threshold power are shown. Figure 3b The results of detuned pumping at a higher power above the threshold power are shown. For Figure 3a and 3b each, the dashed lines show the Zeeman sub-levels of the first (F = 3) manifold and the second (F = 4) manifold, and the dots on the dashed lines show the population of the sub-levels.

[0082] As can be seen, in Figure 3a , at a power below the threshold power, the pump has moved some of the atomic population of the first manifold into the second manifold, but there is alignment; there is a symmetric population distribution in both the first and second manifolds.

[0083] As Figure 3bAs can be seen, in the case of pumping at a power above the threshold power, although alignment still exists in the first manifold, orientation exists in the second manifold because the population of the second manifold is generally only in a single stretched state.

[0084] In this embodiment, the atomic ensemble is cesium. However, cesium is not the only element that can be used. Nevertheless, the atomic ensemble is preferably an alkali metal, especially cesium or rubidium.

[0085] As is clear from the above, in use, the atomic magnetometer implements a method of generating atomic spin orientation in an atomic ensemble, which includes:

[0086] Using a bias magnetic field source, providing a steady magnetic field, i.e., a bias magnetic field, to the atomic ensemble to cause Zeeman splitting within the first and second manifolds of the ground state of the atomic energy levels of the atomic ensemble;

[0087] Using a radiation source 1, pumping the atomic ensemble with an electromagnetic light radiation beam 2 to generate atomic spin orientation in the atomic ensemble.

[0088] When this occurs, the rf coil can be operated in the manner discussed above when adjacent to the sample to provide a primary magnetic field oscillating at the rf frequency, causing the sample to generate a secondary magnetic field 4 oscillating at the rf frequency.

[0089] The evolution of the collective atomic spin of the atomic ensemble, at least in part as a result of the secondary magnetic field 4, is mapped onto the polarization state of the electromagnetic light radiation beam 2, which beam also serves as the magnetometer detection beam. In other words, pumping the ensemble with the beam also detects the ensemble with the beam.

[0090] The detector detects the beam after the electromagnetic light radiation beam 2 has passed through the atomic ensemble in order to detect the oscillating secondary magnetic field 4, and in this embodiment enables material defect imaging to be performed.

[0091] Although Figure 1 The embodiments of have the advantage of using a single electromagnetic light radiation beam 2, but they are most effective at low Larmor frequencies, generally not exceeding 30 kHz, in the range of 20 kHz to 30 kHz, in the range of 1 kHz to 30 kHz, or up to 20 kHz, and thus, the bias magnetic field source is configured and operated to generate a Larmor frequency within one of these ranges in the atomic ensemble. However, the Figure 2 The embodiments described below are more effective than the embodiments from Figure 1 but at the cost of increased complexity.

[0092] Figure 2 The embodiments of are based on the embodiments of, except that they also use a circularly polarized pump beam in the manner discussed below. Figure 1 except that it also uses a circularly polarized pump beam in the manner discussed below.

[0093] Figure 2 The magnetometer includes a beam splitter 13 configured to split a second beam from the linearly polarized electromagnetic optical radiation beam 2 emitted by the radiation source 1. The linearly polarized electromagnetic optical radiation beam 2 continues as described for Figure 1 and the second beam is converted into a circularly polarized pump beam 11 and guided and supplied to the atomic ensemble in the detection unit and used to enhance the transfer of atomic population from the first manifold to the magnetic Zeeman sub-levels of the second manifold as described above.

[0094] In this embodiment, the magnetometer is configured such that the probe beam has a light radiation power above the threshold at the atomic ensemble.

[0095] However, since the pumping is provided by a circularly polarized beam, it is not necessary to provide the pumping by a linearly polarized beam in every embodiment. In some embodiments, it is possible to have the power of the linearly polarized beam less than the threshold and not have it assist in the pumping.

