Photon Shot Noise Research Articles

The “Squeeze Laser”

The level of quantum noise in measurements is bounded from below by the Heisenberg uncertainty principle, but it can be unequally distributed between two non-commuting observables — it can be “squeezed”. Since 2019, all gravitational-wave observatories have been using squeezed light for increasing the astronomical reach. Squeezed laser light is efficiently produced by degenerate parametric down-conversion in a nonlinear crystal located inside an optical resonator. A spontaneously generated initial pair of indistinguishable photons is amplified to a squeezed vacuum state. Overlapped with bright coherent light, the photo electric measurement shows a sub-Poissonian photon statistics. Squeezed states have ample applications in nonlocal quantum sensing, device-independent quantum key distribution, and quantum computing. Here, we present our continuous-wave 1550 nm ‘squeeze laser’ with a footprint of 80 cm × 80 cm. The well-defined output beam has an interference contrast of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gtrsim 99\%$</tex-math></inline-formula> with an overlapped 10 mW beam being in an almost perfect TEM00 mode. The interference result shows 13 dB squeezing of the photon shot noise in balanced detection.

Front Cover: Magneto‐Optical Sensing Beyond the Shot Noise Limit (Adv. Quantum Technol. 1/2022)

Classical magneto-optical microscopies are workhorse tools for materials characterization, but they are fundamentally limited in sensitivity by the photon shot noise limit. Quantum mechanical light sources guarantee that the aforementioned “standard quantum limit” is beaten. In article number 2100107, Yun-Yi Pai, Raphael C. Pooser, Benjamin J. Lawrie, and co-workers describe quantum enhanced magneto-optical Kerr effect measurements that are accessible with today's quantum optical resources – an optical parametric amplifier. This approach to quantum sensing of quantum materials enables 10 nrad/√Hz sensitivity at temperatures well below 100 mK. [Cover design by Yun-Yi Pai]

Reducing Number Fluctuations in an Ultracold Atomic Sample Using Faraday Rotation and Iterative Feedback

We demonstrate a method to reduce number fluctuations in an ultracold atomic sample using real-time feedback. By measuring the Faraday rotation of an off-resonant probe laser beam with a pair of avalanche photodetectors in a polarimetric setup, we produce a proxy for the number of atoms in the sample. We iteratively remove a fraction of the excess atoms from the sample to converge on a target proxy value in a way that is insensitive to environmental perturbations and robust to errors in light polarization. Using absorption imaging for out-of-loop verification, we demonstrate a reduction in the number fluctuations from $3\mathrm{%}$ to $0.45\mathrm{%}$ for samples at a temperature of $16.4\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{K}$ over the time scale of several hours, which is limited by temperature fluctuations, beam-pointing noise, and photon shot noise.

Line-Edge Roughness from Extreme Ultraviolet Lithography to Fin-Field-Effect-Transistor: Computational Study.

Although extreme ultraviolet lithography (EUVL) has potential to enable 5-nm half-pitch resolution in semiconductor manufacturing, it faces a number of persistent challenges. Line-edge roughness (LER) is one of critical issues that significantly affect critical dimension (CD) and device performance because LER does not scale along with feature size. For LER creation and impacts, better understanding of EUVL process mechanism and LER impacts on fin-field-effect-transistors (FinFETs) performance is important for the development of new resist materials and transistor structure. In this paper, for causes of LER, a modeling of EUVL processes with 5-nm pattern performance was introduced using Monte Carlo method by describing the stochastic fluctuation of exposure due to photon-shot noise and resist blur. LER impacts on FinFET performance were investigated using a compact device method. Electric potential and drain current with fin-width roughness (FWR) based on LER and line-width roughness (LWR) were fluctuated regularly and quantized as performance degradation of FinFETs.

