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Maximizing precision in saturation-limited absorption measurements
Abstract
Quantum fluctuations in the intensity of an optical probe is noise which limits measurement precision in absorption spectroscopy. Increased probe power can offer greater precision; however, this strategy is often constrained by sample saturation. Here, we analyze measurement precision for a generalized absorption model in which we account for saturation and explore its effect on both classical and quantum probe performance. We present a classical probe-sample optimization strategy to maximize precision and find that optimal probe powers always fall within the saturation regime. We apply our optimization strategy to two examples, high-precision Doppler broadened thermometry and an absorption spectroscopy measurement of chlorophyll a. We derive a limit on the maximum precision gained from using a nonclassical probe and find a strategy capable of saturating this bound. We evaluate amplitude-squeezed light as a viable experimental probe state and find it capable of providing precision that reaches to within >85% of the ultimate quantum limit with currently available technology.
... For example, in the context of biological imaging applications, where illuminating a live sample with a high probe beam power may alter cell processes and a high probe beam power can lead to cell death (1,2). In absorption measurements, increasing the probe power can also lead to saturation of the sample (3). Further to these applications, low-light imaging is desirable for LiDAR and covert imaging where either low-power eye-safe sources are required or in cases where imaging is performed through scattering media (4,5). ...
Low-light imaging is challenging in regimes where low-noise detectors are not yet available. One such regime is the shortwave infrared where even the best multipixel detector arrays typically have a noise floor in excess of 100 photons per pixel per frame. We present a homodyne imaging system capable of recovering both intensity and phase images of an object from a single frame despite an illumination intensity of ≈ 1 photon per pixel. We interfere this weak signal which is below the noise floor of the detector with a reference beam that is ∼ 300, 000 times brighter, record the resulting interference pattern in the spatial domain on a detector array, and use Fourier techniques to extract the intensity and phase images. We believe our approach could vastly extend the range of applications for low-light imaging by accessing domains where low-noise cameras are not currently available and for which low-intensity illumination is required.
... Finally, our methodology relies on studying the exact dynamics of a pulse interacting with a single atom. This is in contrast to "conventional" approaches [1,19] that relate the induced polarizations in ensembles to the measured signals or treat the matter "effectively" [20][21][22]. ...
We study the fundamental limits of the precision of estimating parameters of a quantum matter system when it is probed by a travelling pulse of quantum light. In particular, we focus on the estimation of the interaction strength between the pulse and a two-level atom, equivalent to the estimation of the dipole moment. Our analysis of single-photon pulses highlights the interplay between the information gained from the photon absorption by the atom, as measured in absorption spectroscopy, and the perturbation to the field temporal mode due to spontaneous emission. Beyond the single-photon regime, we introduce an approximate model to study more general states of light in the limit of short pulses, where spontaneous emission can be neglected. We also show that for a vast class of entangled biphoton states, quantum entanglement provides no fundamental advantage and the same precision can be obtained with a separable state. We conclude by studying the estimation of the electric dipole moment of a sodium atom using quantum light. Our work initiates a quantum information theoretic methodology for developing the theory and practice of quantum light spectroscopy.
... For example, in the context of biological imaging applications, where illuminating a live sample with a high probe beam power may alter cell processes and high probe beam power can lead to cell death [1,2]. In absorption measurements increasing the probe power can also lead to saturation of the sample [3]. Further to these applications, low-light imaging contexts exist within LiDAR and covert imaging where, either low-power eye-safe sources are required, or in cases where imaging is performed through a scattering media [4,5]. ...
We present a wide-field homodyne imaging system capable of recovering intensity and phase images of an object from a single camera frame at an illumination intensity significantly below the noise floor of the camera. By interfering a weak imaging signal with a much brighter reference beam we are able to image objects in the short-wave infrared down to signal intensity of $\sim$$1.1$ photons per pixel per frame incident on the sensor despite the camera having a noise floor of $\sim$$200$ photons per pixel. At this illumination level we operate under the conditions of a reference beam to probe beam power ratio of $\sim$$300$,$000$:$1$. There is a corresponding $29.2\%$ drop in resolution of the image due to the method implemented. For transmissive objects, in addition to intensity, the approach also images the phase profile of the object. We believe our demonstration could open the way to low-light imaging in domains where low noise cameras are not available, thus vastly extending the range of application for low-light imaging.
We study the fundamental limits of the precision of estimating parameters of a quantum matter system when it is probed by a traveling pulse of quantum light. In particular, we focus on the estimation of the interaction strength between the pulse and a two-level atom, equivalent to the estimation of the dipole moment. Our analysis of single-photon pulses highlights the interplay between the information gained from the absorption of the photon by the atom as measured in absorption spectroscopy and the perturbation to the temporal mode of the photon due to spontaneous emission. Beyond the single-photon regime, we introduce an approximate model to study more general states of light in the limit of short pulses, where spontaneous emission can be neglected. We also show that for a vast class of entangled biphoton states, quantum entanglement between the signal mode interacting with the atom and the idler mode provides no fundamental advantage and the same precision can be obtained with a separable state. We conclude by studying the estimation of the electric dipole moment of a sodium atom using quantum light. Our work initiates a quantum information-theoretic methodology for developing the theory and practice of quantum light spectroscopy.