[0096] Regarding the power of the circularly polarized pump beam, it should be noted that the characteristics of polarization pumping by the pump beam and the probe beam are different. Indirect pumping with a circularly polarized beam does not require high power. In fact, the signal saturates at around 200 - 500 μW and for even higher powers, the amplitude of the signal decreases. Only the linearly polarized beam produces non-linearity. Figure 13 is a graph showing the amplitude of the magnetometer relative to the power of the pump beam (published in Appl. Phys. Lett. in 2012). On the other hand, Figure 7 b (discussed below) shows that for a given power of the pump beam, the probe beam can increase the signal (polarization) as long as it is above the threshold. The increased markings are the changes in the steepness of the power-dependence slope (blue).

[0097] Therefore, in this embodiment, the power of the pump beam is in the range of 200 - 500 μW, but values outside this range can still be used in some embodiments.

[0098] In Figure 2 the embodiment, the second beam is redirected through a quarter-wave plate 12 via a mirror to convert the linear polarization into circular polarization and is guided to the detection unit parallel to the direction of the bias field.

[0099] The circular polarization of the pump beam improves the effectiveness of optical pumping. One result of this is that the system can operate more effectively at higher Larmor frequencies. Therefore, in this embodiment, the bias magnetic field source is configured and operated to generate a Larmor frequency greater than 20 kHz in the atomic ensemble. However, the system is not limited to operating at high Larmor frequencies and can operate at lower Larmor frequencies, such as Figure 1 the frequency of the embodiment of

[0100] In Figure 2 the embodiment of, the pump beam provides an increased pump, while the linearly polarized beam acts as a probe beam. However, as explained above, in this embodiment, the linearly polarized beam also contributes to the pump. Those skilled in the art will appreciate that the pump beam and the probe beam are degenerate in terms of frequency. In this embodiment, the radiation source is configured to emit a beam having an optical radiation power of approximately 6 mW to 7 mW, i.e., the combined power of the probe beam and the pump beam. In other embodiments, this power may be greater, up to 10 mW or higher than 10 mW.

[0101] In use, Figure 2 the embodiment of operates and operates in substantially the same manner as Figure 1 the embodiment of. However, in this embodiment, the atomic ensemble is pumped with two beams, i.e., the probe beam and the pump beam, and the two beams contribute to the pump as discussed above.

[0102] Those skilled in the art will appreciate that instead of the radiation source emitting a single beam and the system splitting the beam as in Figure 2 the embodiment of, multiple radiation sources may be used, provided that appropriate polarization and similar frequencies are used, but this increases the cost and complexity of the system.

[0103] Furthermore, it is not necessary for radiation source 1 to emit a linearly polarized beam whose part is split and converted into a circularly polarized beam. It can be performed in the opposite way, where the radiation source emits a circularly polarized beam and a part of it is split and converted into a linearly polarized beam.

[0104] Figure 2 The advantage of the embodiment of is that since the beams are detuned in the described manner, they pump the same type of symmetry (or lack of the same type of symmetry). This means that the beams can be at the same frequency, in other words, degenerate in terms of frequency, thus allowing a single radiation source to conveniently generate both. In the absence of detuning, the circularly polarized beam and the linearly polarized beam would compete, which means that different frequencies would need to be used to prevent this, which is usually the case in conventional systems, which means that multiple radiation sources would be required.

[0105] In another embodiment, the system is as described above in connection with Figure 2configured and operated as described. In this embodiment, the atomic ensemble is rubidium vapor, and the radiation source is a vertical cavity surface emitting laser diode (VCSEL). Rubidium can provide the described functionality with a laser diode of lower power than cesium, which advantageously allows the use of a relatively low power VCSEL diode. This is because the ground state hyperfine splitting in rubidium is about 3 or 6 GHz compared to about 9 GHz in cesium. In this embodiment, the radiation source is configured to emit a beam having an optical radiation power of no more than about 4 mW, typically about 4 mW.

[0106] Those skilled in the art will appreciate that the particular atomic magnetometer described above is not the only type of atomic magnetometer that can be used; for example, the detector can vary, but is preferably a photodetector capable of detecting the polarization and / or amplitude of the probe beam.

