We study experimentally the fundamental limits of sensitivity of an atomic radio-frequency magnetometer. First, we apply an optimal sequence of state preparation, evolution, and the backaction evading measurement to achieve a nearly projection noise limited sensitivity. We furthermore experimentally demonstrate that Einstein-Podolsky-Rosen entanglement of atoms generated by a measurement enhances the sensitivity to pulsed magnetic fields. We demonstrate this quantum limited sensing in a magnetometer utilizing a truly macroscopic ensemble of 1.5x10(12) atoms which allows us to achieve subfemtotesla/square root(Hz) sensitivity.
We study experimentally the fundamental limits of sensitivity of an atomic radio-frequency magnetometer. First, we apply an optimal sequence of state preparation, evolution, and the backaction evading measurement to achieve a nearly projection noise limited sensitivity. We furthermore experimentally demonstrate that Einstein-Podolsky-Rosen entanglement of atoms generated by a measurement enhances the sensitivity to pulsed magnetic fields. We demonstrate this quantum limited sensing in a magnetometer utilizing a truly macroscopic ensemble of 1.5x10(12) atoms which allows us to achieve subfemtotesla/square root(Hz) sensitivity.
Optical atomic magnetometry is a powerful tool for continuous sensing applications, yet, in the absence of quantum correlations, its sensitivity is limited by the standard quantum limit (SQL) stemming from a trade-off between optical probe imprecision and quantum measurement backaction. Beyond-SQL sensitivity requires quantum correlations that modify these measurement noise sources. Here we demonstrate such sensitivity by using entangled state of the probe light and by engineering correlations between measurement imprecision and backaction. Having first explored SQL in a broad range of frequencies, we demonstrate overcoming the limit by combining variational readout with coupling the magnetometer to one mode of a bipartite entangled light state and conditioning the results on the other entangled mode. Tuning the detected light quadratures and combining the signals from the two measurement channels, we achieve sensitivity beyond the SQL in a broad range of acoustic frequencies which has so far remained inaccessible to quantum-noise-limited optical magnetometry.
We demonstrate a new technique for detecting the amplitude of arbitrarily chosen components of radio-frequency waveforms based on stroboscopic backaction evading measurements. We combine quantum nondemolition measurements and stroboscopic probing to detect waveform components with magnetic sensitivity beyond the standard quantum limit. Using an ensemble of 1.5×10^{6} cold rubidium atoms, we demonstrate entanglement-enhanced sensing of sinusoidal and linearly chirped waveforms, with 1.0(2) and 0.8(3) dB metrologically relevant noise reduction, respectively. We achieve volume-adjusted sensitivity of δBsqrt[V]≈3.96 fTsqrt[cm^{3}/Hz], comparable to the best rf magnetometers.
Quantum entanglement, in the form of spin squeezing, is known to improve the sensitivity of atomic sensors to static or slowly varying fields. Sensing transient events presents a distinct challenge, requires different analysis tools, and has not been shown to benefit from entanglement in practically important scenarios such as spin-precession magnetometry. To address this, we apply concepts from continuous quantum measurements and estimation theory to optical atomic magnetometers, aiming to accurately model these devices, interpret their measurement data, control their dynamics, and achieve optimal sensitivity. Quantifying this optimal performance requires determining a fundamental quantum limit on sensitivity. We derive this limit, imposed by noise, and show that it scales at best linearly with sensing time and atom number N, ruling out any super-classical scaling. This limit is independent of the initial state, measurement, estimator, and measurement-based feedback, and depends only on the decoherence model and the strength of field fluctuations. Thus, finding an estimator that attains this bound proves the sensing strategy optimal. To approach this limit, we develop a quantum dynamical model scalable with N, based on a co-moving Gaussian approximation of the stochastic master equation, which includes measurement backaction and decoherence. This enables a real-time estimation and control architecture integrating an extended Kalman filter with a linear quadratic regulator. Simulating the magnetometer with our model and EKF+LQR strategy shows that quantum-limited tracking of constant and fluctuating fields is within reach of current atomic magnetometers. Our sensing strategy can also track biologically relevant signals, such as heartbeat-like waveforms, and drive the atomic ensemble into an entangled state, even when the measurement record is used for feedback but later discarded.
