Method and system for generating atomic spin orientation - Patents.com

Abstract

A method for generating atomic spin orientation in an atomic ensemble is disclosed. The method includes providing a steady magnetic field (5) to the atomic ensemble to induce Zeeman splitting in first and second manifolds of the ground state of atomic energy levels of the atomic ensemble. The method includes exciting the atomic ensemble with a beam of electromagnetic light radiation, the beam being detuned from 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 a magnetic Zeeman sublevel 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 a method and system for generating atomic spin orientation. [Background technology]

[0002] The generation of spin polarization is a key step in the study and application of a wide variety of systems, from solid samples [1] to cold atomic ensembles [2, 3]. In the realm of atomic physics, the standard method (optical excitation) relies on the transfer of angular momentum from polarized light to the atomic system [4]. A typical scheme involves the interaction of an atomic sample with a circularly polarized laser beam propagating along a static magnetic field, whereas other configurations involving different polarizations [5–7] and laser numbers [8] have also been demonstrated. Optical excitation also involves the transfer of optical angular momentum to the target atoms, which is realized via spin exchange collisions (SEC) [9, 10]. Another category of spin polarization processes combines optical excitation with nonlinear spin dynamics [11, 12]. One particular realization, the so-called alignment-to-orientation conversion, involves the generation of population imbalances in mutually orthogonal magnetic and electric fields [13–15]. In this way, tensor polarization (alignment), in which spins are aligned along a preferred axis rather than a preferred direction, can be transformed into vector polarization (orientation), in which spins are biased in one direction

[16] . Summary of the Invention [Problem to be solved by the invention]

[0003] Aspects of the present invention seek to provide improved methods and systems for generating atomic spin orientation. [Means for solving the problem]

[0004] According to one aspect of the present invention, there is provided a method for generating atomic spin orientations in an atomic ensemble, the method comprising: providing a constant magnetic field to the atomic ensemble to induce Zeeman splitting within first and second manifolds of ground states of atomic energy levels of the atomic ensemble; and exciting the atomic ensemble with a beam of electromagnetic light radiation, the beam being detuned from a transition involving a 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 a magnetic Zeeman sublevel of a second manifold.

[0005] In some embodiments, the beam is detuned from a transition involving a first manifold, such that a majority of the atomic population of the first manifold in the atomic ensemble is moved from the first manifold to a magnetic Zeeman sublevel of a second manifold having a maximum or minimum magnetic quantum number.

[0006] In some embodiments, the optical radiation power of the beam exceeds a threshold power to induce an asymmetry in the distribution of the atomic population of the Zeeman sublevels of the second manifold, resulting in atomic spin orientation.

[0007] 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 nonlinear. Those skilled in the art will appreciate that the magneto-optical rotation signal can be obtained from detection of the beam after passing through the atomic ensemble, preferably when the ensemble is subjected to an oscillating magnetic field. The signal can be related to the amplitude of oscillation of the beam polarization. As those skilled in the art will appreciate, the magneto-optical signal arises from coupling caused by the oscillating magnetic field between Zeeman sublevels in the atomic ensemble exposed to a constant magnetic field.

[0008] In some embodiments, the threshold power is 2 mW.

[0009] In some embodiments, the constant magnetic field is configured to induce a Larmor frequency in the atomic ensemble of less than or equal to 30 kHz.

[0010] In some embodiments, the constant magnetic field is configured to induce a Larmor frequency in the atomic ensemble of less than or equal to 20 kHz.

[0011] In some embodiments, the frequency of the beam is one that maximizes the magneto-optical rotation signal from the second manifold.

[0012] In some embodiments, the beam is negatively detuned from the transition involving the first manifold.

[0013] In some embodiments, the beam has linear polarization. In other embodiments, the beam has circular polarization. Preferably, the circularly polarized beam is parallel (or substantially parallel) to the stationary magnetic field.

[0014] In some embodiments, the constant magnetic field is configured to induce a Larmor frequency in the atomic ensemble of greater than 20 kHz.

[0015] According to one aspect of the invention, there is provided a method of detecting an oscillating magnetic field comprising the above method, wherein the beam has linear polarization, the method comprising detecting the beam after passing through an ensemble of atoms to detect the oscillating magnetic field.

[0016] According to one aspect of the invention, there is provided a method of detecting an oscillating magnetic field comprising the above method, wherein the beam has circular polarization, the beam being a magnetometer pump beam, the method comprising probing an atomic ensemble with a magnetometer probe beam having linear polarization and degenerate in frequency with the magnetometer pump beam, the method comprising detecting the magnetometer probe beam after passing through the atomic ensemble to detect the oscillating magnetic field.

[0017] In some embodiments, the method includes providing an oscillating primary magnetic field and causing a secondary magnetic field by a conductive or magnetically permeable object.

[0018] In any of the above embodiments, the polarization of the linearly polarized beam is preferably parallel or substantially parallel to the stationary magnetic field. The linearly polarized beam is transverse, preferably orthogonal, to the stationary magnetic field direction and transverse, preferably orthogonal, to the oscillating magnetic field for detection.

[0019] According to one aspect of the present invention, there is provided a system for generating atomic spin orientations in an atomic ensemble, the system comprising: an atomic ensemble having atomic energy levels including a ground state including a first and a second manifold; and a radiation source configured to excite the atomic ensemble with a beam of electromagnetic light radiation detuned from a transition involving the first manifold, such that a majority of the atomic population of the first manifold within the atomic ensemble is transferred from the first manifold to a magnetic Zeeman sublevel of the second manifold.

[0020] In some embodiments, the system is configured to provide a beam having an optical radiation power exceeding a threshold power to induce an asymmetry in the distribution of the atomic population of the Zeeman sublevels of the second manifold, resulting in atomic spin orientation.

[0021] In some embodiments, the beam has linear polarization.

[0022] In some embodiments, the beam is a pump beam having circular polarization.

[0023] 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, which may be the same radiation source used for excitation.

[0024] 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.

[0025] In some embodiments, the system includes a detector configured to detect the linearly polarized beam to detect the oscillating magnetic field.

