Shot Noise Spectroscopy: Principles & Applications

• Shot noise spectroscopy is a technique that analyzes intrinsic fluctuations in charge or light to reveal microscopic transport mechanisms and effective charge transfer.
• It uses low-frequency current-noise spectral density and photon shot-noise measurements to distinguish Poissonian, sub-Poissonian, and super-Poissonian regimes.
• The approach enables detection of phenomena like Andreev reflection, multiple-charge transfer, and Kondo screening, advancing studies in superconducting, topological, and correlated materials.

Shot noise spectroscopy denotes a class of spectroscopic methods in which information is extracted from fluctuations generated by the discreteness of charge or of light. In electronic transport, the relevant observable is the current-noise spectral density, usually analyzed together with the Fano factor to infer effective charge, transmission probabilities, and temporal correlations of tunnelling events. In optical, Raman, soft X-ray, and spin-noise implementations, the corresponding objective is often to suppress technical noise until the remaining sensitivity is set by photon shot noise, thereby reaching the conventional quantum limit for detecting small absorption, gain, or spectral-parameter changes (Tamir et al., 2021, Karpf et al., 2018, Truong et al., 2015, Guyader et al., 2022).

1. Core observables and formal definitions

The central quantity in transport-based shot-noise spectroscopy is the low-frequency or zero-frequency current-noise spectral density. One common definition is

$$S_I \equiv \int_{-\infty}^{+\infty} dt\, e^{i\omega t}\langle \delta I(t)\delta I(0)\rangle\big|_{\omega\to 0},$$

or, equivalently, the symmetrized current-current correlator at zero frequency. For uncorrelated Poissonian transfer of carriers with charge $q$, the Schottky result is

$S_{\rm shot}=2qI,$

with $I$ the time-averaged current. The Fano factor is then introduced as

$F\equiv \frac{S_{\rm shot}}{2qI},$

so that $F=1$ for fully random tunnelling, $F<1$ for sub-Poissonian noise, and $F>1$ when the chosen normalization makes correlated multi-charge transfer appear super-Poissonian (Thupakula et al., 2021).

For mesoscopic conductors, the same quantity can be written in a transmission-eigenchannel language. At zero temperature, for channels with transmission probabilities $\{\tau_n\}$,

$$S_I = 2 e V G_0 \sum_n \tau_n(1-\tau_n), \qquad G = G_0 \sum_n \tau_n,$$

and

$q$0

This shows explicitly that the tunnelling limit $q$1 is Poissonian, while nearly open channels suppress noise (Tamir et al., 2021).

A finite-temperature formulation interpolates between thermal and shot-noise regimes. One expression used in the literature is

$q$2

For normal tunnel junctions, the thermal-to-shot-noise crossover is also written as

$q$3

In the low-bias limit this reduces to Johnson–Nyquist noise, whereas in the high-bias limit it approaches the Poissonian shot-noise form (Tamir et al., 2021, Zhou et al., 2017).

2. What shot noise adds to spectroscopy

The spectroscopic value of shot noise lies in its sensitivity to microscopic transport mechanisms that are not fixed by the mean current alone. In Coulomb-blockaded quantum dots, this distinction appears sharply between elastic and inelastic cotunnelling. In the elastic cotunnelling regime, the measured Fano factor is Poissonian, $q$4, whereas in the inelastic cotunnelling regime the noise becomes super-Poissonian, with $q$5 and a peak around $q$6. The interpretation given is that elastic cotunnelling transfers a single electron per cycle, while inelastic cotunnelling can be followed by sequential relaxation through an excited state, so that a “bunch” of electrons is transferred in each cycle (Okazaki et al., 2012).

In superconducting tunnelling through Yu–Shiba–Rusinov states, shot noise resolves the coexistence of single-electron and Andreev channels. The current can be decomposed as

$q$7

with total shot noise

$q$8

and an effective Fano factor

$q$9

Within this framework, sub-Poissonian noise signals time-ordering in single-electron flow, whereas $S_{\rm shot}=2qI,$0 signals a finite Andreev contribution. The same measurements were used to extract an intrinsic YSR width $S_{\rm shot}=2qI,$1 and lifetime $S_{\rm shot}=2qI,$2, even though $S_{\rm shot}=2qI,$3 and is therefore inaccessible to conventional thermally limited conductance spectroscopy (Thupakula et al., 2021).

