Coherent anti-Stokes Raman scattering is a widely used imaging technique that provides chemical contrast without the need for labels, making it an extremely valuable tool in physics, chemistry, and biology. In this work, we explore its fundamental precision limits by applying tools from quantum information theory. We identify optimal measurement strategies and show that spatial mode demultiplexing–a technique already accessible in current experimental setups–can achieve these quantum limits and, in many situations, improve the sensitivity of conventional intensity measurements. Building on this, we introduce an advanced imaging scheme based on vortex beams, which we predict to enhance the image information in the final quantum state of light and thereby lead to even higher resolution and sensitivity. These findings establish a clear path for enhancing nonlinear imaging techniques using concepts from quantum science, bridging the gap between established microscopy methods and the emerging capabilities of quantum technologies.
Coherent anti-Stokes Raman scattering is a widely used imaging technique that provides chemical contrast without the need for labels, making it an extremely valuable tool in physics, chemistry, and biology. In this work, we explore its fundamental precision limits by applying tools from quantum information theory. We identify optimal measurement strategies and show that spatial mode demultiplexing–a technique already accessible in current experimental setups–can achieve these quantum limits and, in many situations, improve the sensitivity of conventional intensity measurements. Building on this, we introduce an advanced imaging scheme based on vortex beams, which we predict to enhance the image information in the final quantum state of light and thereby lead to even higher resolution and sensitivity. These findings establish a clear path for enhancing nonlinear imaging techniques using concepts from quantum science, bridging the gap between established microscopy methods and the emerging capabilities of quantum technologies.
Nonlinear optical processes are used in biological microscopy to surpass the diffraction limit on resolution, image deeper into brain tissues, and identify biomolecules without exogenous labels. These techniques typically require high optical intensities to increase the strength of the nonlinear interactions, which can perturb native biochemistry and damage or kill living samples. Stimulated Raman scattering (SRS) microscopy visualizes the spatial distribution of molecules using a nonlinear interaction between light and chemically specific molecular vibrations. However, the detection of biomolecules at low concentrations is limited by the total photon dose that can be applied before photodamage alters the sample, and photon shot noise sets the minimum achievable noise floor for most microscopes. Here we demonstrate a cavity-enhanced SRS microscope that is more sensitive than an equivalent conventional SRS microscope by up to 8.3(7) dB in spectroscopy and 8.6(1) dB in cell imaging. These results approach quantum limits on sensitivity and demonstrate that quantum states of light are sufficient but not necessary to enhance the sensitivity of microscopy techniques that are limited by photodamage.
In theoretical investigations, we review several nonlinear optical approaches towards subdiffraction-limited resolution in label-free imaging via coherent anti-Stokes Raman scattering (CARS). Using a density matrix model and numerical integration, we investigate various level schemes and combinations of the light fields that induce CARS along with additional control laser fields. As the key to techniques that gain far-field resolution below the diffraction limit, we identify the inhibition of the buildup of vibrational molecular coherence via saturation or depletion of population (Beeker et al. Opt Express 17:22632–22638, 2009) or the generation of Stark broadening and spatially dependent Rabi sideband generation (Beeker et al. Phys Rev A 81(1), 2010). Depending on the coherence and population decay rates offered by a particular molecular energy level scheme, we identify various different regimes. In the first case, where an additional state (called the control state) and a vibrational state are able to rapidly exchange population via incoherent processes, a prepopulation of the upper vibrational state inhibits the buildup of vibrational coherence. With increasing control laser intensity, this suppresses CARS emission via an incoherent, saturation type of nonlinear process. Using an intense, donut-shaped control laser beam, similar to stimulated emission depletion (STED) microscopy, this can suppress CARS emission from all sample locations except within a subdiffraction-sized range around the central node. Scanning the control beams across the sample provides subdiffraction-limited resolution imaging. An alternative, which does not require a rapid exchange of population with the control state, applies a control beam that only partially depletes the vibrational ground state. Thereby, a CARS point spread function containing a subdiffraction-limited component is generated. Subdiffraction images can then be retrieved through deconvolution. Further approaches are based on the coherent, nonlinear, resonant response of the sample. In this case, CARS signal depletion by Stark splitting of the weakly populated upper vibrational state or the observation of spatially dependent Rabi oscillation may increase the resolution beyond the diffraction limit.
