Thermodynamic Noise Research Articles

Quantum linewidth limitation of a laser stabilized with a nonlinear microcavity.

We show that the linewidth of a laser locked to an optical cavity characterized with nonzero optical cubic nonlinearity is restricted by the value of the nonlinear frequency shift of the cavity mode per single photon localized in the mode. This effect is masked by the fundamental thermodynamic noise in monolithic microcavities. The quantum limit of the linewidth can be measured using two independent lasers separately locked to spatially overlapping modes of the nonlinear resonator.

Deconstructing magnetization noise: Degeneracies, phases, and mobile fractionalized excitations in tetris artificial spin ice.

Direct detection of spontaneous spin fluctuations, or "magnetization noise," is emerging as a powerful means of revealing and studying magnetic excitations in both natural and artificial frustrated magnets. Depending on the lattice and nature of the frustration, these excitations can often be described as fractionalized quasiparticles possessing an effective magnetic charge. Here, by combining ultrasensitive optical detection of thermodynamic magnetization noise with Monte Carlo simulations, we reveal emergent regimes of magnetic excitations in artificial "tetris ice." A marked increase of the intrinsic noise at certain applied magnetic fields heralds the spontaneous proliferation of fractionalized excitations, which can diffuse independently, without cost in energy, along specific quasi-1D spin chains in the tetris ice lattice.

SDEGen: learning to evolve molecular conformations from thermodynamic noise for conformation generation.

Generation of representative conformations for small molecules is a fundamental task in cheminformatics and computer-aided drug discovery, but capturing the complex distribution of conformations that contains multiple low energy minima is still a great challenge. Deep generative modeling, aiming to learn complex data distributions, is a promising approach to tackle the conformation generation problem. Here, inspired by stochastic dynamics and recent advances in generative modeling, we developed SDEGen, a novel conformation generation model based on stochastic differential equations. Compared with existing conformation generation methods, it enjoys the following advantages: (1) high model capacity to capture multimodal conformation distribution, thereby searching for multiple low-energy conformations of a molecule quickly, (2) higher conformation generation efficiency, almost ten times faster than the state-of-the-art score-based model, ConfGF, and (3) a clear physical interpretation to learn how a molecule evolves in a stochastic dynamics system starting from noise and eventually relaxing to the conformation that falls in low energy minima. Extensive experiments demonstrate that SDEGen has surpassed existing methods in different tasks for conformation generation, interatomic distance distribution prediction, and thermodynamic property estimation, showing great potential for real-world applications.

Spectral Purity Improvement in Flickering Self-Injection Locked Lasers

We study improvements of the Self-Injection Locked (SIL) distributed feedback (DFB) semiconductor laser phase noise as well as integral linewidth on the amount of the SIL feedback and show that SIL reduces the laser noise nearly equally in a broad frequency range, spanning from 1 Hz to 10 MHz. In our experiment SIL operation is supported by a tunable resonant reflector consisting of a high quality factor (high-Q) monolithic whispering gallery mode resonator (WGMR) supplied with a controllable attenuator. Using the experimental setup we validated theoretical formula describing the SIL spectral purity and identified practical parameters of the system allowing reaching the phase noise limit resulting from the fundamental thermodynamic noise of the resonator. We show that the linewidth improvement due to SIL effect is drastically impacted by the frequency spectral dependence of the phase noise of the laser and that it drops significantly in a flickering laser. We also confirmed that the thermorefractive coefficient as well as mode volume of the WGMR imposes the major limitations on the SIL performance. Low intracavity absorption is needed to suppress the attenuation-related thermal effects in the cavity.

Measurement of sub-fm/Hz1/2 displacement spectral densities in ultrahigh-Q single-crystal microcavities with hertz-level lasers

Tracing a resonance frequency of a high quality factor (Q) optical cavity facilitates subpicometer displacement measurements of the optical cavity via Pound–Drever–Hall (PDH) locking scheme, tightly synchronizing a laser frequency to the optical cavity. Here we present observations of subfemtometer displacements on a ultrahigh-Q single-crystal MgF 2 whispering-gallery-mode microcavity by frequency synchronization between a 1 Hz cavity-stabilized laser and a resonance of the MgF 2 cavity using PDH laser-cavity locking. We characterize not only the displacement spectral density of the microcavity with a sensitivity of 1.5 × 10 − 16 m / Hz 1 / 2 over the Fourier offset frequency ranging from 15 mHz to 100 kHz but also a 1.77 nm displacement fluctuation of the microcavity over 4500 s. Such measurement capability not only supports the analysis of integrated thermodynamical and technical cavity noise but allows for minute displacement measurements using laser-cavity locking for ultraprecise positioning, metrology, and sensing.

