Conventional classical sensors are approaching their maximum sensitivity levels in many areas. Yet these levels still are far from the ultimate limits dictated by quantum mechanics. Quantum sensors promise a substantial step ahead by taking advantage of the salient sensitivity of quantum states to the environment. Here, we focus on sensing rotations, a topic of broad application. By resorting to the basic tools of estimation theory, we derive states that achieve the ultimate sensitivities in estimating both the orientation of an unknown rotation axis and the angle rotated about it. The critical enhancement obtained with these optimal states should make of them an indispensable ingredient in the next generation of rotation sensors that is now blossoming.
Ultimate Information Rate for Quantum Sensing under Multilevel Relaxation
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Ulsan National Institute of Science and Technology（蔚山科学技术院）；Chungbuk National University（忠北国立大学）
Ultimate sensitivity of multiparameter estimation in quantum sensing with undetected photons
Australian National University（澳大利亚国立大学）；A*STAR Quantum Innovation Centre (Q.InC), Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局量子创新中心）；Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学联合量子研究所和联合量子信息与计算科学中心）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）
We report on experimental observation of electromagnetically induced transparency and slow-light (vg ~ c/607) in atomic sodium vapor, as a potential medium for a recently proposed experiment on slow-light enhanced relative rotation sensing [11]. We have performed an interferometric measurement of the index variation associated with a two-photon resonance to estimate the dispersion characteristics of the medium that is relevant to the slow-light based rotation sensing scheme. We also show that the presence of counter-propagating pump beams in an optical Sagnac loop produces a backward optical p…
This work theoretically study the Bose-Hubbard model in a ring geometry in a rotating frame. We obtain an effective Hamiltonian by using unitary transformation, where the effect of the rotating reference frame is introducing additional phases to the hopping constant. Within the mean-field theory, the phase transition edge of the Bose-Hubbard model not only depends on the particle numbers and the ring radius, but also depends on the rotation velocity. Therefore, we propose a sensing method of the rotation velocity using the phase transition edge of the Bose-Hubbard model. At the exact phase tra…
We theoretically propose a scheme to realize rotation sensing based on two coupled whispering-gallery-mode resonators with loss and gain. We consider that the active resonator with gain is rotated while the passive one with loss is stationary. The rotation will induce Sagnac effect and we show that the eigenfrequencies of the supermodes are sensitive to the Sagnac-Fizeau shift. Therefore, we can measure the average photon number in the steady state or the fluctuation spectrum of the output fields to detect the angular velocity of the rotation. We hope that our investigation will be useful in t…
We describe a resonator based optical gyroscope whose sensitivity for measuring absolute rotation is enhanced via use of the anomalous dispersion characteristic of superluminal light propagation. The enhancement is given by the inverse of the group index, saturating to a bound determined by the group velocity dispersion. We also show how the offsetting effect of the concomitant broadening of the resonator linewidth may be circumvented by using an active cavity. For realistic conditions, the enhancement factor is as high as 106. We also show how normal dispersion used for slow light can enhance…
We theoretically propose a scheme to perform rotation sensing in a Whispering-gallery-mode resonator setup. With the assistance of a large detuned two-level atom, which induces the effective coupling between clockwise and counterclockwise propagating modes in the resonator, we realize an effective interferometry with SU(2) algebraic structure. By studying the quantum Fisher information of the system, we find that the estimate accuracy for the angular velocity of the rotation can achieve and even break the Heisenberg limit in linear and nonlinear setup, respectively. The high performance of qua…
We find and investigate the optimal scheme of quantum distributed Gaussian sensing for estimation of the average of independent phase shifts. We show that the ultimate sensitivity is achievable by using an entangled symmetric Gaussian state, which can be generated using a single-mode squeezed vacuum state, a beam-splitter network, and homodyne detection on each output mode in the absence of photon loss. Interestingly, the maximal entanglement of a symmetric Gaussian state is not optimal although the presence of entanglement is advantageous as compared to the case using a product symmetric Gaus…
