Limits on Lorentz Invariance Violation from Coulomb Interactions in Nuclei and Atoms

Comprehensive analysis of the effects of magnetic field gradient on the performance of the SERF co-magnetometer

The magnetic field gradient affects the improvement of sensitivity and magnetic field suppression ability of the spin-exchange relaxation-free co-magnetometer. This paper proposes a response model of a co-magnetometer considering magnetic field gradient based on state-space method. The effects of transverse and longitudinal magnetic field gradients on the system's scale factor, bandwidth and magnetic field response are analyzed. The analysis shows that transverse gradient affects the whole frequency band of system response, including steady-state and dynamic performance, while longitudinal gradient only affects steady-state response. With the increase of the gradient, the effect becomes more significant. The test results are in agreement with the theory, proving the accuracy of the theoretical analysis. The rotational sensitivity at 1 Hz decreases from 6.51 ×10^-6 °/s/Hz^1/2 to 5.05×10^-5 °/s/Hz^1/2 in the presence of a magnetic field gradient of -40 nT/cm, so the effect of the magnetic field gradient is critical. This work provides an accurate model for evaluating the effects of magnetic field gradients and provides a method for suppressing gradients using gradient coils, which are important for improving the sensitivity and accuracy of co-magnetometers.

Study on the Magnetic Noise Characteristics of Amorphous and Nanocrystalline Inner Magnetic Shield Layers of SERF Co-Magnetometer

With the widespread use of magneto-sensitive elements, magnetic shields are an important part of electronic equipment, ultra-sensitive atomic sensors, and in basic physics experiments. Particularly in Spin-exchange relaxation-free (SERF) co-magnetometers, the magnetic shield is an important component for maintaining the SERF state. However, the inherent noise of magnetic shield materials is an important factor limiting the measurement sensitivity and accuracy of SERF co-magnetometers. In this paper, both amorphous and nanocrystalline materials were designed and applied as the innermost magnetic shield of an SERF co-magnetometer. Magnetic noise characteristics of different amorphous and nanocrystalline materials used as the internal magnetic shielding layer of the magnetic shielding system were analyzed. In addition, the effects on magnetic noise due to adding aluminum to amorphous and nanocrystalline materials were studied. The experimental results show that compared with an amorphous material, a nanocrystalline material as the inner magnetic shield layer can effectively reduce the magnetic noise and improve the sensitivity and precision of the rotation measurement. Nanocrystalline material is very promising for inner shield composition in SERF co-magnetometers. Furthermore, its ultra-thin structure and low cost have significant application value in the miniaturization of SERF co-magnetometers.

Analysis on the effect of electron spin polarization on a hybrid optically pumped K-Rb-21Ne co-magnetometer

In this paper, the effect of longitudinal electron spin polarization under the combined action of alkali metal density ratio and pump laser power density on the hybrid optically pumped co-magnetometer operated in the spin-exchange relaxation-free (SERF) regime is studied. The AC response model of rotation velocity and magnetic noise of the SERF co-magnetometer system is proposed, and the factors of frequency and system bandwidth are considered. Based on the proposed response model, the error equation of the system is obtained, and the relationship between alkali metal density ratio and pump laser power density and the system noise response is theoretically analyzed and experimentally tested. The results show that when the product of pumping rate and alkali metal density ratio is greater than the electron spin relaxation rate, there is a longitudinal electron spin polarization point that minimizes the system error. In addition, the range of minimum error calculated results obtained by changing the pumping rate for the cells with different alkali metal density ratios is within 5% of the average value, that is, their minimum error potential is roughly the same within a certain range. Under the experimental conditions in this paper, due to the limitation of the electron spin relaxation rate and the operating capacity of the pump laser, the optimal alkali metal density ratio range is about 1/100-1/300.

Investigation on the pulse response of a spin-exchange relaxation-free comagnetometer

We investigate the magnetic pulse response of the optically pumped comagnetometer operated in the spin-exchange relaxation-free (SERF) regime. The pulse response model describing the evolution of the coupled spin ensemble of alkali metal and noble gas during and after the pulse is established for the first time. A three-beam comagnetometer is created with a circularly and two linearly polarized lasers to detect the responses in the three axes of the comagnetometer simultaneously and independently. The results indicate that the response to the small pulse excitation is dominated by the electron spins, while the response to the large pulse excitation and both responses after the pulse excitation consist of a fast and a slow oscillation, which are dominated by the electron spins and nuclear spins, respectively. We also observe novel dynamics of the coupled spin ensemble when the nuclear spins are tipped far away from equilibrium. The theory and method presented here can not only facilitate the investigation on the dynamics of the optically pumped coupled spin ensemble, but also shed light on the application of the pulse modulation technology in the SERF comagnetometer.