We present a homodyne imaging system capable of imaging an object under a level of illumination comparable to the noise floor of the detector.
The performance of light microscopes is limited by the stochastic nature of light, which exists in discrete packets of energy known as photons. Randomness in the times that photons are detected introduces shot noise, which fundamentally constrains sensitivity, resolution and speed¹. Although the long-established solution to this problem is to increase the intensity of the illumination light, this is not always possible when investigating living systems, because bright lasers can severely disturb biological processes2,3,4. Theory predicts that biological imaging may be improved without increasing light intensity by using quantum photon correlations1,5. Here we experimentally show that quantum correlations allow a signal-to-noise ratio beyond the photodamage limit of conventional microscopy. Our microscope is a coherent Raman microscope that offers subwavelength resolution and incorporates bright quantum correlated illumination. The correlations allow imaging of molecular bonds within a cell with a 35 per cent improved signal-to-noise ratio compared with conventional microscopy, corresponding to a 14 per cent improvement in concentration sensitivity. This enables the observation of biological structures that would not otherwise be resolved. Coherent Raman microscopes allow highly selective biomolecular fingerprinting in unlabelled specimens6,7, but photodamage is a major roadblock for many applications8,9. By showing that the photodamage limit can be overcome, our work will enable order-of-magnitude improvements in the signal-to-noise ratio and the imaging speed.
The utility of transmission measurement has made it a target for quantum enhanced measurement strategies. Here we find if the length of an absorbing object is a controllable variable, then, via the Beer-Lambert law, classical strategies can be optimized to reach within 83% of the absolute quantum limit in precision. Our analysis includes experimental losses, detector noise, and input states with arbitrary photon statistics. We derive optimal operating conditions for both classical and quantum sources, and observe experimental agreement with theory using Fock and thermal states.
We review the rapid recent progress in single-photon sources based on multiplexing multiple probabilistic photon-creation events. Such multiplexing allows higher single-photon probabilities and lower contamination from higher-order photon states. We study the requirements for multiplexed sources and compare various approaches to multiplexing using different degrees of freedom.
The theory of open quantum systems is one of the most essential tools for the development of quantum technologies. Furthermore, the Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) master equation plays a key role as it is the most general generator of Markovian dynamics in quantum systems. In this paper, we present this equation together with its derivation and methods of resolution. The presentation tries to be as self-contained and straightforward as possible to be useful to readers with no previous knowledge of this field.
Wave-particle duality is an inherent peculiarity of the Quantum world. The double-slit experiment has been frequently used for understanding different aspects of this fundamental concept. The occurrence of interference rests on the lack of which-way information and on the absence of decoherence mechanisms, which could scramble the wave fronts. Here, we report on the observation of two-center interference in the molecular-frame photoelectron momentum distribution upon ionization of the neon dimer by a strong laser field. Postselection of ions, which are measured in coincidence with electrons, allows choosing the symmetry of the residual ion, leading to observation of both, gerade and ungerade, types of interference.
Loss measurements are at the base of spectroscopy and imaging, thus perme- ating all the branches of science, from chemistry and biology to physics and material science. However, quantum mechanics laws set the ultimate limit to the sensitivity, constrained by the probe mean energy. This can be the main source of uncertainty, for example when dealing with delicate system such as biological samples or photosensitive chemicals. It turns out that ordinary (clas- sical) probe beams, namely with Poissonian photon number distribution, are fundamentally inadequate to measure small losses with the highest sensitivity. Conversely, we demonstrate that a quantum-correlated pair of beams, known as twin-beam state, allows reaching the ultimate sensitivity for all energy regimes (even less than one photon per mode) with the simplest measurement strategy. One beam of the pair addresses the sample, while the second one is used as a reference to compensate both for classical drifts and for uctuation at the most fundamental quantum level. This scheme is also absolute and accurate, since it self-compensates for unavoidable instability of the sources and detectors, which could otherwise lead to strongly biased results. Moreover, we report the best sensitivity per photon ever achieved in loss estimation experiments.
Harnessing the unique properties of quantum mechanics offers the possibility of delivering alternative technologies that can fundamentally outperform their classical counterparts. These technologies deliver advantages only when components operate with performance beyond specific thresholds. For optical quantum metrology, the biggest challenge that impacts on performance thresholds is optical loss. Here, we demonstrate how including an optical delay and an optical switch in a feed-forward configuration with a stable and efficient correlated photon-pair source reduces the detector efficiency required to enable quantum-enhanced sensing down to the detection level of single photons and without postselection. When the switch is active, we observe a factor of improvement in precision of 1.27 for transmission measurement on a per-input-photon basis compared to the performance of a laser emitting an ideal coherent state and measured with the same detection efficiency as our setup. When the switch is inoperative, we observe no quantum advantage.
