The theory of spin noise spectroscopy: a review

Nonergodic Measurements of Qubit Frequency Noise

Slow fluctuations of a qubit frequency are one of the major problems faced by quantum computers. To understand their origin it is necessary to go beyond the analysis of their spectra. We show that characteristic features of the fluctuations can be revealed using comparatively short sequences of periodically repeated Ramsey measurements, with the sequence duration smaller than needed for the noise to approach the ergodic limit. The outcomes distribution and its dependence on the sequence duration are sensitive to the nature of the noise. The time needed for quantum measurements to display quasiergodic behavior can strongly depend on the measurement parameters.

Mesoscopic critical fluctuations

We investigate the magnetic fluctuations in a mesoscopic critical region formed at the interface due to smooth time-independent spatial variations of a control parameter around its critical value. In the proximity of the spatial critical point, the order parameter fluctuations exhibit a mesoscopic nature, characterized by their significant size compared to the lattice constant, while gradually decaying away from the critical region. To explain this phenomenon, we present a minimal model that effectively captures this behavior and demonstrates its connection to the integrable Painlevé-II equation governing the local order parameter. By leveraging the well-established mathematical properties of this equation, we gain valuable insights into the nonlinear susceptibilities exhibited within this region.

Noise analysis of the atomic superheterodyne receiver based on flat-top laser beams

Since its theoretical sensitivity is limited by quantum noise, radio wave sensing based on Rydberg atoms has the potential to replace its traditional counterparts with higher sensitivity and has developed rapidly in recent years. However, as the most sensitive atomic radio wave sensor, the atomic superheterodyne receiver lacks a detailed noise analysis to pave its way to achieve theoretical sensitivity. In this work, we quantitatively study the noise power spectrum of the atomic receiver versus the number of atoms, where the number of atoms is precisely controlled by changing the diameters of flat-top excitation laser beams. The results show that under the experimental conditions that the diameters of excitation beams are less than or equal to 2 mm and the read-out frequency is larger than 70 kHz, the sensitivity of the atomic receiver is limited only by the quantum noise and, in the other conditions, limited by classical noise. However, the experimental quantum-projection-noise-limited sensitivity this atomic receiver reaches is far from the theoretical sensitivity. This is because all atoms involved in light-atom interaction will contribute to noise, but only a fraction of them participating in the radio wave transition can provide valuable signals. At the same time, the calculation of the theoretical sensitivity considers both the noise and signal are contributed by the same amount of atoms. This work is essential in making the sensitivity of the atomic receiver reach its ultimate limit and is significant in quantum precision measurement.

Quantum nonlinear spectroscopy of single nuclear spins

Conventional nonlinear spectroscopy, which use classical probes, can only access a limited set of correlations in a quantum system. Here we demonstrate that quantum nonlinear spectroscopy, in which a quantum sensor and a quantum object are first entangled and the sensor is measured along a chosen basis, can extract arbitrary types and orders of correlations in a quantum system. We measured fourth-order correlations of single nuclear spins that cannot be measured in conventional nonlinear spectroscopy, using sequential weak measurement via a nitrogen-vacancy center in diamond. The quantum nonlinear spectroscopy provides fingerprint features to identify different types of objects, such as Gaussian noises, random-phased AC fields, and quantum spins, which would be indistinguishable in second-order correlations. This work constitutes an initial step toward the application of higher-order correlations to quantum sensing, to examining the quantum foundation (by, e.g., higher-order Leggett-Garg inequality), and to studying quantum many-body physics.

Signals that look the same from their low-order correlations can often be distinguished by looking at higher-order ones. Here, the authors exploit the sensitivity of quantum nonlinear spectroscopy to fourth-order correlations to identify Gaussian noises, random-phased AC fields, and quantum spins.

Enhancement of spin noise spectroscopy of rubidium atomic ensemble by using the polarization squeezed light

We measured the spin noise spectroscopy (SNS) of rubidium atomic ensemble with two different kinds of atomic vapor cells (filled with buffer gas or coated with paraffin film on the inner wall) and demonstrated the enhancement of the signal-to-noise ratio (SNR) by using polarization squeezed state (PSS) of 795-nm light field with Stokes operator S Λ ₂ squeezed. The PSS is prepared by locking the relative phase between the squeezed vacuum state of light obtained with a sub-threshold optical parametric oscillator and the orthogonally polarized local oscillator beam by means of the quantum noise lock. Under the same conditions, the PSS can be employed not only to improve the SNR, but also to keep the full width at half maximum (FWHM) of SNS, compared with the case of using the polarization coherent state (PCS), enhancement of SNR is positively correlated with the squeezing level of the PSS. With increasing probe laser power and atomic number density, the SNR and FWHM of SNS will increase correspondingly. With the help of the PSS of the Stokes operator S Λ ₂, quantum improvements of both the SNR and FWHM of SNS signal has been demonstrated by controlling optical power of polarization squeezed light beam or atomic number density in our experiments.

