Quantum Sensing (I): Fundamental Theory and Methods

|Authors: Guo Hong^1,† Wu Teng¹ Luo Bin²

(1 Peking University, School of Electronics, Quantum Information Technology Center)

(2 Beijing University of Posts and Telecommunications, School of Electronic Engineering, National Key Laboratory of Information Photonics and Optical Communication)

This article is selected from “Physics” 2024 Issue 4

Abstract

As one of the three core quantum technologies today, quantum sensing technology serves as an important physical realization basis for quantum information perception and acquisition. It is also the most mature, historically longest developed, and widely applicable quantum technology with the most potential applications. This article is the first part of quantum sensing, primarily introducing the fundamental theory and methods of quantum sensing. Firstly, it theoretically summarizes the definition and basic concepts of quantum sensing, points out the origin of the “quantum nature” of quantum sensing, and proposes the technical extension and classification basis of quantum sensing from the perspective of practical applications. Next, it details the basic implementation architecture related to quantum sensing and describes the core technical indicators that characterize quantum sensing performance, summarizing the physical principles and technical methods used to improve quantum sensing performance.

Keywords Quantum Sensing, Atomic Energy Levels, Quantum Coherence, Quantum Sensors, Quantum Information Perception and Acquisition

1Introduction

Quantum sensing is one of the core development directions in the three major quantum technology fields. It serves as the physical realization basis for quantum information perception and, along with quantum communication and quantum computing, constitutes the three pillars of current quantum technology. Various quantum sensors formed based on the principles of quantum sensing play significant roles in many fields. Compared to quantum computing and quantum communication, the development history of quantum sensing technology is longer, its technological maturity is higher, its applications are broader, and its effects are more significant. With the development of quantum theory and information technology, the concept and technical extension of quantum sensing have also been continuously expanded, and its technical manifestations have become increasingly diverse. This article mainly introduces the basic concepts, technical extensions, and fundamental methods of quantum sensing.

2Basic Concepts of Quantum Sensing

In the traditional sense, sensing refers to the response characteristics of macro objects to certain physical quantities to achieve detection and perception of physical quantities. For example, by utilizing the electrical properties of macro materials and their dependency on the physical quantity to be measured, temperature sensors, pressure sensors, etc., can be constructed. Early quantum sensing technologies (primarily referring to quantum electronics technologies formed around the 1930s) were based on this idea, with the distinction being that the physical effects responding to the measured physical quantity transitioned from macro physical effects to the quantum states of micro particles. For instance, various sensors based on atomic energy levels utilize the discreteness of micro particle quantum states—the physical quantity to be measured causes changes in the probability distribution of micro particles being in different states. By measuring the changes in this probability distribution, detection of the physical quantity to be measured is achieved. The coupling between the quantum state and the physical quantity to be measured constitutes the core of quantum sensing.

Quantum sensing technology has developed alongside the discovery of quantum theory and the quantum characteristics of micro particles, as well as advances in physics and information technology. From an application perspective, quantum characteristics can be summarized as: discreteness, coherence, and randomness. Among them, the coherence of micro particles (such as atoms) is reflected not only in the coherent superposition of single particle states (in fact, early quantum sensing technologies primarily utilized this characteristic) but also in the coherent superposition of multiple particle states, namely quantum entanglement, including how entangled states are prepared, how they are manipulated and evolve under the influence of the physical quantity to be measured, and how they are detected after evolution, all of which are fundamentally different from early quantum sensing technologies. Additionally, advancements in microwave oscillators, quantum frequency standards, atomic clocks, lasers, semiconductors, integrated circuits, nonlinear optics, quantum optics, etc., have greatly facilitated the development of techniques for preparing, controlling, evolving, and reading quantum states, bringing more possibilities and broader space for the development of quantum sensing technology.