Quantum information processing with geometric features of quantum states may provide promising noise-resilient schemes for quantum metrology. In this work, we theoretically explore phase-space geometric Sagnac interferometers with trapped atomic clocks for rotation sensing, which could be intrinsically robust to certain decoherence noises and reach high precision. With the wave guide provided by sweeping ring-traps, we give criteria under which the well-known Sagnac phase is a pure or unconventional geometric phase with respect to the phase space. Furthermore, corresponding schemes for geometr…
We propose to implement a solid-state rotation sensor by employing a many-body quantum spin system which takes the advantages of the easy controllability of the electron spin and the robustness provided by the collective nuclear spin state. The sensor consists of a central electron spin coupled to many surrounding nuclear spins. Previously, this central spin system has been suggested to realize a quantum memory. Here, we further utilize the collective nuclear spins, which store a certain quantum state, to detect the macroscopic rotation. Different from other nuclear spin-based gyroscopes, our …
We have recently proposed [9], the use of fast-light media to obtain ultrahigh precision rotation sensing capabilities. The scheme relies on producing a critically anomalous dispersion, in a suitable dispersive medium, which is introduced in the arms of a Sagnac interferometer. We present here an experimental investigation of the anomalous dispersion properties of bi-frequency Raman gain in rubidium vapor, with the goal of using this medium for producing the critically anomalous dispersion condition. A heterodyne phase measurement technique is used to measure accurately the index variation ass…
The nature of dark matter is unknown and calls for a systematical search. For axion dark matter, such a search relies on finding feeble random noise arising from the weak coupling between dark matter and microwave haloscopes. We model such process as a quantum channel and derive the fundamental precision limit of noise sensing. An entanglement-assisted strategy based on two-mode squeezed vacuum is thereby demonstrated optimal, while the optimality of a single-mode squeezed vacuum is found limited to the lossless case. We propose a `nulling' measurement (squeezing and photon counting) to achiev…
Critical quantum sensing via backaction-evading continuous measurement
Research Center for Quantum Physics and Technologies, Inner Mongolia University（内蒙古大学量子物理与技术研究中心）；School of Physical Science and Technology, Inner Mongolia University（内蒙古大学物理科学与技术学院）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）
Diamond-based quantum magnetometers are more sensitive to oscillating (AC) magnetic fields than static (DC) fields because the crystal impurity-induced ensemble dephasing time $T_2^*$, the relevant sensing time for a DC field, is much shorter than the spin coherence time $T_2$, which determines the sensitivity to AC fields. Here we demonstrate measurement of DC magnetic fields using a physically rotating ensemble of nitrogen-vacancy centres at a precision ultimately limited by $T_2$ rather than $T_2^*$. The rotation period of the diamond is comparable to $T_2$ and the angle between the NV axis…
We address the problem of estimating the mass of a quantum particle in a gravitational field and seek the ultimate bounds to precision of quantum-limited detection schemes. In particular, we study the effect of the field on the achievable sensitivity and address the question of whether quantumness of the probe state may provide a precision enhancement. The ultimate bounds to precision are quantified in terms of the corresponding Quantum Fisher Information. Our results show that states with no classical limit perform better than semiclassical ones and that a non-trivial interplay exists between…
Ultimate quantum sensitivity in the 3D relative localisation of two single-photon emitters via two-photon interference
School of Mathematics and Physics, University of Portsmouth（朴茨茅斯大学数学与物理学院）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯大学宇宙学与引力研究所）
We present a protocol for using trapped ions to measure rotations via matter-wave Sagnac interferometry. The trap allows the interferometer to enclose a large area in a compact apparatus through repeated round-trips in a Sagnac geometry. We show how a uniform magnetic field can be used to close the interferometer over a large dynamic range in rotation speed and measurement bandwidth without losing contrast. Since this technique does not require the ions to be confined in the Lamb-Dicke regime, thermal states with many phonons should be sufficient for operation.