[0107] In some embodiments, it is possible to use the Earth's magnetic field as the bias field and thus omit the bias magnetic field source.

[0108] Applications of the methods and systems described herein include: detection of corrosion under insulation, such as for oil and gas pipelines and the energy sector; monitoring of reinforced concrete structures for the transportation sector; object detection; surveillance; and monitoring in nuclear waste containers in nuclear power plants.

[0109] Advantages that can be obtained include: the system can be safe and non-invasive (non-ionizing radiation), may be able to detect corrosion on the inner and / or outer walls of pipelines, may be able to distinguish between corrosion and changes in pipeline geometry due to bends / T-joints / welds in the pipeline, may be able to scan all insulation types, can be low-cost, and may be able to provide improvements in resolution and switching scan modes.

[0110] Although the embodiments mainly described relate to atomic magnetometers, systems and / or methods for generating atomic spin orientation can be used in other fields, such as for chemical analysis of materials or non-destructive testing. In such embodiments, the detector can be omitted or modified, and the rf coil can be omitted, for example, when appropriate.

[0111] Experimental results and discussions

[0112] Experimental results and discussions are presented below that explore the mechanism for generating spin orientation in room temperature cesium vapor, which combines three elements: (1) off-resonant optical pumping, (2) non-linear spin dynamics, and (3) SEC (selective relaxation and coherence transfer [17-20]). The details discussed below can of course be used in the embodiments described above.

[0113] (1) A linearly polarized laser beam moves atomic population from the F = 3 manifold to the F = 4 manifold by off-resonant optical pumping, while creating a population imbalance (alignment) within the two energy levels.Figure 4 (a). The specific frequency detuning of the beam ensures that most of the population transferred to the F = 4 energy level becomes either the stretched state, i.e., the sublevel with the maximum or minimum magnetic quantum number. While the dynamics within the F = 3 energy level is defined by the resonant coupling to the laser field, the F = 4 atomic spin evolves only in the presence of weak far - off - resonance optical and SEC couplings.

[0114] (2)The weak coupling to the optical field drives non - linear spin dynamics that breaks the symmetry of the population distribution. Specifically, it moves some of the population out of one of the stretched states, thus effectively making the atoms more prone to SEC relaxation (3).

[0115] Due to these two factors (non - linear spin dynamics and SEC), we observe the suppression of the component representing one of the spin directions, which contributes to alignment and atomic orientation generation at low magnetic fields. A direct implementation of the technology described is in the field of radio - frequency (rf) atomic magnetometry [21, 22], but possible applications span a wide range of technologies from chemical analysis of materials

[23] to non - destructive testing [24, 25].

[0116] The following section contains a brief description of the experimental apparatus. The components of the atomic spin orientation mechanism are explored through the dependence of the rf spectroscopy signal on three measurement parameters (laser frequency detuning, beam power, and magnetic field strength) discussed in the subsequent sections.

[0117] Experimental setup.

[0118] Measurements are performed in a shielded environment [12, 20, 26] using a system according to Figure 1 , but it should be noted that this is not necessary for every embodiment.

[0119] The ambient magnetic field is suppressed by using a five - layer cylindrical shield with end caps made of 2 - mm - thick high - permeability alloy (mu - metal). A solenoid inside the shield generates a well - controlled offset magnetic field B off , where the relative homogeneity over the length of the cell exceeds 10 -4 . The atoms used are cesium atomic vapor (atomic density n Cs = 0.33 - 1.0x10 11 cm -3 ) contained in a paraffin - coated cell 3 at ambient temperature. These atoms are optically pumped by a linearly polarized electromagnetic light radiation beam 2 with a diameter of 20 mm, and the linearly polarized laser beam propagates orthogonally to the direction of B off . Figure 4 (b). The polarization of the electromagnetic light radiation beam 2 is parallel to B off . The beam is at the cesium D2 line Figure 4The DBR diode laser 1 operating (a) provides and can use frequency stabilization offset-locked within ±10 GHz relative to the main laser frequency. The same linearly polarized beam also serves as a probe for polarization precession via the Faraday effect

[27] , where the evolution of the collective atomic spin is mapped onto the polarization state of the linearly polarized probe beam [8, 21, 28 - 30]. The laser transmitted through the cell is analyzed by a polarimeter 6 consisting of a crystal polarizer oriented at 45° relative to the incident polarization and a commercial balanced photodetector. The two orthogonal components of the resulting signal are measured by a lock-in amplifier, referencing the first harmonic of the driving rf field (B rf ).

