Session E07: Quantum Metrology and Sensing I

Optimizing quantum-metrology protocols with Heisenberg limit scaling

Optical lattice clocks operating near the standard quantum limit (SQL) employ uncorrelated ensembles of cold trapped atoms to reach unprecedented accuracy. Their phase-detection precision is proportional to the square root of the number of atoms. That scaling can be improved when including quantum effects such as entanglement and non-classical correlations. Nonlinear interactions such as the one-axis twisting (OAT) Hamiltonian can generate many-body entangled states such as spin squeezed states (SSSs) that can improve the precision scaling beyond the SQL. Recently, it has been shown that an effective time-reversal protocol consisting of an OAT pulse which is time-reversed after a perturbation can give rise to the more fundamental Heisenberg limit (HL) scaling [1]. In the HL, precision improves proportionally to the number of atoms. This remains true even when considering experimental limitations that further reduce the metrological gain (increasing the distance to the HL but not the scaling). For example, photon scattering into free space when using light-mediated interactions to implement one-axis twisting induces contrast loss in the measured signal.

In our work, we generalize the time-reversed OAT approach by considering a short pulse sequence of alternating OAT and rotations instead of a single OAT pulse. By doing so, we can optimize the precision and minimize the contrast loss. While our proposed method can be applied to any existing OAT experiment, we will focus our discussion on the potential implementation in an optical lattice clock atom experiment, where the OAT is created by cavity feedback.

[1] S. Colombo et al, Time-reversal-based quantum metrology with many-body entangled states, arXiv:2106.03754 (2021).   

Extensions of One Axis Twisting to more than One Degree of Freedom

The creation and manipulation of quantum entanglement is central to improving precision measurements. A principal method of generating entanglement for use in atomic interferometry is the process of spin squeezing, whereupon the states become more sensitive to SU(2) rotations. This entanglement is typically generated via one axis twisting (OAT), where a many particle entangled state of one degree of freedom is generated by a non-linear Hamiltonian. We introduce a straightforward extension of OAT that creates squeezing and entanglement across two distinct degrees of freedom. We present this extension in the physical context of entanglement between collective atomic dipoles, and discrete collective momentum states. Our method may be considered as an SU(4) extension of the typical SU(2) one axis twisting. The states therefore prepared by this system are sensitive to SU(4) rotations, and therefore are a potential platform for realizing more intricate measurement schemes.   

Quantum Fisher Information of Schrödinger Cat States

A general expression for the quantum Fisher information (QFI) of atomic Schrödinger cat states is presented. We analyze the dependence of the QFI on the cat state parameters and demonstrate a possibility to achieve the Heisenberg limit scaling of the Ramsey interferometric measurements. Interplay between non-classical correlations between atoms and maximization of QFI of the cat states is discussed.   

Fundamental limits of pulsed quantum light spectroscopy

Quantum light spectroscopy is an emerging field wherein the quantum nature of light is exploited to reveal information about the properties of matter. Although there is evidence that spectroscopy with quantum light may have certain advantages compared to classical spectroscopic methods, this advantage has not been rigorously assessed. 

We use quantum estimation theory to identify the ultimate limit in the precision of estimating parameters of a matter system when probed by a (travelling) pulse of quantum light. Concretely, we consider the estimation of the dipole moment of a two-level atom interacting with different quantum states of quantum light, such as squeezed and entangled light, and compare their performance. We then study the attainability of the quantum limit. This should allow the identification of optimal quantum light spectroscopy setups.   

A geometric perspective: experimental evaluation of the quantum Cramer-Rao bound

Quantum parameter estimation plays a central role in quantum metrology. Its ultimate precision limit is known as the quantum Cramer-Rao bound. In multi-parameter estimation, the quantum Cramer-Rao bound is usually not saturated due to incompatibility of observables in quantum physics. In this work, we explore the connection between multi-parameter estimation and quantum geometry, and provide experimental evaluation of the Cramer-Rao bound through geometric measurements. A concrete example of estimating two (three) parameters in a spin-1/2 (spin-1) system is analyzed in detail, where fundamental uncertainty principles prevent saturating the Cramer-Rao bound. We measure the quantum fisher information and Berry curvature, and for the first time, experimentally extract the attainable Cramer-Rao bound for three-parameter estimations.   

