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arXiv:2309.00207 · Advanced Quantum Technologies

Quantum Nonlinear Spectroscopy via Correlations of Weak Faraday‐Rotation Measurements

Brian Chung Hang Cheung, Ren‐Bao Liu

Published Jun 16, 2024• 3 citations
arXivHTMLPDF

Abstract

Abstract The correlations of fluctuations are key to studying fundamental quantum physics and quantum many‐body dynamics. They are also useful information for understanding and combating decoherence in quantum technology. Nonlinear spectroscopy and noise spectroscopy are powerful tools to characterize fluctuations, but they can access only very few among the many types of higher‐order correlations. A systematic quantum sensing approach, called quantum nonlinear spectroscopy (QNS), is recently proposed for extracting arbitrary types and orders of time‐ordered correlations, using sequential weak measurement via a spin quantum sensor. However, the requirement of a central spin as the quantum sensor limits the versatility of the QNS since usually a central spin interacts only with a small number of particles in proximity and the measurement of single spins needs stringent conditions. Here, the aim is to employ the polarization (a pseudo‐spin) of a coherent light beam as a quantum sensor for QNS. After interacting with a target system (such as a transparent magnetic material), the small Faraday rotation of the linearly polarized light can be measured, which constitutes a weak measurement of the magnetization in the target system. Using a Mach–Zehnder interferometer with a designed phase shift, one can post‐select the effects of the light–material interaction to be either a quantum evolution or a quantum measurement of the material magnetization. This way, the correlated difference photon counts of a certain number of measurement shots, each with a designated interference phase, can be made proportional to a certain type and order of correlations of the magnetic fluctuations in the material. The analysis of the signal‐to‐noise ratios shows that the second‐order correlations are detectable in general under realistic conditions and higher‐order correlations are significant when the correlation lengths of the fluctuations are comparable to the laser spot size (such as in systems near the critical points). Since the photon sensor can interact simultaneously with many particles and interferometry is a standard technique, this protocol of QNS is advantageous for studying quantum many‐body systems.

