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

TL;DR

This work introduces two-tone tomography to achieve complete, phase-sensitive characterization of unitary spectral-temporal transformations in quantum frequency conversion (QFC). By probing a QFC with a bichromatic seed and analyzing spectral interference, the authors reconstruct the complex Green's function $G(\omega_{out},\omega_{in})$, including its phase $\phi(\omega_{out},\omega_{in})$, up to an output-only term. They validate the method on a Bragg-scattering four-wave mixing module in Ge-doped photonic crystal fiber, revealing internal dynamics such as passive dispersion before active conversion and achieving a dispersion slope in agreement with theory. The technique provides a platform-agnostic diagnostic tool for full process tomography of QFC devices, with potential to optimize spectral-temporal mode matching in future quantum networks, and suggests hardware improvements to reach femtosecond-scale phase retrieval.

Abstract

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.

Figures (5)

• Figure 1: (a) The complex spectral transfer (Green's) function, $G(\omega_\mathrm{out},\omega_\mathrm{in})$, for the case of unchirped pulsed pumps. The heatmap shows the phase, $\phi(\omega_\mathrm{out},\omega_\mathrm{in})$, whereas the white concentric lines denote contours of the (normalized) magnitude, $|G(\omega_\mathrm{out},\omega_\mathrm{in})|$. (b) Same as (a) but with chirped pumps. (c) The optimized input mode, $f(\omega_\mathrm{in})$, for maximum conversion in the two cases: unchirped pumps (blue), and chirped pumps (red). The spectral amplitude is shown with a solid line in the unchirped case and with a dashed line in the chirped case. The spectral phase is shown with dash-dotted lines in both cases. (d) The optimized input pulse in the time domain in the unchirped case (blue, solid) and chirped case (red, dashed), respectively.
• Figure 2: (a) Experimental schematic. A Ti:Sapphire laser supplies the NIR pump with a small portion picked off to create the modulation signals for the C-Band pump (Q) and probe fields, which are independently controlled by analog delay boxes. The monitoring PD drives the pulse carving for Pump Q, while the fast PD signal is bandpass-filtered and amplified to modulate the probe around 560MHz (highlighted pink). The Green's function $G(\omega_{\mathrm{out}},\omega_{\mathrm{in}})$ characterizes the complete frequency conversion module (shaded green) consisting of a dispersive fiber (1.9km SMF-28E+), C-Band field combination in fiber beam splitter (FBS), amplification (EDFA), wavelength division multiplexer (WDM), and the Ge-PCF (20m). The output is measured by an optical spectrum analyzer (OSA). (b) Wavelength scheme for near-degenerate Bragg-scattering four-wave mixing with monochromatic pumps, illustrating frequency conversion span $\Delta\omega_{\text{BS}}$ and probe spectral shear $\Omega$. Photons are annihilated at the probe $\omega_{\text{probe}}$ and pump frequency $\omega_{\text{pump}}$, and created in the C-band pump $\omega_{\text{Q}}$ and target frequency $\omega_{\text{T}}$. (c) Variation in intensity of converted signal ($\lambda_{\text{T}}=922.63nm$) as the probe ($\lambda_{\text{probe}}=1555.5nm$) delay $\tau$ is swept from 0.5ns to 2.5ns.
• Figure 3: (a) Measured output intensity $I_{\text{out}}(\lambda_{\text{T}},\tau)$ recorded at the output wavelength for which peak conversion is achieved $\lambda_{\text{T}}=922.63nm$ (corresponding to a fixed probe wavelength $\lambda_{\text{probe}}=1555.5nm$), as the relative delay $\tau$ between the pumps and the probe is incremented in 0.5ns steps. Black dots represent experimental data, while the solid red line denotes the interpolation used for resampling. (b) Spectrogram of the target emission intensity across the full probe tuning range. The data is displayed over 0-4ns temporal window to highlight the diagonal fringes resulting from the group velocity dispersion, emphasized by two parallel dashed lines separated by $1/560MHz$. (c) Fourier transform of the time domain trace shown in (a) into the conjugate frequency space, $\bar{\omega}$, revealing a peak at the modulation frequency $\Omega=560MHz$ (the adjacent sixth harmonic is also prominent). (d) The magnitude of the spectrally resolved Fourier transform, $|\tilde{I}_{\text{out}}(\omega_{\text{out}},\bar{\omega})|$, for all probe wavelengths, from which the phase information is extracted.
• Figure 4: (a) Measured relative group delay, $\tau_{g}$, as a function of probe wavelength for the primary shear frequency $\Omega=560MHz$. The dashed line represents the linear fit yielding a dispersion slope of 34.63ps/nm with a mean $1\sigma$ uncertainty of $\pm34.2ps$. (b)-(d) Group delay retrieval for adjacent harmonics of the laser repetition rate used for validation: (b) 480MHz ($33.69ps/nm$, $\pm 33.9ps$); (c) 640MHz ($33.21ps/nm$ , $\pm 33.4ps$ ); and (d) 720MHz ($36.62ps/nm$ , $\pm 52.6ps$). All error bars represent $1\sigma$ r.m.s. deviation from the linear fit.
• Figure 5: Retrieval of the complex Green's function. (a) Reconstructed spectral intensity, $|G(\omega_{\text{out}},\omega_{\text{in}})|^2$. (b) Two dimensional map of the relative group delay $\tau_g = \frac{\partial\phi}{\partial\omega}$.