Harnessing non-adiabatic excitations for quantum technological tasks

Non-adiabatic excitations are usually considered detrimental in many scenarios, and consequently several approaches have been developed to circumvent their formation. In contrast, here we show that non-adiabatic excitations formed because of the vanishing energy gap at a quantum critical point can be controlled and harnessed to perform certain tasks advantageously. Our results highlight the interplay between quantum thermodynamics and metrology with critical nonequilibrium dynamics.   

Correlated many-body noise and emergent 1/f behavior

Fluctuating electric fields emanating from surfaces are a major possible source of decoherence in a number of quantum applications, including trapped ions and near-surface NV diamond qubits. We show that at low temperatures, due to superradiant decay, phonon-induced excitation exchange between adsorbed atoms can counterintuitively mitigate the electric field noise. This contrasts with perhaps the anticipated behavior of corrrelated dynamics amplifying detrimental noise. We derive an exact mapping between the noise spectrum of N interacting fluctuators with M vibrational levels to (N+M-1 \choose N)-1 noninteracting two-level dipoles. The anharmonic interaction of the fluctuators with the surface is semiempirical and physically motivated. This anharmonicity affects the noise spectral power intensity at higher temperatures which we simulate numerically. We describe conditions for which the ubiquitous 1/f noise emerges naturally from the coupled dynamics of, remarkbly, identical fluctuators and whose behavior depends critically on correlation among the fluctuators. We believe this work constitutes the first derivation of correlated superradiant noise and emergent 1/f behavior.   

Single-shot Coherent-State Optical Phase Estimation with Adaptive Photon Counting Measurements

Single-shot phase estimation for coherent states has a wide variety of applications for quantum information sciences including quantum metrology, enhanced quantum sensing, and quantum optics. The optimal measurement for phase estimation corresponds to the canonical phase measurement, which minimizes the error of phase estimators. However, physical implementations of the canonical phase measurement for the optical phase are unknown. Here, we investigate a practical realization of non-Gaussian measurements based on adaptive photon-counting and optimized displacements operations. We show that the optimization of coherent displacement operations by a suitable cost function, such as mutual information, allows these non-Gaussian measurements to surpass the standard heterodyne limit and outperform adaptive homodyne measurements. We numerically show that adaptive photon counting measurements maximizing information gain approach the canonical phase measurement in the asymptotic limit with a high convergence rate.

    

Inversion interferometry for resolving point sources in real microscopes

Modal imaging can provide unprecedented resolution for imaging point sources, such as single-molecule fluorescent tags that are used to study biological samples. Theoretical work has shown that modal imaging can approach the quantum limits in optical resolution [1],  albeit assuming highly idealized measurements described by complex quantum operators. To make the potential of quantum measurements available for super-resolution microscopy it is imperative to understand the critical parameters in optical systems for realizing such quantum measurements under realistic conditions. Our efforts focus on understanding these critical parameters and developing an optical system for super-resolving two incoherent point sources (i.e. fluorophore tags) for the study of biological samples. We use a Mach-Zehnder interferometer with optical field inversion to realize image inversion interferometry, in principle allowing for near-optimal imaging of point sources.  We use laser light collimated with a microscope objective to mimic point sources imaged in a microscope. We investigate different methods for image inversion and the effects of aberrations and source bandwidth in the interference visibility.  In a second stage will use this setup with a fluorescence microscope, allowing measurements of sub-diffraction limit sized fluorescent beads, single-molecule fluorescence and finally, protein organization and dynamics in biological samples.

[1] M. Tsang, et al., Phys. Rev. X 6, 031033 (2016)