Subdiffraction-Limited Quantum Imaging within a Living Cell

We report both subdiffraction-limited quantum metrology and quantum-enhanced spatial resolution for the first time in a biological context. Nanoparticles are tracked with quantum-correlated light as they diffuse through an extended region of a living cell in a quantum-enhanced photonic-force microscope. This allows spatial structure within the cell to be mapped at length scales down to 10 nm. Control experiments in water show a 14% resolution enhancement compared to experiments with coherent light. Our results confirm the long-standing prediction that quantum-correlated light can enhance spatial resolution at the nanoscale and in biology. Combined with state-of-the-art quantum light sources, this technique provides a path towards an order of magnitude improvement in resolution over similar classical imaging techniques.

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Quantum physics could enable exciting new applications in computing, encryption, and measurement. When applied to imaging, quantum effects can be utilized to overcome classical imaging constraints, such as those posed by noise and diffraction. This will be particularly significant in biology: Since many subcellular structures have nanometer-size scales, surpassing the diffraction limit would be beneficial to observe key details of a living cell. However, until now, no demonstration of quantum-enhanced resolution in biological imaging has been reported. In this paper, we demonstrate a new approach to quantum imaging that allows mapping subcellular structures with a spatial resolution of about 10 nanometers.

Our method is based on the use of quantum-squeezed states of light in photonic force microscopy (PFM). PFM is an imaging method in which a nanoscale particle is embedded in a cell and moved with optical tweezers to probe the cellular structure in vivo. By tracking the probe motion as it drifts through an extended region of the cell, a spatial map of the viscous and elastic properties of the cellular cytoplasm can be constructed. The quantum advantage stems from the fact that the resolution of PFM along the direction of particle motion depends on the measurement’s signal-to-noise ratio, which limits the precision with which the particle position can be determined. By utilizing squeezed states of light—which are engineered to have better noise properties than classical light—we were thus able to enhance the spatial resolution of the technique.

The method was applied to image one-dimensional profiles of yeast cells. The comparison with controlled experiments with classical light revealed that squeezed light could improve the resolution by 14%. If combined with state-of-the-art squeezed light sources, we envision that this method could lead to an order-of-magnitude enhancement, potentially allowing angstrom resolution in PFM imaging.

Figure 1

Experimental setup. (a) Counterpropagating trapping fields (orange) confine particles between two objectives and are isolated from the detector with polarizing beam splitters (PBS) and wave plates ($\lambda /2$). An imaging field (green) allows visual identification of the particles near the optical trap on a CCD camera. The particle tracking measurement relies only on an amplitude-squeezed local oscillator and an amplitude-modulated probe (red), with the probe providing dark-field illumination, and the particle tracking signal arising from interference between scattered light from the probe and the local oscillator. (b) Measured particle motion, which is the $x$ projection of the 3D motion (shown schematically in the inset). (c) The MSD is constructed with both squeezed light (dark red) and coherent light (gold), and $\alpha$ is determined by fitting this to Eq. (2). The classical and squeezed example traces here both yield $\alpha =0.83$. (d) The raw data are divided into 100 ms segments and the value of $\alpha$ established for each (solid dots). The light red shaded region represents the moving mean and standard error with a 0.5-s width. (e) The normalized power spectral density (PSD) shows that squeezing suppresses the noise floor by 2.4 dB.

Figure 2

1D profiles of $\alpha$. Each circle represents a single measurement of $\alpha$ versus $x$ using a 100-ms set of data. The shaded regions represent the running mean and standard error with 10-nm resolution (thick black bar). Each profile is recorded minutes apart to allow the particle time to diffuse to different regions of the cell with qualitatively different spatial structures. The particle confinement is greatest where $\alpha$ is lowest, such as the dip about 40 nm in (b), and the particle movement is most free when $\alpha$ is highest, such as the peak at $-55\mathrm{nm}$ in (d). To verify that the changes in $\alpha$ are spatial, correlations between sequential measurements of $\alpha (x)$ are analyzed for three sets of data in (e). The circles are experimentally determined correlations between a series of measurements, which are well fitted by the predicted relation (lines) explained in the Supplemental Material, Sec. S1 [38]. By fitting data to this theory, the characteristic time $T_c$ for the particle to diffuse into uncorrelated regions of the cell can be determined. Note that the decay in correlation restricts the duration over which $\alpha (x)$ profiles can be constructed. Although the characteristic times found here are in the range of 0.1 s, correlations are found to persist for sufficient time to construct the 10-s $\alpha (x)$ profiles shown here.

Figure 3

Characterization of the spatial resolution. To calibrate the resolution enhancement achieved here, a profile of $\alpha (x)$ is constructed by tracking particles in water. The individual measurements are shown in (a), while (b) shows the corresponding moving mean and standard error calculated over a 200-nm range with spatial resolution of 2, 10, and 50 nm. The data closely follow the expected $\alpha =1$ result (horizontal line). (c), The ratio of spatial resolutions with squeezed and coherent light is shown as a function of contrast in $\alpha$. The $\alpha$ contrast values shown are normalized into units of $\mathrm{Hz}{}^{-1/2}$ to account for the improvement in absolute contrast as data are accumulated. For a fixed contrast, the spatial resolution achievable with squeezing ($R_{\mathrm{sqz}}$) is improved by approximately 14% when compared to coherent light ($R_0$). The absolute spatial resolution achievable using squeezed light is plotted in the inset. Since the number of points being averaged is proportional to the spatial resolution, the sensitivity scales as the inverse square root of spatial resolution until the averaging window width becomes comparable to the spatial range of the measured data.