Thermal Noise Limit Research Articles

First upper limits on the 21 cm signal power spectrum from cosmic dawn from one night of observations with NenuFAR (Corrigendum)

The redshifted 21 cm signal from neutral hydrogen is a direct probe of the physics of the early universe and has been an important science driver of many present and upcoming radio interferometers. In this study we use a single night of observations with the New Extension in Nan cay Upgrading LOFAR (NenuFAR) to place upper limits on the 21 cm power spectrum from cosmic dawn at a redshift of $z$ = 20.3. NenuFAR is a new low-frequency radio interferometer, operating in the 10--85 MHz frequency range, currently under construction at the Nan cay Radio Observatory in France. It is a phased array instrument with a very dense $u coverage at short baselines, making it one of the most sensitive instruments for 21 cm cosmology analyses at these frequencies. Our analysis adopts the foreground subtraction approach, in which sky sources are modeled and subtracted through calibration and residual foregrounds are subsequently removed using Gaussian process regression. The final power spectra are constructed from the gridded residual data cubes in the $u plane. Signal injection tests are performed at each step of the analysis pipeline, the relevant pipeline settings are optimized to ensure minimal signal loss, and any signal suppression is accounted for through a bias correction on our final upper limits. We obtain a best 2sigma upper limit of $2.4 mK $ at $z$ = 20.3 and $k$ = 0.041 $h\ cMpc $. We see a strong excess power in the data, making our upper limits two orders of magnitude higher than the thermal noise limit. We investigate the origin and nature of this excess power and discuss further improvements to the analysis pipeline that can potentially mitigate it and consequently allow us to reach thermal noise sensitivity when multiple nights of observations are processed in the future.

Thermal-noise-limited ultra-stable laser operated at 698 nm

Ultra-stable lasers are indispensable in high precision measurements. Here we demonstrate an ultra-stable laser system that reaches the thermal noise limit of the optical cavity for the 698 nm clock transition laser of strontium atomic optical clock. This is achieved by locking the frequency of the external-cavity diode laser (ECDL) to a full ULE optical cavity with a length of 10 cm. By suppressing noise such as temperature disturbance, vibration, residual amplitude modulation (RAM), and fiber phase noise, the measured laser linewidth is less than 0.9 Hz. After subtracting the linear drift of 60 mHz/s, the frequency instability of the beat signal reaches 1.2 × 10−15 at 1 s averaging time, which is close to the thermal noise limit of the optical cavity.

Feature correlation method for image reconstruction evaluation in under-sampled scanning probe microscopy

We introduce an advanced feature-correlation approach for evaluating the accuracy of data completion in scanning probe microscopy (SPM). Our method utilizes characteristic patterns from conventional SPM images and their reconstructions via data interpolation. We develop a refined comparative evaluation algorithm based on correlation coefficients. This algorithm provides a precise assessment by effectively addressing SPM-specific distortions such as thermal drift, feedback error, and noise limitations often overlooked by traditional metrics such as peak signal-to-noise ratio and structural similarity index measure. The effectiveness of our approach is demonstrated through its application in high-resolution and extensive scanning tunneling microscopy assessments.

A torsion balance as a weak-force testbed for novel optical inertial sensors

Torsion balances (TBs) are versatile instruments known for their ability to measure tiny forces and accelerations with high precision. We are currently commissioning a new TB facility to support the development and testing of novel optical inertial sensor units for future gravity-related space missions. Here, we report on the status of our apparatus and present first sensitivity curves that demonstrate acceleration and torque sensitivities of 5⋅10−11ms−2 and 1⋅10−12NmHz−1 at frequencies around 4mHz , respectively. Capacitive sensors and optical levers measure the dynamics of the system with a displacement sensitivity of down to 9⋅10−10mHz−1 for the former and 2⋅10−11mHz−1 for the latter. Combining the readout of the suspended inertial member (IM) with environmental sensor signals, the system is characterized, and limiting noise sources are identified. We find that, in particular, the coupling of ambient seismic motion is limiting over a broad frequency range and show that due to its high susceptibility to ground motion, our TB is also a promising platform for exploring ground motion sensing in multiple degrees of freedom. Future upgrades will focus on mitigating seismic noise by controlling the torsion fiber suspension point using piezoelectric actuators and the integration of precision interferometric readout of the IM. These improvements will further increase the sensitivity towards the thermal noise limit which constrains the performance to 1⋅10−13ms−2Hz−1 at 4mHz .