Reaching the quantum optics limit of strong light-matter interactions between a single exciton and a plasmon mode is highly desirable, because it opens up possibilities to explore room-temperature quantum devices operating at the single-photon level. However, two challenges severely hinder the realization of this limit: the integration of single-exciton emitters with plasmonic nanostructures and making the coupling strength at the single-exciton level overcome the large damping of the plasmon mode. Here, we demonstrate that these two hindrances can be overcome by attaching individual J aggregates to single cuboid Au@Ag nanorods. In such hybrid nanosystems, both the ultrasmall mode volume of ∼71 nm3 and the ultrashort interaction distance of less than 0.9 nm make the coupling coefficient between a single J-aggregate exciton and the cuboid nanorod as high as ∼41.6 meV, enabling strong light-matter interactions to be achieved at the quantum optics limit in single open plasmonic nanocavities.
The interaction of a single photon with an individual two-level system is the textbook example of quantum electrodynamics. Achieving strong coupling in this system so far required confinement of the light field inside resonators or waveguides. Here, we demonstrate strong coherent coupling between a single Rydberg superatom, consisting of thousands of atoms behaving as a single two-level system due to the Rydberg blockade, and a propagating light pulse containing only a few photons. The strong light-matter coupling in combination with the direct access to the outgoing field allows us to observe for the first time the effect of the interactions on the driving field at the single photon level. We find that all our results are in quantitative agreement with the predictions of the theory of a single two-level system strongly coupled to a single quantized propagating light mode. The demonstrated coupling strength opens the way towards interfacing photonic and atomic qubits and preparation of propagating non-classical states of light, two crucial building blocks in future quantum networks.
Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational-wave interferometers and some atomic sensors do not appear to fit this description, because there is no external constraint on particle number. Here we develop the theory of particle-number-unconstrained quantum sensing, and describe how optimal particle numbers emerge from the competition of particle-environment and particle-particle interactions. We apply the theory to optical probing of an atomic medium modeled as a resonant, saturable absorber, and observe the emergence of well-defined finite optima without external constraints. The results contradict some expectations from number-constrained quantum sensing, and show that probing with squeezed beams can give a large sensitivity advantage over classical strategies, when each is optimized for particle number.
Absorption spectroscopy is routinely used to characterise chemical and biological samples. For the state-of-the-art in laser absorption spectroscopy, precision is theoretically limited by shot-noise due to the fundamental Poisson-distribution of photon number in laser radiation. In practice, the shot-noise limit can only be achieved when all other sources of noise are eliminated. Here, we use wavelength-correlated and tuneable photon pairs to demonstrate how absorption spectroscopy can be performed with precision beyond the shot-noise limit and near the ultimate quantum limit by using the optimal probe for absorption measurement---single photons. We present a practically realisable scheme, which we characterise both the precision and accuracy of by measuring the response of a control feature. We demonstrate that the technique can successfully probe liquid samples using two spectrally similar types of haemoglobin we show that obtaining a given precision in resolution requires fewer heralded single probe photons compared to using an idealised laser.
Spectroscopy has an illustrious history delivering serendipitous discoveries and providing a stringent testbed for new physical predictions, including applications from trace materials detection, to understanding the atmospheres of stars and planets, and even constraining cosmological models. Reaching fundamental-noise limits permits optimal extraction of spectroscopic information from an absorption measurement. Here, we demonstrate a quantum-limited spectrometer that delivers high-precision measurements of the absorption lineshape. These measurements yield a very accurate measurement of the excited-state (6P1/2) hyperfine splitting in Cs, and reveals a breakdown in the well-known Voigt spectral profile. We develop a theoretical model that accounts for this breakdown, explaining the observations to within the shot-noise limit. Our model enables us to infer the thermal velocity dispersion of the Cs vapour with an uncertainty of 35 p.p.m. within an hour. This allows us to determine a value for Boltzmann's constant with a precision of 6 p.p.m., and an uncertainty of 71 p.p.m.
The aim of this paper is to introduce the subject of chirality within pharmaceuticals and its implications in environmental contamination. The paper describes contemporary techniques and stationary phases in the analysis of chiral pharmaceuticals and illicit drugs, the main focus being on liquid chromatography coupled with mass spectrometry. A critical review of the methods employed including sample collection, preparation and analysis is undertaken. Special attention is paid to the possible analytical pitfalls of chromatographic separations at enantiomeric level, which could potentially lead to erroneous measurements of enantiomers. Several applications of chiral analysis and results gained in the field are also discussed. Among them are: (i) study of fate and effects of chiral pharmaceuticals in the environment and during wastewater treatment, (ii) estimation of community-wide drugs use via newly emerging field of sewage epidemiology and (iii) usage of chiral drugs as chemical markers of water contamination with sewage. The paper also aims to identify gaps within current knowledge.
Super-resolution optical microscopy is opening a new window to unveil the unseen details on the nanoscopic scale. Current far-field super-resolution techniques rely on fluorescence as the read-out(1-5). Here, we demonstrate a scheme for breaking the diffraction limit in far-field imaging of non-fluorescent species by using spatially controlled saturation of electronic absorption. Our method is based on a pump-probe process where a modulated pump field perturbs the charge-carrier density in a sample, thus modulating the transmission of a probe field. A doughnut shape laser beam is then added to transiently saturate the electronic transition in the periphery of the focal volume, thus the induced modulation in the sequential probe pulse only occurs at the focal center. By raster scanning the three collinearly aligned beams, high-speed sub-diffraction-limited imaging of graphite nano-platelets was performed. This technique potentially enables super-resolution imaging of nano-materials and non-fluorescent chromophores, which may remain out of reach for fluorescence-based methods.