Superconducting bolometer with high-frequency readout circuit at 400 mK

The detection of a terahertz optical signal using a bolometric detector with a planar niobium resonator loaded with a hafnium micromotor using the nonlinearity of the impedance of an electron gas at a frequency of 1.5 GHz near the critical temperature of the micromotor is demonstrated for the first time. The temperature of the electron gas was shifted by the resonator current, and the superconducting transition of the micromotor occurred under the action of a terahertz signal. The test thermodynamic signal from a thin-film Fe-Cr-Ni absorber heated in the range of 1-10 K was focused from a distance of 10 mm with an immersion lens made of sapphire onto a planar antenna matched with a micro-bridge in the range of 600-700 GHz. The measured power transmission coefficient of the bolometer was +5.5 dB with a saturation power of ~1 pW and a threshold sensitivity of the receiving system (3±1)·10-17 W/sqrt(Hz)sqrt sqrt, which is close to the theoretical values for the investigated bridge with a size of 2.5x2.5x0.08 μm. The tested detector can be used to create imaging terahertz matrices with frequency multiplexing in sorption-type cryostats. Keywords: RFTES bolometer, superconducting micro bridge, high-frequency impedance of superconductor, hafnium film, electron gas, planar resonator, frequency multiplexing, planar antenna, black body, thermodynamic noise. Keywords: RFTES bolometer, superconducting microbridge, high-frequency impedance, hafnium film, electron gas, coplanar resonator, frequency-division multiplexing, planar antenna, blackbody, noise.

Superconducting noise-source for ultra-low temperatures

The device operates at temperatures <300 mK and comprises a hafnium microbridge and a superconducting aluminum tunnel junction both integrated into a common coplanar waveguide. The microbridge matches with a planar antenna and operates as an optical blackbody at frequencies 600-700 GHz. The coplanar terminal is the blackbody output in the 1-2 GHz frequency range. The microbridge temperature can be set in the range of 0.4-9 K and calibrated using the shot noise of the tunnel junction. Temperature modulation of each of the sources can be performed independently using a direct current which transit them from the superconducting to the normal state with characteristic times <0.1 ms and heating power ~ 1 μW. Keywords: Superconducting microbridge, superconducting tunnel junction, thermodynamic noise, shot noise, noise thermometry.

Superconducting noise-source for ultra-low temperatures

The device operates at temperatures <300 mK and comprises a hafnium microbridge and a superconducting aluminum tunnel junction both integrated into a common coplanar waveguide. The microbridge matches with a planar antenna and operates as an optical blackbody at frequencies 600-700 GHz. The coplanar terminal is the blackbody output in the 1-2 GHz frequency range. The microbridge temperature can be set in the range of 0.4-9 K and calibrated using the shot noise of the tunnel junction. Temperature modulation of each of the sources can be performed independently using a direct current which transit them from the superconducting to the normal state with characteristic times <0.1 ms and heating power ~ 1 μW. Keywords: Superconducting microbridge, superconducting tunnel junction, thermodynamic noise, shot noise, noise thermometry.

Double Rayleigh scattering in a digitally enhanced, all-fiber optical frequency reference.

We demonstrate a passive, all-optical fiber frequency reference using a digitally enhanced homodyne interferometric phase readout. We model the noise contributions from fiber thermal noise and the coupling of double Rayleigh scattering in a digitally enhanced homodyne interferometer. A system frequency stability of 0.1 Hz/Hz is achieved above 100 Hz, which coincides with the double Rayleigh scattering estimate and is approximately a factor of five above the thermo-dynamic noise limit.