We challenge the current thinking and approach to the design of photonic integrated circuits (PICs) for applications in communications, quantum information and sensing. The standard PICs are based on directional couplers, that provide a wide range of functionalities but do not fully respond to the major technological challenges: massive parallelisation of transmission channels, low-energy dissipation and small footprint. We propose a new concept for design of PICs with the ultimate downscaling capability, the absence of geometric loss and a high-fidelity throughput. This is achieved by a perio…
We study a transverse-field Ising model (TFIM) in a rotational reference frame. We find that the effective Hamiltonian of the TFIM of this system depends on the system's rotation velocity. Since the rotation contributes an additional transverse field, the dynamics of TFIM sensitively responses to the rotation velocity at the critical point of quantum phase transition. This observation means that the TFIM can be used for quantum sensing of rotation velocity that can sensitively detect rotation velocity of the total system at the critical point. It is found that the resolution of the quantum sen…
Quantum metrology of electric and magnetic dipole moments: ultimate limits and optimal regimes
Università di Modena e Reggio Emilia（摩德纳与雷焦艾米利亚大学）；CNR-Istituto di Nanoscienze（国家研究委员会纳米科学研究所）；Università degli Studi di Milano（米兰大学）；INFN, Sezione di Milano（意大利国家核物理研究所米兰分部）
Based on two-photon entanglement, quantum remote sensing enables the measurement and detection to be done non-locally and remotely. However, little attention has been paid to implement a noncontact way to sense a real objects angular rotation, which is a key step towards the practical applications of precise measurements with entangled twisted photons. Here, we use photon pairs entangled in orbital angular momentum (OAM) to show that a real object's angular rotation can be measured non-locally. Our experiment reveals that the angular sensitivity of the object encoded with idler photons is prop…
Quantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an unambiguous discrimination strategy, an inconclusive decision (abstention) is allowed to vanish any possibility of errors when a conclusive result is obtained. In both scenarios, the testing between quantum states are relatively well-understood, for example, the ultimate limits of the performance are established decades ago; however, the testing between quantum channe…
A quantum device for measuring two-body interactions, scalar magnetic fields and rotations is proposed using a Bose--Einstein condensate (BEC) in a ring trap. We consider an imbalanced superposition of orbital angular momentum modes with opposite winding numbers for which a rotating minimal atomic density line appears. We derive an analytical model relating the angular frequency of the minimal density line rotation to the strength of the non-linear atom-atom interactions and the difference between the populations of the counter-propagating modes. Additionally, we propose a full experimental pr…
SU(1,1) interferometer (SUI) is a novel type of interferometer that uses directly entangled quantum fields for sensing phase change. For rotational sensing, Sagnac geometry is usually adopted. However, because SUI depends on the phase sum of the two arms, traditional Sagnac geometry, when applied to SUI, will result in null signal. In this paper, we modify the traditional Sagnac interferometer by nesting SU(1,1) interferometers inside. We show that the rotational signal comes from two parts labeled as "classical" and "quantum", respectively, and the quantum part, where quantum entangled fields…
Atom interferometers provide exquisite measurements of the properties of non-inertial frames. While atomic interactions are typically detrimental to good sensing, efforts to harness entanglement to improve sensitivity remain tantalizing. Here we explore the role of interactions in an analogy between atomic gyroscopes and SQUIDs, motivated by recent experiments realizing ring shaped traps for ultracold atoms. We explore the one-dimensional limit of these ring systems with a moving weak barrier, such as that provided by a blue-detuned laser beam. In this limit, we employ Luttinger liquid theory …
A point source atom interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses during the expansion of a cloud of cold atoms behaving approximately as a point source. Unlike a conventional light pulse atom interferometer, the PSI can produce a signal that corresponds to multi-axis rotation only, independent of acceleration. In addition, it can be used to measure acceleration along one direction, independent of rotation. Here, we describe a modified PSI that can be used to measure multi-axis rotation and multi-axis acceleration. Specifi…
Point source atom interferometry is a promising approach for implementing robust, high-sensitivity, rotation sensors using cold atoms. However, its scale factor, i.e., the ratio between the interferometer signal and the actual rotation rate, depends on the initial conditions of the atomic cloud, which may drift in time and result in bias instability, particularly in compact devices with short interrogation times. We present two methods to stabilize the scale factor, one relying on a model-based correction which exploits correlations between multiple features of the interferometer output and wo…
Sensitive and accurate rotation sensing is a critical requirement for applications such as inertial navigation [1], north-finding [2], geophysical analysis [3], and tests of general relativity [4]. One effective technique used for rotation sensing is Sagnac interferometry, in which a wave is split, traverses two paths that enclose an area, and then recombined. The resulting interference signal depends on the rotation rate of the system and the area enclosed by the paths [5]. Optical Sagnac interferometers are an important component in present-day navigation systems [6], but suffer from limited…