Nearly a century after Einstein first predicted the existence of gravitational waves, a global network of Earth-based gravitational wave observatories1, 2, 3, 4 is seeking to directly detect this faint radiation using precision laser interferometry. Photon shot noise, due to the quantum nature of light, imposes a fundamental limit on the attometre-level sensitivity of the kilometre-scale Michelson interferometers deployed for this task. Here, we inject squeezed states to improve the performance of one of the detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) beyond the quantum noise limit, most notably in the frequency region down to 150 Hz, critically important for several astrophysical sources, with no deterioration of performance observed at any frequency. With the injection of squeezed states, this LIGO detector demonstrated the best broadband sensitivity to gravitational waves ever achieved, with important implications for observing the gravitational-wave Universe with unprecedented sensitivity.
In this tutorial article the authors provide a discussion of squeezed states of light from an elementary point of view. An outline of the topics considered is provided in the contents list below. Following the presentation of topics 1-3, which are of a general nature, they discuss two kinds of nonclassical light: quadrature-squeezed light (topics 4-6) and photon-number-squeezed light (topics 7-9). In the last part of the article they provide a listing of early nonclassical light experiments and consider a number of applications (and potential applications) of squeezed light. Finally, they provide a survey of the available general literature.
We review recent experimental advances in the field of efficient coupling of single atoms and light in free space. Furthermore, a comparison of efficient free space coupling and strong coupling in cavity quantum electrodynamics (QED) is given. Free space coupling does not allow for observing oscillatory exchange between the light field and the atom which is the characteristic feature of strong coupling in cavity QED. Like cavity QED, free space QED does, however, offer full switching of the light field, a 180° phase shift conditional on the presence of a single atom as well as 100% absorption probability of a single photon by a single atom. Furthermore, free space cavity QED comprises the interaction with a continuum of modes.
The estimation of parameters characterizing dynamical processes is central to
science and technology. The estimation error changes with the number N of
resources employed in the experiment (which could quantify, for instance, the
number of probes or the probing energy). Typically, it scales as 1/N^(1/2).
Quantum strategies may improve the precision, for noiseless processes, by an
extra factor 1/N^(1/2). For noisy processes, it is not known in general if and
when this improvement can be achieved. Here we propose a general framework for
obtaining attainable and useful lower bounds for the ultimate limit of
precision in noisy systems. We apply this bound to lossy optical interferometry
and atomic spectroscopy in the presence of dephasing, showing that it captures
the main features of the transition from the 1/N to the 1/N^(1/2) behaviour as
N increases, independently of the initial state of the probes, and even with
use of adaptive feedback.
Optical interferometry is amongst the most sensitive techniques for precision
measurement. By increasing the light intensity a more precise measurement can
usually be made. However, in some applications the sample is light sensitive.
By using entangled states of light the same precision can be achieved with less
exposure of the sample. This concept has been demonstrated in measurements of
fixed, known optical components. Here we use two-photon entangled states to
measure the concentration of the blood protein bovine serum albumin (BSA) in an
aqueous buffer solution. We use an opto-fluidic device that couples a waveguide
interferometer with a microfluidic channel. These results point the way to
practical applications of quantum metrology to light sensitive samples.
We review the current status of single-photon-source and single-photon-detector technologies operating at wavelengths from the ultraviolet to the infrared. We discuss applications of these technologies to quantum communication, a field currently driving much of the development of single-photon sources and detectors.
A short review of recent developments of the Dicke model in quantum optics is presented. The focus is on the model in a cavity at zero temperature and in the rotating wave approximation. Topics discussed include spectroscopic structures, the giant quantum oscillator, entanglement and phase transitions.
The LIGO-II gravitational-wave interferometers (ca. 2006–2008) are designed to have sensitivities near the standard quantum limit (SQL) in the vicinity of 100 Hz. This paper describes and analyzes possible designs for subsequent LIGO-III interferometers that can beat the SQL. These designs are identical to a conventional broad band interferometer (without signal recycling), except for new input and/or output optics. Three designs are analyzed: (i) a squeezed-input interferometer (conceived by Unruh based on earlier work of Caves) in which squeezed vacuum with frequency-dependent (FD) squeeze angle is injected into the interferometer’s dark port; (ii) a variational-output interferometer (conceived in a different form by Vyatchanin, Matsko and Zubova), in which homodyne detection with FD homodyne phase is performed on the output light; and (iii) a squeezed-variational interferometer with squeezed input and FD-homodyne output. It is shown that the FD squeezed-input light can be produced by sending ordinary squeezed light through two successive Fabry-Pérot filter cavities before injection into the interferometer, and FD-homodyne detection can be achieved by sending the output light through two filter cavities before ordinary homodyne detection. With anticipated technology (power squeeze factor e-2R=0.1 for input squeezed vacuum and net fractional loss of signal power in arm cavities and output optical train ε*=0.01) and using an input laser power Io in units of that required to reach the SQL (the planned LIGO-II power, ISQL), the three types of interferometer could beat the amplitude SQL at 100 Hz by the following amounts μ≡sqrt[Sh]/sqrt[ShSQL] and with the following corresponding increase V=1/μ3 in the volume of the universe that can be searched for a given noncosmological source: Squeezed input —μ≃sqrt[e-2R]≃0.3 and V≃1/0.33≃30 using Io/ISQL=1. Variational-output—μ≃ε*1/4≃0.3 and V≃30 but only if the optics can handle a ten times larger power: Io/ISQL≃1/sqrt[ε*]=10. Squeezed varational —μ=1.3(e-2Rε*)1/4≃0.24 and V≃80 using Io/ISQL=1; and μ≃(e-2Rε*)1/4≃0.18 and V≃180 using Io/ISQL=sqrt[e-2R/ε*]≃3.2.