Abstract Stimulated Raman scattering (SRS) is a powerful technique for imaging and spectroscopy, in particular in chemistry and biology. By introducing a full quantum description, we determine the ultimate quantum limits of precision and optimal strategies to approach them within the rigorous framework offered by quantum metrology. This approach reveals optimal uses of squeezed states, and the possibility of enhancing the resolution beyond recent experiments. Our work establishes a basis for approaching quantum precision limits in SRS and integrating nonlinear spectroscopy and imaging with emerging quantum technologies.
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.
We theoretically investigate ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering (CARS) microscopy. We propose a scheme based on ground-state depopulation, which is achieved via a control laser light field incident prior to the CARS excitation light fields. This ground-state depopulation results in a reduced CARS signal generation. With an appropriate choice of spatial beam profiles, the scheme can be used to increase the spatial resolution. Based on the density matrix formalism we calculate the CARS signal generation and find a CARS signal suppression by 75 due to ground-state depletion with a single control light field and by using two control light fields the CARS signal suppression can be enhanced to 94. Additional control light fields will enhance the CARS suppression even further. In case of a single control light field we calculate resulting CARS images using a computer-generated test image including quantum and detector noise and show that the background from the limited CARS suppression can be removed by calculating difference images, yielding subdiffraction-limited resolution where the resolution achievable depends only on the intensity used.
In optical microscopy, as in any biological measurement performed with light, there is a compromise between increasing power to improve resolution and decreasing power to prevent photodamage to the biological structure. Quantum optics allows this compromise to be overcome, enabling improved precision without increased illumination intensity. This thesis demonstrates, for the first time, absolute quantum advantage in microscopy, with a specific focus on Stimulated Raman Scattering (SRS) microscopy.SRS microscopy is a powerful tool widely used in many fields, especially in biomedical sciences. It uses a two-photon process where the light is downshifted in frequency by being absorbed and subsequently inelastically scattered by the intrinsic molecular vibrations in the sample. Each element or molecule has a different response, allowing selective imaging of biological systems. SRS microscopy is particularly useful because it is label-free (no addition of dyes, beads or any implanted tracer), meaning that imaging contrast is achieved without modification of, or interference with, the specimen. Here I present our newly built state-of-the-art shot-noise limited SRS microscope. I also characterize the Raman microscope, describe the developped imaging system and show SRS spectroscopy and imaging of both polystyrene beads and living yeast cells.The quantisation of light introduces a fundamental uncertainty, or quantum noise, in both the amplitude and phase quadratures of an optical field. A squeezed state of light is a state of the optical field where the uncertainty of one of these quadratures is reduced below the quantum noise. Therefore, it provides an approach to reduce the noise level below this quantum noise limit and consequently increases measured signal-to-noise ratio. Here I describe the concepts involved in this technique and present our newly built light squeezer. I characterize the squeezing and show up to -1.3 dB of noise floor reduction for a 6 picosecond pulsed laser, which is the pulse duration that maximises the Raman interaction.In this thesis we apply squeezed states of light in SRS, developping a quantum-enhanced micro- scope. Our SRS Raman intensity noise is ∆I/I ≈ 10^(−7) and the measured quantum efficiency of the built photodiode is η = 72%. In this proof of principle we show a reduction of the noise floor of at least 13% below the quantum noise limit for Raman imaging of polystyrene beads and living yeast cells. This enhancement allowed us to resolve the cell membrane where with conventional microscope would be unresolvable. It also allowed sub-micron spatial resolution. The improved image contrast and reduced imaging time, while avoiding photodamage in the sample, surpasses the current state-of-the-art Raman microscopes and opens opportunities for new discoveries in biophysics.