[0026] In some embodiments, the atomic ensemble is rubidium and the radiation source is configured to emit a beam having an optical radiation power of 4mW or less.

[0027] In some embodiments, the radiation source is a vertical cavity surface emitting laser diode.

[0028] In some embodiments, the system includes a magnetic field source configured to provide a constant magnetic field to the atomic ensemble to induce Zeeman splitting within first and second manifolds of ground states of atomic energy levels of the atomic ensemble.

[0029] In some embodiments, the system is an atomic magnetometer.

[0030] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which: [Brief description of the drawings]

[0031] [Figure 1] Schematic setup of a single linearly polarized beam that creates a population imbalance (polarization) in the atomic ground state by transferring populations between ground state manifolds. A static bias magnetic field creates an energy split in 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 polarizing beam splitter. [Diagram 2] Schematic setup in which a single beam is split into two beams with degenerate optical frequencies. The linearly polarized beam works similarly to that described in Fig. 1. The circularly polarized beam is used to enhance the population transfer between ground state manifolds. [Diagram 3] FIG. 13 is a schematic diagram illustrating the evolution of orientations within a second manifold of an atomic ensemble. [Figure 4(a)] FIG. 1 is a schematic depicting a linearly polarized laser beam transferring populations between the ground state manifolds of F=3 and F=4 cesium, resulting in a population imbalance (atomic spins) within the ground state manifolds of F=3 and F=4 cesium. [Figure 4(b)] Schematic depicting a weak radio frequency field Brf that induces coherence between adjacent F=4 Zeeman sublevels and causes the atomic spin polarization to precess around Boff, as indicated by the black arrows. The spin precession is monitored by a linearly polarized probe beam. [Diagram 5] Dependence of the rf signal amplitude R on detuning the probe beam from the 62S1 / 2F=3 → 62P3 / 2F'=2 transition. The F=3 and F=4 resonances are indicated by the red and black arrows, respectively. Measurements were performed with a laser beam power of 5.9 mW. [Figure 6] Figure 3 shows the rf spectroscopy signal recorded with the laser beam frequency tuned around the 62S1 / 2F=3 → 62P3 / 2F'=2 transition (-100 MHz detuning). The F=3 and F=4 resonances are indicated by red and black arrows, respectively. The transition from alignment (a) to orientation (b) can be seen in the spectral profile brought about by the F=4 coherence. The measurements were performed with laser beam powers of (a) 200 μW and (b) 9.1 mW. [Figure 7(a)] Magneto-optic rotation signal recorded with a linearly polarized beam only (black solid line) in the presence of a circularly polarized pump beam with orthogonal polarization components (red dashed and blue dotted lines). The linearly polarized beam power is 12.4 mW and the pump power is 17 μW. [Figure 7(b)]Dependence of signal amplitude on laser beam power for linearly polarized beam only (black triangles) in combination with a Boff-parallel circularly polarized beam (red dots and blue diamonds represent measurements with either of the two orthogonal circular polarizations to the pump beam). [Figure 8] Dependence of the quadrature components of the rf signal amplitude (a) and phase (b) on the offset magnetic field strength (Larmor frequency). The frequencies of the rf spectrum are expressed in terms of detuning from the center of the rf spectrum. Measurements were performed with a laser beam power of 4.6 mW. [Figure 9-11] FIG. 2 illustrates how the magnetometer signal, also called magneto-optical rotation signal, is provided in three phases. [Figure 12] FIG. 1 is a diagram showing an example of an rf spectrum. [Figure 13] 1 is a graph showing magnetometer amplitude versus pump beam power for a circularly polarized beam. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0032] Embodiments of the present invention can efficiently provide for the generation of atomic spin orientation in alkali metal vapor at room temperature in some embodiments with linearly polarized beams, as described below.

[0033] Traditionally, atomic spin orientation is achieved by the transfer of angular momentum from polarized light to the atomic system.

[0034] The measurement configuration discussed below enables a simple and robust radio-frequency atomic magnetometer based on a single low-power laser diode that matches the performance of multi-laser pump-probe systems.

[0035] Some embodiments of the invention described below provide an orientation generating mechanism, for example in room temperature cesium vapor, that combines three elements: optical excitation, nonlinear spin dynamics, and spin exchange collisions. Fluctuations in the spin exchange relaxation rate indicate transitions between alignments and orientations of atomic samples. Observations are performed by monitoring the atomic radio frequency spectrum.

[0036] FIG. 1 shows a radio frequency atomic magnetometer, which in some embodiments may be tunable. The magnetometer is for use with a primary magnetic field source (not shown) configured to provide an oscillating primary magnetic field. In this embodiment, the primary magnetic field source is an rf coil, although in other embodiments, other variable magnetic field sources may be used. The rf coil is configured to provide a primary magnetic field substantially orthogonal to a surface of the sample to be investigated. In this embodiment, this surface is the surface under investigation, which is the main surface of the sample.

[0037] In this embodiment, the rf coil is a 1000 turn coil of 0.02 mm diameter copper wire, with a height of 10 mm, an inner diameter of 2 mm, and an outer diameter of 4 mm, although those skilled in the art will appreciate that these dimensions may vary depending on the application.

[0038] The rf coil is configured such that it may be positioned adjacent to the sample, but generally to one side of the sample, in a non-overlapping relationship with the sample, and is operable to generate an oscillating primary magnetic field resulting in a secondary magnetic field 4 oscillating through the sample at the same frequency as the primary magnetic field. The secondary magnetic field is indicative of the material response of the sample.

[0039] The sample must be electrically conductive (not necessarily highly conductive) and / or magnetically permeable, and thus the sample can be given a tense.

[0040] The atomic magnetometer is configured to detect secondary magnetic fields to perform imaging of, for example, material defects.

[0041] In this embodiment, the atomic magnetometer includes a detection cell 3, which in this embodiment has a resolution of 1 cm at ambient temperature. 3 1. A glass cell coated with paraffin of 1000 nm and containing an atomic ensemble. In this embodiment, the atomic ensemble is a vapor of cesium atoms (atom density is n Cs =3.3×10 10 cm -3 ).