Enhancement of electromagnetically induced transparency based Rydberg-atom electrometry through population repumping

We demonstrate improved sensitivity of Rydberg electrometry based on electromagnetically induced transparency (EIT) with a ground state repumping laser. Though there are many factors that limit the sensitivity of radio frequency field measurements, we show that repumping can enhance the interaction strength while avoiding additional Doppler or power broadening. Through this method, we nearly double the EIT amplitude without an increase in the width of the peak. A similar increase in amplitude without the repumping field is not possible through simple optimization. We also establish that one of the key limits to detection is the photon shot noise of the probe laser. We show an improvement on the sensitivity of the device by a factor of nearly 2 in the presence of the repump field.

Squeezed-Light Enhancement and Backaction Evasion in a High Sensitivity Optically Pumped Magnetometer.

We study the effect of optical polarization squeezing on the performance of a sensitive, quantum-noise-limited optically pumped magnetometer. We use Bell-Bloom (BB) optical pumping to excite a ^{87}Rb vapor containing 8.2×10^{12} atoms/cm^{3} and Faraday rotation to detect spin precession. The sub-pT/sqrt[Hz] sensitivity is limited by spin projection noise (photon shot noise) at low (high) frequencies. Probe polarization squeezing both improves high-frequency sensitivity and increases measurement bandwidth, with no loss of sensitivity at any frequency, a direct demonstration of the evasion of measurement backaction noise. We provide a model for the quantum noise dynamics of the BB magnetometer, including spin projection noise, probe polarization noise, and measurement backaction effects. The theory shows how polarization squeezing reduces optical noise, while measurement backaction due to the accompanying ellipticity antisqueezing is shunted into the unmeasured spin component. The method is compatible with high-density and multipass techniques that reach extreme sensitivity.

Self-Bayesian aberration removal via constraints for ultracold atom microscopy.

High-resolution imaging of ultracold atoms typically requires custom high numerical aperture (NA) optics, as is the case for quantum gas microscopy. These high NA objectives involve many optical elements, each of which contributes to loss and light scattering, making them unsuitable for quantum backaction limited "weak" measurements. We employ a low-cost high NA aspheric lens as an objective for a practical and economical-although aberrated-high-resolution microscope to image 87Rb Bose-Einstein condensates. Here, we present a methodology for digitally eliminating the resulting aberrations that is applicable to a wide range of imaging strategies and requires no additional hardware. We recover nearly the full NA of our objective, thereby demonstrating a simple and powerful digital aberration correction method for achieving optimal microscopy of quantum objects. This reconstruction relies on a high-quality measure of our imaging system's even-order aberrations from density-density correlations measured with differing degrees of defocus. We demonstrate our aberration compensation technique using phase-contrast imaging, a dispersive imaging technique directly applicable to quantum backaction limited measurements. Furthermore, we show that our digital correction technique reduces the contribution of photon shot noise to density-density correlation measurements which would otherwise contaminate the desired quantum projection noise signal in weak measurements.

Advanced high dynamic range fluorescence microscopy with Poisson noise modeling and integrated edge-preserving denoising

In the last decades, fluorescence microscopy has evolved into a powerful tool for modern cell biology and immunology. However, while modern fluorescence microscopes allow to study processes at subcellular level, the informative content of the recorded images is frequently constrained by the limited dynamic range of the camera mounted to the optical system. In addition, the quality of acquired images is generally affected by the typically low-light conditions that lead to comparatively high levels of noise in the data. Addressing these issues, we introduce a variational method for high dynamic range (HDR) imaging in the context of fluorescence microscopy that explicitly accounts for the Poisson statistics of the unavoidable signal-dependent photon shot noise and complements HDR image reconstruction with edge-preserving denoising. Since the proposed model contains a weight function to confine the influence of under- and overexposed pixels on the result, we briefly discuss the choice of this function. We evaluate our approach by showing HDR results for real fluorescence microscopy exposure sequences acquired with the recently developed MACSimaTM System for fully automated cyclic immunofluorescence imaging. These results are obtained using a first-order primal-dual implementation. On top of this, we also provide the corresponding saddle-point and dual formulations of the problem.

Helium-4 magnetometers for room-temperature biomedical imaging: toward collective operation and photon-noise limited sensitivity.