The measurement of circular dichroism (CD) has widely been exploited to distinguish the different enantiomers of chiral structures. It has been applied to natural materials (e.g. molecules) as well as to artificial materials (e.g. nanophotonic structures). However, especially for chiral molecules the signal level is very low and increasing the signal-to-noise ratio is of paramount importance to either shorten the necessary measurement time or to lower the minimum detectable molecule concentration. As one solution to this problem, we propose here to use quantum states of light in CD sensing to …
Sensing local environment through the motional response of small molecules lays the foundation of many fundamental technologies. The information of local viscosity, for example, is contained in the random rotational Brownian motions of molecules. However, detection of the motions is challenging for molecules with sub-nanometer scale or high motional rates. Here we propose and experimentally demonstrate a novel method of detecting fast rotational Brownian motions of small magnetic molecules. With electronic spins as sensors, we are able to detect changes in motional rates, which yield different…
Nuclear magnetic resonance (NMR) has enormous applications. Two-dimensional NMR is an essential technique to characterize correlations between nuclei and, hence, molecule structures. Towards the ultimate goal of single-molecule NMR, dynamical-decoupling- (DD) enhanced diamond quantum sensing enables the detection of single nuclear spins and nanoscale NMR. However, there is still the lack of a standard method in DD-based quantum sensing to characterize correlations between nuclear spins in single molecules. Here we present a scheme of two-dimensional DD-based quantum sensing, as a universal met…
Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However the spectral resolution in such protocols is limited ultimately by sensor lifetime. Here we demonstrate a heterodyne detection method for microwaves (MW) leading to a lifetime independent spectral resolution in the GHz range. We reference the MW-signal to a local oscillator by generating the initial superposition state from a coherent source. Experimentally we achieve a spectral resolution below $1\ \rm{Hz}$ for a $4\ \rm{GHz}$ signal far below the sensor lifetime limit of kilohert…
Faraday rotation is one way to realize quantum non-demolition measurement of electron spin in quantum dots. To describe Faraday rotation, semiclassical models are typically used, based on quantized electron spin states and classical electromagnetic fields. Such treatments neglect the entanglement between electronic and photonic degrees of freedom that produce intrinsic quantum noise, limiting the ultimate sensitivity of this technique. We present a fully quantum-mechanical description of Faraday rotation, and quantify this intrinsic noise. A method for measuring the purity of a given spin stat…
High precision interferometers are the building blocks of precision metrology and the ultimate interferometric sensitivity is limited by the quantum noise. Here we propose and experimentally demonstrate a compact quantum interferometer involving two optical parametric amplifiers and the squeezed states generated within the interferometer are directly used for the phase-sensing quantum state. By both squeezing shot noise and amplifying phase-sensing intensity the sensitivity improvement of $4.86\pm 0.24$ dB beyond the standard quantum limit is deterministically realized and a minimum detectable…
A point source interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses during the expansion of a cloud of cold atoms behaving approximately as a point source. The PSI can work as a sensitive multi-axes gyroscope that can automatically filter out the signal from accelerations. The phase shift arising from rotations is proportional to the momentum transferred to each atom from the Raman pulses. Therefore, by increasing the momentum transfer, it should be possibly to enhance the sensitivity of the PSI. Here, we investigate the degree o…
We show that light-pulse atom interferometry with atomic point sources and spatially resolved detection enables multi-axis (two rotation, one acceleration) precision inertial sensing at long interrogation times. Using this method, we demonstrate a light-pulse atom interferometer for Rb-87 with 1.4 cm peak wavepacket separation and a duration of 2T = 2.3 seconds. The inferred acceleration sensitivity of each shot is 6.7 * 10^(-12) g, which improves on previous limits by more than two orders of magnitude. We also measure the Earth's rotation rate with a precision of 200 nrad/s.
Quantum sensing exploits fundamental features of quantum mechanics and quantum control to realise sensing devices with potential applications in a broad range of scientific fields ranging from basic science to applied technology. The ultimate goal are devices that combine unprecedented sensitivity with excellent spatial resolution. Here, we propose a new platform for all-electric nanoscale quantum sensing based on a carbon nanotube double quantum dot. Our analysis demonstrates that the platform can achieve sensitivities that allow for the implementation of single-molecule magnetic resonance sp…
I consider the role of detection noise in quantum-enhanced metrology in collective spin systems, and derive a fundamental bound for the maximum obtainable sensitivity for a given level of added detection noise. I then present an interaction-based readout utilising the commonly used one-axis twisting scheme that approaches this bound for states generated via several commonly considered methods of generating quantum enhancement, such as one-axis twisting, two-axis counter-twisting, twist-and-turn squeezing, quantum non-demolition measurements, and adiabatically scanning through a quantum phase t…