Coherent photo-thermal noise cancellation in a dual-wavelength optical cavity for narrow-linewidth laser frequency stabilisation.

Optical resonators are used for the realisation of ultra-stable frequency lasers. The use of high reflectivity multi-band coatings allows the frequency locking of several lasers of different wavelengths to a single cavity. While the noise processes for single wavelength cavities are well known, the correlation caused by multi-stack coatings has as yet not been analysed experimentally. In our work, we stabilise the frequency of a 729 nm and a 1069 nm laser to one mirror pair and determine the residual-amplitude modulation (RAM) and photo-thermal noise (PTN). We find correlations in PTN between the two lasers and observe coherent cancellation of PTN for the 1069 nm coating. We show that the fractional frequency instability of the 729 nm laser is limited by RAM at 1 × 10-14. The instability of the 1069 nm laser is at 3 × 10-15 close to the thermal noise limit of 1.5 × 10-15.

First upper limits on the 21 cm signal power spectrum from cosmic dawn from one night of observations with NenuFAR

The redshifted 21 cm signal from neutral hydrogen is a direct probe of the physics of the early universe and has been an important science driver of many present and upcoming radio interferometers. In this study we use a single night of observations with the New Extension in Nançay Upgrading LOFAR (NenuFAR) to place upper limits on the 21 cm power spectrum from cosmic dawn at a redshift of z = 20.3. NenuFAR is a new low-frequency radio interferometer, operating in the 10–85 MHz frequency range, currently under construction at the Nançay Radio Observatory in France. It is a phased array instrument with a very dense uv coverage at short baselines, making it one of the most sensitive instruments for 21 cm cosmology analyses at these frequencies. Our analysis adopts the foreground subtraction approach, in which sky sources are modeled and subtracted through calibration and residual foregrounds are subsequently removed using Gaussian process regression. The final power spectra are constructed from the gridded residual data cubes in the uv plane. Signal injection tests are performed at each step of the analysis pipeline, the relevant pipeline settings are optimized to ensure minimal signal loss, and any signal suppression is accounted for through a bias correction on our final upper limits. We obtain a best 2σ upper limit of 2.4 × 107 mK2 at z = 20.3 and k = 0.041 h cMpc−1. We see a strong excess power in the data, making our upper limits two orders of magnitude higher than the thermal noise limit. We investigate the origin and nature of this excess power and discuss further improvements to the analysis pipeline that can potentially mitigate it and consequently allow us to reach thermal noise sensitivity when multiple nights of observations are processed in the future.

Near thermal noise limit, 5W single frequency fiber laser base on the ring cavity configuration.

In this study, we present an ultralow noise single-frequency fiber laser operating at 1550 nm, utilizing a traveling-wave ring cavity configuration. The frequency noise of the laser approaches the thermal noise limit, achieving a white noise level of 0.025 Hz2/Hz, resulting in an instantaneous linewidth of 0.08 Hz. After amplification, the output power reaches 4.94 W while maintaining the same low white noise level as the laser oscillator. The integration linewidths of the laser oscillator and amplifier are 221 Hz and 665 Hz, respectively, with both exhibiting relative intensity noises that approach the quantum shot noise limit. To the best of our knowledge, this work shows the lowest frequency noise combined with relatively high power for this type of ring cavity fiber laser.

Single-molecule mid-infrared spectroscopy and detection through vibrationally assisted luminescence

Room-temperature detection of molecular vibrations in the mid-infrared (MIR, λ = 3–30 µm) has numerous applications, including real-time gas sensing, medical imaging and quantum communication. However, existing technologies rely on cooled semiconductor detectors because of thermal noise limitations. One way to overcome this challenge is to upconvert the low-energy MIR photons into high-energy visible wavelengths (λ = 500–800 nm) where detection of single photons is easily achieved using silicon technologies. This process suffers from weak cross-sections and the MIR-to-visible wavelength mismatch, limiting its efficiency. Here we exploit molecular emitters possessing both MIR and visible transitions from molecular vibrations and electronic states, coupled through Franck–Condon factors. By assembling molecules into a plasmonic nanocavity resonant at both MIR and visible wavelengths, and optically pumping them below the electronic absorption band, we show transduction of MIR light. The upconverted signal is observed as enhanced visible luminescence. Combining Purcell-enhanced visible luminescence with enhanced rates of vibrational pumping gives transduction efficiencies of >10%. MIR frequency-dependent upconversion gives the vibrational signatures of molecules assembled in the nanocavity. Transient picocavity formation further confines MIR light down to the single-molecule level. This allows us to demonstrate single-molecule MIR detection and spectroscopy that is inaccessible to any previous detector.