Optically-pumped magnetometers constitute a valuable tool for imaging biological magnetic signals without cryogenic cooling. Nowadays, numerous developments are being pursued using alkali-based magnetometers, which have demonstrated excellent sensitivities in the spin-exchange relaxation free (SERF) regime that requires heating to >100 °C. In contrast, metastable helium-4 based magnetometers work at any temperature, which allows a direct contact with the scalp, yielding larger signals and a better patient comfort. However former 4He magnetometers displayed large noises of >200 fT/Hz1/2 with 300-Hz bandwidth. We describe here an improved magnetometer reaching a sensitivity better than 50 fT/Hz1/2, nearly the photon shot noise limit, with a bandwidth of 2 kHz. Like other zero-field atomic magnetometers, these magnetometers can be operated in closed-loop architecture reaching several hundredths nT of dynamic range. A small array of 4 magnetometers operating in a closed loop has been tested with a successful correction of the cross-talks.

Accurate Determination of Conversion Gains of SVOM VT CCDs Based on a Signal-Dependent Charge-Sharing Mechanism

The signal-variance method and the photon transfer curve method are the most valuable tools for calculating the conversion gains of charge-coupled device (CCD) detectors. This paper describes the phenomena that arise in the conversion gain measurements of space multi-band variable object monitor (SVOM) visible telescope (VT) CCDs, where the results of the signal-variance method increase with the image gray level, and the results of the photon transfer curve method appear with nonlinearity, which is caused by the signal-dependent charge sharing mechanism of back-illuminated CCDs. A numerical simulation model based on random variables was adopted to analyze the influence of the mechanism on the gain determination. The model simulates all the signals and noise in the flat field image, including the photon signal and photon-shot noise, readout noise, fixed pattern noise, and the signal-dependent charge-sharing signal, and it demonstrated agreement with the experimental data. Then, we proposed a quadratic polynomial curve-fitting formula for the photon transfer curve, and we quantitatively analyzed the relationship between the fitting coefficients and the gain, the signal-dependent charge sharing coefficient, and the full well capacity using the control variable method. Finally, the formula was used to accurately determine the conversion gains of SVOM VT CCDs.

Online adaptive quantum characterization of a nuclear spin

The characterization of quantum systems is both a theoretical and technical challenge. Theoretical because of the exponentially increasing complexity with system size and the fragility of quantum states under observation. Technical because of the requirement to manipulate and read out individual atomic or photonic elements. Adaptive methods can help to overcome these challenges by optimizing the amount of information each measurement provides and reducing the necessary resources. Their implementation, however, requires fast-feedback and complex processing algorithms. Here, we implement online adaptive sensing with single spins and demonstrate close to photon shot noise limited performance with high repetition rate, including experimental overheads. We further use fast feedback to determine the hyperfine coupling of a nuclear spin to the nitrogen-vacancy sensor with a sensitivity of 445,{mathrm{nT}}{sqrt{mathrm{Hz}}}^{- 1}. Our experiment is a proof of concept that online adaptive techniques can be a versatile tool to enable faster characterization of the spin environment.

Cavity-enhanced microwave readout of a solid-state spin sensor

Overcoming poor readout is an increasingly urgent challenge for devices based on solid-state spin defects, particularly given their rapid adoption in quantum sensing, quantum information, and tests of fundamental physics. However, in spite of experimental progress in specific systems, solid-state spin sensors still lack a universal, high-fidelity readout technique. Here we demonstrate high-fidelity, room-temperature readout of an ensemble of nitrogen-vacancy centers via strong coupling to a dielectric microwave cavity, building on similar techniques commonly applied in cryogenic circuit cavity quantum electrodynamics. This strong collective interaction allows the spin ensemble’s microwave transition to be probed directly, thereby overcoming the optical photon shot noise limitations of conventional fluorescence readout. Applying this technique to magnetometry, we show magnetic sensitivity approaching the Johnson–Nyquist noise limit of the system. Our results pave a clear path to achieve unity readout fidelity of solid-state spin sensors through increased ensemble size, reduced spin-resonance linewidth, or improved cavity quality factor.