[0042] The magnetometer includes a bias magnetic field source (not shown) configured to provide a bias magnetic field 5 at the detection cell 3 and thus to the atomic ensemble in the bias magnetic field direction. The terms "bias" and "offset" are used interchangeably in this magnetic field context. The bias magnetic field is a constant or static magnetic field, which can be varied but is stabilized and does not oscillate. The bias magnetic field is configured to induce Zeeman splitting in the first and second manifolds of the ground states of the atomic energy levels of the atomic ensemble. The strength of the bias field defines the Larmor frequency.

[0043] In this embodiment, the offset field is actively stabilized by three pairs of nested orthogonal square Helmholtz coils, which provide the bias field source, although other bias field sources may be used in other embodiments.

[0044] The magnetometer includes a radiation source 1, in this embodiment a laser, configured to excite atoms of an atomic sample in a detection cell 3 with a beam of electromagnetic light radiation 2 transverse, in this embodiment orthogonal, to a bias magnetic field.

[0045] Beam 2 is configured to excite the atomic sample and induce orientation within the atomic ensemble.

[0046] Beam 2 also probes detection cell 3 to probe the atomic ensemble, and in particular acts as a probe beam to probe atomic coherence precession within the atomic ensemble.

[0047] The collective atomic spin evolution of the atomic ensemble is mapped onto the polarization state of beam 2.

[0048] The atomic magnetometer includes a detector, which in this embodiment includes a balanced polarimeter 6 configured to receive and detect beam 2 after it has passed through the atomic ensemble in detection cell 3 and detect the oscillating magnetic field in the region of the atomic ensemble. Polarimeter 6 includes a polarizing beam splitter 9, a half wave plate 10 configured for beam 2 to pass through on its way to beam splitter 9, and a photodiode configured to receive both outputs of beam splitter 9, one of which is routed from beam splitter 9 via mirror 8 to photodiode 7.

[0049] The laser light transmitted through cell 3 is analyzed by a polarimeter.

[0050] The detector is configured to output a detection signal in response to detection of the beam 2. This detection signal is typically a voltage or current signal representative of the polarization and / or amplitude of the detected beam 2. In this embodiment, the detector output is an output of a balanced photodetector providing a voltage signal representative of the polarization of the beam 2. The amplitude and phase of this signal can be used, for example, by a computer, to detect the secondary magnetic field 4 and thereby detect the material response of the sample and possibly perform imaging of material defects.

[0051] As will be appreciated by those skilled in the art, the magnetometer signal, also called the magneto-optical rotation signal, comes in three phases. Figures 9-11 illustrate this based on a conventional pump and probe beam system. However, as described herein, in the embodiment under discussion, a single beam serves both of these roles.

[0052] First, referring to Figure 9, coupling to the pump beam induces a polarization of the atomic population in the atomic ensemble (or in other words a spin component aligned with the bias field, shown by the black arrow in Figure 9). In Figure 9, the pump beam is conveniently shown as a circularly polarized beam parallel to the bias field, as in many conventional systems, but in the embodiment of Figure 1, this is the same beam as the probe beam.

[0053] 10, an oscillating magnetic field (e.g., a secondary magnetic field) creates atomic coherence, or in other words tilts the atomic spins and causes them to precess about the bias field. The spin component perpendicular to the bias field (i.e., the atomic coherence) precesses at a Larmor frequency defined by the strength of the bias field.

[0054] Referring to FIG. 11, the oscillations of atomic spins are monitored by a linearly polarized probe beam.

[0055] The precession of the spins is mapped to the beam polarization, i.e. the oscillation of the spins leads to oscillation of the beam polarization (Faraday effect). A photodetector records the amplitude of the oscillations at a characteristic drive frequency. Scanning the drive frequency gives an rf spectrum, otherwise known 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 for F=3 and F=4 spins are different). The amplitude and phase of the F=4 resonance profile gives rise to the amplitude and phase images in non-destructive testing.

[0056] As explained above, many conventional magnetometers use a circularly polarized pump beam at a different frequency than the linearly polarized probe beam. In contrast, in the embodiment of Figure 1, the radiation source 1 is configured to emit a single linearly polarized beam 2 that is used as both the pump and the probe beam. The polarization of beam 2 is substantially parallel to the bias magnetic field, optimally parallel polarization.

[0057] The inventors have found that by detuning the beam from a transition involving a first manifold of the ground state of the atomic energy levels of the atomic ensemble, it is possible to move a large portion of the atomic population of a first manifold in the atomic ensemble from the first manifold to a magnetic Zeeman sublevel of a second manifold of the ground state. Furthermore, the inventors have found that, for a linearly polarized beam, increasing the optical radiation power of the beam breaks the symmetry of the distribution in the second manifold above a threshold power, and then orientation is obtained within the second manifold.

[0058] In atomic physics, population refers to the probability of occupancy of a particular energy level within an atomic ensemble. If the population of the sublevel with the highest magnetic number is said to be 0.5, this means that on average 50% of the atoms in a given ensemble occupy that level.

[0059] Accordingly, beam 2 is detuned from a transition involving a first manifold of ground states of atomic energy levels of the atomic ensemble (in this embodiment, the first manifold is 6 2 S 1 / 2 F=3 and the second manifold is 6 2 S 1 / 2 F=4 and beam 2 is 6 2 S 1 / 2 F=3→6 2 P 3 / 2The F'=4 transition is detuned), thus transferring most of the atomic population of the first manifold in the atomic ensemble from the first manifold to the magnetic Zeeman sublevel 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 in some embodiments, this can be done automatically, but one skilled in the art will appreciate that frequencies around this maximum that still have an observable signal can also be used. With reference to FIG. 5, discussed in detail below, FIG. 5 consists of about 700 rf spectra recorded for different detunings of the probe beam (without pump), showing resonances for F=3 and F=4, indicated by red and black arrows, respectively. FIG. 8, also discussed below, is recorded in the same way (as a group of rf spectra recorded for different Larmor frequencies). In this embodiment, the detuning can range from about -416 MHz (for 3.3 mW) to about -290 MHz (for 10 mW).