Laser frequency stabilization based on Fano resonance in a microcylinder cavity.

We investigate the application of Fano resonance in microcylinder cavities for laser frequency stabilization. By combining Fano resonance and the differential subtraction method, we successfully reproduce the error signal of the traditional Pound-Drever-Hall (PDH) technique. The frequency noise of the laser, when locked to both microsphere and microcylinder cavities, approaches the thermal noise limit. The microcylinder cavity, with a high Q factor of ∼108, benefiting from its large mode volume, exhibits a significant reduction in frequency noise by one order of magnitude compared with a microsphere in the frequency range of 0.1 to 10 kHz, achieving a minimum noise of ∼2.25 Hz2/Hz at 10 kHz. As this approach eliminates the need for additional electronic circuits typically used in the PDH technique, it holds promise as a cost-effective and reliable solution for laser frequency stabilization.

Ultra-stable cryogenic sapphire cavity laser with an instability reaching 2 × 10-16 based on a low vibration level cryostat.

Cryogenic ultra-stable lasers have extremely low thermal noise limits and frequency drifts, but they are more seriously affected by vibration noise from cryostats. Main material candidates for cryogenic ultra-stable cavities include silicon and sapphire. Although sapphire has many excellent properties at low temperature, the development of sapphire-based cavities is less advanced than that of silicon-based. Using a homemade cryogenic sapphire cavity, we develop an ultra-stable laser source with a frequency instability of 2(1) × 10-16. This is the best frequency instability level among similar systems using cryogenic sapphire cavities reported so far. Low vibration performance of the cryostat is demonstrated with a two-stage vibration isolation, and the vibration suppression is optimized by tuning the mixing ratio of the gas-liquid-helium. With this technique, the linear power spectral densities of vibrations at certain frequencies higher than tens of hertz are suppressed by two orders of magnitude in all directions.

Entanglement-enhanced optomechanical sensing

Optomechanical systems have been exploited in ultrasensitive measurements of force, acceleration and magnetic fields. The fundamental limits for optomechanical sensing have been extensively studied and now well understood—the intrinsic uncertainties of the bosonic optical and mechanical modes, together with backaction noise arising from interactions between the two, dictate the standard quantum limit. Advanced techniques based on non-classical probes, in situ ponderomotive squeezed light and backaction-evading measurements have been developed to overcome the standard quantum limit for individual optomechanical sensors. An alternative, conceptually simpler approach to enhance optomechanical sensing rests on joint measurements taken by multiple sensors. In this configuration, a pathway to overcome the fundamental limits in joint measurements has not been explored. Here we demonstrate that joint force measurements taken with entangled probes on multiple optomechanical sensors can improve the bandwidth in the thermal-noise-dominant regime or the sensitivity in the shot-noise-dominant regime. Moreover, we quantify the overall performance of entangled probes with the sensitivity–bandwidth product and observe a 25% increase compared with that of classical probes. The demonstrated entanglement-enhanced optomechanical sensors would enable new capabilities for inertial navigation, acoustic imaging and searches for new physics. Joint force measurements with entangled optical probes on two optomechanical sensors are demonstrated. The force sensitivity is improved by 40% in the shot-noise-dominant regime. The sensing bandwidth is improved by 20% in the thermal noise limit.

Gyro-Free Inertial Navigation Systems Based on Linear Opto-Mechanical Accelerometers.

