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High-precision magnetic field measurement is an ubiquitous issue in physics and a critical task in metrology. Generally, magnetic field has DC and AC components and it is hard to extract both DC and AC components simultaneously. The conventional Ramsey interferometry can easily measure DC magnetic fields, while it becomes invalid for AC magnetic fields since the accumulated phases may average to zero. Here, we propose a scheme for simultaneous measurement of DC and AC magnetic fields by combining Ramsey interferometry and rapid periodic pulses. In our scheme, the interrogation stage is divided into two signal accumulation processes linked by a unitary operation. In the first process, only DC component contributes to the accumulated phase. In the second process, by applying multiple rapid periodic $pi$ pulses, only the AC component gives rise to the accumulated phase. By selecting suitable input state and the unitary operations in interrogation and readout stages, and the DC and AC components can be extracted by population measurements. In particular, if the input state is a GHZ state and two interaction-based operations are applied during the interferometry, the measurement precisions of DC and AC magnetic fields can approach the Heisenberg limit simultaneously. Our scheme provides a feasible way to achieve Heisenberg-limited simultaneous measurement of DC and AC fields.
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Sensing static or slowly varying magnetic fields with high sensitivity and spatial resolution is critical to many applications in fundamental physics, bioimaging and materials science. Several versatile magnetometry platforms have emerged over the past decade, such as electronic spins associated with Nitrogen Vacancy (NV) centers in diamond. However, their high sensitivity to external fields also makes them poor sensors of DC fields. Indeed, the usual method of Ramsey magnetometry leaves them prone to environmental noise, limiting the allowable interrogation time to the short dephasing time T2*. Here we introduce a hybridized magnetometery platform, consisting of a sensor and ancilla, that allows sensing static magnetic fields with interrogation times up to the much longer T2 coherence time, allowing significant potential gains in field sensitivity. While more generally applicable, we demonstrate the method for an electronic NV sensor and a nuclear ancilla. It relies on frequency upconversion of transverse DC fields through the ancilla, allowing quantum lock-in detection with low-frequency noise rejection. In our experiments, we demonstrate sensitivities better than 6uT/vHz, comparable to the Ramsey method, and narrow-band signal noise filtering better than 64kHz. With technical optimization, we expect more than an one order of magnitude improvement in each of these parameters. Since our method measures transverse fields, in combination with the Ramsey detection of longitudinal fields, it ushers in a compelling technique for sensitive vector DC magnetometry at the nanoscale.
The convention in Atomic, Molecular, and Optical (AMO) physics of employing the dipole approximation to describe laser-induced processes replaces four source-free Maxwell equations governing laser fields with a single Maxwell equation for a proxy field that requires a virtual source current for its existence. Laser fields are transverse, but proxy fields are longitudinal; there can be no gauge equivalence. The proxy field is sometimes serviceable, but its limitations are severe. One example is the above-threshold ionization (ATI) phenomenon; surprising by proxy-field understanding, but natural and predicted in advance of observation with a laser-field method. An often-overlooked limitation is that numerical solution of the time-dependent Schrodinger equation (TDSE) is exact for proxy fields, but not for laser fields. Acceptance of proxy-field concepts has been costly in terms of inefficiently deployed research resources. Calculations with a nearly-40-year old transverse-field method remain unmatched with proxy fields. The transverse-field method is applicable in the tunneling domain, the multiphoton domain, and, as shown here, in the low-frequency magnetic domain. Attempts to introduce low-frequency magnetic field corrections into TDSE cannot be expected to produce meaningful results. They would be based on inappropriate Maxwell equations, a non-existent virtual source, and would approach constant electric field properties as the field frequency declines. Laser fields propagate at the speed of light for all frequencies; they cannot approach a constant-field limit. Extremely strong laser fields are unambiguously relativistic; a nonrelativistic limit that connects continuously to the relativistic domain is simpler conceptually and mathematically than is a theory constructed with a proxy field that is certain to fail as intensities increase.
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