[0060] Furthermore, in this embodiment, the optical radiation power of beam 2 exceeds a threshold power, which causes an asymmetry in the distribution of the atomic population of the Zeeman sublevels of the second manifold, resulting in spin orientation. In this embodiment, the threshold power is 2 mW, but the threshold power for other embodiments may be different and depends on the atomic magnetometer configuration, in particular the atomic ensemble. The threshold power may be the power at which the dependence of the magneto-optical rotation signal of the atomic ensemble on the optical radiation beam power becomes nonlinear, so that a person skilled in the art can determine the appropriate threshold power for use in any particular embodiment.

[0061] The embodiment of Figure 1 has the advantage that a linearly polarized beam, rather than a circularly polarized beam, can provide orientation to the atomic ensemble, meaning that the same beam can be used to probe the polarization, which can reduce the number of radiation sources required, resulting in smaller power consumption and sensor dimensions.

[0062] In this embodiment, the beam 2 is negatively detuned from the transition involving the first manifold, so that a large portion of the atomic population of the first manifold in the atomic ensemble is transferred from the first manifold to the magnetic Zeeman sublevel of the second manifold with the largest or smallest magnetic quantum number, which are the states with the highest momentum, otherwise called the extended states of the second manifold. Negative detuning means that the frequency of the beam is reduced with respect to the frequency of the transition.

[0063] 3 provides a schematic diagram illustrating the occurrence of orientation in the second manifold. The orientation is characterized by the excitation of the population to a Zeeman sublevel having a high or low magnetic quantum number, preferably to a Zeeman sublevel having a maximum or minimum quantum number.

[0064] On the left side of Figure 3, a schematic diagram of the energy levels of cesium is shown.

[0065] Figure 3a shows the result of detuned excitation at a lower power below the threshold power, and Figure 3b shows the result of detuned excitation at a higher power above the threshold power. In each of Figures 3a and 3b, the dashed lines indicate the Zeeman sublevels of the first manifold (F=3) and the second manifold (F=4), and the points on the dashed lines indicate the population of the sublevels.

[0066] As can be seen in Figure 3 a, below the threshold power, the excitation moves some of the atomic population of the first manifold into the second manifold, but alignment exists and there is a symmetric population distribution in both the first and second manifolds.

[0067] As can be seen in Fig. 3b, when the excitation is above a threshold power, alignment still exists in the first manifold, but orientation arises in the second manifold as the population of the second manifold is virtually exclusively in a single stretched state.

[0068] In this embodiment, the atomic ensemble is cesium, but cesium is not the only element that can be used, nevertheless the atomic ensemble is preferably an alkali metal, in particular cesium or rubidium.

[0069] As is apparent from the above, in use the atomic magnetometer implements a method for generating atomic spin orientations within an atomic ensemble, the method comprising: providing a bias magnetic field, a constant magnetic field, to the atomic ensemble by a bias magnetic field source to induce Zeeman splitting within first and second manifolds of ground states of atomic energy levels of the atomic ensemble; The method includes exciting the atomic ensemble with a beam of electromagnetic light radiation 2 by a radiation source 1 to produce atomic spin orientation within the atomic ensemble.

[0070] While this is occurring, an rf coil can be operated adjacent to the sample in the manner discussed above to provide a primary magnetic field oscillating at the rf frequency, and a secondary magnetic field 4 oscillating at the rf frequency through the sample.

[0071] 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 beam 2, which is also used as a magnetometer probe beam: in other words, exciting the ensemble with this beam also means probing the ensemble with this beam.

[0072] A detector detects the beam 2 after passing through the atomic ensemble to detect the oscillating secondary magnetic field 4 and thus in this embodiment imaging of material defects can be performed.

[0073] The embodiment of Figure 1 has the advantage of using a single beam 2, which is most effective at low Larmor frequencies, typically below 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 the bias magnetic field source is accordingly configured and operated to bring about a Larmor frequency within one of these ranges in the atomic ensemble. However, the embodiment of Figure 2 described below is more effective than the embodiment of Figure 1, albeit at the expense of increased complexity.

[0074] The embodiment of FIG. 2 is similar to that of FIG. 1, except that it also uses a circularly polarized pump beam, as discussed below.

[0075] The magnetometer of Figure 2 includes a beam splitter 13 configured to split a second beam from the linearly polarized beam 2 emitted by the radiation source 1. The linearly polarized beam 2 continues as described with respect to Figure 1, and the second beam is converted into a circularly polarized pump beam 11, guided and provided to the atomic ensemble in the detection cell and used to enhance the transfer of the atomic population from the first manifold to the magnetic Zeeman sublevel of the second manifold, as described above.

[0076] In this embodiment, the magnetometer is configured such that the probe beam has an optical emission power above a threshold at the atomic ensemble.

[0077] However, since excitation is provided by a circularly polarized beam, not all embodiments require excitation by a linearly polarized beam, and in some embodiments, the power of the linearly polarized beam may be below a threshold and not support excitation.

[0078] It should be noted that, with respect to the power of the circularly polarized pump beam, the characteristics of the polarized excitation by the pump and probe beams are different. Indirect excitation by a circularly polarized beam does not require high powers, in fact the signal saturates at about 200-500 μW, and for even higher powers the signal amplitude decreases. Only linearly polarized beams introduce nonlinearities. Figure 13 shows a graph of the magnetometer amplitude versus pump beam power (Appl. Phys. Lett. 2012). On the other hand, Figure 7b (discussed below) shows that for a given power of the pump beam, it is possible for the probe beam to increase the signal (polarization) as long as it is above a threshold. The increase is shown by the change in the steepness of the power-dependent gradient (blue).

[0079] Accordingly, in this embodiment, the power of the pump beam is in the range of 200-500 μW, although in some embodiments values ​​outside this range can still be used.