High-sensitivity uniaxial opto-mechanical accelerometers provide very accurate linear acceleration measurements. In addition, an array of at least six accelerometers allows the estimation of linear and angular accelerations and becomes a gyro-free inertial navigation system. In this paper, we analyze the performance of such systems considering opto-mechanical accelerometers with different sensitivities and bandwidths. In the six-accelerometer configuration adopted here, the angular acceleration is estimated using a linear combination of accelerometers' read-outs. The linear acceleration is estimated similarly but requires a correcting term that includes angular velocities. Accelerometers' colored noise from experimental data is used to derive, analytically and through simulations, the performance of the inertial sensor. Results for six accelerometers, separated by 0.5 m in a cube configuration show noise levels of 10-7 m s-2 and 10-5 m s-2 (in Allan deviation) for time scales of one second for the low-frequency (Hz) and high-frequency (kHz) opto-mechanical accelerometers, respectively. The Allan deviation for the angular velocity at one second is 10-5 rad s-1 and 5×10-4 rad s-1. Compared to other technologies such as MEMS-based inertial sensors and optical gyroscopes, the high-frequency opto-mechanical accelerometer exhibits better performance than tactical-grade MEMS for time scales shorter than 10 s. For angular velocity, it is only superior for time scales less than a few seconds. The linear acceleration of the low-frequency accelerometer outperforms the MEMS for time scales up to 300 s and for angular velocity only for a few seconds. Fiber optical gyroscopes are orders of magnitude better than the high- and low-frequency accelerometers in gyro-free configurations. However, when considering the theoretical thermal noise limit of the low-frequency opto-mechanical accelerometer, 5×10-11 m s-2, linear acceleration noise is orders of magnitude lower than MEMS navigation systems. Angular velocity precision is around 10-10 rad s-1 at one second and 5×10-7 rad s-1 at one hour, which is comparable to fiber optical gyroscopes. While experimental validation is yet not available, the results shown here indicate the potential of opto-mechanical accelerometers as gyro-free inertial navigation sensors, provided the fundamental noise limit of the accelerometer is reached, and technical limitations such as misalignments and initial conditions errors are well controlled.

Frequency stability of cryogenic silicon cavities with semiconductor crystalline coatings

State-of-the-art optical oscillators employing cryogenic reference cavities are limited in performance by the Brownian thermal noise associated with the mechanical dissipation of the mirror coatings. Recently, crystalline Al1−xGa x As/GaAs coatings have emerged as a promising candidate for improved coating thermal noise. We present measurements of the frequency noise of two fully crystalline cryogenic reference cavities with Al0.92Ga0.08As/GaAs optical coatings. We report on birefringent noise associated with anticorrelated frequency fluctuations between the polarization modes of the crystalline coatings and identify variables that affect its magnitude. Comparing the birefringent noise between the two cryogenic reference cavities reveals a phenomenological set of scalings with intracavity power and mode area. We implement an interrogation scheme that cancels this noise by simultaneous probing of both polarization modes. The residual noise remaining after this cancellation is larger than both cavities’ thermal noise limits but still lower than the instabilities previously measured on equivalent resonators with dielectric coatings. Though the source of these noise mechanisms is unclear, we demonstrate that crystalline coatings can provide stability and sensitivity competitive with resonators employing dielectric coatings.

Finite element analysis of the zero-crossing temperature of a long Fabry–Perot cavity

An ultra-stable Fabry–Perot (F–P) cavity is designed, whose spacer is made of an ultra-low-expansion (ULE) glass and mirrors made of fused silicon (FS). The spacer aperture is composed of three holes, among which a long and small hole is in the middle, and a short and large hole is on each side. The fused silicon (FS) mirrors are placed in the large holes of the spacer aperture, and the FS rings are mounted on the end face of the spacer. FS mirrors, aperture and FS rings are coaxial. The thermal noise limit of the cavity is $$9.1\times 10^{-17}$$ . By finite element analysis, the specific FS rings are choose to successfully tune the zero-crossing temperature from −10 to 27 K, which enables the cavity zero-crossing temperature easily be tuned above room temperature. In the meantime, this design makes the machining error has little effect on the zero-crossing temperature of the cavity, and it is convenient to manufacture a long F–P cavity.

All-fiber-device-coupled compact, transportable ultra-stable laser.

In response to the demand for operation in non-laboratory environments, there has been a trend toward the development of compact, transportable ultra-stable lasers. This paper reports on this sort of laser system assembled in a cabinet. The whole optical part utilizes fiber-coupled devices to simplify the integration. In addition, spatial beam collimation and alignment into the high-finesse cavity are realized by a five-axis positioner and a focus-adjustable fiber collimator, which significantly relax the alignment and adjustment. A theoretical analysis is performed on how the collimator adjusts the beam profile and coupling efficiency. The support structure of the system is specially designed as well so that it features robustness and transportation without performance degradation. The observed linewidth is 1.4Hz within a duration of 1s. After subtracting the linear drift of 70 mHz/s, the fractional frequency instability is better than 4 × 10-15, for the averaging time ranging from 1 to 100s, which is close to the thermal noise limit of the high-finesse cavity.