For Kondo systems, the Fano factor itself acquires a spectroscopic lineshape. A large-$S_{\rm shot}=2qI,$4 plus Keldysh treatment predicts that $S_{\rm shot}=2qI,$5 exhibits a characteristic bias dependence arising from Kondo screening that is similar to the Kondo resonance in the differential conductance, but that its precise form is strongly dependent on the tunnelling-amplitude ratio $S_{\rm shot}=2qI,$6. The predicted low-bias behavior,

$S_{\rm shot}=2qI,$7

connects the noise directly to the same effective transmission that governs the conductance, while the interference term proportional to $S_{\rm shot}=2qI,$8 allows enhancement or suppression of $S_{\rm shot}=2qI,$9 by quantum interference between tunnelling into the conduction band and into the adatom level (Cocklin et al., 2019).

Shot-noise spectroscopy can also be used in periodically driven systems. In a weakly backscattered fractional quantum Hall edge with $I$0, the zero-frequency photoassisted noise takes the form

$I$1

where $I$2, $I$3, and $I$4. Because the chiral-Luttinger-liquid tunnelling rates exhibit a power-law singularity near zero energy, sweeping $I$5 and $I$6 allows the photoassisted absorption and emission probabilities $I$7 to be reconstructed from the peak structure of the noise (Vannucci et al., 2017).

3. Experimental architectures and detection strategies

The experimental implementations of shot-noise spectroscopy are diverse, but they share a common design principle: the relevant fluctuation signal is small, so the front-end electronics or photodetection must be configured to suppress technical backgrounds and preserve bandwidth.

Platform	Detection strategy	Characteristic capability
STM single-atom junctions	Broadband low-temperature amplifier close to the junction; cross-correlation of two channels	Local shot-noise measurements through single-atom junctions (Tamir et al., 2021)
hBN tunnel junctions	RF excess-noise detection with bias modulation and lock-in demodulation	Excess shot noise consistent with theoretical expectations (Zhou et al., 2017)
Soft X-ray transient absorption	Beam-splitting off-axis zone plate and shot-by-shot simultaneous normalization	Approaching the photon shot-noise limit at EuXFEL (Guyader et al., 2022)

In a low-temperature STM implementation for single-atom junctions, a commercial ultra-high-vacuum STM is operated at 4.3 K, and a dual-channel low-temperature broadband amplifier is mounted within a few centimeters of the junction. The tip current line is shunted via a precision resistor, the two amplifier outputs are cross-correlated to remove uncorrelated noise, and the measured voltage-noise spectral density is converted back to current noise using the parallel combination of junction and shunt. The flat gain window lies above approximately 40 kHz up to approximately 500 kHz, while the shot-noise plateau is identified in the range $I$8 to avoid both $I$9 noise and RC roll-off (Tamir et al., 2021).

A different high-frequency strategy was implemented in Au/hBN/Au tunnel devices. There, a square-wave bias switching between 0 and $F\equiv \frac{S_{\rm shot}}{2qI},$0 at 5 kHz is applied through the low-frequency port of a bias tee, while high-frequency current fluctuations in the 250–600 MHz range are routed through the RF port, filtered, amplified, and sent to a logarithmic power detector. Lock-in demodulation yields the excess noise $F\equiv \frac{S_{\rm shot}}{2qI},$1. Because the on-chip leads, wire bonds, and coaxial cables introduce significant attenuation, the measured power is related to the true noise by a collection efficiency $F\equiv \frac{S_{\rm shot}}{2qI},$2–$F\equiv \frac{S_{\rm shot}}{2qI},$3, which is calibrated with benchmark devices (Zhou et al., 2017).

Shot-noise-limited detection also appears in ultrafast photon spectroscopies. At the Spectroscopy & Coherent Scattering instrument of the European XFEL, a dedicated soft X-ray setup uses a beam-splitting off-axis zone plate in transmission to create three copies of the incoming beam. These are used to measure the transmitted intensity through the excited sample, the unexcited sample, and the incoming intensity monitor. Because the three signals are detected shot-by-shot and simultaneously, normalized shot-by-shot analysis of the transmission becomes possible. Photon detection is performed with the DSSC imaging detector, capable of recording up to 800 images at a 4.5 MHz frame rate during the FEL burst, thereby allowing the experiment to approach the photon shot-noise limit (Guyader et al., 2022).