Quantum-Enhanced Measurement
The single electron spin in a molecule, atom, or quantum dot precesses in a magnetic field and so can be used as a magnetic field sensor. As the number of spins in a sensor increases, so too does the sensitivity. Quantum mechanical entanglement of the spin ensemble should then allow the sensitivity to increase much more than would be expected from a simple increase in the number of individual spins in the ensemble. Using the highly symmetric molecule, trimethyl phosphite, a molecule containing a central P atom surrounded by nine hydrogen atoms, Jones et al. (p. 1166 , published online 23 April) quantum mechanically entangled the 10 spins (or qubits) to generate a nearly 10-fold enhancement in the magnetic field sensitivity. The results pave the way for the further development of quantum sensors.
The Beer-Lambert-Bouguer absorption law, known as Beer's law for absorption in an optical medium, is precise only at power densities lower than a few kW. At higher power densities this law fails because it neglects the processes of stimulated emission and spontaneous emission. In previous models that considered those processes, an analytical expression for the absorption law could not be obtained. We show here that by utilizing the Lambert W-function, the two-level energy rate equation model is solved analytically, and this leads into a general absorption law that is exact because it accounts for absorption as well as stimulated and spontaneous emission. The general absorption law reduces to Beer's law at low power densities. A criterion for its application is given along with experimental examples.
Squeezed light enables measurements with sensitivity beyond the quantum noise limit (QNL) for optical techniques such as spectroscopy, gravitational wave detection, magnetometry, and imaging. Precision of a measurement—as quantified by the variance of repeated estimates—has also been enhanced beyond the QNL using squeezed light. However, sub-QNL sensitivity is not sufficient to achieve sub-QNL precision. Furthermore, demonstrations of sub-QNL precision in estimating transmission have been limited to picowatts of probe power. Here we demonstrate simultaneous enhancement of precision and sensitivity to beyond the QNL for estimating modulated transmission with a squeezed amplitude probe of 0.2 mW average (25 W peak) power, which is 8 orders of magnitude above the power limitations of previous sub-QNL precision measurements of transmission. Our approach enables measurements that compete with the optical powers of current classical techniques, but have both improved precision and sensitivity beyond the classical limit.
An invaluable text for the teaching, design, and development of gas sensor technology. This excellent resource synthesizes the fundamental principles of spectroscopy, laser physics, and photonics technology and engineering to enable the reader to fully understand the key issues and apply them in the design of optical gas absorption sensors. It provides a straightforward introduction to low-cost and highly versatile near-IR systems, as well as an extensive review of mid-IR systems. Fibre laser systems for spectroscopy are also examined in detail, especially the emerging technique of frequency comb spectroscopy. Featuring many examples of real-world application and performance, as well as MATLAB computer programs for modeling and simulation, this exceptional work is ideal for postgraduate students, researchers, and professional engineers seeking to gain an in-depth understanding of the principles and applications of fibre-optic and laser-based gas sensors.
Optical absorption measurements characterize a wide variety of systems from atomic gases to in vivo diagnostics of living organisms. Here we study the potential of nonclassical techniques to reduce statistical noise below the shot-noise limit in absorption measurements with concomitant phase shifts imparted by a sample. We consider both cases where there is a known relationship between absorption and a phase shift, and where this relationship is unknown. For each case we derive the fundamental limit and provide a practical strategy to reduce statistical noise. Furthermore, we find an intuitive correspondence between measurements of absorption and of lossy phase shifts, which both show the same analytical form for precision enhancement for bright states. Our results demonstrate that nonclassical techniques can aid real-world tasks with present-day laboratory techniques.
The minimum resolvable signal in sensing and metrology platforms that rely on optical readout fields is increasingly constrained by the standard quantum limit, which is determined by the sum of photon shot noise and backaction noise. A combination of backaction and shot noise reduction techniques will be critical to the development of the next generation of sensors for applications ranging from high energy physics to biochemistry and for novel microscopy platforms capable of resolving material properties that were previously obscured by quantum noise. This perspective reviews the dramatic advances made in the use of squeezed light for sub-shot-noise quantum sensing in recent years, and highlights emerging applications that enable new science based on signals that would otherwise be obscured by noise at the standard quantum limit.
