BACKGROUND

In atom magnetometry, spin-polarized atoms in an external magnetic field precess at the Larmor frequency. This precession is typically measured via Faraday rotation, i.e., the spin-polarized atoms rotate the linear polarization of a weak laser beam that passes through the atoms. This rotation of the laser polarization can be detected with a polarimeter, and the resulting electronic signal can be processed into a value of the external magnetic field. Since the gyromagnetic ratio of the atoms (i.e., the Larmor frequency per unit magnetic-field strength) is determined primarily by the energy-level structure of the atoms, atomic magnetometry benefits from high accuracy, as compared to other forms of magnetometry (e.g., SQUID, fluxgate, Hall effect, magnetoresistance, etc.).

In addition, recent advances in the development of millimeter-size vapor cells has enabled the placement of atom-vapor-based magnetometer heads close to the sample to be measured (e.g., within one centimeter of the sample). This improves sensitivity since the magnetic field strength generated by a sample drops at least as 1/r, where r is the distance between the sample and the magnetometer head. In some cases (e.g., a magnetic dipole), the magnetic field drops as rapidly as 1/r3, further emphasizing the need to miniaturize sensor heads so that they can be placed closer to the sample.

SUMMARY

An atomic magnetometer is typically operated in an alternating sequence of pumping and probing stages. In each pumping stage, a pump laser beam is directed through a vapor cell to spin-polarize gaseous atoms therein. An external magnetic field may be applied to establish a quantization axis. The polarization (e.g., circular or linear), propagation direction, and modulation (e.g., AM or FM) of the pump laser beam is selected such that the optical pumping results in a ground-state coherence (i.e., a coherence between two or more magnetic ground-state sublevels of the atoms). During the probing stage, a linear polarized probe laser beam passes through the vapor cell. The spin-polarized atoms rotate the polarization of the probe laser beam synchronously with the Larmor precession. The rotated polarization is then measured with a polarimeter.

The duration of each probing stage is limited by a dephasing time of the atoms (i.e., the transverse spin relaxation time T2). Specifically, collisions between atoms disrupt the ground-state coherences, washing out the Larmor precession, and hence the measured signal. Although techniques exist for increasing the dephasing time (e.g., spin-relaxation coatings and buffer gasses), dephasing times are still typically on the order of milliseconds. Furthermore, as the size of the vapor cell decreases, the rate of collisions between the atoms and the walls increases, leading to shorter dephasing times (even if the walls have a spin-relaxation coating).

The duration of each pumping stage is typically between a few hundred microseconds and a few milliseconds, depending on the available power of the pump laser beam and the transition strengths of the atomic species used. Thus, for each cycle of one pumping stage followed by one probing stage, the atoms may be measured for as little as 50% of the time. That is, half of the time is wasted preparing the atoms, which limits the signal-to-noise ratio (SNR). Gaps in the measured time record of the atoms can also introduce aliasing and other deleterious signal-processing artifacts that mask the true magnetic signal to be measured.

To solve these problems, the present embodiments feature systems and methods for time-multiplexed atomic magnetometry performed with two vapor cells located adjacent to (e.g., on opposite sides of) the sample to be measured. The first vapor cell is operated according to a first sequence of alternating pumping and probing stages. Similarly, the second vapor cell is operated according to a second sequence of alternating pumping and probing stages. However, the second sequence is delayed relative to the first sequence such that the second vapor cell is pumped while the first vapor cell is probed, and the first vapor cell is pumped while the second vapor cell is probed. With this time-multiplexed operation, the magnetic field generated by the sample can be measured without any time gaps. More specifically, and as described in more detail below, the signals from the two vapor cells can be interleaved to form a single gapless time sequence that represents the time-varying magnetic field generated by the sample over the entire time sequence.

By using two vapor cells, the present embodiments advantageously have twice the signal-to-noise ratio of conventional atomic magnetometers that use only one vapor cell (assuming equal vapor pressures, vapor cell sizes, atomic species, etc.). However, the present embodiments also offer advantages over simply doubling the size or pressure of one vapor cell. For example, doubling the vapor cell size results in the extra atoms being located farther from the sample, where they are less sensitive to the magnetic field. As a result, doubling the vapor cell size does not necessarily double the SNR. On the other hand, in the present embodiments the two vapor cells may be located on opposite sides of the sample, in which case both vapor cells are located proximate to the sample, ensuring equal sensitivity to the magnetic field. Increasing the vapor pressure inside the cell can help, although the resulting pressure broadening can reduce T2. More than two vapor cells can be used to achieve even greater increases in signal-to-noise ratio.