Probe noise characteristics of the spin-exchange relaxation-free (SERF) magnetometer.

In the spin-exchange relaxation-free (SERF) magnetometer, the probe noise is a consequential factor affecting the gradiometric measurement sensitivities. In this paper, we proposed a new characteristics model of the probe noise based on noise separation. Different from noise analysis on single noise source, we considered most of the noise sources influencing the probe system and realized noise sources level measurement experimentally. The results demonstrate that the major noise type changes with the signal frequency. Below 10 Hz, the probe noise mainly comes from the sources independent of light intensity such as the vibration, which accounts for more than 50%; while at 30 Hz, the photon shot noise and the magnetic noise are the main origins, with proportion about 43% and 32%, respectively. Moreover, the results indicate that the optimal probe light intensity with highest sensitivity appears when the response of the magnetic noise is equal to the sum of the electronic noise and half of the shot noise. The optimal intensity gets larger with higher signal frequency. The noise characteristics model could be applied in modulating or differential optical systems and helps sensitivity improvement in SERF magnetometer.

Single-molecule orientation localization microscopy I: fundamental limits.

Precisely measuring the three-dimensional position and orientation of individual fluorophores is challenging due to the substantial photon shot noise in single-molecule experiments. Facing this limited photon budget, numerous techniques have been developed to encode 2D and 3D position and 2D and 3D orientation information into fluorescence images. In this work, we adapt classical and quantum estimation theory and propose a mathematical framework to derive the best possible precision for measuring the position and orientation of dipole-like emitters for any fixed imaging system. We find that it is impossible to design an instrument that achieves the maximum sensitivity limit for measuring all possible rotational motions. Further, our vectorial dipole imaging model shows that the best quantum-limited localization precision is 4%-8% worse than that suggested by a scalar monopole model. Overall, we conclude that no single instrument can be optimized for maximum precision across all possible 2D and 3D localization and orientation measurement tasks.

First Demonstration of 6dB Quantum Noise Reduction in a Kilometer Scale Gravitational Wave Observatory.

Photon shot noise, arising from the quantum-mechanical nature of the light, currently limits the sensitivity of all the gravitational wave observatories at frequencies above one kilohertz. We report a successful application of squeezed vacuum states of light at the GEO 600 observatory and demonstrate for the first time a reduction of quantum noise up to 6.03±0.02 dB in a kilometer scale interferometer. This is equivalent at high frequencies to increasing the laser power circulating in the interferometer by a factor of 4. Achieving this milestone, a key goal for the upgrades of the advanced detectors required a better understanding of the noise sources and losses and implementation of robust control schemes to mitigate their contributions. In particular, we address the optical losses from beam propagation, phase noise from the squeezing ellipse, and backscattered light from the squeezed light source. The expertise gained from this work carried out at GEO 600 provides insight toward the implementation of 10dB of squeezing envisioned for third-generation gravitational wave detectors.

Low-Light Demosaicking and Denoising for Small Pixels Using Learned Frequency Selection

Low-light imaging is a challenging task because of the excessive photon shot noise. Color imaging in low-light is even more difficult because one needs to demosaick and denoise simultaneously. Existing demosaicking algorithms are mostly designed for well-illuminated scenarios, which fail to work with low-light. Recognizing the recent development of small pixels and low read noise image sensors, we propose a learning-based joint demosaicking and denoising algorithm for low-light color imaging. Our method combines the classical theory of color filter arrays and modern deep learning. We use an explicit carrier to demodulate the color from the input Bayer pattern image. We integrate trainable filters into the demodulation scheme to improve flexibility. We introduce a guided filtering module to transfer knowledge from the luma channel to the chroma channels, thus offering substantially more reliable denoising. Extensive experiments are performed to evaluate the performance of the proposed method, using both synthetic datasets and real data. Results indicate that the proposed method offers consistently better performance over the current state-of-the-art, across several standard evaluation metrics.

Shot noise limited soft x-ray absorption spectroscopy in solution at a SASE-FEL using a transmission grating beam splitter.