This book treats the interaction of radiation with matter, particular attention being paid to the laser. Knowledge is assumed of the usual half-year introduction of quantum mechanics found in undergraduate physics curricula. The material can be covered in two semesters, or, alternatively, the first part (Chaps 1-13) can be used as a one-semester course in which quantum mechanical aspects of the electromagnetic field are ignored. Each chapter is accompanied by problems that illustrate the text and give useful (occasionally new) results. Existing laser media are intrinsically quantum mechanical and are most easily studied with the quantum theory. Understanding the laser along these lines enlivens one’s understanding of quantum mechanics itself. In fact, the material constitutes a viable, applied alternative for the usual second and third semesters of quantum mechanics.
Structured‐illumination microscopy allows widefield fluorescence imaging with resolution beyond the classical diffraction limit. Its linear form extends resolution by a factor of two, and its nonlinear form by an in‐principle infinite factor, the effective resolution in practice being determined by noise. In this paper, we analyse the noise properties and achievable resolution of linear and nonlinear 1D and 2D patterned SIM from a frequency–space perspective. We develop an analytical theory for a general case of linear or nonlinear fluorescent imaging, and verify the analytical calculations with numerical simulation for a special case where nonlinearity is produced by photoswitching of fluorescent labels. We compare the performance of two alternative implementations, using either two‐dimensional (2D) illumination patterns or sequentially rotated one‐dimensional (ID) patterns. We show that 1D patterns are advantageous in the linear case, and that in the nonlinear case 2D patterns provide a slight signal‐to‐noise advantage under idealised conditions, but perform worse than 1D patterns in the presence of nonswitchable fluorescent background.
Lay Description
Structured‐illumination microscopy (SIM) is a high‐resolution light microscopy technique that allows imaging of fluorescence at a resolution about twice the classical diffraction limit. There are various ways that the illumination can be structured, but it is not obvious how the choice of illumination pattern affects the final image quality, especially in view of the noise. We present a detailed performance analysis considering two illumination techniques: sequential illumination with line‐gratings that are shifted and rotated during image acquisition and two‐dimensional (2D) illumination structures requiring only shift operations. Our analysis is based on analytical theory, supported by simulations of images considering noise. We also extend our analysis to a nonlinear variant of SIM, with which enhanced resolution can be achieved, limited only by noise. This includes nonlinear SIM based on the light‐induced switching of the fluorescent molecules between a bright and a dark state. We find sequential illumination with line‐gratings to be advantageous in ordinary (linear) SIM, whereas 2D patterns provides a slight signal‐to‐noise advantage under idealised conditions in nonlinear SIM if there is no nonswitching background.
Squeezed states of light belong to the most prominent nonclassical resources. They have compelling applications in metrology, which has been demonstrated by their routine exploitation for improving the sensitivity of a gravitational-wave detector since 2010. Here, we report on the direct measurement of 15 dB squeezed vacuum states of light and their application to calibrate the quantum efficiency of photoelectric detection. The object of calibration is a customized InGaAs positive intrinsic negative (p-i-n) photodiode optimized for high external quantum efficiency. The calibration yields a value of 99.5% with a 0.5% (k=2) uncertainty for a photon flux of the order 1017 s−1 at a wavelength of 1064 nm. The calibration neither requires any standard nor knowledge of the incident light power and thus represents a valuable application of squeezed states of light in quantum metrology.
Quantum metrology provides a route to overcome practical limits in sensing devices. It holds particular relevance to biology, where sensitivity and resolution constraints restrict applications both in fundamental biophysics and in medicine. Here, we review quantum metrology from this biological context, focusing on optical techniques due to their particular relevance for biological imaging, sensing, and stimulation. Our understanding of quantum mechanics has already enabled important applications in biology, including positron emission tomography (PET) with entangled photons, magnetic resonance imaging (MRI) using nuclear magnetic resonance, and bio-magnetic imaging with superconducting quantum interference devices (SQUIDs). In quantum metrology an even greater range of applications arise from the ability to not just understand, but to engineer, coherence and correlations at the quantum level. In the past few years, quite dramatic progress has been seen in applying these ideas into biological systems. Capabilities that have been demonstrated include enhanced sensitivity and resolution, immunity to imaging artifacts and technical noise, and characterization of the biological response to light at the single-photon level. New quantum measurement techniques offer even greater promise, raising the prospect for improved multi-photon microscopy and magnetic imaging, among many other possible applications. Realization of this potential will require cross-disciplinary input from researchers in both biology and quantum physics. In this review we seek to communicate the developments of quantum metrology in a way that is accessible to biologists and biophysicists, while providing sufficient detail to allow the interested reader to obtain a solid understanding of the field. We further seek to introduce quantum physicists to some of the central challenges of optical measurements in biological science. We hope that this will aid in bridging the communication gap that exists between the fields, and thereby guide the future development of this multidisciplinary research area.
Cavity quantum electrodynamics studies the behaviour of atoms inside a low-loss cavity. The composite atom–cavity system constitutes a new ‘molecule’ with radiative properties which differ radically from those of the individual components. For example, spontaneous emission becomes reversible, the spectrum splits into several peaks and the intensity fluctuations of the light transmitted by this novel ‘molecule’ are below the classical shot noise limit. In terms of practical applications, the system renders possible, first, the detection of single atoms with a high sensitivity and, second, optical bistability for a few atoms and photons only.
