Fundamental Quantum Limit Research Articles

Nonlinear optical response of 1H-indene-based donor-acceptor chromophores. Influence of the higher-lying states on the first hyperpolarizability

The hyperpolarizabilities often fall short of the fundamental quantum limits. However, in case of 5-(diphenylamino)thiophen-2-yl substituted 1H-indene based donor-π-acceptor (D-π-A) chromophores, in spite of the preponderance of twisted intramolecular charge transfer state, we find that the first hyperpolarizability is modulated (limited!) due to the possible interference of the higher-lying excited states of significant oscillator strength with the lower-lying excited state.

Fundamental quantum limit for linear measurements with instability

The fundamental quantum limit, or the quantum Cramér-Rao bound, defines the sensitivity limit for quantum measurements. For linear measurement systems, such as gravitational-wave detectors, it is inversely proportional to the noise spectrum of the dynamical variable that couples to the measured signal. Defining a physically meaningful spectrum, however, requires that the system is stable and a steady state exists. We relax such a stability requirement and prove that the fundamental quantum limit can be derived simply by considering the open-loop dynamics in the Fourier domain.

Efficient Superoscillation Measurement for Incoherent Optical Imaging

I propose a superoscillation measurement method for subdiffraction incoherent optical sources, with potential applications in astronomy, remote sensing, fluorescence microscopy, and spectroscopy. The proposal, based on coherent optical processing, can capture all the light on the aperture in principle, perform better than direct imaging on statistical terms, and approach the fundamental quantum limit.

Fundamental quantum limits of magnetic nearfield measurements

Major advances in the precision of magnetic measurements bring us closer to quantum detection of individual spins at the single-atom level. On the quest for reducing both classical and quantum measurement noise, it is intriguing to look forward and search for precision limits arising from the fundamental quantum nature of the measurement process itself. Here, we present the limits of magnetic quantum measurements arising from quantum information considerations, and apply these limits to a concrete example of magnetic force microscopy (MFM). We show how such microscopes have a fundamental limit on their precision arising from the theory of imperfect quantum cloning, manifested by the entanglement between the measured system and the measurement probe. We show that counterintuitively, increasing the probe complexity decreases both the measurement noise and back action, and a judicious design of the magnetic interaction reveals optimal schemes already at spin-1 probes.

Demonstration of Entanglement-Enhanced Covert Sensing.

The laws of quantum physics endow superior performance and security for information processing: quantum sensing harnesses nonclassical resources to enable measurement precision unmatched by classical sensing, whereas quantum cryptography aims to unconditionally protect the secrecy of the processed information. Here, we present the theory and experiment for entanglement-enhanced covert sensing, a paradigm that simultaneously offers high measurement precision and data integrity by concealing the probe signal in an ambient noise background so that the execution of the protocol is undetectable with a high probability. We show that entanglement offers a performance boost in estimating the imparted phase by a probed object, as compared to a classical protocol at the same covertness level. The implemented entanglement-enhanced covert sensing protocol operates close to the fundamental quantum limit by virtue of its near-optimum entanglement source and quantum receiver. Our work is expected to create ample opportunities for quantum information processing at unprecedented security and performance levels.

Quantum Variational Optimization of Ramsey Interferometry and Atomic Clocks

We discuss quantum variational optimization of Ramsey interferometry with ensembles of $N$ entangled atoms, and its application to atomic clocks based on a Bayesian approach to phase estimation. We identify best input states and generalized measurements within a variational approximation for the corresponding entangling and decoding quantum circuits. These circuits are built from basic quantum operations available for the particular sensor platform, such as one-axis twisting, or finite range interactions. Optimization is defined relative to a cost function, which in the present study is the Bayesian mean square error of the estimated phase for a given prior distribution, i.e. we optimize for a finite dynamic range of the interferometer. In analogous variational optimizations of optical atomic clocks, we use the Allan deviation for a given Ramsey interrogation time as the relevant cost function for the long-term instability. Remarkably, even low-depth quantum circuits yield excellent results that closely approach the fundamental quantum limits for optimal Ramsey interferometry and atomic clocks. The quantum metrological schemes identified here are readily applicable to atomic clocks based on optical lattices, tweezer arrays, or trapped ions.