In embodiments, a time-multiplexed dual atomic magnetometer operates as a pair of free-induction-decay atomic magnetometers. In these embodiments, the signal from each of the two vapor cells is continuously recorded over several oscillations. For a single probing stage, the resulting signal is approximately equal to an exponentially decaying sinusoid, which can be fitted to extract a center frequency which equals the average Larmor frequency over the probing phase. The Larmor frequency may then be converted into a corresponding value of the magnetic field. Repeating this process over several consecutive cycles produces a time sequence of magnetic field values. The bandwidth of this approach is limited by the duration of one cycle. However, the sequence can be used to identify low-frequency components spanning over several cycles.

To increase the bandwidth, instantaneous-phase retrieval may be implemented on the recorded signals. This technique was recently demonstrated for atomic magnetometers in “Wide-bandwidth atomic magnetometry via instantaneous-phase retrieval” by N. Wilson et al. (arXiv:2003.04526v1), although it has been used in geosciences for several decades. For example, see “The calculation of instantaneous frequency and instantaneous bandwidth” by A. E. Barnes (Geophysics 57, 1520-1539, 1992). In addition to these references, details about instantaneous phase and frequency can be found in “Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals” by B. Boashash (Proc. IEEE 80, 520-538, 1992). With instantaneous-phase retrieval, the present embodiments are expected to operate at bandwidths exceeding 10 kHz.

The present embodiments may be used to enhance magnetometry in a host of applications, including geosciences, magnetic communication, threat detection, the measurement of bio-magnetic signals (e.g., magnetoencephalography), nuclear magnetic resonance (NMR), and magnetic resonance imaging (MRI). In another application, the present embodiments are used to measure the time-varying magnetic field generated by molecules in an aqueous solution. It is hypothesized that the motion of these molecules (e.g., stretching, rotating, translating, etc.) causes electric charges therein to accelerate, which produces magnetic fields at the femtotesla level. When the time-varying magnetic field is later “played” to cells (e.g., by applying electric currents to coils to replicate the time-varying magnetic field), the cells may behave as if the original molecules were present. In this regard, the time-varying magnetic field may be used to replicate the pharmacological effects of a compound on the cells, but without physically exposing the cells to the actual compound. As such, the present embodiments may be used to identify new therapies for treating cancer. Examples of molecules whose time-varying magnetic fields can be measured and subsequently used for such therapeutic purposes include small interfering RNA (siRNA) and messenger RNA (mRNA) from genes.

In embodiments, a time-multiplexed dual atomic magnetometer includes first and second vapor cells located adjacent to a sample cell such that a magnetic field generated by a sample within the sample cell induces Larmor precession of atoms within the first and second vapor cells. The dual atomic magnetometer also includes a first polarimeter that measures a first polarization of a first probe beam after the first probe beam propagates through the first vapor cell. The first polarimeter outputs a first polarization signal indicative of the first polarization. The dual atomic magnetometer also includes a second polarimeter that measures a second polarization of a second probe beam after the second probe beam propagates through the second vapor cell. The second polarimeter outputs a second polarization signal indicative of the second polarization. The time-multiplexed dual atomic magnetometer also includes a signal processor that processes alternating data blocks of the first and second polarization signals to generate a single gapless temporal sequence that represents the magnetic field generated by the sample.

In other embodiments, a method for time-multiplexed dual atomic magnetometry includes generating, by a sample within a sample cell, a magnetic field that induces Larmor precession of atoms within first and second vapor cells located adjacent to the sample cell. The method also includes measuring, with a first polarimeter, a first polarization of a first probe beam after the first probe beam propagates through the first vapor cell. The first polarimeter outputs a first polarization signal indicative of the first polarization. The method also includes measuring, with a second polarimeter, a second polarization of a second probe beam after the second probe beam propagates through the second vapor cell. The second polarimeter outputs a second polarization signal indicative of the second polarization. The method also includes processing alternating data blocks of the first and second polarization signals to generate a single gapless temporal sequence that represents the magnetic field generated by the sample.