2.1 Origin of the “Quantum Nature” of Quantum SensingAlthough quantum sensing has been researched for a long time, there has never been a standardized definition. In 2003, J. P. Dowling and G. J. Milburn published a significant paper titled “Quantum Technology: The Second Quantum Revolution,” which first explicitly proposed the concept and definition of the “Second Quantum Revolution”^[1]. In the paper, the concept of “quantum technology” is established based on quantum principles such as quantization (discreteness), uncertainty principle, quantum superposition, quantum tunneling, quantum entanglement, and quantum decoherence. Quantum technology is divided into quantum information technology (including quantum algorithms, quantum cryptography, and quantum information theory), quantum electromechanical technology, and coherent quantum electronics (mainly superconducting quantum circuits). Furthermore, quantum photonics is proposed independently from quantum technology, including spintronics, molecular coherent quantum electronics, solid-state quantum computing, quantum optics, quantum optical interference technology, quantum lithography and microscopy, quantum squeezing, non-interacting imaging, quantum teleportation, coherent matter technology (i.e., atomic interferometry), atomic optics, atomic gravity gradient meters, atomic lasers, etc. It can be seen that the initial classification of quantum technology was relatively chaotic in terms of hierarchy. With the proposal of the concept of the “Second Quantum Revolution” and its development over the past two decades, quantum technology has gradually refined and formed three core development directions: quantum computing (including but not limited to quantum computation, quantum simulation, quantum acceleration, and quantum algorithms), quantum communication (including but not limited to quantum key distribution, quantum teleportation, quantum direct communication), and quantum sensing (including but not limited to quantum precision measurement, quantum metrology, quantum sensors, and quantum information perception). For quantum sensing, its earlier sources can even be traced back to 1879^[2], which means that even before the establishment of quantum theory, people had already realized that certain properties of micro particles could be used to measure physical quantities (Figure 1), emphasizing that the advantage of this method lies in the intrinsic properties of micro particles’ states being independent of changes in time and space^[2]. For example, the fixed energy intervals determined by the discrete energy levels of electrons outside the atomic nucleus are the basis of atomic clock technology; the determined proportional relationship between the amplitude of the external magnetic field and the energy level shift, dictated by the discrete values that angular momentum can take in space orientation, is the basis of atomic magnetometer technology; and so on.Figure 1 Left: William Thomson (the first Baron Kelvin) and his discussion on utilizing atomic energy levels for precise measurement of physical quantities; Middle: Cover of Thomson’s published book Treatise on Natural Philosophy (1879, second edition), which mentioned the text quoted in the left image, meaning “the wavelength of specific rays emitted by atoms, i.e., the distance covered by light of a specific frequency in a fixed time period (period time), can provide a length standard that is completely independent of time changes”; Right: The basic idea of using the energy level structure of micro particles for physical quantity sensing and precise measurementThus, it can be seen that early quantum sensing utilized the discreteness of micro particles to provide certainty and consistency in measurements, and in terms of enhancing sensing performance, did not deviate from the framework of classical sensing technology, still employing classical sensing techniques for noise suppression and signal extraction methods. With the introduction of special quantum states, such as entangled states and squeezed states, and the rapid development of laser technology, particularly the semiconductor laser technology and nonlinear optical technology that developed rapidly in the late 1980s, the technical barriers and difficulties in preparing, controlling, and reading special quantum states were significantly lowered, allowing quantum sensing to truly differ from classical sensing—evolving from classical independent sensing (detection) to correlation sensing (detection) based on quantum effects. Overall, the scientific and standardized academic definition of the concept and technical connotation of quantum sensing took a long time, with many attempts made by various individuals. In 2017, C. Degen, F. Reinhard, and P. Cappellaro published a lengthy review paper titled “Quantum Sensing” in Reviews of Modern Physics, which can be regarded as the greatest effort to date in defining the concept and technical extension of quantum sensing technology academically^[3]. The paper provided the most comprehensive coverage of quantum sensing available and further emulated the criteria method proposed by D. DiVincenzo in 2000 for quantum computers^[4], proposing criteria (or classification basis) for quantum sensing. Based on this, the paper attempted to propose a universal quantum sensing protocol (or technical classification method). In this paper, the definition, sources of quantum nature, and technical extensions of quantum sensing can be classified into three categories according to the following criteria: (1) using quantum objects to measure physical quantities characterized by quantized energy levels (quantum states). Specific examples include energy levels from superconductors, neutral atoms, trapped ions, or other spin systems; (2) using quantum coherence (i.e., spatial and temporal superposition states with wave-like properties) to measure physical quantities; (3) using quantum entanglement to enhance measurement sensitivity or precision, thus surpassing the statistical limits of classical measurement.2.2 Technical Classification of Quantum SensingAccording to the aforementioned three categories, early quantum sensing technologies can basically be classified into the first two categories. With the realization of quantum entanglement and the development of laser technology, researchers began to fully explore the enormous potential of special quantum states and quantum state manipulation methods in reducing measurement uncertainty, leading to the development of quantum precision measurement, quantum parameter estimation, and other technologies. In this paper, we collectively refer to these technologies as quantum sensing. On one hand, this aligns with the definitions above; on the other hand, the core of different technologies is to utilize the coupling between quantum states and the physical quantities to be measured, ultimately converging on the same goal. However, the emphasis of development at this stage differs: the first two categories focus more on enhancing the ability to perceive small changes in physical quantities, while the third category focuses more on how to further reduce the measurement uncertainty of the physical quantities to be measured under limited resources. From the perspective of practical applications of quantum sensing, in 2022, the United States released a report titled “Bringing Quantum Sensors to Fruition”^[5], defining quantum sensors as: “Quantum sensors are devices that utilize quantum mechanical properties (such as atomic energy levels, photon states, or the spins of fundamental particles) for measurement,” emphasizing the extension of the concept and only providing examples of which technologies belong to quantum sensors—whether a sensor itself is sufficiently “quantum” does not affect its effectiveness at this stage. Therefore, based on inductive reasoning, a framework for quantum sensors can be established. Based on this idea, since quantum technology has risen to the status of a national strategic technology in many developed countries, we can first list representative documents related to quantum strategies from developed countries to attempt to describe the concept and classification of quantum sensors (Table 1). Overall, as of now, the quantum sensing technologies that have garnered widespread attention in developed countries are gradually converging. Currently, the common quantum sensing technologies can also be divided into three major categories. It can be seen that the classification results align closely with the aforementioned academic classification standards.Table 1 Examples of Quantum Sensor Technologies in Major Scientific NationsThe first category includes mature technological directions that have already formed representative practical products and are gradually constructing new industrial structures, mainly including atomic clocks, atomic magnetometers, superconducting interference magnetometers, atomic interferometric gravity meters, nuclear magnetic resonance technology, etc.The second category includes technologies in the practical development process, mainly including optical lattice clocks, diamond color center (NV color center) technology, quantum correlated imaging, etc. The third category includes technologies that are still in the laboratory and academic research stage, mainly including (Rydberg) atomic electric field detectors, quantum illumination, and quantum precision measurement technologies and methods based on special quantum states (such as squeezed states, entangled states), etc.3Description of Quantum Sensing Performance and Methods for Enhancement

