We report a direct demonstration of quantum-enhanced sensing in the Fourier domain by comparing single- and two-photon interference in a fiber-based interferometer under strictly identical noise conditions. The simultaneous acquisition of both signals provides a common-mode reference that enables a fair and unambiguous benchmark of quantum advantage. Spectral analysis of the interferometric outputs reveals that quantum correlations do not increase the amplitude of the modulation peak, but instead lower the associated noise floor, resulting in the expected 3 dB improvement in signal-to-noise ratio. This enhancement persists in the sub-shot-noise regime, where the classical signal becomes buried in the spectral background while the two-photon contribution remains resolvable. These observations establish Fourier-domain quantum super-sensitivity as an operational and broadly applicable resource for precision interferometric sensing.
Interferometric sensors, from gravitational-wave detectors and distributed fiber systems to acoustic and optical probes, are operated and characterized in the frequency domain. Weak physical signals are identified as narrow spectral lines emerging from a continuous background in the power spectral density (PSD), rather than as absolute phase shifts in the time domain [1][2][3][4]. Their sensitivity is therefore determined by the spectral contrast, namely by how clearly a signal peak rises above the noise floor in Fourier space. In practice, detection thresholds and integration times are set by the measured noise spectra and by the resulting spectral signal-to-noise ratios [5][6][7].
Spectral-domain analysis is widely used in both classical interferometry [1][2][3][4][5][6][7] and quantum optics, for instance for state characterization [8], spatial and spectral interference [9,10], acoustic-wave detection [11], coherence tomography [12], and fractional Fourier-domain sensing [13][14][15]. By contrast, quantum-enhanced sensitivity is almost exclusively formulated in the time or phase domain, in terms of variances, Fisher information, and Cramér-Rao bounds [16][17][18][19]. As a result, quantum advantage is usually benchmarked through phase estimation, while practical interferometric sensors are optimized and compared through their PSD. Whether quantum correlations can provide a direct and operational advantage at the level of the PSD itself, by reducing the spectral noise floor against which signals are detected, has so far remained an open question.
Here we demonstrate a quantum enhancement that manifests directly in the Fourier domain of an interferometric signal. By comparing single-and two-photon interference under strictly identical technical-noise conditions, we analyze the corresponding power spectral densities and show that quantum correlations do not modify the spectral amplitude of the signal peak, but instead reduce noise background. This leads to an increased spectral signal-to-noise ratio and provides a direct, operational form of quantum-enhanced sensitivity in the frequency domain. Our results establish spectral noise reduction as a key resource for quantum-enhanced interferometric sensing, expressed in the same quantities that are used to characterize and optimize broadband, noiselimited sensors.
Since interferometric sensors are usually characterized in the frequency domain, we first formulate quantumenhanced sensitivity in terms of the PSD associated with a Poissonian photon flux. For a source with mean emission rate λ, discretely detected with time bins of duration ∆t = f -1 0 , each bin contains a random number of counts I k with mean ⟨I k ⟩ = λ∆t. The corresponding PSD, obtained from the discrete Fourier transform of the sequence {I k }, is flat and reads
which defines the shot-noise-limited spectral background (see Appendix A). Expressed in units of counts 2 /Hz, this quantity represents the variance of photon-number fluctuations per unit bandwidth and thus sets the noise floor against which any spectral signal must be resolved. We now consider an interferometric configuration in which the probe field is prepared in a correlated Nphoton state and injected into a folded Franson interferometer [20], shown in Fig. 1(a). The input state reads
where a and b denote the two arms of the interferometer. Such path-entangled states constitute a canonical arXiv:2602.16350v1 [quant-ph] 18 Feb 2026 resource for quantum-enhanced interferometry [21,22].
The N -fold phase factor reflects the collective response of the probe to the accumulated phase and is responsible for phase super-resolution. The probability to register an N -fold coincidence at the output is
where V N is the interference visibility. The prefactor 1/N ensures a fair comparison between probes of different photon number by fixing the total optical energy per measurement.
To connect with realistic sensing scenarios, we consider a small phase modulation of the form
with modulation amplitude A m , frequency f m , and operating point ϕ 0 set at mid-fringe, ϕ 0 = π/2N , such that A m ≪ V N . In this linear regime, the detection probability can be expanded to first order as
The corresponding PSD then takes the form
It consists of a flat noise floor, set by the quantum statistics of the detected probes, and a narrow spectral line at the modulation frequency. Crucially, while the height of the spectral peak is independent of N , the noise floor scales as 1/N . Quantum correlations therefore do not amplify the signal in Fourier space; they suppress the background on which it is detected. Physically, the time-domain modulation P N (t) exhibits the same oscillation amplitude for all N , but the fluctuations associated with photon counting decrease as √ N , as illustrated in Fig. 1(b,c). For unit visibility, the signalto-noise ratio of the spectral line is
leading to the scaling SNR(N )/SNR(1) = N . The quantum advantage in the Fourier d
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