[0080] In the embodiment of FIG. 2, the second beam is redirected through a quarter wave plate 12 via a mirror to convert the linear polarization to circular polarization and is directed at the detection cell parallel to the bias field direction.

[0081] Circular polarization of the pump beam improves the effectiveness of the optical excitation. One consequence of this is that the system can be operated more effectively at higher Larmor frequencies. Thus, in this embodiment, the bias magnetic field source is configured and operated to provide a Larmor frequency of greater than 20 kHz in the atomic ensemble. However, the system is not limited to operating at high Larmor frequencies, but can also be operated at lower Larmor frequencies, such as those of the embodiment of FIG. 1.

[0082] In the embodiment of FIG. 2, the pump beam provides increased excitation and the linearly polarized beam serves as a probe beam, although as explained above, in this embodiment the linearly polarized beam also contributes to excitation. As will be appreciated by those skilled in the art, the pump and probe beams are degenerate in frequency. In this embodiment, the radiation source is configured to emit a beam having an optical radiation power in the region of 6 mW to 7 mW, which is the combined power of the probe and pump beams. In other embodiments, this power can be greater, which can be up to 10 mW or can exceed 10 mW.

[0083] In use, the embodiment of Figure 2 operates and is operated in much the same way as the embodiment of Figure 1. However, in this embodiment, the atomic ensemble is excited by two beams, a probe beam and a pump beam, both of which contribute to the excitation as discussed above.

[0084] As will be appreciated by those skilled in the art, instead of the radiation source emitting a single beam and the system splitting the beam as in the embodiment of FIG. 2, multiple radiation sources can be used, provided that appropriate polarization and similar frequencies are used, but this will increase the cost and complexity of the system.

[0085] Furthermore, it is not necessary for the radiation source 1 to emit a linearly polarized beam, a part of which is split and converted into a circularly polarized beam: it is also possible to do this the other way around, with the radiation source emitting a circularly polarized beam, a part of which is split and converted into a linearly polarized beam.

[0086] The advantage of the embodiment of Fig. 2 is that it excites (or lacks) the same type of symmetry because the beams are detuned as described. This means that the beams can be of the same frequency, or in other words degenerate in frequency, and a single radiation source can conveniently generate both. Without detuning, the circularly and linearly polarized beams would compete, which means that to prevent this, as in conventional systems, it would be necessary to use different frequencies and multiple radiation sources would be required.

[0087] In another embodiment, the system is configured and operated as described above in connection with FIG. 2. 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 lower power laser diode than cesium, and advantageously allows for the use of relatively low power VCSEL diodes. This is because the hyperfine splitting of the ground state of rubidium is about 3 or 6 GHz, compared to about 9 GHz for cesium. In this embodiment, the radiation source is configured to emit a beam having an optical radiation power of about 4 mW or less, typically about 4 mW.

[0088] 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 be modified, but preferably the detector is an optical detector capable of detecting the polarization and / or amplitude of the probe beam.

[0089] In some embodiments, it is possible to use the Earth's magnetic field as the bias field, thus eliminating the bias field source.

[0090] Applications of the methods and systems described herein include, for example, detection of corrosion under insulation in oil and gas pipes and energy sectors, monitoring of reinforced concrete structures in the transportation sector, object detection, monitoring, and monitoring of nuclear waste containers in nuclear power plants.

[0091] The advantages gained include: the system can be safe and non-invasive (non-ionizing radiation), allows detection of corrosion on the inner and / or outer walls of the pipeline, allows differentiation between corrosion and changes in the pipeline geometry from bends / T-junctions / welds in the pipe, allows scanning of all insulation types, can be low cost, allows offering improvements in resolution and switch scanning modes.

[0092] Although the primary described embodiment relates to an atomic magnetometer, the system and / or method for generating atomic spin orientations may be used in other areas, such as chemical analysis or non-destructive testing of materials, etc. In such embodiments, for example, the detector may be omitted or modified as appropriate, and the rf coil may be omitted.

[0093] Experimental results and discussion Below we present experimental results and discussion investigating the mechanism of spin orientation generation in room temperature cesium vapor, combining three elements: (1) nonresonant optical excitation, (2) nonlinear spin dynamics, and (3) SEC (selective relaxation and coherence transfer [17-20]). Of course, the details discussed below can be used in the embodiments described above.

[0094] (1) A linearly polarized laser beam moves the atomic population from the F=3 manifold to the F=4 manifold by non-resonant optical excitation, resulting in population imbalance (alignment) within both levels, as shown in Figure 4(a). A specific frequency detuning of the beam ensures that most of the population moved to the F=4 level proceeds to either the elongated state, i.e., the sublevel with the largest or smallest magnetic quantum number. The dynamics within the F=3 level is defined by the resonant coupling to the laser field, while the atomic spins in F=4 arise only in the presence of a weak far-resonant optical SEC coupling.

[0095] (2) Weak coupling to the optical field drives nonlinear spin dynamics that break the symmetry of the population distribution. In particular, this moves a fraction of the population out of one of the elongated states, effectively making these atoms more susceptible to SEC relaxation. (3)

[0096] As a result of these two factors (nonlinear spin dynamics and SEC), the suppression of the component representing one of the spin directions contributing to the alignment and the generation of atomic orientation at low magnetic fields are observed. A direct implementation of the discussed techniques is within the realm of radio frequency (rf) atomic magnetometry [21, 22], but possible applications include a wide range of techniques ranging from chemical analysis of materials

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

[0097] The following contains a brief description of the experimental setup. The components of the atomic spin orientation mechanism are investigated by the dependence of the rf spectroscopy signal on three measurement parameters (laser frequency detuning, beam power, and magnetic field strength) which are discussed later.

[0098] Experimental setup The measurements are performed in a shielded environment using a system according to FIG. 1 [12, 20, 26], although it should be noted that this is not necessary for all embodiments.