[0120] Off-resonance pumping.

[0121] Simple rate equations based on the transition probabilities of the D2 line confirm that the optimal conditions (laser detuning) for population transfer between the F = 3 and F = 4 levels and the generation of population imbalance within the F = 4 manifold are mutually exclusive. The former is optimized when tuning the laser frequency near the 6 2 S 1 / 2 F = 3 → 6 2 P 3 / 2 F' = 4 transition, in which case the latter effect is minimized. In the following sections, we identify the frequency range that optimizes the construction of the orientation in the F = 4 level.

[0122] Figure 5 Showing the magnitude of the rf signal when scanning the frequency of a linearly polarized laser beam across a group of D2 line transitions involving the F = 3 ground state (zero detuning represents the 6 2 S 1 / 2 F = 3 → 6 2 P 3 / 2 F' = 2 transition), R , where X and Y are the two orthogonal components of the rf spectroscopy signal. B off 's relatively small magnitude (Larmor frequency ~22 kHz) ensures that, on the one hand, the contributions from the two ground state levels can be individually distinguished, and on the other hand, the Zeeman levels in a particular manifold are degenerate. The splitting between the components of the F = 3 spectral profile is only limited by the tensor light shift. Specifically, as the laser frequency approaches the atomic resonance, the tensor light shift in F = 3 increases, and thus, the splitting between the components of the relevant profile also increases. Due to the relatively large detuning from resonance, there is no significant splitting in the F = 4 profile. At 6 2 S 1 / 2 F = 3 → 6 2 P 3 / 2Efficient pumping from the F=3 level to the F=4 level near the F'= 4 transition produces an asymmetry in the F=3 signal amplitude with respect to laser detuning. The exact detuning where the maximum in the F=4 signal is observed varies with laser power and ranges from ~ -416 MHz (3.3 mW) to ~ -290 MHz (10 mW).

[0123] Although the observations for off-resonance F = 4 pumping are similar to those observed on the D1 transition

[31] , there are two differences worth pointing out. First, for non-zero laser detuning (for Figure 5 The measurements shown in Figure 2 are ~ -310 MHz), achieving maximum pumping between the manifolds. Second, the characteristics of the polarizations generated in the F=3 (alignment) level and the F=4 (orientation) level are different.

[0124] Nonlinear dynamics.

[0125] Linearly polarized light ( ) through the tensor AC polarization rate α2 (single-spin Hamiltonian, scalar part of the light-free displacement ~α2( ) 2 ,in is the total angular momentum operator of the ith atom) is coupled to the atomic ground state, so the atomic spin dynamics will generally exhibit nonlinear characteristics [11, 12].

[0126] Figure 6 Figure 2 shows rf spectra recorded with laser powers of 200 μW (a) and 9.1 mW (b). The positions of the F=3 and F=4 resonances are marked with red and black arrows, respectively. off Polarization rotation resonances are observed when the introduced splitting between adjacent Zeeman sublevels matches. In an aligned system, the RF response consists of two profiles with opposite signs, resulting in a dispersion-like line shape. At low power, Figure 6 (a) The rf spectrum consists of large, broad features due to alignment in the F=3 level generated by direct optical pumping, which has much smaller structure due to off-resonance excitation into the F=4 manifold. An increase in laser beam power does not simply translate into an increase in the amplitude of the F=3 and F=4 signals, Figure 6 (b). While the properties of the F=3 profile remain unchanged, the change in the symmetry of the F=4 signal indicates the presence of atomic orientation. The resonant coupling of the laser to the F=3 Zeeman sublevel causes a power broadening of its corresponding spectral profile, which contributes to Figure 6 The broad low-amplitude background visible in (b).