Transverse light-shift in a spin-exchange relaxation-free co-magnetometer: measurement, decoupling, and suppression

The transverse light-shift can induce non-negligible polarization error in the output signal of spin-exchange relaxation-free (SERF) co-magnetometer. In this paper, a novel method for rapid measurement of transverse light-shift based on the error of steady-state response of co-magnetometer is proposed firstly, then the sources of transverse light-shift in a compact SERF co-magnetometer is modeled and analyzed from three aspects: the non-ideal linear polarization of probe laser, the circular dichroism of the atomic spin ensembles, and the stress-induced birefringence effect of the cell wall. Furthermore, the decoupling and suppression methods of transverse light-shift based on a degree of circular polarization (DOCP) regulation scheme is presented, to realize the decoupling measurement of the transverse light-shift introduced by the whole co-magnetometer cell, and cancel it out with the non-ideal linear polarization of the probe laser. Eventually, the DOCP regulation scheme suggested in this paper achieves more than a 67% suppression ratio in transverse light-shift, and the short- and long-term performance of SERF co-magnetometer are improved due to the reduction of the coupling effect between the probe laser power and transverse field. Moreover, the measurement, decoupling and suppression methods provided in this paper also have the potential to be applied to other atomic sensors, such as the SERF magnetometers and nuclear spin co-magnetometers.

Optimized gas pressure of an Rb vapor cell in a single-beam SERF magnetometer

We present a theoretical and experimental study of a single-beam spin-exchange relaxation-free magnetometer in ⁸⁷Rb vapor cells under different nitrogen gas pressures. The spin relaxation rate is a key component to limit the magnetic sensitivity, and the zero-field resonance method was used to measure the spin relaxation rates of different alkali metal cells. Simultaneously, in a single-beam spin-exchange-relaxation-free (SERF) magnetometer, we demonstrated that the fundamental magnetic field sensitivity was also limited by the pumping light intensity. Based on our theoretical analysis and experimental results, we determined the optimal pumping light intensity and optimal gas pressure. We experimentally demonstrated that the magnetic field sensitivity was 8.89 fT/Hz in the single-beam configuration, with an active measurement volume of 3 × 3 × 3~mm³.

High-sensitivity operation of a single-beam atomic magnetometer for three-axis magnetic field measurement

We demonstrate a single-beam atomic magnetometer (AM) capable of measuring a three-axis magnetic field with high-sensitivity, achieved by applying a small DC offset field and a high frequency modulation field. To satisfy the miniaturization demand of AMs, an elliptically polarized light detuned by 50 GHz from the resonance transition center is employed. The circularly polarized component is used to polarize the alkali-metal atoms, while the linearly polarized light is used to detect the dynamics of the polarized spin under a magnetic field. Based on theoretical analysis, parameters that significantly affect the performance are optimized, and a sensitivity of 20 fT/Hz^1/2 in x-axis, 25 fT/Hz^1/2 in y-axis, 30 fT/Hz^1/2 in z-axis is achieved with a miniature 4 × 4 × 4 mm ⁸⁷Rb vapor cell. Moreover, we also verify that the operation principle of AMs can be used to null background magnetic fields in-situ with isotropic compensation resolution of 6.7 pT, which provides an effectively precise method for zeroing ambient magnetic field. The high-sensitivity operating of an elliptically-polarized-laser-based magnetometer provides prospective futures for constructing a compact, low-cost AM, which is particularly applicable for non-invasive bio-magnetic imaging such as array-based magnetoencephalography (MEG) and magnetocardiography (MCG).

Transient dynamics of atomic spin in the spin-exchange-relaxation-free regime

In this paper, we experimentally study transient dynamics of spin polarized atoms in the spin-exchange-relaxation-free (SERF) regime with a single-beam configuration. We pumped atoms with a weak detuning pumping beam, along with a sequence of magnetic field pulses orthogonal to the pumping beam were applied. The dynamics of atomic spin, which experiences Larmor precession under the perturbation of magnetic field, is detected by the transmitted pumping beam. Benefited from the long coherence time of atomic spin in the SERF regime, the dependence of precession frequency and decay rate, which is equal to the magnetic resonance linewidth of atomic spin, on magnetic fields is studied with the transient dynamics of atomic spin in the limit of low spin polarization. Moreover, we demonstrate that coil constants can be calibrated by analyzing the precession frequency of the transient dynamics of atomic spin. And the experimental results show that the coil constants are 114.25 ± 0.02 nT/mA and 114.12 ± 0.04 nT/mA in x- and y-axis, respectively. This method is particularly applicable to study the atomic spin dynamics and calibrate the coil constant in situ of a miniature single-beam SERF magnetometer.

Non-Minimal Lorentz Violation in Macroscopic Matter

The effects of Lorentz and CPT violations on macroscopic objects are explored. Effective composite coefficients for Lorentz violation are derived in terms of coefficients for electrons, protons, and neutrons in the Standard-Model Extension, including all minimal and non-minimal violations. The hamiltonian and modified Newton’s second law for a test body are derived. The framework is applied to free-fall and torsion-balance tests of the weak equivalence principle and to orbital motion. The effects on continuous media are studied, and the frequency shifts in acoustic resonators are calculated.