[0099] The ambient magnetic field is suppressed by the use of five layers of cylindrical shielding with end caps made from 2 mm thick mu metal. A solenoid within the shield creates a well-controlled offset magnetic field B off and the relative homogeneity is 10 over the length of the cell. -4 The atoms used are cesium atomic vapors contained in a paraffin-covered cell 3 at ambient temperature (atom density is n Cs =0.33-1.0×10 11 cm -3 These atoms are photoexcited by a linearly polarized laser beam 2 with a diameter of 20 mm, and the B off The polarization of beam 2 is B off The laser beam is provided by a DBR diode laser 1 operating on the caesium D2 line [Fig. 4(a)] and can be frequency stabilized to within ±10 GHz relative to the master laser frequency using offset locking. The same linearly polarized beam also acts as a probe of the polarization precession via the Faraday effect

[27] , and the evolution of the collective atomic spins is mapped onto the polarization state of the linearly polarized probe beam [8, 21, 28–30]. The laser light transmitted through the cell is analyzed by a polarimeter 6 consisting of a crystal polarizer oriented at 45° to the incident polarization and a commercial balanced photodetector 7. The two orthogonal components of the resulting signal are measured by a lock-in amplifier and are coupled to the driving rf field (B rf ) frequency fundamental.

[0100] Non-resonant excitation Simple rate equations based on the transition probabilities of the D2 line confirm that the optimum conditions (laser detuning) for population transfer from the F=3 level to the F=4 level and for the creation of population imbalances in the F=4 manifold are mutually exclusive. The former occurs when the laser frequency is 6 2 S 1 / 2 F=3→6 2 P 3 / 2It is optimized when tuned near the F'=4 transition, where the latter effect is minimal. In the following section, we identify the frequency range that optimizes the increase in orientation at the F=4 level.

[0101] Figure 5 shows the magnitude of the rf signal.

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[31] , but two differences are worth pointing out. First, the inter-manifold excitation maximum is reached at a non-zero laser detuning (about -310 MHz for the measurement depicted in Figure 5). Second, the characteristics of the polarization generated within the F=3 level (alignment) and the F=4 level (orientation) are different.

[0102] Nonlinear Dynamics Linearly polarized

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[0103] Figure 6 shows the 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 indicated by red and black arrows, respectively. The rf field frequency is off A polarization rotation resonance is observed when the alignment of the F=3 level with the splitting between adjacent Zeeman sublevels introduced by the rf-resonance excitation is aligned to the splitting between adjacent Zeeman sublevels introduced by the rf-resonance excitation. In this aligned system, the rf response consists of two profiles with opposite signs, resulting in a dispersive lineshape. As shown in Fig. 6(a), at low power, the rf spectrum consists of large and broad features due to the alignment within the F=3 level brought about by the direct photoexcitation, while the structures become much smaller due to the non-resonant excitation into the F=4 manifold. An increase in the laser beam power not only translates into an increase in the F=3 and F=4 signal amplitudes, as shown in Fig. 6(b). The change in the symmetry of the F=4 signal indicates the presence of atomic alignment, whereas the features of the F=3 profile remain unchanged. The resonant coupling of the laser light into the F=3 Zeeman sublevel results in a broadening of the power of the corresponding spectral profile, which contributes to the broad, low amplitude background seen in Fig. 6(b).

[0104] To confirm that the F = 4 spectral profile represents atomic orientation, Boff Excitation was added by a circularly polarized (pump) beam propagating along the direction of the nucleus

[26] . The pump beam was generated by a diode laser and consisted of cesium-6 2 S 1 / 2 F=3→6 2 P 3 / 2 The crossover is frequency-locked to the F'=2,3 crossover. The solid black line in Figure 7(a) shows the rf spectrum for the F=4 profile recorded with only a linearly polarized beam. The dashed red and dotted blue lines represent the case where one of the two orthogonal circular polarizations of the pump beam is added. The presence of the pump beam leads to atomic orientation in the sample (B off ) when the orientations produced by the linearly polarized and pump beams coincide, the amplitude of the observed profile increases [blue dotted line in Fig. 7(a)]. For opposite pump polarizations, the signal amplitude decreases and the spectral features change (red dashed line). The dependence of the signal amplitude on opposite pump beam polarization is shown in Fig. 7(b) (red dots and blue diamonds). The amplitude of the signal produced by the orthogonally polarized pump beam is below 2 mW of the probe power. The asymmetry in the amplitude above this power is caused by the sample orientation induced by the linearly polarized beam. Signatures of this effect are also present in the amplitude data for the signal produced by the linearly polarized beam only (black triangles). The change from a linear to a quadratic slope of the amplitude power dependence seen above 2 mW confirms the nonlinear character of the underlying mechanism. Calculation and splitting of the spectrum in Fig. 6(a) shows that the tensor light shift (0.2 Hz) is smaller than the SEC relaxation rate (3 Hz). However, even such small values ​​can give rise to nonlinear spin dynamics, as shown in figure 6 of

[12] .

[0105] Spin exchange collisions The effect of nonlinear spin dynamics is enhanced by SEC-driven coherence transfer. It has been demonstrated that the degeneracy between the transition frequencies of the Zeeman sublevels leads to a reduction in the decoherence rate governed by SEC

[20] . In contrast to the nondegenerate case, the frequency mismatch (dephasing) between the precessing spins is negligible, whether or not it is affected by SEC, and the SEC process, which does not involve a change in the manifold, does not contribute to the relaxation. One of the features of this effect, the so-called coherence transfer process [17–20], is that the spectral profile representing the relevant coherence clusters around the main component of the spectrum [20, 32].

[0106] Figure 8 shows B off 4 shows the dependence of the two normalized quadratures (X, Y) of the rf spectroscopy signal on B. The normalization takes into account the variation of the amplitude and phase of the rf spectroscopy signal with the operating frequency, off was performed in the standard pump-probe configuration

[26] over the same range of off The spectral profile in FIG. 8(a) for (the Larmor frequency is about 200 kHz) has a shape typical of the atomic alignment in FIG. 8(a). off As β decreases, the overlap of the components with opposite signs increases, which results in a reduced signal amplitude. As a result of nonlinear spin dynamics, the profile positioned at a detuning of about -0.05 kHz from resonance reduces the population of the stretched state depicted in Fig. 5(a). This results in a higher relaxation rate for the coherence, which contributes to the negatively detuned portion of the spectrum. As a result, the amplitude of the negatively detuned component is larger than that of the other profiles, which is shown in Fig. 5(b). off The small frequency mismatch between the various components (B off The decrease in coherence transfer and atomic orientation observed over the frequency range below 20 kHz is enhanced by the decrease in off The intensity of the other perpendicular components is shown along with their occurrence.