[0127] To confirm that the F = 4 spectral profile represents the atomic orientation, add offPumping with a circularly polarized (pump) beam propagating in the direction of

[26] . The pump beam is generated by a diode laser and frequency locked to cesium 6 2 S 1 / 2 F = 3 → 6 2 P 3 / 2 F' = 2, 3 crossing. Figure 7 The solid black line in (a) shows the rf spectrum of the F = 4 profile recorded with only a linearly polarized beam. The red dash and blue dotted lines represent the cases where one of the two orthogonal circular polarizations of the pump beam is added. The presence of the pump beam creates atomic orientation in the sample (parallel or antiparallel to B off ). If the orientations generated by the linearly polarized beam and the pump beam are consistent, the amplitude of the observed profile increases Figure 7 [blue dotted line in (a)]. For the case with opposite pump polarization, the signal amplitude decreases and the characteristics of the spectrum change (red dash). Figure 7 (b) shows the dependence of the signal amplitude for opposite pump beam polarizations (red dots and blue diamonds). The amplitude of the signal generated by the orthogonally polarized pump beams is equal to the probe power below 2 mW. The amplitude asymmetry above this power is caused by the sample orientation induced by the linearly polarized beam.

[0128] Distinct features of this effect are also present in the amplitude data of the signal generated by only the linearly polarized beam (black triangles). The change in the amplitude power dependence from linear to quadratic slope seen above 2 mW confirms the nonlinear nature of the underlying mechanism. Figure 6 The calculated and split spectra in (a) indicate that the tensor light shift (0.2 Hz) is less than the SEC relaxation rate (3 Hz). However, as shown in

[12] in Figure 6 even such small values can trigger nonlinear spin dynamics.

[0129] Spin-exchange collisions.

[0130] The effect of nonlinear spin dynamics is enhanced by SEC-driven coherence transfer. It has been confirmed that the degeneracy between the Zeeman sublevel transition frequencies leads to a decrease in the SEC-dominated decoherence rate

[20] .

[0131] In contrast to the non-degenerate case, the frequency mismatch (phase shift) between the precessing spins affected and not affected by SEC is negligible, and SEC processes not involving manifold changes do not contribute to relaxation. One of the distinct features of this effect, the so-called coherence transfer process [17 - 20], is that the spectral profiles representing the relevant coherence are grouped around the leading component of the spectrum [20, 32].

[0132] Figure 8 Showing two normalized orthogonal (X, Y) pairs of the rf spectroscopy signal versus Boff dependence. Normalization takes into account the variations in the amplitude and phase of the rf spectroscopy signal with the operating frequency, and in the same range of B off is performed in an intrinsic standard pump - probe configuration

[26] . For large B off (Larmor frequency ~200 kHz), Figure 8 the spectral profile in (a) has a shape typical for atomic alignment, Figure 8 (a). B off decrease increases the overlap of components with opposite signs and thus increases the reduction of the signal amplitude.

[0133] Nonlinear spin dynamics is caused by the profile located at a resonance detuning of ~ - 0.05 kHz Figure 5 and the decrease in the population of the stretched state represented in (a).

[0134] This leads to a higher relaxation rate that contributes to the coherence of the part of the spectrum with negative detuning. Thus, the amplitude of the component with negative detuning decreases more rapidly with B off than that of the other profile. The small frequency mismatches between the various components (which decrease with the decrease in B off ) enhance the coherence transfer and the build - up of atomic alignment observed in the frequency range below 20 kHz. For completeness, we show in Figure 8 (b) the evolution of another orthogonal component with intensity B off .

[0135] Conclusions. Radio-frequency atomic magnetometer.