The core of sensing or measurement reflects the ability to measure physical quantities or respond to changes in physical quantities. In addition, the repeatability and consistency of sensing performance and results is also one of the key development directions at present. This section will first provide the basic framework of quantum sensing and introduce the descriptive methods for quantum sensing performance indicators. Based on this, it will describe how to enhance the performance indicators of quantum sensing technology from both physical and technical methods.

3.1 Basic Framework of Quantum SensingQuantum sensing mainly relies on the precise control and reading of micro particle states (quantum states). In fact, the basic framework and implementation methods of quantum sensing can be described using the general framework of quantum technology, that is, the preparation of quantum states, the evolution of quantum states, and the reading of quantum states. Therefore, from this perspective, quantum sensing and quantum computing are equivalent. The distinction between the two lies in the complexity of the preparation and evolution of quantum states; quantum computing is generally more complex than quantum sensing, primarily because quantum computing requires transforming (or compiling) the problem to be solved or the algorithm to be implemented into a series of interaction Hamiltonians that realize quantum state evolution, while for quantum sensing, the evolution of the state only needs to consider the evolution form of the quantum state under the influence of the physical quantity to be measured. In other words, quantum sensing focuses more on how to precisely control and read the evolution of quantum states. Additionally, quantum computing has higher requirements for quantum entangled states, while entanglement is not a necessary condition for quantum sensing. Specifically, the general framework of quantum sensing includes seven basic steps. This section mainly references the review paper “Quantum Sensing”^[3]. This paper is based on this and supplements and explains the basic structure of the quantum sensing framework in conjunction with representative quantum sensing technologies such as atomic magnetometers, atomic clocks, and nuclear magnetic resonance. The first step: initialization of the quantum state. The state of the micro particle needs to be prepared into an initial state, which can generally be chosen as an eigenstate of the micro particle (e.g., the energy eigenstate of a two-level atom). For quantum sensors based on atomic ensembles, this step is also referred to as polarization. For example, strong magnetic fields in nuclear magnetic resonance, magnetic selection state technology in atomic clocks, and optical pumping technology in atomic magnetometers. The second step: preparation of the quantum state. This step mainly transforms the quantum state into a state that can be used for sensing. This state needs to evolve under the influence of the physical quantity to be measured. Generally, this is achieved by applying certain state control pulses. For example, a 90° magnetic field pulse in nuclear magnetic resonance; in addition, a series of more complex control methods can be designed to prepare some special quantum states, such as entangled states, squeezed states, etc. The third step: evolution of the quantum state. The prepared quantum state evolves under the influence of the physical quantity to be measured, which is the key to achieving quantum sensing. For example, under the influence of a magnetic field, the intrinsic magnetic moment of the micro particle interacts with the external magnetic field. If the state of the micro particle is not the eigenstate of this interaction, evolution will occur. The evolution process can be phenomenologically reflected by the Larmor precession of the magnetic moment under the action of the magnetic field. By measuring the angle (or frequency) of the precession, information about the magnetic field can be obtained; atomic clocks utilize the intrinsic interactions of atoms to accurately extract the evolution frequency of micro particles’ states under intrinsic actions by shielding all external influences. The fourth step: transformation of the quantum state. The main purpose of this step is to convert the evolved quantum state into an observable state. For example, in atomic clocks, after preparing the atomic state into a superposition state using a 90° pulse and evolving under intrinsic interactions, another 90° pulse needs to be applied. This step mainly depends on the subsequent observation methods. If the chosen observation method can directly observe the evolved superposition state, this operation is unnecessary. The fifth step: reading the quantum state. Compared to the initial state, the evolved state is generally a superposition state of the original eigenstates, so the result obtained from a single measurement is random and can only yield one of the eigenstates. The reading (or measurement) is a Bernoulli process, with a probability of 1-p of obtaining state A and a probability of p of obtaining state B. This probability cannot be obtained through a single measurement and requires multiple measurements. The sixth step: repeated measurement. Repeat the above steps 1-5. In an ideal situation, the measurement results obtained will be the probabilities of different eigenstates. Repetition has two meanings: on one hand, it reflects the repetition of the above steps for a single particle, and on the other hand, it reflects the average of the detection results of the particle ensemble. Both meanings of repetition can be conducted in parallel. The seventh step: estimation of the physical quantity to be measured. According to the analysis of the previous steps, the measurement of the probability distribution of different eigenstates and its changes contains information about the physical quantity to be measured. By measuring the probability, information about the value of the physical quantity can be obtained. This framework basically summarizes all technologies related to quantum sensing at present, and the differences between different technological directions mainly reflect the differing emphases of the seven steps described above.3.2 Performance Indicators of Quantum SensingThe core technical indicators of quantum sensing include noise, sensitivity, precision, etc. These indicators are