Recovery of absolute gas absorption line shapes from first harmonic residual AM (RAM) signals in tunable diode laser spectroscopy with wavelength modulation (TDLS-WM) offers sig- nificant advantages in terms of measurement accuracy (for gas concentration and pressure), freedom from the need for calibra- tion and resilience to errors, or drift in system parameters/scaling factors. However, the signal strength and SNR are compromised somewhat relative to conventional WM spectroscopy (WMS) by the signal dependence on the laser's intensity modulation ampli- tude rather than on the direct intensity, and by the need to operate at low modulation index, , in the previously reported study. In part 1 of this two-part publication, we report a more uni- versal approach to the analysis of recovered RAM signals and ab- solute absorption line shapes. This new approach extends the use of RAM techniques to arbitrary m values up to 2.2. In addition, it provides the basis for a comparison of signal strength between the RAM signals recovered by the phasor decomposition approach and conventional first and second harmonic TDLS-WM signals. The experimental study reported here validates the new model and demonstrates the use of the RAM techniques for accurate recovery of absolute gas absorption line shapes to and above. Fur- thermore, it demonstratesthat theRAM signalstrengths canbe in- creased significantly by increasing the modulation frequency and defines regimes of operation such that the directly recovered RAM signalsare comparableto orevengreaterthanthewidelyusedcon- ventional second harmonic TDLS-WM signal. Finally, a critique of the RAM techniques relative to the conventional approaches is given.
Near infrared spectroscopy (NIRS) has been recognized as a valuable quality control tool in the flour, grain and forage industry since the mid-1960s, but the application of the technique within the food industry has become increasingly recognized in the 1980s. This short review provides brief theoretical background and a discussion of the techniques, particularly mathematical. These are integral to the development of off-line applications prior to on-line implementation. Examples are given of current on-line applications of NIR within the food industry.
Thylakoid membranes can be immobilized to enhance their stability in photoelectrochemical cells exposed to strong continuous illumination. We studied the effect of such immobilization in a glutaraldehyde-albumin crosslinked matrix on the rates of photoinhibition of electron transfer and chlorophyll photobleaching. The immobilization matrix constituted an efficient oxygen diffusion barrier that prevents chlorophyll photobleaching to a great extent. The photoprotection was less efficient against photoinhibition as seen by monitoring oxygen evolution after given periods of preillumination or by measuring the energy storage yield in condensed samples decaying under continuous illumination in the cell of a photoacoustic spectrophotometer. The results also indicated that light dispersion by the immobilization matrix was not a critical factor for photoprotection.
The interaction of a resonant radiation field with two-level atoms (in the long-wavelength limit) is described by a Hamiltonian trilinear in the boson operators. It is shown that the dynamics of the system can be determined nearly exactly if either at least one of the three modes is strongly populated for all times or any two modes are separately strong in two complementary time domains. Explicit results are given in two important specific cases: (i) pumping of a ground-state atomic system by a coherent radiation field and (ii) coherent spontaneous emission. The results are compared with previously known approximate results. Our results are also applicable to certain parametric processes such as parametric amplification, frequency conversion, Raman and Brillouin scattering, etc., where an identical trilinear Hamiltonian is used to describe these processes.
Guiding light through hollow optical waveguides has opened the field of photonics to the investigation of non-solid materials that have all the convenience of integrated optics. Of particular interest is the confinement of atomic vapours, such as rubidium, because of its wide range of applications, including slow and stopped light1, single-photon nonlinear optics2, quantum information processing3, precision spectroscopy4 and frequency stabilization5. Here, we present the first monolithically integrated rubidium vapour cell using hollow-core antiresonant reflecting optical waveguides (ARROWs) on a silicon chip. The cells have a footprint of less than 1 cm2, fully planar fibre-optical access, and a cell volume more than 7 orders of magnitude less than conventional bulk cells. The micrometre-sized mode areas enable high beam intensities over near centimetre lengths. We demonstrate optical densities in excess of 2, and saturation absorption spectroscopy on a chip. These results allow the study of atoms and molecules on a platform that combines the advantages of photonic-crystal-like structures with integrated optics.
Many chemical sensors based on fiber optics and absorption spectroscopy have been reported in applications ranging from biomedical and environmental monitoring to industrial process control. In these diverse applications, the analyte can be probed directly, by measuring its intrinsic absorption, or by incorporating some transduction mechanism such as a reagent chemistry to enhance sensitivity and selectivity. Physical and performance requirements are placed on a device depending on its intended use. In applications such as chemical process monitoring, survivability and the assurance of the long-term quality of the analytical data are paramount. The above needs have resulted in devices that now employ multivariate data analysis, complex sampling interfaces, and reagent renewal mechanisms. The response from such systems can provide information not only about target analyte(s), but can also signal the presence of interferences, and may potentially be used to follow sensor degradation. Examples are given of devices currently being investigated along with a discussion of some of the remaining material, chemical, and optical challenges.