[0136] We have demonstrated the generation of atomic spin alignment in room - temperature cesium vapor. The presence of atomic polarization is important for the operation of rf atomic magnetometers. In the context of non - destructive testing based on magnetic induction, the rf frequency range (1 kHz - 30 KHz) of the single - beam technique is interesting, where the low operating frequency translates into a deeper penetration depth of the (so - called primary) magnetic field

[25] . The measurement configuration discussed here combines the efficient generation of F = 4 atomic alignment and the off - resonance detection typically achieved with two / three independent lasers. The obvious benefit of the presented scheme is the simplicity of the instrument. Systematic measurements of the signal - to - noise ratio (SNR) confirm that the SNR delivered by the option discussed is only 1.3 - 1.4 times lower than the SNR recorded in an optimized pump - probe configuration

[26] . Despite the strong saturation of the F = 3 resonance, Figure 5 the relatively sharp peak in the signal frequency dependence allows for the stabilization of the laser frequency.

[0137] As discussed above, it can be overcome, for example, by Figure 2 the implementation of a degenerate pump - probe configuration in the embodiments such as in a relatively narrow range of B offDifficulties in observing the orientation generated by linearly polarized beams, where the degenerate pump - probe configuration involves circularly polarized (pump) and linearly polarized (probe) beams operating at the same frequency (e.g., ~290 MHz due to the 2 1 / 2 2 3 / 2 6 85 85 2 S 1 / 2 F = 3 → 6 2 3 / 2 2 P 3 / 2 transition). It is worth noting that this frequency for the pump beam is not far from the frequency used to optimize the indirect pumping scheme

[26] . The cesium ground - state hyperfine splitting (9.172 GHz) defines the detuning of the laser frequency from F = 4, which affects the signal amplitude and the intensity of non - linearity. Thus, using 85 Rb vapor (with a hyperfine splitting of 3 GHz) can increase the recorded signal amplitude. Tests indicate that the combination of degenerate pump - probe and 85 the use of Rb vapor enables the efficient operation of an atomic magnetometer with a laser power of 4 mW, which can be achieved based on a single vertical - cavity surface - emitting laser diode.

[0138] All optional and preferred features and modifications of the described embodiments and the appended claims can be used in all aspects of the invention taught herein. Additionally, the individual features of the appended claims and all optional and preferred features and modifications of the described embodiments can be combined with and interchanged with each other.

[0139] The disclosure in UK Patent Application No. 1914464.1, for which this application claims priority, and in the abstract appended to this application are incorporated herein by reference.

[0140] References

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Claims

1. A method for detecting an oscillating magnetic field, comprising: Generating atomic spin orientation in an atomic ensemble, comprising: Providing a steady magnetic field to the atomic ensemble to cause Zeeman splitting within a first manifold and a second manifold of the ground state of the atomic energy levels of the atomic ensemble; Pumping the atomic ensemble with an electromagnetic light radiation beam, the beam having linear polarization and being detuned due to transitions involving the first manifold, such that most of the atomic population of the first manifold in the atomic ensemble is transferred to the magnetic Zeeman sublevels of the second manifold; Detecting the beam after the beam has passed through the atomic ensemble in order to detect the oscillating magnetic field.

2. The method according to claim 1, wherein the optical radiation power of the beam exceeds a threshold power to cause an asymmetry in the distribution of the atomic population of the Zeeman sublevels of the second manifold, so as to generate atomic spin orientation.

3. The method according to claim 2, wherein the threshold power is the power at which the dependence of the optical radiation beam power on the magneto-optical rotation signal of the atomic ensemble becomes non-linear.