Single-photon nonlinearity at room temperature.

The recent progress in nanotechnology1,2 and single-molecule spectroscopy3-5 paves the way foremergent cost-effective organic quantum optical technologies with potential applications in useful devices operating at ambient conditions. We harness a π-conjugated ladder-type polymer strongly coupled to a microcavity forming hybrid light-matter states, so-called exciton-polaritons, to create exciton-polariton condensates with quantum fluid properties. Obeying Bose statistics, exciton-polaritons exhibit an extreme nonlinearity when undergoing bosonic stimulation6, which we have managed to trigger at the single-photon level, thereby providing an efficient way for all-optical ultrafast control over the macroscopic condensate wavefunction. Here, we utilize stable excitons dressed with high-energy molecular vibrations, allowing for single-photon nonlinear operation at ambient conditions. This opens new horizons for practical implementations like sub-picosecond switching, amplification and all-optical logic at the fundamental quantum limit.

Superresolution in interferometric imaging of strong thermal sources

Imaging using interferometer arrays based on the Van Cittert--Zernike theorem has been widely used in astronomical observation. Recently it was shown that superresolution can be achieved in this system for imaging two weak thermal point sources. Using quantum estimation theory, we consider the fundamental quantum limit of resolving the transverse separation of two strong thermal point sources using interferometer arrays, and show that the resolution is not limited by the longest baseline. We propose measurement techniques using linear beam splitters and photon-number-resolving detection to achieve our bound. Our results demonstrate that superresolution for resolving two thermal point sources of any strength can be achieved in interferometer arrays.

Quantum Statistical Transport Phenomena in Memristive Computing Architectures

The advent of reliable, nanoscale memristive components is promising for next generation compute-in-memory paradigms, however, the intrinsic variability in these devices has prevented widespread adoption. Here we show coherent electron wave functions play a pivotal role in the nanoscale transport properties of these emerging, non-volatile memories. By characterizing both filamentary and non-filamentary memristive devices as disordered Anderson systems, the switching characteristics and intrinsic variability arise directly from the universality of electron transport in disordered media. Our framework suggests localization phenomena in nanoscale, solid-state memristive systems are directly linked to circuit level performance. We discuss how quantum conductance fluctuations in the active layer set a lower bound on device variability. This finding implies there is a fundamental quantum limit on the reliability of memristive devices, and electron coherence will play a decisive role in surpassing or maintaining Moore's Law with these systems.

Quantum-limited discrimination of laser light and thermal light.

Understanding the fundamental sensitivity limit of an optical sensor requires a full quantum mechanical description of the sensing task. In this work, we calculate the fundamental (quantum) limit for discriminating between pure laser light and thermal noise in a photon-starved regime. The Helstrom bound for discrimination error probability for single mode measurement is computed along with error probability bounds for direct detection, coherent homodyne detection and the Kennedy receiver. A generalized Kennedy (GK) receiver is shown to closely approach the Helstrom limit. We present an experimental demonstration of this sensing task and demonstrate a 15.4 dB improvement in discrimination sensitivity over direct detection using a GK receiver and an improvement of 19.4% in error probability over coherent detection.

Single-Photon Cooling in Microwave Magnetomechanics.

Cavity optomechanics, where photons are coupled to mechanical motion, provides the tools to control mechanical motion near the fundamental quantum limits. Reaching single-photon strong coupling would allow to prepare the mechanical resonator in non-Gaussian quantum states. Preparing massive mechanical resonators in such states is of particular interest for testing the boundaries of quantum mechanics. This goal remains however challenging due to the small optomechanical couplings usually achieved with massive devices. Here we demonstrate a novel approach where a mechanical resonator is magnetically coupled to a microwave cavity. We measure a single-photon coupling of g_{0}/2π∼3 kHz, an improvement of one order of magnitude over current microwave optomechanical systems. At this coupling we measure a large single-photon cooperativity with C_{0}≳10, an important step to reach single-photon strong coupling. Such a strong interaction allows us to cool the massive mechanical resonator to a third of its steady state phonon population with less than two photons in the microwave cavity. Beyond tests for quantum foundations, our approach is also well suited as a quantum sensor or a microwave to optical transducer.