Optical studies of single molecules in ambient environments, which have led to broad applications, are primarily based on fluorescence detection. Direct detection of optical absorption with single-molecule sensitivity at room temperature is difficult because absorption is not a background-free measurement and is often complicated by sample scattering. Here we report ground-state depletion microscopy for ultrasensitive detection of absorption contrast. We image 20 nm gold nanoparticles as an initial demonstration of this microscopy. We then demonstrate the detection of an absorption signal from a single chromophore molecule at room temperature. This is accomplished by using two tightly focused collinear continuous-wave laser beams at different wavelengths, both within a molecular absorption band, one of which is intensity modulated at a high frequency (>MHz). The transmission of the other beam is found to be modulated at the same frequency due to ground state depletion. The signal of single chromophore molecules scanned across the common laser foci can be detected with shot-noise limited sensitivity. This measurement represents the ultimate detection sensitivity of nonlinear optical spectroscopy at room temperature.Keywords (keywords): single molecule spectroscopy; single molecule detection; ground state depletion; microscopy
We develop an analytical approach to the dynamics of band populations of reverse saturable absorbers modeled by the three-level approximation of the five-level rate equations. We find high-accuracy approximate solutions to these rate equations, taking into account the temporal shape of the incident laser pulse for different regimes of excitation. The results obtained are confirmed by direct numerical integration of the rate equations and are verified by solution of the full system of the rate and the propagation equations. The validity ranges of the approximations are determined. We also prove that for input pulses that are much longer than the lifetime of the first excited state the ground-state depletion obeys the same functional dependence on the input fluence as in the case of rectangular input pulses. The dynamics of the excited states, however, explicitly depends on the pulse shape. We quantitatively estimate the effect of various parameters on the nonlinear absorption coefficient and discuss implementation of the approach by a beam propagation method to reduce the computational time.
We show that the uncertainty in the relative quantum phase of two fields propagating in the arms of a Mach-Zehnder interferometer can be reduced to the Heisenberg limit by driving the interferometer with two Fock states containing equal numbers of photons. This leads to a minimum detectable phase shift far below that of any interferometer driven by a coherent light source.
The dynamic nonlinear absorption of a chloroform solution of chlorophyll A was investigated using the Z-scan technique with
picosecond pulses at 532nm. The nonlinear absorption exhibits a reverse saturation, indicating a strong intersystem crossing
(singlet–triplet) process. The time evolution of the optical nonlinearity, modeled by means of a five-level energy diagram,
allows the determination of excited-state cross sections and the lifetime of the intersystem crossing based on its absorption
characteristics and efficient formation of triplet states. Chlorophyll A was found to be a good candidate for a sensitizer
in photodynamic therapy.
This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.
The concentrations of copper, iron, magnesium, and zinc in the hair of eighteen different adult male subjects have been determined by atomic absorption spectroscopy over periods ranging from 4 to 10 months. The mean for each of the four analysis elements is shown for each subject. A mean, median, and range are given for each subject. A mean, median, and range are given for each element taking all subjects into consideration. A study was made of the pre-treatment of hair, including a comparison of detergent washed and organic solvent washed hair and an investigation of other wash parameters. Recovery studies were made for each analysis element.
We present an object-oriented open-source framework for solving the dynamics
of open quantum systems written in Python. Arbitrary Hamiltonians, including
time-dependent systems, may be built up from operators and states defined by a
quantum object class, and then passed on to a choice of master equation or
Monte-Carlo solvers. We give an overview of the basic structure for the
framework before detailing the numerical simulation of open system dynamics.
Several examples are given to illustrate the build up to a complete
calculation. Finally, we measure the performance of our library against that of
current implementations. The framework described here is particularly
well-suited to the fields of quantum optics, superconducting circuit devices,
nanomechanics, and trapped ions, while also being ideal for use in classroom
instruction.
We present a theoretical framework for studying spatially dependent absorption in a thermal vapor of multilevel atoms, of arbitrary optical thickness. The atomic state dynamics, governed by a standard atom-optical master equation, are self-consistently coupled to the axial evolution of the probe beam intensity and the effusive gas dynamics. We derive steady-state equations for the spatially varying distributions of atomic populations and the probe beam intensity. From the latter, absorption coefficients in both the saturated and unsaturated regimes can be calculated. We present solutions to the resulting equations at various levels of approximation, including an example of the full numerical solution of a saturated, optically thick vapor of three-level atoms, demonstrating a breakdown of Beer's law, among other measurable effects. 2010 The American Physical Society.
Recent advances in laser technology, computational power, and imaging algorithms have extended the application of fluorescence lifetime method into medical imaging. Initial applications of fluorescence lifetime in cell studies focused on autofluorescence lifetimes of endogenous fluorophores. The lifetime signatures of these biomolecules can be altered by changes in normal cell physiology or pathologic conditions. Scientists have accelerated the development of new fluorophores and luminescent materials for lifetime studies. Depending on the ultimate goal of the study, molecular probes with fixed or variable lifetimes can be used. The availability of a commercial small animal imaging system has extended the application of fluorescence lifetime studies in small animal beyond the confines of instrumentation experts. The emergence of newer diffuse optical tomography (DOT)-based lifetime devices will further enhance the quantitative accuracy and imaging depth by this technique.