Thermal decoherence and laser cooling of Kerr microresonator solitons

Thermal noise is ubiquitous in microscopic systems and high-precision measurements. The control of thermal noise would reveal quantum regimes1 and enable fundamental physics searches2. Recently, nonlinearity in microresonators has enabled laser devices such as Kerr microresonator soliton frequency combs3. Soliton microcombs explore nonlinear dynamics and enable optical synthesizers4, optical clockwork5 and data communications systems6. Here, we explore how thermal noise leads to the fundamental decoherence of microcombs. We show that a particle-like soliton, which is an ensemble of comb modes, is closely coupled to the thermal fluctuations of its silicon-chip-based resonator. The microcomb modal linewidth is thus thermally broadened, and we characterize these thermal-noise correlations through a soliton effective temperature. Moreover, we demonstrate that passive laser cooling reduces soliton thermal decoherence to far below the ambient-temperature limit. We implement laser cooling by photothermal forcing, and we observe cooling of the frequency comb modes to 84 K. Our work illuminates inherent connections between nonlinear photonics and microscopic fluctuations. Observations of decoherence from thermodynamic noise in microresonator soliton frequency combs and laser cooling that reduces soliton thermal decoherence to far below the ambient-temperature limit are described, linking nonlinear photonics and microscopic fluctuations.

Oscillations in feedback-driven systems: Thermodynamics and noise.

Oscillations in nonequilibrium noisy systems are important physical phenomena. These oscillations can happen in autonomous biochemical oscillators such as circadian clocks. They can also manifest as subharmonic oscillations in periodically driven systems such as time crystals. Oscillations in autonomous systems and, to a lesser degree, subharmonic oscillations in periodically driven systems have been both thoroughly investigated, including their relation with thermodynamic cost and noise. We perform a systematic study of oscillations in a third class of nonequilibrium systems: feedback-driven systems. In particular, we use the apparatus of stochastic thermodynamics to investigate the role of noise and thermodynamic cost in feedback-driven oscillations. For a simple two-state model that displays oscillations, we analyze the relation between precision and dissipation, revealing that oscillations can remain coherent for an indefinite time in a finite system with thermal fluctuations in a limit of diverging thermodynamic cost. We consider oscillations in a more complex system with several degrees of freedom, an Ising model driven by feedback between the magnetization and the external field. This feedback-driven system can display subharmonic oscillations similar to the ones observed in time crystals. We illustrate the second law for feedback-driven systems that display oscillations. For the Ising model, the oscillating dissipated heat can be negative. However, when we consider the total entropy that also includes an informational term related to measurements, the oscillating total entropy change is always positive. We also study the finite-size scaling of the dissipated heat, providing evidence for the existence of a first-order phase transition for certain parameter regimes.

Thermorefractive noise in silicon-nitride microresonators

Thermodynamic noise places a fundamental limit on the frequency stability of dielectric optical resonators. Here, we present the characterization of thermo-refractive noise in photonic-chip-based silicon nitride microresonators and show that thermo-refractive noise is the dominant thermal noise source in the platform. We employed balanced homodyne detection to measure the thermo-refractive noise spectrum of microresonators of different diameters. The measurements are in good agreement with theoretical models and finite element method simulations. Our characterization sets quantitative bounds on the scaling and absolute magnitude of thermal noise in photonic chip-based microresonators. An improved understanding of thermo-refractive noise can prove valuable in the design considerations and performance limitations of future photonic integrated devices.

Chasing the thermodynamical noise limit in whispering-gallery-mode resonators for ultrastable laser frequency stabilization

Ultrastable high-spectral-purity lasers have served as the cornerstone behind optical atomic clocks, quantum measurements, precision optical microwave generation, high-resolution optical spectroscopy, and sensing. Hertz-level lasers stabilized to high-finesse Fabry-Pérot cavities are typically used for these studies, which are large and fragile and remain laboratory instruments. There is a clear demand for rugged miniaturized lasers with stabilities comparable to those of bulk lasers. Over the past decade, ultrahigh-Q optical whispering-gallery-mode resonators have served as a platform for low-noise microlasers but have not yet reached the stabilities defined by their fundamental noise. Here, we show the noise characteristics of whispering-gallery-mode resonators and demonstrate a resonator-stabilized laser at this limit by compensating the intrinsic thermal expansion, allowing a sub-25 Hz linewidth and a 32 Hz Allan deviation. We also reveal the environmental sensitivities of the resonator at the thermodynamical noise limit and long-term frequency drifts governed by random-walk-noise statistics.