4. Superconducting, topological, and strongly correlated matter

Superconducting junctions are among the most developed arenas for shot-noise spectroscopy because the effective transferred charge is not fixed to $F\equiv \frac{S_{\rm shot}}{2qI},$4. In an $F\equiv \frac{S_{\rm shot}}{2qI},$5-wave-tip/topological-superconductor junction, a real-time Keldysh formulation yields analytical expressions for the Andreev current and the associated current noise. In the regime $F\equiv \frac{S_{\rm shot}}{2qI},$6, where single-particle tunnelling is suppressed and Andreev reflection dominates, the Fano factor becomes

$F\equiv \frac{S_{\rm shot}}{2qI},$7

which reflects the transfer of charge $F\equiv \frac{S_{\rm shot}}{2qI},$8 per Andreev event. The same theory provides a catalog of $F\equiv \frac{S_{\rm shot}}{2qI},$9 spectra and Fano-factor behavior for BW $F=1$0-wave, chiral or helical $F=1$1-wave, polar $F=1$2, and $F=1$3 pairing states (Tei et al., 20 Jan 2026).

In superconducting STM with tunable transparency, the effective charge evolves continuously with junction conditions. Measurements on Pb(111) at 2.2 K show that, as transparency increases, the shot noise evolves from a single-electron tunnelling regime to a multiple-charge-transfer regime. In a symmetric SIS junction with a Pb-coated tip, the conductance exhibits subharmonic peaks at $F=1$4, characteristic of $F=1$5th-order multiple Andreev reflection, while the simultaneously measured $F=1$6 steps from approximately $F=1$7 at large bias through $F=1$8, $F=1$9, and beyond $F<1$0 at low bias. The reported measurements are quantitatively consistent with single-channel MAR theory and with full-counting-statistics calculations once the same $F<1$1, $F<1$2, and bias-dependent transparency are used (Sato et al., 23 Mar 2026).

A major contemporary use of shot-noise spectroscopy is to test whether a zero-bias conductance peak is genuinely Majorana-like. In Fe(Se,Te), differential conductance alone can exhibit an apparently robust zero-bias peak at defect sites, but atomic-scale shot-noise measurements reveal a different fingerprint. The extracted $F<1$3 shows both enhancement and suppression around zero bias, directly signaling unequal particle and hole amplitudes and mixed single-electron and Andreev processes. The reported range $F<1$4–$F<1$5 at $F<1$6 departs from the Majorana expectation $F<1$7 at low bias. In that study, all five measured impurity sites showed $F<1$8, and the conclusion was that the zero-bias peaks arose from trivial Yu–Shiba–Rusinov states rather than Majorana zero modes (Maiti et al., 28 Apr 2026).

The same logic extends to other correlated systems. In Kondo impurities and Kondo lattices, the Fano factor can peak or dip near zero bias depending on the sign of the tunnelling-amplitude ratio, and spatially resolved $F<1$9 is predicted to display $F>1$0 oscillations around the impurity. A plausible implication is that shot-noise spectroscopy serves not only as a “charge-counting” probe, but also as a local interferometric probe of many-body screening and tunnelling-path interference (Cocklin et al., 2019).

5. Photon shot-noise-limited Raman, absorption, and spin-noise methods

In photonic spectroscopies, shot noise usually enters as the fundamental detection floor rather than as the signal itself. For broadband stimulated Raman detection, the relevant one-sided shot-noise current spectral density of a photodiode carrying a dc photocurrent $F>1$1 is

$F>1$2

and the instantaneous signal-to-noise ratio for a small stimulated Raman gain signal with additional ac photocurrent $F>1$3 is

$F>1$4

Time-encoded Raman uses a wavelength-swept Fourier Domain Mode Locked laser and dual-balanced detection in both analog and digital domains to suppress common-mode laser noise to the shot-noise floor. The reported system has a 400 MHz detection bandwidth, a measured relative RMS noise floor of $F>1$5 at 2 mW probe power, and a benzene C–H stretch at $F>1$6 measured with $F>1$7 in a single 9 ms sweep. After averaging 1000 sweeps, the SNR rises near the ideal $F>1$8 behavior to above 500, or above 1500 when excluding small XPM baselines (Karpf et al., 2018).