4. The method according to claim 2 or 3, wherein the threshold power is 2 mW.

5. A method for detecting an oscillating magnetic field, comprising: Generating atomic spin orientation in an atomic ensemble, which comprises: Providing a steady magnetic field to the atomic ensemble to cause Zeeman splitting within a first manifold and a second manifold of the ground state of the atomic energy levels of the atomic ensemble; Pumping the atomic ensemble with an electromagnetic light radiation beam, wherein the beam is a magnetometer pumping beam having circular polarization and the beam is detuned due to transitions involving the first manifold, such that most of the atomic population of the first manifold in the atomic ensemble is transferred to the magnetic Zeeman sublevels of the second manifold; Probing the atomic ensemble with a magnetometer probe beam having linear polarization and degenerate in frequency with the magnetometer pumping beam, the method comprising detecting the magnetometer probe beam after the magnetometer probe beam has passed through the atomic ensemble in order to detect the oscillating magnetic field; wherein the method comprises splitting a beam emitted by a radiation source to provide the magnetometer pumping beam and the magnetometer probe beam.

6. The method according to claim 5, wherein The pumping beam is detuned due to transitions involving the first manifold, such that most of the atomic population of the first manifold in the atomic ensemble is transferred to the magnetic Zeeman sublevels of the second manifold having the maximum or minimum magnetic quantum number.

7. The method according to claim 1 or 5, wherein the steady magnetic field is configured to generate a Larmor frequency of no more than 30 kHz in the atomic ensemble.

8. The method according to claim 1 or 5, wherein the steady magnetic field is configured to generate a Larmor frequency of no more than 20 kHz in the atomic ensemble.

9. The method according to claim 1 or 5, wherein the beam is negatively detuned due to transitions involving the first manifold.

10. The method according to claim 1 or 5, wherein the frequency of the beam is the frequency that maximizes the magneto-optical rotation signal from the second manifold.

11. The method according to claim 5, wherein the static magnetic field is configured to generate a Larmor frequency greater than 20 kHz in the atomic ensemble.

12. The method according to claim 1 or 5, comprising providing an oscillating primary magnetic field to cause a secondary magnetic field to be generated in a conductive or magnetically permeable object.

13. A system for generating atomic spin orientation in an atomic ensemble, comprising: An atomic ensemble having atomic energy levels including a ground state, the ground state including a first manifold and a second manifold; A radiation source configured to pump the atomic ensemble with an electromagnetic light radiation beam having linear polarization, the electromagnetic light radiation beam being detuned due to a transition involving the first manifold such that a majority of the atomic population of the first manifold in the atomic ensemble is transferred from the first manifold to magnetic Zeeman sub-levels of the second manifold; A detector configured to detect the linearly polarized beam in order to detect an oscillating magnetic field.

14. The system according to claim 13, wherein the system is configured to provide the beam having an optical radiation power exceeding a threshold power to cause an asymmetry in the distribution of the atomic population of the Zeeman sub-levels of the second manifold in order to generate atomic spin orientation.

15. A system for generating atomic spin orientation in an atomic ensemble, comprising: An atomic ensemble having atomic energy levels including a ground state, the ground state including a first manifold and a second manifold; A radiation source configured to pump the atomic ensemble with an electromagnetic light radiation beam, the electromagnetic light radiation beam being a pump beam having circular polarization and being detuned due to a transition involving the first manifold such that a majority of the atomic population of the first manifold in the atomic ensemble is transferred from the first manifold to magnetic Zeeman sub-levels of the second manifold; wherein the radiation source is configured to probe the atomic ensemble with a linearly polarized probe beam that is degenerate in frequency with the circularly polarized pump beam; wherein the system includes a detector configured to detect the linearly polarized probe beam in order to detect an oscillating magnetic field; wherein the radiation source is configured to emit a single beam, and the system includes a beam splitter configured to split the single beam into the pump beam and the probe beam.

16. The system according to any one of claims 13 to 15, wherein the atomic ensemble is rubidium, and the radiation source is configured to emit the beam having an optical radiation power not exceeding 4 mW.

17. The system according to any one of claims 13 to 15, wherein the radiation source is a vertical cavity surface emitting laser diode.

18. The system according to any one of claims 13 to 15, comprising a magnetic field source configured to provide a static magnetic field to the atomic ensemble to cause Zeeman splitting within the first and second manifolds of the ground state of the atomic energy levels of the atomic ensemble.

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