DOI
10.1002/qute.202300286

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Abstract The correlations of fluctuations are key to studying fundamental quantum physics and quantum many‐body dynamics. They are also useful information for understanding and combating decoherence in quantum technology. Nonlinear spectroscopy and noise spectroscopy are powerful tools to characterize fluctuations, but they can access only very few among the many types of higher‐order correlations. A systematic quantum sensing approach, called quantum nonlinear spectroscopy (QNS), is recently proposed for extracting arbitrary types and orders of time‐ordered correlations, using sequential weak measurement via a spin quantum sensor. However, the requirement of a central spin as the quantum sensor limits the versatility of the QNS since usually a central spin interacts only with a small number of particles in proximity and the measurement of single spins needs stringent conditions. Here, the aim is to employ the polarization (a pseudo‐spin) of a coherent light beam as a quantum sensor for QNS. After interacting with a target system (such as a transparent magnetic material), the small Faraday rotation of the linearly polarized light can be measured, which constitutes a weak measurement of the magnetization in the target system. Using a Mach–Zehnder interferometer with a designed phase shift, one can post‐select the effects of the light–material interaction to be either a quantum evolution or a quantum measurement of the material magnetization. This way, the correlated difference photon counts of a certain number of measurement shots, each with a designated interference phase, can be made proportional to a certain type and order of correlations of the magnetic fluctuations in the material. The analysis of the signal‐to‐noise ratios shows that the second‐order correlations are detectable in general under realistic conditions and higher‐order correlations are significant when the correlation lengths of the fluctuations are comparable to the laser spot size (such as in systems near the critical points). Since the photon sensor can interact simultaneously with many particles and interferometry is a standard technique, this protocol of QNS is advantageous for studying quantum many‐body systems.
Conventional nonlinear spectroscopy, which use classical probes, can only access a limited set of correlations in a quantum system. Here we demonstrate that quantum nonlinear spectroscopy, in which a quantum sensor and a quantum object are first entangled and the sensor is measured along a chosen basis, can extract arbitrary types and orders of correlations in a quantum system. We measured fourth-order correlations of single nuclear spins that cannot be measured in conventional nonlinear spectroscopy, using sequential weak measurement via a nitrogen-vacancy center in diamond. The quantum nonlinear spectroscopy provides fingerprint features to identify different types of objects, such as Gaussian noises, random-phased AC fields, and quantum spins, which would be indistinguishable in second-order correlations. This work constitutes an initial step toward the application of higher-order correlations to quantum sensing, to examining the quantum foundation (by, e.g., higher-order Leggett-Garg inequality), and to studying quantum many-body physics.
Central spin decoherence is useful for detecting many-body physics in environments and moreover, the spin echo control can remove the effects of static thermal fluctuations so that the quantum fluctuations are revealed. The central spin decoherence approach, however, is feasible only in some special configurations and often requires uniform coupling between the central spin and individual spins in the baths, which are very challenging in experiments. Here, by making analogue between central spin decoherence and depolarization of photons, we propose a scheme of Faraday rotation echo spectroscopy (FRES) for studying quantum fluctuations in interacting spin systems. The echo control of the photon polarization is realized by flipping the polarization with a birefringence crystal. The FRES, similar to spin echo in magnetic resonance spectroscopy, can suppress the effects of the static magnetic fluctuations and therefore reveal dynamical magnetic fluctuations. We apply the scheme to a rare-earth compound LiHoF4 and calculate the echo signal, which is related to the quantum fluctuations of the system. We observe enhanced signals at the phase boundary. The FRES should be useful for studying quantum fluctuations in a broad range of spin systems, including cold atoms, quantum dots, solid-state impurities, and transparent magnetic materials.
Abstract Magneto‐optical sensors including spin noise spectroscopies and magneto‐optical Kerr effect microscopies are now ubiquitous tools for materials characterization that can provide new understanding of spin dynamics, hyperfine interactions, spin‐orbit interactions, and charge‐carrier g‐factors. Both interferometric and intensity‐difference measurements can provide photon‐shot‐noise‐limited sensitivity, but further improvements in sensitivity with classical resources require either increased laser power that can induce unwanted heating and electronic perturbations or increased measurement times that can obscure out‐of‐equilibrium dynamics and slow experimental throughput. Proof‐of‐principle measurements have already demonstrated quantum enhanced spin noise measurements with a squeezed readout field that are likely to be critical to the nonperturbative characterization of spin excitations in quantum materials that emerge at low temperatures. Here, a truncated nonlinear interferometric readout for low‐temperature magneto‐optical Kerr effect and related magneto‐optical microscopies that is accessible with today's quantum optical resources is proposed. 10 sensitivity is achievable with optical power as small as 1 µW. As a result, measurements may be performed at temperatures as low as 83 mK in commercially available dilution refrigerators. This combination of high sensitivity and low operating temperature is impossible to achieve with any classical measurement. The quantum advantage for the proposed measurements persists even in the limit of large loss and small squeezing parameters.
Quantum correlations are key information about the structures and dynamics of quantum many-body systems. There are many types of high-order quantum correlations with different time orderings, but only a few of them are accessible to the existing detection methods. Recently, a quantum-sensing approach based on sequential weak measurement was proposed to selectively extract arbitrary types of correlations. However, its experimental implementation is still elusive. Here we demonstrate the extraction of arbitrary types of quantum correlations. We generalized the original weak measurement scheme to a protocol using synthesized quantum channels, which can be applied to more universal scenarios including both single and ensemble quantum systems. In this quantum channel method, various controls on the sensors are superimposed to select the sensor-target evolution along a specific path for measuring a desired quantum correlation. Using the versatility of nuclear magnetic resonance techniques, we successfully extract the second- and fourth-order correlations of a nuclear-spin target by another nuclear-spin sensor. The full characterization of quantum correlations provides a new tool for understanding quantum many-body systems, exploring fundamental quantum physics, and developing quantum technologies.
Correlations of fluctuations are the driving forces behind the dynamics and thermodynamics in quantum many-body systems. For qubits embedded in a quantum bath, the correlations in the bath are key to understanding and combating decoherence-a critical issue in quantum information technology. However, there is no systematic method for characterizing the many-body correlations in quantum baths beyond the second order or the Gaussian approximation. Here we present a scheme to characterize the correlations in a quantum bath to arbitrary order. The scheme employs a weak measurement of the bath via the projective measurement of a central system. The bath correlations, including both the "classical" and the "quantum" parts, can be reconstructed from the correlations of the measurement outputs. The possibility of full characterization of many-body correlations in a quantum bath forms the basis for optimizing quantum control against decoherence in realistic environments, for studying the quantum characteristics of baths, and for the quantum sensing of correlated clusters in quantum baths.
Techniques for making quantum-limited nonlinear measurements have attracted a great deal of recent attention because they allow a measurement sensitivity that improves as the number of measuring particles (e.g. photons) increases faster than an equivalent linear measurement. This super-Heisenberg scaling was recently demonstrated in a proof-of-principle experiment [1], in which a measurement Hamiltonian of the form studied in Ref. [2] was carefully engineered by exploiting nonlinearities in a Faraday rotation based measurement of atomic spins. However, despite the improved scaling, the absolute measurement sensitivity in this experiment remained significantly worse than a linear Faraday rotation measurement due to the weak atom-light coupling strength of the nonlinear Faraday rotation, and effect of higher-order nonlinearities at large photon number. This leaves open the question of whether it is possible to make a nonlinear measurement that both benefits from the improved scaling, and competes in absolute sensitivity with linear techniques.