Intrinsic and induced quantum quenches for enhancing qubit-based quantum noise spectroscopy

Quantum sensing protocols that exploit the dephasing of a probe qubit are powerful and ubiquitous methods for interrogating an unknown environment. They have a variety of applications, ranging from noise mitigation in quantum processors, to the study of correlated electron states. Here, we discuss a simple strategy for enhancing these methods, based on the fact that they often give rise to an inadvertent quench of the probed system: there is an effective sudden change in the environmental Hamiltonian at the start of the sensing protocol. These quenches are extremely sensitive to the initial environmental state, and lead to observable changes in the sensor qubit evolution. We show how these new features give access to environmental response properties. This enables methods for direct measurement of bath temperature, and for detecting non-thermal equilibrium states. We also discuss how to deliberately control and modulate this quench physics, which enables reconstruction of the bath spectral function. Extensions to non-Gaussian quantum baths are also discussed, as is the application of our ideas to a range of sensing platforms (e.g., nitrogen-vacancy (NV) centers in diamond, semiconductor quantum dots, and superconducting circuits).

Generation of squeezed light vacuum enabled by coherent population trapping

We demonstrate the possibility to generate squeezed vacuum states of light by four wave mixing (FWM) enabled coherent population trapping in a metastable helium cell at room temperature. Contrary to usual FWM far detuned schemes, we work at resonance with an atomic transition. We investigate the properties of such states and show that the noise variances of the squeezed and anti-squeezed quadratures cannot be explained by the simple presence of losses. A specific model allows us to demonstrate the role played by spontaneous emitted photons, which experience squeezing while propagation inside of the cell. This theoretical model, which takes into account both residual absorption and spontaneous emission, leads to an excellent agreement with the experimental data without any adjusted parameter.

Raman scattering model of the spin noise

The mechanism of formation of the polarimetric signal observed in the spin noise spectroscopy (SNS) is analyzed from the viewpoint of the light scattering theory. A rigorous calculation of the polarimetric signal (Faraday rotation or ellipticity) recorded in the SNS is presented in the approximation of single scattering. We show that it is most correctly to consider this noise as a result of scattering of the probe light beam by fluctuating susceptibility of the medium. Fluctuations of the gyrotropic (antisymmetric) part of the susceptibility tensor lead to appearance of the typical for the SNS Faraday rotation noise at the Larmor frequency. At the same time, fluctuations of linear anisotropy of the medium (symmetric part of the susceptibility tensor) give rise to the ellipticity noise of the probe beam spectrally localized at the double Larmor frequency. The results of the theoretical analysis well agree with the experimental data on the ellipticity noise in cesium vapor.

Spin-noise spectrum in a pulse-modulated field

We measure the spin noise spectrum (SNS) of a thermal Rubidium vapor in a pulse-modulated transverse magnetic field and develop a simple theory to describe the main structure of the SNS. Notably, when the pulse area is equal to π, the SNS consists of resonances centered at half-odd-integer multiples of the modulation frequency, while revealing the spin dynamics of the system in a zero field. Our study opens a promising way of studying zero-field spin dynamics by spin noise spectrum free from any low-frequency environmental disturbances.

Spatiotemporal Spin Noise Spectroscopy

We report on the potential of a new spin noise spectroscopy approach by demonstrating all-optical probing of spatiotemporal spin fluctuations. This is achieved by homodyne mixing of a spatially phase-modulated local oscillator with spin-flip scattered light, from which the frequency and wave vector dependence of the spin noise power is unveiled. As a first application of the method we measure the spatiotemporal spin noise in weakly n-doped CdTe layers, from which the electron spin diffusion constant and spin relaxation rates are determined. The absence of spatial spin correlations is also shown for this particular system.

Johnson Noise Thermometry

Johnson noise thermometers infer thermodynamic temperature from measurements of the thermally-induced current fluctuations that occur in all electrical conductors. This paper reviews the status of Johnson noise thermometry and its prospects for both metrological measurements and for practical applications in industry. The review begins with a brief description of the foundations and principles of Johnson noise thermometry before outlining the many different techniques and technological breakthroughs that have enabled the application of JNT to high-accuracy, cryogenic, and industrial thermometry. Finally, the future of noise thermometry is considered. As the only purely electronic approach to thermodynamic temperature measurement, Johnson noise thermometry has appeal for metrological applications at temperatures ranging from below 1 μK up to 800 K. With the rapid advances in digital technologies, there are also expectations that noise thermometry will become a practical option for some industrial applications reaching temperatures above 2000 K.