[0107] Conclusion Radio Frequency Atomic Magnetometer We have demonstrated the generation of atomic spin orientations in cesium vapor at room temperature. The presence of atomic polarization is important for the operation of radio frequency atomic magnetometers. The rf frequency range (1 kHz-30 kHz) of single beam techniques is interesting in the context of non-destructive testing based on magnetic induction, 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 and non-resonant probing of F=4 atomic orientations, which is usually realized by two / three independent lasers. A clear benefit of the presented scheme is the simplicity of the instrument. Systematic measurements of the signal-to-noise ratio (SNR) confirm that the discussed option gives only 1.3-1.4 times lower SNR than that recorded with the optimized pump-probe configuration

[26] . The relatively steep peak of the signal frequency dependence shown in Figure 5 allows the stabilization of the laser frequency, despite the strong saturation of the F=3 resonance.

[0108] As discussed above, the orientation produced by a linearly polarized beam is B off The challenge is that the frequency of the signal is observed over a relatively narrow range of frequencies 2 S 1 / 2 F=3→6 2 P 3 / 2 This can be overcome by the implementation of a degenerate pump-probe configuration such as the embodiment of Figure 2 with a circularly polarized (pump) beam and a linearly polarized (probe) beam operating at about 290 MHz from the F'=2 transition. It is worth pointing out that this frequency for the pump beam is not far from the frequency used in the optimized indirect excitation scheme

[26] . The hyperfine splitting of the cesium ground state (9.172 GHz) defines the detuning of the laser frequency from F=4, which affects the signal amplitude and the nonlinearity strength. Thus, 85 The use of Rb vapor (hyperfine splitting of 3 GHz) allows the recorded signal amplitude to be increased. 85 The combination of the use of Rb vapor can enable efficient operation of the atomic magnetometer with 4 mW of laser optical power, which is shown to be achievable from a single vertical-cavity surface-emitting laser diode.

[0109] All optional and preferred features and modifications of the described embodiments, as well as the dependent claims, can be used in any aspect of the invention taught herein. Furthermore, the individual features of the dependent claims, as well as all optional and preferred features and modifications of the described embodiments, can be combined with each other and are interchangeable.

[0110] The disclosures in UK Patent Application No. 1914464.1 from which this application claims priority and in the abstract accompanying this application are hereby incorporated by reference.

[0111] References 1. DD Awschalom, Ronald Hanson, J. Wrachtrup, and BB Zhou, Nat. Photonics 12, 516 (2018). 2. A. Smith, BE Anderson, H. Sosa-Martinez, CA Riofrio, IH Deutsch, and PS Jessen, Phys. Rev. Lett. 111, 170502 (2013). 3. T. Chalopin, C. Bouazza, A. Evrard, V. Makhalov, D. Dreon, J. Dalibard, LA Sidorenkov, and S. Nascimbene, Nat. Commun. 9, 4955 (2018). 4. W. Happer, Rev. Mod. Phys. 44, 169 (1972). 5. N. Fortson, and B. Heckel, Phys. Rev. Lett. 59, 1281 (1987). 6. WM Klipstein, SK Lamoreaux, and N. Fortson, Phys. Rev. Lett. 76, 2266 (1996). 7. A. Andalkar, R. B. Warrington, M. V. Romalis, S. K. Lamoreaux, B. Heckel, and N. Fortson, Phys. Rev. A 65, 023407 (2002). 8. W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, Phys. Rev. Lett. 104, 133601 (2010). 9. T. G. Walker, and W. Happer, Rev. Mod. Phys. 69, 629 (1997). 10. S. Appelt, B.-A. Barnga, C. J. Erikson, M. V. Romalis, A. R. Young, and W. Happer, Phys. Rev. A 58, 1412 (1998); 11. G. A. Smith, S. Chaudhury, A. Silberfarb, I. H. Deutsch, and P. S. Jessen, Phys. Rev. Lett. 93, 163602 (2004). 12. W. Chalupczak, and P. Josephs-Franks, Phys. Rev. Lett. 115, 033004 (2015). 13. D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, Phys. Rev. Lett. 85, 2088 (2000). 14. M. C. Kuntz, R. C. Hilborn, and A. M. Spencer, Phys. Rev. A 65, 023411 (2002). 15. S. M. Rochester, M. P. Ledbetter, T. Zigdon, A. D. Wilson-Gordon, D. Budker, Phys. Rev. A 85, 022125 (2012). 16. M. Auzinsh, D. Budker, and S. M. Rochester, Optically polarized atoms, Oxford University Press (2010). 17. G. A. Ruff and T. R. Carver, Phys. Rev. Lett. 15, 282 (1965). 18. S. Haroche and C. Cohen-Tannoudji, Phys. Rev. Lett. 24, 974 (1970). 19. J. Skalla, G. Wackerle, and M. Mehring, Opt. Commun. 127, 31 (1996). 20. W. Chalupczak, P. Josephs-Franks, B. Patton, and S. Pustelny, Phys. Rev. A 90, 042509 (2014). 21. M. Savukov, S. J. Seltzer, M. V. Romalis, and K. L. Sauer, Phys. Rev. Lett. 95, 063004 (2005). 22. W. Chalupczak, R. M. Godun, and S. Pustelny, Advances in At. Mol. and Opt. Phys. 67, 297-336 (2018). 23. G. Bevilacqua, V. Biancalana, Y. Dancheva, A. Vigilante, A. Donati, and C. Rossi, J. Phys. Chem. Lett. 8, 6176 (2017) 24. A. Wickenbrock, S. Jurgilas, A. Dow, L. Marmugi, and F. Renzoni, Opt. Lett. 39, 6367 (2014). 25. P. Bevington, R. Gartman and W. Chalupczak, J. Appl. Phys. 125, 094503 (2019). 26. W. Chalupczak, RM Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, Phys. Rev. A 85, 043402 (2012). 27. Y. Takahashi, K. Honda, N. Tanaka, K. Toyoda, K. Ishikawa, and T. Yabuzaki, Phys. Rev. A 60, 4974 (1999). 28. MP Ledbetter, IM Savukov, VM Acosta, D. Budker, and MV Romalis, Phys. Rev. A 77, 033408 (2008) 29. W. Chalupczak, RM Godun, S. Pustelny, and W. Gawlik, Appl. Phys. Lett. 100, 242401 (2012). 30. G. Bevilacqua, V. Biancalana, P. Chessa, and Y. Dancheva, Appl. Phys. B 122, 103 (2016). 31. W. Chalupczak, P. Josephs-Franks, S. Pustelny, and W. Gawlik, Phys. Rev. A 81, 013422 (2010). 32. W. Happer and AC Tam, Phys. Rev. A 16, 1877 (1977).