Coherent light transmission properties of commercial photonic crystal hollow core optical fiber

Photonic crystal hollow core fiber (PC-HCF) has enabled many exciting new applications in nonlinear optics and spectroscopy. However, to date there has been less impact in coherent applications where preservation of optical phase over long fiber lengths is crucial. This paper presents characteristics of three commercially available PC-HCFs relevant to coherent applications including higher-order mode analysis, birefringence and polarization-dependent loss, and their impact on coherent light transmission in PC-HCF. Multipath interference due to higher-order mode propagation and Fresnel reflection is shown to generate excess intensity noise in transmission, which can be suppressed by up to 20 dB through high frequency phase modulation of the source laser. To demonstrate the potential of PC-HCF in high performance sensing, a Mach-Zehnder interferometer (MZI) incorporating 10 m of PC-HCF in each arm is characterized and demonstrates a phase resolution (59×10(-9) rad/Hz(1/2) at 30 kHz) close to the shot noise limit, which is better than can be achieved in a MZI made with the same length of single mode solid core fiber because of the limit set by fundamental thermodynamic noise (74×10(-9) rad/Hz(1/2) at 30 kHz).

ENSO dynamics and diversity resulting from the recharge oscillator interacting with the slab ocean

El Nino-Southern Oscillation (ENSO) is the leading mode of interannual global climate variability, which in its essence is often described by the equatorial dynamics of the recharge oscillator with a fixed pattern. Here we explore the idea that ENSO can be simulated in a model with a fixed pattern of sea surface temperature variability following the recharge oscillator mechanism, which interacts with the thermodynamic red noise of a slab ocean. This model is capable of simulating the leading modes of sea surface temperature variability in the tropical Pacific in good agreement with the observations and most coupled general circulation models. ENSO dynamics, amplitude, seasonality, the structure of the leading patterns, its meridional extension, its variations in an eastern and central Pacific pattern and associated positive feedbacks are all influenced and simulated well by including the interaction of recharge oscillator and the thermodynamic coupling to the slab ocean model. We further point out that much of the ENSO diversity in the spatial structure is a reflection of this interaction. However, it also has to be noted that some equatorial dynamics are missing in this model and in coupled general circulation models that are important for the ENSO diversity.

Low-noise Brillouin laser on a chip at 1064 nm

We demonstrate narrow-linewidth-stimulated Brillouin lasers at 1064 nm from ultra-high-Q silica wedge disk resonators on silicon. Fundamental Schawlow-Townes frequency noise of the laser is on the order of 0.1 Hz2/Hz. The technical noise spectrum of the on-chip Brillouin laser is close to the thermodynamic noise limit of the resonator (thermorefractive noise) and is comparable to that of ultra-narrow-linewidth Nd:YAG lasers. The relative intensity noise of the Brillouin laser also is reduced by using an intensity-stabilized pump laser. Finally, low-noise microwave synthesis up to 32 GHz is demonstrated by heterodyne of first and third Brillouin Stokes lines from a single resonator.

Transient Thermodynamic Performance and Passby Noise from the Silencer of a Modern Diesel Engine in an Actual Vehicle

Transient Thermodynamic Performance and Passby Noise from the Silencer of a Modern Diesel Engine in an Actual Vehicle

Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators

In its most basic form an oscillator consists of a resonator driven on resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonator's anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nanoelectromechanical system based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables suppressing the most significant contributions to the oscillator's phase noise, as predicted by our model.

Comment on “Probing the Ultimate Limit of Fiber-Optic Strain Sensing”

Gagliardi et al. (Reports, 19 November 2010, p. 1081) described an ultrahigh-resolution fiber-optic strain sensor. This comment addresses an error in the calculation of the fundamental thermodynamic noise in optical fiber resonators and shows that the actual thermodynamic noise level is lower by a factor of at least 11 than that calculated.

Fundamental frequency noise properties of extended cavity erbium fiber lasers

A multimode linear cavity and a single-mode unidirectional ring cavity fiber laser with meter-long cavity lengths are shown to exhibit frequency noise limited by fundamental thermodynamic noise from 100 Hz to 100 kHz. Their measured spectra agree closely with theoretically derived thermodynamic noise and the characteristic dependence of the frequency noise power spectrum on the inverse of the cavity length is observed. The unidirectional ring laser exhibits a frequency noise of 2 Hz/Hz(1/2) at 1 kHz, one of the lowest published values to date from a free-running laser. The multimode linear cavity laser is shown to be a suitable candidate for thermal-noise-limited, meter-long fiber laser strain sensors with a strain resolution of 14 fϵ/Hz(1/2) at 1 kHz.