Advanced Virgo Plus: Future Perspectives

While completing the commissioning phase to prepare the Virgo interferometer for the next joint Observation Run (O4), the Virgo collaboration is also finalizing the design of the next upgrades to the detector to be employed in the following Observation Run (O5). The major upgrade will concern decreasing the thermal noise limit, which will imply using very large test masses and increased laser beam size. But this will not be the only upgrade to be implemented in the break between the O4 and O5 observation runs to increase the Virgo detector strain sensitivity. The paper will cover the challenges linked to this upgrade and implications on the detector’s reach and observational potential, reflecting the talk given at 12th Cosmic Ray International Seminar - CRIS 2022 held in September 2022 in Napoli.

Research on Brownian Thermal Noise Limit of a Cylindrical Ultra-Stable Cavity with Support Pads

Brownian thermal noise (TN) of ultra-stable cavities (USCs) imposes a fundamental limitation on the frequency stability of ultra-narrow linewidth lasers. This work investigates the TN in cylindrical USCs with the four support pads in detail through theoretical estimation and simulation. To evaluate the performance of state-of-the-art ultra-narrow linewidth lasers, we derive an expression of the TN for a cylindrical spacer according to the fluctuation–dissipation theorem, which takes into account the front face area of the spacer. This estimation is more suitable for the TN of the cylindrical USC than the previous one. Meanwhile, we perform detailed studies of the influence of the four support pads on the TN in cylindrical USCs for the first time by numerical simulations. For a 400 mm long cylindrical USC with an ultra-low expansion spacer and fused silica substrates, the displacement noise contributed from the four support pads is roughly four times that of the substrates and the GaAs/AlGaAs crystalline coating. The results show that the four support pads are the primary TN contributors under some materials and geometries of USCs.

Precision Calibration of Radio Interferometers for 21 cm Cosmology with No Redundancy and Little Knowledge of Antenna Beams and the Radio Sky

We introduce CALibration AMITY (calamity), a precision bandpass calibration method for radio interferometry. calamity can solve for direction-independent gains with arbitrary frequency structure to the high precision required for 21 cm cosmology with minimal knowledge of foregrounds or antenna beams and does not require any degree of redundancy (repeated identical measurements of the same baseline). We have achieved this through two key innovations. First, we model the foregrounds on each baseline independently using a flexible and highly efficient set of basis functions that have minimal overlap with 21 cm modes and enforce spectral smoothness in the calibrated foregrounds. Second, we use an off-the-shelf GPU accelerated API (tensorflow) to solve for per-baseline foregrounds simultaneously with per-frequency antenna gains in a single optimization loop. GPU acceleration is critical for our technique to be able to solve for the large numbers of foreground and gain parameters simultaneously across all frequencies for an interferometer with ≳10 antennas in a reasonable amount of time. In this paper, we give an overview of our technique and, using realistic simulations, demonstrate its performance in solving for and removing pathological gain structures down to 4.5 orders of magnitude below the level of foregrounds and consistent with our simulated thermal noise limit. If readers want to start using calamity now, they can find a tutorial notebook online.

Sub-femto-Newton sensing torsion pendulum for detection of light force.

Mechanical oscillators are widely used in many fields of physics, including ultrahigh precision measurements, gravity experiments, and optical mechanical systems. A sub-gram-scale silicon wafer is suspended by a tungsten wire with a diameter of 8 µm, forming a torsion pendulum to detect the laser radiation pressure. We demonstrate the application of a low-frequency, highly sensitive torsion pendulum for the measurement of light forces. In the feedback cooling state, the system exhibits a force sensitivity at the end of the pendulum close to 0.1 fN, approaches the thermal noise limit, and reaches the detection level of the laser radiation pressure of 60 nW.

Digital control of residual amplitude modulation at the 10-7 level for ultra-stable lasers.

The stabilization of lasers on ultra-stable optical cavities by the Pound-Drever-Hall (PDH) technique is a widely used method. The PDH method relies on the phase-modulation of the laser, which is usually performed by an electro-optic modulator (EOM). When approaching the 10-16 fractional frequency stability level, this technology requires an active control of the residual amplitude modulation (RAM) generated by the EOM in order to bring the frequency stability of the laser down to the thermal noise limit of the ultra-stable cavity. In this article, we report on the development of an active system of RAM reduction based on a free space EOM, which is used to perform PDH-stabilization of a laser on a cryogenic silicon cavity. A minimum RAM instability of 1.4 × 10-7 is obtained by employing a digital servo that stabilizes the EOM DC electric field, the crystal temperature and the laser power. Considering an ultra-stable cavity with a finesse of 2.5 × 105, this RAM level would contribute to the fractional frequency instability at the level of about 5 × 10-19, well below the state of the art thermal noise limit of a few 10-17.