interrelated yet distinct. Generally speaking, noise primarily reflects a class of physical factors that affect measurement results and has random characteristics. Sensitivity, while closely related to noise, also depends on signal strength, reflecting the minimum change in physical quantities that the system can distinguish. Precision (or accuracy) concerns the difference between measurement results and actual results, which is related to noise (statistical error) and also depends on the errors introduced by the measurement methods (systematic errors).Noise.In quantum sensing, noise can primarily be divided into two categories: classical noise and quantum noise. Classical noise is often referred to as technical noise (mainly referring to noise introduced by macro systems, such as intensity noise from lasers, frequency noise, detector shot noise, etc.), and dark current noise, which actually originates from spontaneous radiation, a quantum effect, but is usually categorized as technical/classical noise. Quantum noise primarily arises from the measurement of quantum states; its essence is the uncertainty principle and is an inevitable result of projecting measurements on unknown quantum states. For instance, if the probability of obtaining result A is p, and the probability of obtaining result B is 1-p, according to the previous discussion, probability p contains information about the physical quantity to be measured. If the total number of measurements is n, the number of times A is obtained would be np, and the number of times B is obtained would be n(1-p). The uncertainty (or variance) of p can be calculated as p(1-p)/n, and this uncertainty is the quantum projection noise. Quantum projection noise can be controlled by setting different quantum states (e.g., squeezed states), but it is not necessarily better to have smaller quantum projection noise. For example, in the aforementioned case, when p is 0 or 1, the uncertainty of p is 0, indicating that the micro particle is in an eigenstate (basis vector), but this state is not optimal for sensing—sensing is more concerned with the signal-to-noise ratio.Sensitivity.Sensitivity refers to the minimum change in a physical quantity that the sensing system can reflect, mainly depending on the signal-to-noise ratio within a certain bandwidth range. It can be divided into sensitivity indicators determined by classical or quantum noise. For example, for atomic magnetometers, the formula for sensitivity under classical noise can be written as [(T₂)(SNR)γ]^-1, where T₂ is the transverse relaxation time (which reflects the coherence time of the quantum superposition state to some extent), SNR is the signal-to-noise ratio within a certain bandwidth (the longer the average time, the smaller the bandwidth, the lower the noise, and the greater the SNR), and γ is a constant (describing the conversion coefficient between magnetic field and frequency under specific atomic states); while the sensitivity under quantum noise, such as quantum projection noise, is generally written as [(T₂)(NT)γ²]^-1/2, where N is the number of interacting particles, and T is the total measurement time. T/T₂ can also be viewed as the average number of measurements (the upper limit of single measurement time is determined by the relaxation time of the quantum state). The sensitivity limit determined by quantum projection noise is inversely proportional to the number of interacting particles and the measurement time, commonly referred to as the standard quantum limit. This can be further improved by preparing special quantum states, such as entangled states and squeezed states, but is currently limited to systems consisting of a small number of particles.Precision.Also known as accuracy, it primarily reflects the measurement errors introduced during the sensing process, including statistical errors and systematic errors. Statistical errors depend on the noise level; the smaller the noise, the smaller the measurement dispersion, and thus the smaller the statistical error. Systematic errors mainly arise from the measurement methods and non-idealities of the system, primarily reflecting the offset from the actual physical quantity. Precision reflects the long-term stability and repeatability of the sensing system. The reason quantum sensing can achieve high performance in precision is largely due to the high-precision control and protection of the quantum states of micro particles. In addition, indicators describing quantum sensing performance should also include range, bandwidth, etc. These indicators have not been elaborated on here, mainly because they still use definitions from classical sensing and have not technically deviated from classical frameworks. On the other hand, from the current technical development status, the quantum characteristics of micro particles have not brought about disruptive effects in terms of the conceptual connotation and performance improvement of the aforementioned indicators, and even, given the high sensitivity of quantum states to external environments, quantum sensing may be limited in dynamic range and bandwidth. For instance, the bandwidth and sensitivity of atomic magnetometers are mutually constrained. In recent years, with the development of diamond color centers and miniaturized atomic gas chambers combined with optical cavities, quantum sensing has achieved high spatial resolution while ensuring high sensing sensitivity indicators. Especially for sensing technologies based on diamond color centers, they have gradually moved towards a direction that combines high sensing sensitivity, high spatial resolution, large dynamic range, and high bandwidth (detailed content will be introduced in another article).3.3 Methods for Enhancing Quantum Sensing PerformanceBased on the descriptions and analyses of the core performance indicators of quantum sensing mentioned above, we will attempt to summarize and generalize the sources and main technical means to enhance the detection sensitivity, reduce detection noise, and improve detection precision of quantum sensing technology from both physical principles and technical methods. Since this attempt is based on inductive reasoning, it cannot encompass all methods for enhancing the sensitivity of quantum sensing technology. From the introduction below, it can be seen that most of the technologies in Table 1 (excluding those related to safety) can be included.