Absorption spectroscopy can also be run at the conventional quantum limit imposed by photon shot noise. In one implementation, a ratio measurement of the transmission

$F>1$9

between sample and reference photodiodes removes common-mode laser-power noise. With sufficient optical power and suppression of systematic etalons and optical-pumping effects, the remaining uncertainty in transmission is set by photon shot noise. Such measurements reached a 2 ppm noise level, yielded a ten-fold improvement in the accuracy of the Cs $\{\tau_n\}$0 hyperfine splitting, and enabled determination of Boltzmann’s constant with a precision of 6 ppm and an uncertainty of 71 ppm (Truong et al., 2015).

A related differential transmission experiment recorded an absorption profile of cesium vapor at the 2 parts-per-million level and directly observed the homogeneous lineshape component while Doppler broadening was 100 times wider. By measuring the spectral profile more than 200 natural linewidths from line center, the study reported direct measurements of a low-intensity optically induced broadening process distinct from standard power broadening (Truong et al., 2012).

Noise spectroscopy in the stricter sense also appears in optically detected spin fluctuations. For spin-noise spectra modeled by a Lorentzian peak on top of a white photon shot-noise background, estimation theory gives a Fisher information matrix

$\{\tau_n\}$1

or, in the continuum,

$\{\tau_n\}$2

This framework leads to “local” standard quantum limits at fixed probe power and atom number, and “global” standard quantum limits when both are optimized. The same work reported sensitivity beyond the atom- and photon-number-optimized global standard quantum limit using squeezed light, with variances in $\{\tau_n\}$3 and $\{\tau_n\}$4 reduced by a factor approximately 0.61 relative to the coherent-probe global SQL (Lucivero et al., 2016).

6. Resolution limits, misconceptions, and broader significance

A recurrent misconception is that shot noise is merely an unwanted background. The literature instead uses it as a spectroscopic observable in its own right. In electronic systems, measuring $\{\tau_n\}$5 and $\{\tau_n\}$6 can reveal effective charge, transmission-channel structure, bunching, temporal ordering, and interference effects that are either hidden or strongly underdetermined in $\{\tau_n\}$7 or $\{\tau_n\}$8 alone (Tamir et al., 2021, Okazaki et al., 2012).

Another misconception is that conventional energy resolution always sets the ultimate limit of spectroscopy. The YSR case provides a counterexample: at a base temperature of 0.7 K, $\{\tau_n\}$9, yet shot-noise measurements inferred an intrinsic width $$S_I = 2 e V G_0 \sum_n \tau_n(1-\tau_n), \qquad G = G_0 \sum_n \tau_n,$$0 because the finite dwell time appears as a suppression of $$S_I = 2 e V G_0 \sum_n \tau_n(1-\tau_n), \qquad G = G_0 \sum_n \tau_n,$$1 below $$S_I = 2 e V G_0 \sum_n \tau_n(1-\tau_n), \qquad G = G_0 \sum_n \tau_n,$$2 by up to 10%. This shows that noise spectroscopy can access time scales and coupling rates that are thermally invisible to standard conductance measurements (Thupakula et al., 2021).

In photon-based methods, the corresponding conceptual shift is that the goal is not to eliminate shot noise altogether, but to eliminate all excess technical noise so that sensitivity is limited only by shot noise. This is the organizing principle behind dual-balanced TICO-Raman detection, quantum-limited absorption spectroscopy, shot-noise-limited soft X-ray transient absorption at an FEL, and the estimation-theoretic treatment of spin-noise measurements (Karpf et al., 2018, Truong et al., 2015, Guyader et al., 2022, Lucivero et al., 2016).

Taken together, these developments show that shot-noise spectroscopy is not a single technique but a unifying measurement paradigm. In tunnel junctions it acts as a charge- and correlation-sensitive probe of microscopic transport; in superconductors it distinguishes single-electron, Andreev, and multiple-Andreev-reflection processes; in strongly correlated systems it tracks screening and interference; and in optical and X-ray spectroscopies it defines the quantum-limited sensitivity frontier. This suggests that its most durable significance lies in converting irreducible fluctuation into quantitative spectral information rather than treating fluctuation solely as measurement error.