Fundamental relations between measurement, radiation, and decoherence in gravitational wave laser interferometer detectors

As laser interferometer gravitational wave (GW) detectors become quantum noise dominated, understanding the fundamental limit on measurement sensitivity imposed by quantum uncertainty is crucial to guide the search for further noise reduction. Recent efforts have included applying ideas from quantum information theory to GW detection -- specifically the quantum Cramer Rao bound, which is a minimum bound on error in parameter estimation using a quantum state and is determined by the state's quantum Fisher information (QFI) with respect to the parameter. Identifying the QFI requires knowing the interaction between the quantum measurement device and the signal, which was rigorously derived for GW interferometer detectors in [Phys. Rev. D 98, 124006]. In this paper, we calculate the QFI and fundamental quantum limit (FQL) for GW detection, and furthermore derive explicit reciprocity relations involving the QFI which summarize information exchange between the detector and a surrounding weak quantum GW field. Specifically, we show that the GW power radiation by the detector's quantum fluctuations are proportional to the QFI, and therefore inversely proportional to its FQL. Similarly, the detector's decoherence rate in a white noise GW bath can be explicitly related to the QFI/FQL. These relations are fundamental and appear generalizable to a broader class of quantum measurement systems.

Quantum-optimal detection of one-versus-two incoherent optical sources with arbitrary separation

We analyze the fundamental quantum limit of the resolution of an optical imaging system from the perspective of the detection problem of deciding whether the optical field in the image plane is generated by one incoherent on-axis source with brightness epsilon or by two epsilon {mathrm{/}}2-brightness incoherent sources that are symmetrically disposed about the optical axis. Using the exact thermal-state model of the field, we derive the quantum Chernoff bound for the detection problem, which specifies the optimum rate of decay of the error probability with increasing number of collected photons that is allowed by quantum mechanics. We then show that recently proposed linear-optic schemes approach the quantum Chernoff bound—the method of binary spatial-mode demultiplexing (B-SPADE) is quantum-optimal for all values of separation, while a method using image inversion interferometry (SLIVER) is near-optimal for sub-Rayleigh separations. We then simplify our model using a low-brightness approximation that is very accurate for optical microscopy and astronomy, derive quantum Chernoff bounds conditional on the number of photons detected, and show the optimality of our schemes in this conditional detection paradigm. For comparison, we analytically demonstrate the superior scaling of the Chernoff bound for our schemes with source separation relative to that of spatially resolved direct imaging. Our schemes have the advantages over the quantum-optimal (Helstrom) measurement in that they do not involve joint measurements over multiple modes, and that they do not require the angular separation for the two-source hypothesis to be given a priori and can offer that information as a bonus in the event of a successful detection.

Fundamental quantum limits in optical metrology from rate-distortion theory

We derive fundamental lower bounds on the performance of optical metrology and communication systems in a Bayesian framework. The derivation uses classical rate-distortion theory in conjunction with bounds on the capacity to transmit classical information of various optical channels specified by the system design. The bounds are expressed in terms of the system parameters, the prior probability distribution of the parameter, and the average energy, i.e. number of photons E in the probe state. For phase estimation, the bounds pertain to a cyclic mean squared error criterion incorporating the cyclic nature of the phase. In the absence of optical loss, our bounds are applicable to multimode linear phase modulation schemes (including ancilla-assisted ones), and to nonlinear modulations on a single mode. The bounds display inverse-quadratic Heisenberg-limit scaling of the cyclic mean square error with respect to E. In the presence of any finite amount of loss, a lower bound on ancilla-assisted phase estimation with standard quantum limit scaling is derived, which is shown to be little different from a similar bound for coherent-state probes. For systems involving a single optical mode, we also obtain lower bounds on the mean squared error of estimating any classical parameter, and on the average error probability of any M-ary communication system under an average energy constraint. The bounds are valid for arbitrary quantum measurements, for any prior probability distribution, and do not rely on unbiasedness assumptions.

Towards the Fundamental Quantum Limit of Linear Measurements of Classical Signals.

The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the standard quantum limit that arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum nondemolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric gravitational-wave detectors.