3.3.1 Physical Principles

The improvement of sensitivity and precision in quantum sensing technology, known as the “quantum enhancement” effect, can be simply divided into two main parts: quantization and quantum coherence. This is also what we currently understand regarding the fundamental properties of micro particles (Figure 2).Figure 2 Fundamental properties of micro particles: discreteness (discrete energy levels), coherence (quantum superposition states, entangled states), randomness (quantum noise)Quantization.The quantization (or discreteness) of the microstructure of the basic sensing unit is the physical foundation of almost all quantum sensors and is fundamental to the application of various quantum effects and their control methods. Its precision is embodied in the “quantization” itself. The quantum characteristics of some physical systems provide theoretical support for the limits of sensitivity (for example, superconductors). It should be noted that, contrary to traditional definitions, this paper believes that “quantization” does not merely refer to “discreteness,” which primarily involves natural conclusions related to quantum bound states, but also emphasizes the full homogeneity of the basic assumptions of quantum mechanics (strict academic proof of bound states and quantum mechanical postulates is not pursued here). Importantly, the quantization of atomic energy levels and the basic assumption of homogeneity in quantum mechanics fundamentally guarantee the high consistency of the transition frequencies between different atomic energy levels, and the high precision of frequency measurement constitutes the core capability of modern precision measurement, serving as one of the fundamental guarantees for measuring quantization (i.e., tracing back to fundamental physical constants). To date, frequency measurement is the highest physical quantity humans can measure—not only in terms of measurement precision but also in ensuring long-term consistency and repeatability of measurements.Quantum Coherence.Quantum coherence mainly involves the coherent superposition characteristics of quantum states (including the control and maintenance of quantum entanglement characteristics), which are key to enhancing and improving the sensitivity and precision of quantum sensing technology. For early quantum sensing technologies, such as atomic clocks, atomic magnetometers, and atomic gyroscopes, one of the key factors determining their sensing performance is how to maintain the coherent characteristics of quantum states. Coherence can largely be characterized by the Q value of the characteristic signal, such as the resonance signal linewidth in quantum sensing technologies of atomic clocks and atomic magnetic sensors. This is also represented in the formula [(T₂)(SNR)γ]^-1, where T₂ is generally inversely proportional to the linewidth. Therefore, the longer the coherence time, the narrower the signal linewidth, the greater the Q value, and the higher the sensitivity performance indicators of the sensor. With the development of matter wave interference technology alongside cold atom technology, we can boldly attribute the improvements in measurement precision and detection sensitivity brought about by quantum coherence to the further manifestation of the “wave-like” nature of quantum systems. The improvements in measurement precision and detection sensitivity of quantum sensing technologies can largely be attributed to the quantum version of classical optical interference measurement technologies (optical interference represents the highest level of classical measurement, such as gravitational wave detection). Together with other classical theories, they follow the transition from classical wave amplitude interference to probability amplitude interference of “quantum waves,” thus unifying within the theoretical framework of quantum coherence and quantum statistical theory. Furthermore, the use of special quantum states (such as quantum squeezed states, NOON states, etc.) and quantum control methods (such as dynamical decoupling, quantum non-demolition measurement, etc.) to enhance the sensitivity and precision of sensing technology ultimately reflects the control and maintenance of the coherent and entangled characteristics of quantum states.3.3.2 Technical MethodsBased on the analysis of the physical principles of quantum sensing mentioned above, the current main technical implementations to enhance the performance indicators of quantum sensing technology can be divided into three main ideas. (1) Preparation and maintenance of high Q value systems. The quantization of the microstructure of the basic sensing unit is the physical foundation of almost all quantum sensors, but quantization itself does not guarantee improved measurement precision. If we do not consider quantum systems that introduce quantum entanglement, the improvement of measurement precision fundamentally parallels that of classical systems, relying on the high Q value of the sensing unit. This is true not only for circuits or optical cavities but also for atomic systems, which are the most important quantum sensing systems. The discreteness of the “atoms” does not guarantee measurement precision (but can ensure measurement consistency); a high Q value atomic system is essential for ensuring measurement precision—this essentially reflects the atomic system’s responsiveness to the physical quantity to be measured. The higher the Q value, the stronger the atomic system’s response to the physical quantity to be measured. The Q value of an atomic system can be defined as the ratio of the transition frequency to the transition linewidth. This is also the fundamental reason for the inevitable transition from atomic clocks to optical clocks^[16] (increasing transition frequency) and from hot atoms to cold atoms^[17] (decreasing transition linewidth). (2) Quantum enhancement technology of interferometers. Optical interferometers have played an important role in the history of precision measurement, with the Michelson-Morley experiment being the most famous. The improvement of measurement precision in classical optical interferometers requires shorter wavelengths and stronger coherence (diffraction limits), which is often achieved through the selection of light sources (from visible light to ultraviolet, X rays, etc.), stability of light sources (increasing coherence time), and lengthening the interferometer arms. The statistical principles of their measurement values still follow classical statistical laws of 1/N^1/2. The quantum coherence brought about by quantum mechanics provides more options for the “light source” of interferometers. Atomic interferometers have made significant strides towards short wavelength matter wave interferometers. Furthermore, interference can also be realized using electrons, neutrons, antimatter particles, etc. The introduction of entangled light and special light field states based on it provides the fundamental conditions for improving the measurement precision of interferometers to the Heisenberg limit of 1/N, and the technical implementation of injecting entangled light completes this leap^[18]. Additionally, ghost imaging technology based on intensity interference and superconducting quantum interference devices can also be included in this category. (3) Conversion from physical quantity measurement to frequency measurement. Modern quantum optical technologies represented by lasers and high-finesse (high Q) optical cavities are fundamental to enhancing quantum sensing capabilities. With the continuous maturation of quantum frequency standard technologies centered on atomic clocks, human precision measurement capabilities for frequency as a fundamental unit have improved to an astonishing level—the uncertainty of frequency measurement has reached the level of 10^-19[19], and operational atomic clocks (fountain clocks) can reach levels of 10^-15[20], which is far superior to the measurement precision of other physical quantities. Therefore, converting other physical quantities into frequency measurements through interaction with quantum systems (especially atomic energy levels) has become an important means, with representative technologies including light-pumped atomic magnetometers (which relate magnetic fields and frequencies through gyromagnetic ratios based on specific atomic energy levels), Rydberg atomic electric field measurements^[21,22], and dual optical comb ranging, etc. Additionally, some technical solutions, including but not limited to multipath techniques in atomic gas chambers, zero difference and heterodyne detection, dual optical comb technologies, etc., have not been listed here, as these involve technical means to enhance quantum sensing performance and are fundamentally similar to classical optical interferometers, microwave radar detection, and telecom signal time detection technologies, thus not belonging to the typical quantum effects (i.e., discreteness, coherence).4Definition of Quantum Sensors