X-ray absorption near-edge structure (XANES) spectroscopy provides element specificity and is a powerful experimental method to probe local unoccupied electronic structures. In the soft x-ray regime, it is especially well suited for the study of 3d-metals and light elements such as nitrogen. Recent developments in vacuum-compatible liquid flat jets have facilitated soft x-ray transmission spectroscopy on molecules in solution, providing information on valence charge distributions of heteroatoms and metal centers. Here, we demonstrate XANES spectroscopy of molecules in solution at the nitrogen K-edge, performed at FLASH, the Free-Electron Laser (FEL) in Hamburg. A split-beam referencing scheme optimally characterizes the strong shot-to-shot fluctuations intrinsic to the process of self-amplified spontaneous emission on which most FELs are based. Due to this normalization, a sensitivity of 1% relative transmission change is achieved, limited by fundamental photon shot noise. The effective FEL bandwidth is increased by streaking the electron energy over the FEL pulse train to measure a wider spectral window without changing FEL parameters. We propose modifications to the experimental setup with the potential of improving the instrument sensitivity by two orders of magnitude, thereby exploiting the high peak fluence of FELs to enable unprecedented sensitivity for femtosecond XANES spectroscopy on liquids in the soft x-ray spectral region.

Continuous High-Sensitivity and High-Bandwidth Atomic Magnetometer

Here we demonstrate an atomic magnetometer that has a bandwidth of more than 100 kHz and a sensitivity of $180\phantom{\rule{0.2em}{0ex}}\mathrm{fT/}\ensuremath{\surd}\mathrm{Hz}$ at a Fourier frequency of 8 Hz, and $0.7\phantom{\rule{0.2em}{0ex}}\mathrm{nT/}\ensuremath{\surd}\mathrm{Hz}$ at 100 kHz. These sensitivity measurements are achieved at geophysically useful magnetic field magnitudes (approximately $50\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{T}$ inside a three-layer $\ensuremath{\mu}$-metal shield) and are limited by the photon shot noise for frequencies above 8 Hz. This device is based on a nonlinear magneto-optical rotation sensor that is operated with an active feedback to the pump modulation frequency. We present a theoretical description of the response functions of the components in the magnetometer. We show that the range of operation of atomic magnetometers can thus be expanded beyond the conventional high-sensitivity, low-bandwidth domain, to provide a high-linearity, high-bandwidth, and high-sensitivity sensor.

Statistical properties of spontaneous synchrotron radiation with arbitrary degree of coherence

We study turn-by-turn fluctuations in the number of spontaneously emitted photons from an undulator, installed in the Integrable Optics Test Accelerator (IOTA) electron storage ring at Fermilab. A theoretical model is presented, showing the relative contributions due to the discrete nature of light emission and to the incoherent sum of fields from different electrons in the bunch. The model is compared with a previous experiment at Brookhaven and with new experiments we carried out at IOTA. Our experiments focused on the case of a large number of longitudinal and transverse radiation modes, a regime where photon shot noise is significant and the total magnitude of the fluctuations is very small. The experimental and data analysis techniques, required to reach the desired sensitivity, are detailed. We discuss how the model and the experiment provide insights into this emission regime, enable diagnostics of small beam sizes, and improve our understanding of beam lifetime in IOTA.

Spectral characterization of non-Gaussian quantum noise: Keldysh approach and application to photon shot noise

Having accurate tools to describe non-classical, non-Gaussian environmental fluctuations is crucial for designing effective quantum control protocols and understanding the physics of underlying quantum dissipative environments. We show how the Keldysh approach to quantum noise characterization can be usefully employed to characterize frequency-dependent noise, focusing on the quantum bispectrum (i.e., frequency-resolved third cumulant). Using the paradigmatic example of photon shot noise fluctuations in a driven bosonic mode, we show that the quantum bispectrum can be a powerful tool for revealing distinctive non-classical noise properties, including an effective breaking of detailed balance by quantum fluctuations. The Keldysh-ordered quantum bispectrum can be directly accessed using existing noise spectroscopy protocols.