Claims

1. A method for detecting an oscillating magnetic field, comprising: generating atomic spin orientations in an atomic ensemble, the generating of the atomic spin orientations comprising: providing a constant magnetic field to the atomic ensemble to induce Zeeman splitting within first and second manifolds of ground states of atomic energy levels of the atomic ensemble; exciting the atomic ensemble with a beam of electromagnetic light radiation, the beam having a linear polarization and detuned from a transition involving the first manifold, such that a majority of the atomic population of the first manifold within the atomic ensemble is transferred from the first manifold to a magnetic Zeeman sublevel of the second manifold; The method further comprises: detecting the beam after passing through the atomic ensemble to detect an oscillating magnetic field. method.

2. A method for detecting an oscillating magnetic field, comprising: generating atomic spin orientations in an atomic ensemble, the generating of the atomic spin orientations comprising: providing a constant magnetic field to the atomic ensemble to induce Zeeman splitting within first and second manifolds of ground states of atomic energy levels of the atomic ensemble; exciting the atomic ensemble with a beam of electromagnetic light radiation, the beam being a magnetometer pump beam having circular polarization and detuned from 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 a magnetic Zeeman sublevel of the second manifold; The method further comprises: probing the atomic ensemble with a magnetometer probe beam having linear polarization and degenerate in frequency with the magnetometer pump beam; The method further comprises: detecting the magnetometer probe beam after passing through the atomic ensemble to detect an oscillating magnetic field; The method further comprises: splitting a beam emitted by a radiation source into a magnetometer pump beam and a magnetometer probe beam; method.

3. The method of claim 2, wherein the pump beam is detuned from a transition involving the first manifold, such that a majority of the atomic population of the first manifold in the atomic ensemble is moved from the first manifold to a magnetic Zeeman sublevel of the second manifold having a maximum or minimum magnetic quantum number.

4. The optical radiation power of the beam exceeds a threshold power to cause an asymmetry in the distribution of the atomic population of Zeeman sublevels of the second manifold, resulting in atomic spin orientation; the threshold power being a power at which the dependence of the magneto-optical rotation signal of the atomic ensemble on the optical radiation beam power becomes nonlinear; The method of claim 1.

5. The constant magnetic field is configured to produce a Larmor frequency of 30 kHz or less in the atomic ensemble; and / or the beam is negatively detuned from the transition involving the first manifold; The method according to any one of claims 1 to 4.

6. A method according to any one of claims 1 to 5, wherein the frequency of the beam is a frequency that maximizes the magneto-optical rotation signal from the second manifold.

7. The method of claim 2, wherein the constant magnetic field is configured to produce a Larmor frequency greater than 20 kHz within the atomic ensemble.

8. A method according to any preceding claim, comprising providing an oscillating primary magnetic field and causing a secondary magnetic field by means of a conductive or magnetically permeable object.

9. 1. A system for generating atomic spin orientation in an atomic ensemble, comprising: an atomic ensemble having atomic energy levels including a ground state including a first and a second manifold; a magnetic field source configured to provide a constant magnetic field to the atomic ensemble to induce Zeeman splitting within first and second manifolds of ground states of atomic energy levels of the atomic ensemble; a radiation source configured to excite the atomic ensemble with a beam of electromagnetic light radiation having linear polarization, the beam being detuned from a transition involving the first manifold such that a majority of the atomic population of the first manifold within the atomic ensemble is transferred from the first manifold to a magnetic Zeeman sublevel of the second manifold; The system further comprises: a detector configured to detect the linearly polarized beam to detect an oscillating magnetic field; system.

10. 10. The system of claim 9, configured to provide an optical radiation power to the beam that exceeds a threshold power to induce an asymmetry in the distribution of the atomic population of Zeeman sublevels of the second manifold, resulting in atomic spin orientation.

11. A system for generating atomic spin orientation in an atomic ensemble, comprising: the system comprising: an atomic ensemble having atomic energy levels including a ground state including first and second manifolds; a magnetic field source configured to provide a constant magnetic field to the atomic ensemble to induce Zeeman splitting within first and second manifolds of ground states of atomic energy levels of the atomic ensemble; a radiation source configured to excite the atomic ensemble with a beam of electromagnetic light radiation, the beam being a pump beam having circular polarization and detuned from a transition involving the first manifold such that a majority of the atomic population of the first manifold within the atomic ensemble is transferred from the first manifold to a magnetic Zeeman sublevel of the second manifold; 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; The system further comprises: a detector configured to detect the linearly polarized beam to detect an oscillating magnetic field; the radiation source is configured to emit a single beam; The system further comprises: a beam splitter configured to split the single beam into the pump beam and the probe beam. system.

12. the atomic ensemble is rubidium and the radiation source is configured to emit the beam having an optical radiation power of 4 mW or less; and / or the radiation source is a vertical cavity surface emitting laser diode; A system according to any one of claims 9 to 11.

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