Similar to the three elements of quantum sensing, the review[3] attempts to provide a definition of quantum sensors:

(1) The state of the quantum system must possess distinguishable, discrete basic conditions, equivalent to a two-level system;

(2) The state of the quantum system must have the possibility of initialization to any state and being read;

(3) The state of the quantum system can be manipulated, typically by alternating electromagnetic fields;

(4) There is a fixed conversion relationship between the state of the quantum system and the physical quantity to be measured, generally written as γ=∂^qE/∂V^q, where ∂V represents the change in the physical quantity to be measured, and correspondingly, ∂E represents the change in the energy of the quantum system, q=1 represents a linear relationship, q=2 represents a quadratic relationship (and so on).

It can be seen that, unlike previous definitions related to sensing, there is no deliberate emphasis on quantum entanglement effects here; the definition of quantum sensors is given entirely from a practical perspective. Therefore, typical representatives of quantum sensors that have entered the practical stage include atomic clocks, atomic magnetometers, atomic interferometric gravity meters, etc. Meanwhile, diamond color centers and Rydberg atomic electric field detection are gradually becoming important technological development directions due to their unique advantages and have garnered considerable attention. This section involves the practical applications of quantum sensing technology, which will be discussed in detail in another article due to space limitations regarding the overall development status and further trends of quantum sensing technology and quantum sensors in applications.

5Conclusion

This article primarily introduces the fundamental theory and methods of quantum sensing, theoretically summarizing the definition and basic concepts of quantum sensing, pointing out the origin of the “quantum nature” of quantum sensing, and providing the technical extension and classification basis of quantum sensing from the perspective of practical applications. The article also details the basic implementation architecture related to quantum sensing and describes the core technical indicators that characterize quantum sensing performance, summarizing the core physical principles and technical methods used to improve quantum sensing performance. It should be noted that quantum sensing technology has continuously developed alongside the development of quantum theory, and its conceptual connotation and technical extension have also been continuously expanded over the past century.