New Test of Lorentz Invariance Using the MICROSCOPE Space Mission

We use data from the T-SAGE instrument on board the MICROSCOPE space mission to search for Lorentz violation in matter-gravity couplings as described by the Lorentz violating standard model extension (SME) coefficients (a[over ¯]_{eff})_{μ}^{w}, where (μ=T, X, Y, Z) and (w=e, p, n) for the electron, proton, and neutron. One of the phenomenological consequences of a nonzero value of those coefficients is that test bodies of different composition fall differently in an external gravitational field. This is similar to "standard" tests of the universality of free fall, but with a specific signature that depends on the orbital velocity and rotation of Earth. We analyze data from five measurement sessions of MICROSCOPE spread over a year finding no evidence for such a signature, but setting constraints on linear combinations of the SME coefficients that improve on best previous results by 1 to 2 orders of magnitude. Additionally, our independent linear combinations are different from previous ones, which increases the diversity of available constraints, paving the way towards a full decorrelation of the individual coefficients.

Overview of the Phenomenology of Lorentz and CPT Violation in Atomic Systems

This is an overview of recent publications on the prospects of searching for nonminimal Lorentz-violating effects in atomic spectroscopy experiments. The article discusses the differences in the signals for Lorentz violation in the presence of minimal and nonminimal operators and what systems are more sensitive to certain types of Lorentz-violating operators.

Effects of pump laser power density on the hybrid optically pumped comagnetometer for rotation sensing

We investigate the effects of pump laser power density on the hybrid optically pumped comagnetometer operated in the spin-exchange relaxation-free (SERF) regime. The analytic steady-state output model for the comagnetometer considering two alkali metal species and one nuclear species is presented for the first time. And the effects of pump laser power density on the rotation sensitivity, suppression of low-frequency magnetic noise and long-term stability of the comagnetometer are studied experimentally. The results indicate that when the product of pumping rate and density ratio of pumped atom to probed atom is equal to the spin relaxation rate of the probed atom, the maximum response and highest sensitivity of the comagnetometer are achieved. However, the suppression of low-frequency magnetic noise and long-term stability improve with the increasing of pump laser power density due to the increasing of nuclear spin polarization. Our focus is to optimize the performance of the comagnetometer for rotation sensing, but the theory and method presented here are relevant to all applications of the hybrid optical pumping technique.

Spacetime Symmetries and Classical Mechanics

Physics students are rarely exposed to the style of thinking that goes into theoretical developments in physics until late in their education. In this work, we present an alternative to the traditional statement of Newton’s second law that makes theory questions accessible to students early in their undergraduate studies. Rather than a contrived example, the model considered here arises from a popular framework for testing Lorentz symmetry used extensively in contemporary experiments. Hence, this work also provides an accessible introduction to some key ideas in ongoing tests of fundamental symmetries in physics.

New Methods for Testing Lorentz Invariance with Atomic Systems

We describe a broadly applicable experimental proposal to search for the violation of local Lorentz invariance (LLI) with atomic systems. The new scheme uses dynamic decoupling and can be implemented in current atomic clock experiments, with both single ions and arrays of neutral atoms. Moreover, the scheme can be performed on systems with no optical transitions, and therefore it is also applicable to highly charged ions which exhibit a particularly high sensitivity to Lorentz invariance violation. We show the results of an experiment measuring the expected signal of this proposal using a two-ion crystal of ^{88}Sr^{+} ions. We also carry out a systematic study of the sensitivity of highly charged ions to LLI to identify the best candidates for the LLI tests.

Lorentz-symmetry test at Planck-scale suppression with a spin-polarized 133 Cs cold atom clock

We present the results of a Local Lorentz Invariance (LLI) test performed with the 133Cs cold atom clock FO2 [1], hosted at SYRTE. Such test, relating the frequency shift between 133Cs hyperfine Zeeman substates to the Lorentz violating coefficients of the Standard Model Extension (SME), has already been realized in [2] and led to state-of-the-art constraints on several SME proton coefficients. In this second analysis we used an improved model, based on a second order Lorentz transformation and a SCRMF nuclear model, which enables us to extend the scope of the analysis from purely proton to both proton and neutron coefficients. We have also become sensitive to the isotropic coefficient ~cTT, another SME coefficient that was not constrained in [2]. The resulting limits on SME coefficients improve by up to 13 orders of magnitude the present maximal sensitivities for laboratory tests and reach the generally expected suppression scales at which signatures of Lorentz violation could appear [3].

Nuclear Matrix Elements for Tests of Local Lorentz Invariance Violation

The nuclear matrix elements for the spin operator and the momentum quadrupole operator are important for the interpretation of precision atomic physics experiments that search for violations of local Lorentz and CPT symmetry and for new spin-dependent forces. We use the configuration-interaction nuclear shell model and self-consistent mean-field theory to calculate the momentum matrix elements for ^{21}Ne, ^{23}Na, ^{133}Cs, ^{173}Yb, and ^{201}Hg. We show that these momentum matrix are strongly suppressed by the many-body correlations, in contrast to the well-known enhancement of the spatial quadrupole nuclear matrix elements.