Optical magnetometers use magnetically-sensitive atomic ensembles and optical read-out to detect the amplitude of magnetic fields. They have become the most sensitive instruments for measuring low-frequency magnetic fields surpassing competing technologies like superconducting quantum interface devices (SQUIDs), and find applications in a variety of fields ranging from medicine, biology and geophysics, as well as tests of fundamental physics. However, their fundamental sensitivity is bounded by quantum mechanical behavior of the atoms, which gives rise to the standard quantum limit (SQL). As many instruments are approaching this fundamental limit, it becomes necessary to explore ways to overcome the SQL. Quantum metrology studies strategies to increase the sensitivity beyond the SQL by means of quantum engineering the atomic states. In this thesis, we investigate the quantum enhanced detection of time varying radio-frequency magnetic fields using a cold atomic ensemble of 87Rb atoms held in an optical dipole trap. We first theoretically develop a new measurement technique based on stroboscopic back-action evading measurements that takes advantage of the atomic coherence. This measurement scheme is suitable for the detection of arbitrarily-chosen components of radio-frequency waveforms and includes radio-frequency magnetometry as a special case. Experimentally, we demonstrate the capabilities of this technique using a linearly chirped waveform as a test case. As a first experiment, we demonstrate the selective response of the method in the coherently accumulated signal by the atoms. For this, we dispersively probe the atoms via Faraday rotation and non-destructively measure the induced magnetization. In the last part of the thesis we demonstrate quantum enhanced magnetic field detection. In a measure-evolve-measure (MEM) sequence, a first stroboscopic quantum non-demolition (QND) measurement produces a state with reduced projection noise, followed by a period of free evolution where the atoms accumulate signal. A second QND measurement detects the change relative to the first measurement. We demonstrate entanglement-enhanced sensing of sinusoidal and linearly chirped waveforms, with metrologically-relevant noise reduction of _2m =0.84(8) and _2m =0.80(3), respectively. We achieve volume-adjusted sensitivity of _B p V _ 3.96 fT p cm3/Hz, comparable to the best radio-frequency magnetometers. Els magnetòmetres òptics utilitzen conjunts d’àtoms sensibles magnèticament i lectura òptica per detectar l’amplitud de camps magnètics. S’han convertit en els instruments més sensibles per mesurar camps magnètics de baixa freqüència, superant tecnologies rivals com els dispositius superconductors d’interfície quàntica (SQUID), alhora que troben aplicacions en camps tan diversos com la medicina, la biologia, la geofísica, fins a proves de física fonamental. No obstant això, la seva sensibilitat està fonamental limitada pel comportament quàntic dels àtoms que dóna lloc al límit quàntic estàndard (SQL). Donat que molts instruments s’aproximen a aquest límit fonamental, es imprescindible explorar maneres de superar-ho. La metrologia quàntica estudia estratègies per augmentar la sensibilitat més enllà del SQL mitjançant enginys quàntics en l’estat dels àtoms. En aquesta tesi investiguem la detecció de camps magnètics de freqüència de ràdio amb un conjunt d’atòms freds de 87Rb mantinguts en una trampa de dipol òptic. En primer lloc, desenvolupem teòricament una nova tècnica de mesura basada en mesures estroboscòpiques que eviten la contra-acció de la mesura alhora que permet aprofitar la coherència atòmica. Aquest esquema de mesura és compatible amb la detecció de components elegits arbitràriament de formes d’ona de freqüència de ràdio i inclou la magnetometria de radiofreqüència com a cas especial. Demostrem experimentalment les capacitats d’aquesta tècnica utilitzant una forma d’ona de prova amb canvi de freqüència lineal. Al primer experiment, demostrem la resposta selectiva del mètode en la senyal coherent acumulada pels àtoms. Per aconseguir-ho, provem de forma dispersiva els àtoms amb la sonda Faraday i mesurem no destructivament oscil·lació de Rabi de la població atòmica entre els subnivells magnètics dels nivells hiperfins de l’àtom. A la darrera part de la tesi, demostrem la detecció de l’amplitud de camps magnètics amb precisió millorada gràcies a efectes quàntics. En una seqüència de mesura-evolució-mesura (MEM), una primera mesura quàntica, estroboscòpica i no destructiva (QND) produeix un estat amb soroll de projecció atòmic reduït. El segueix un període d’evolució lliure on els àtoms s’acumulen senyal. Una segona mesura QND detecta el canvi relatiu a la primera mesura. Demostrem detecció millorada per entrellaçament quàntic per a formes d’ona sinusoïdals i amb canvi de freqüència lineal, amb reduccions de soroll metrològicament rellevants ξ2m =0.84(8) i ξ2m =0.80(3), respectivament. Aconseguim una sensibilitat ajustada pel volum B p V 3.96 fT p cm3/Hz, comparable als millors magnetòmetres operant a freqüència de ràdio.
The ability to measure magnetic fields with high sensitivity is a key requirement in many physical, biological and medical applications. Currently the most sensitive magnetometers are optical magnetometers, in which the polarization of an atomic sample responds to the field and is read out by an optical measurement. These instruments are limited by two fundamental sources of quantum noise: projection noise of the atoms and shot noise of the light. For magnetometers designed to have a high statistical sensitivity, contributions from both sources are comparable. Here we show that the sensitivity can be improved by the application of non-classical light.