Quantum-limited biochemical magnetometers designed using the Fisher information and quantum reaction control

Radical-ion pairs and their reactions have triggered the study of quantum effects in biological systems. This is because they exhibit a number of effects best understood within quantum information science, and at the same time are central in understanding the avian magnetic compass and the spin transport dynamics in photosynthetic reaction centers. Here we address radical-pair reactions from the perspective of quantum metrology. Since the coherent spin motion of radical-pairs is effected by an external magnetic field, these spin-dependent reactions essentially realize a biochemical magnetometer. Using the quantum Fisher information, we find the fundamental quantum limits to the magnetic sensitivity of radical-pair magnetometers. We then explore how well the usual measurement scheme considered in radical-pair reactions, the measurement of reaction yields, approaches the fundamental limits. In doing so, we find the optimal hyperfine interaction Hamiltonian that leads to the best magnetic sensitivity as obtained from reaction yields. This is still an order of magnitude smaller than the absolute quantum limit. Finally, we demonstrate that with a realistic quantum reaction control reminding of Ramsey interferometry, here presented as a quantum circuit involving the spin-exchange interaction and a recently proposed molecular switch, we can approach the fundamental quantum limit within a factor of 2. This work opens the application of well-advanced quantum metrology methods to biological systems.

Non-Markovianity Hierarchy of Gaussian Processes and Quantum Amplification.

We investigate the dynamics of Gaussian states of continuous variable systems under Gaussianity-preserving channels. We introduce a hierarchy of such evolutions encompassing Markovian and weakly and strongly non-Markovian processes and provide simple criteria to distinguish between the classes, based on the degree of positivity of intermediate Gaussian maps. We present an intuitive classification of all one-mode Gaussian channels according to their non-Markovianity degree and show that weak non-Markovianity has an operational significance, as it leads to a temporary phase-insensitive amplification of Gaussian inputs beyond the fundamental quantum limit. Explicit examples and applications are discussed.

Nonlinear optics near the fundamental limit: introduction

Nonlinear optics is the study of all effects that can be described as multi-photon interactions in various material systems, including cases where the frequency of one or more photons tends to zero. This feature issue is dedicated to works on both second-order nonlinear optics (three-photon interactions) and third-order nonlinear optics (four-photon interactions) that focus on understanding the fundamental mechanisms of the nonlinear optical response when the nonlinearity is large and approaches the fundamental quantum limit—a regime required by applications and characterized by interesting physics. Slightly more than half of the papers focus on theoretical analysis, with a strong emphasis on understanding model systems in view of the fundamental limits to the nonlinear optical response, which are dictated by quantum mechanics, and with several discussions of new theoretical approaches to understand and model the nonlinear optical response. The remaining papers provide an experimental counterpoint that includes examples of nonlinear optical responses in a variety of systems, an overview of how the fundamental limits can be approached in real materials, and of how the nonlinear response scales with spatial dimensions. The latter is quantified by identifying scale-invariant intrinsic quantities such as the dimensionless ratios between experimental results and the quantum limits.

Quantum model of cooling and force sensing with an optically trapped nanoparticle

Optically trapped nanoparticles have recently emerged as exciting candidates for tests of quantum mechanics at the macroscale and as versatile platforms for ultrasensitive metrology. Recent experiments have demonstrated parametric feedback cooling, nonequilibrium physics, and temperature detection, all in the classical regime. Here we provide the first quantum model for trapped nanoparticle cooling and force sensing. In contrast to existing theories, our work indicates that the nanomechanical ground state may be prepared without using an optical resonator; that the cooling mechanism corresponds to nonlinear friction; and that the energy loss during cooling is nonexponential in time. Our results show excellent agreement with experimental data in the classical limit, and constitute an underlying theoretical framework for experiments aiming at ground state preparation. Our theory also addresses the optimization of, and the fundamental quantum limit to, force sensing, thus providing theoretical direction to ongoing searches for ultra-weak forces using levitated nanoparticles.

Quantum Squeezing of Micromechanical Motion

The act of a quantum measurement reduces the uncertainty in the motion of a vibrating membrane below the fundamental quantum limit.