To date, quantum sensing has become one of the three core development directions of current quantum technology. It is also the most historically developed, technologically mature, and widely applicable or potentially applicable quantum technology. However, even so, quantum sensing, like quantum computing and quantum communication, faces the challenge of resisting the decoherence mechanisms introduced by external environments on quantum states—quantum states are highly sensitive to external environments, which is both an advantage of quantum sensing and poses technical challenges for its stable and reliable use in complex environments. In comparison, addressing the decoherence mechanisms caused by the environment is more direct for quantum computing—simply shielding all external interference as much as possible. The core objective of quantum sensing is to perceive external information; how to fully leverage the disruptive performance advantages brought by quantum sensing in more complex and practical environments is currently one of the core problems that quantum sensing needs to resolve.

In summary, although quantum sensing has undergone a century of development, it is still in its infancy, involving a wide range of technologies, diverse conceptual connotations, and various descriptive methods. Against this background, this article attempts to summarize and consolidate the core concepts, key theories, and technical methods of quantum sensing. Given that the author’s research direction cannot cover all technological fields of quantum sensing, there may inevitably be shortcomings and incompleteness in the descriptions of certain technologies and theories, and constructive criticism is welcomed.

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• List of Outstanding Papers, Outstanding Review Experts, and Outstanding Young Scholars of “Physics and Engineering” in 2021

• Professor Wang Qing: Socratic Problem-Driven Education—Learning and Growing Together in Interaction

• Reflections: Reality and Distance in Education

• Professor Wang Qing: Last night (June 9), the final exam of the Tsinghua Electrodynamics course

• Academician Zhu Bangfen: The Misunderstanding of “Reducing Burdens” and the Challenges Facing Scientific Education in China

• Directory of “Physics and Engineering” 2024 Issue 1

• Yongkang Le: Physics Experiment Teaching in the US under COVID-19 Prevention and Control and Comparison of China-US Situations

• Gu Mu: Understanding and Experience of the Revised “Basic Requirements for Teaching University Physics Courses in Non-Physics Disciplines”

• Academician Zhu Bangfen: From the Basic Science Class to the Tsinghua University Physics Class

• Academician Zhu Bangfen: Thoughts on Cultivating First-Class Innovative Talents

• Professor Li Xueqian: Physics as a Culture

• Professor Li Xueqian: How to Help Physics Department Students Transition from High School to College

• Mu Liangzhu: The Core of Ideological Education in Physics Courses is the Cultivation of Scientific Cognitive Ability

• Mu Liangzhu: What is Physics and Physics Culture?

• Mu Liangzhu: What is the ETA Physics Cognitive Model?

• Mu Liangzhu: What is the ETA Physics Teaching Method?

• Professor Wu Guozhen: Impressions of My Experience as a Graduate Student Abroad—Written for the 20th Anniversary of the Tsinghua University Physics Department’s “Basic Class” and the 10th Anniversary of the “Classroom Class”

• Chen Jiaer, Zhao Kaihua, Wang Zhidong: Facing the 21st Century, Urgently Rebuilding China’s Engineering Physics Education

• Professor Wang Yayu: The Undergraduate Talent Cultivation Philosophy and Practice of the Tsinghua Physics Department

• Professor Ge Weikun: A Few Thoughts on Talent Cultivation in China and Abroad

• Professor An Yu: Why the Traditional Classroom Teaching Model Needs to Change

• Professor An Yu: Actually, Teaching is a Process of Accumulation

• Professor Liu Yuxin: Some Thoughts on Teaching and Textbook Compilation for Undergraduate Physics Basic Courses

• Shen Qianru: The Impact of American and Canadian Curriculum Reforms on Science Education

• Henderson C: The Impact of Physics Education Research Supported by American Research Funds on Higher Physics Education

The journal “Physics and Engineering” focuses on research in physics education and is a core journal of Chinese science and technology, founded in 1981. We welcome enthusiastic submissions, Journal Submission and Review Platform:

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