Phase-sensitive characterization of a quantum frequency converter by spectral interferometry

We introduce an experimental technique for complete phase-sensitive characterization of arbitrary unitary spectral-temporal transformations of optical modes. Our method recovers the complex spectral transfer function, or Green’s function, of a frequency converter by analyzing spectral interference in the response to a tunable bichromatic probe. We perform a proof-of-concept experiment on a frequency conversion module based on Bragg-scattering four-wave mixing in photonic crystal fiber. Our results validate our technique by recovering useful information in the phase of the Green’s function, revealing the relative positions of regions of active frequency conversion and passive dispersive propagation within the module. Our work introduces a new approach to characterizing the performance of a variety of active devices with diverse applications in emerging quantum technologies.

💡 Research Summary

The paper introduces a novel experimental method, termed “two‑tone tomography,” for the complete phase‑sensitive characterization of quantum frequency converters (QFCs). Conventional QFC characterizations typically report only conversion efficiencies, which provide information about the magnitude of the Green’s function |G(ω_out, ω_in)|² but omit the crucial spectral phase ϕ(ω_out, ω_in)=arg G. The phase determines how non‑monochromatic quantum states interact with the device, influences optimal input pulse shaping, and reveals internal dynamics such as the spatial distribution of active nonlinear interaction versus passive dispersive propagation.

The authors model a QFC as a linear, unitary transformation under undepleted‑pump conditions, described by the Green’s function G(ω_out, ω_in). To retrieve both amplitude and phase, they probe the device with a bichromatic (two‑tone) coherent state consisting of two narrow spectral lines separated by a tunable frequency shear Ω and delayed by τ. The output intensity I_out(ω_out, τ) contains a τ‑independent term I₀(ω_out) and an interference term ˜I_out(ω_out) e^{iΩτ}+c.c., where ˜I_out(ω_out)=G(ω_out, ω₀+Ω/2) G⁎(ω_out, ω₀−Ω/2). By scanning τ over one period (0 → 2π/Ω) and Fourier‑transforming with respect to τ, the interference component is isolated in the frequency domain at ±Ω. The complex argument of ˜I_out yields the phase difference Δϕ(ω_out, ω₀)=ϕ(ω_out, ω₀+Ω/2)−ϕ(ω_out, ω₀−Ω/2). If Ω is sufficiently small, Δϕ≈(∂ϕ/∂ω_in)·Ω, allowing the derivative of the phase with respect to input frequency to be measured. Integrating Δϕ over the range of ω₀ reconstructs the full phase map ϕ(ω_out, ω_in) up to an additive term χ(ω_out) that corresponds to post‑conversion dispersion and does not affect conversion efficiency or optimal input shaping.

Experimentally, the technique is demonstrated on a Bragg‑scattering four‑wave‑mixing (BS‑FWM) frequency converter implemented in a 20 m germanium‑doped photonic crystal fiber (Ge‑PCF). The pump is a 35 ps, 923 nm Ti:Sapphire pulse, while the C‑band (≈1550 nm) pump and probe are generated from continuous‑wave lasers and modulated by electro‑optic modulators (EOMs). The probe is frequency‑sheared by driving its EOM with the seventh harmonic (Ω≈560 MHz) of the Ti:Sapphire repetition rate, maximizing the shear within the 600 MHz bandwidth of the detection electronics. The probe delay τ is scanned electronically with 0.5 ns steps, and the output spectrum is recorded on an optical spectrum analyzer. A known dispersive segment (1.9 km SMF‑28) is inserted before the converter to validate the phase extraction; the recovered phase correctly reproduces the added dispersion, confirming the method’s accuracy.

The recovered Green’s function shows that the amplitude |G|² matches conventional efficiency measurements, while the phase map reveals distinct features: (i) a nearly flat phase for unchirped pumps, and (ii) a quadratic phase across both input and output axes when the pumps are linearly chirped. This quadratic phase directly dictates that the optimal input pulse must carry a matching quadratic spectral phase; otherwise, overlap with the active conversion region is reduced, leading to >50 % loss in efficiency. Moreover, the phase profile indicates the position of the active nonlinear region relative to passive dispersive sections, effectively “opening the black box” of the device.

Key advantages of two‑tone tomography are: (1) it requires only a simple bichromatic probe rather than a large set of shaped pulses, dramatically reducing experimental complexity; (2) the measured phase difference scales with Ω, so larger shears improve signal‑to‑noise ratio; (3) the method is agnostic to the specific nonlinear process and can be applied to any unitary time‑frequency converter based on χ^(2) or χ^(3) interactions. Limitations include the need for sufficiently small Ω to maintain linearity of ϕ across the shear, the requirement for high‑speed RF electronics, and the fact that only relative phase (up to χ(ω_out)) is obtained, necessitating separate calibration for absolute timing.

Overall, the work provides a powerful, experimentally accessible tool for fully characterizing quantum frequency converters, enabling precise optimization of input quantum states, diagnosis of internal device structure, and benchmarking of emerging quantum photonic technologies such as quantum networks, multiplexed single‑photon sources, and frequency‑domain quantum processors.