Quantum-enhanced time-domain spectroscopy

Abstract

The time-resolved detection of mid- to far-infrared electric fields absorbed and emitted by molecules is among the most sensitive spectroscopic approaches and has the potential to transform sensing in fields such as security screening, quality control, and medical diagnostics. However, the sensitivity of the standard detection approach, which relies on encoding the far-infrared electric field into amplitude modulation of a visible or near-infrared probe laser pulse, is limited by the shot noise of the latter. This constraint cannot be overcome without using a quantum resource. Here, we show that this constraint can be overcome using a two-mode squeezed state. Quantum-correlated ultrashort pulses, generated by parametric down-conversion, enhance the sensitivity of far-infrared detection beyond the classical limit, achieving a twofold reduction in measured noise. This advancement paves the way for further development of ultrafast quantum metrology, moving toward quantum-enhanced time-resolved electric field spectroscopy with sensitivities beyond the standard quantum limit.

Fig. 1.. Schematic of the experimental setup.

A 1030-nm, 250-fs-duration, 100-kHz-repetition-rate laser is split into two branches. The bottom branch (in red in the figure) pumps a GaP crystal, leading to the generation of a single-cycle THz pulse (yellow). The top branch (p-polarized, also in red) seeds a parametric amplifier pumped by a synchronized laser (s-polarized, green in the figure) at 515 nm, generating a two-mode squeezed vacuum (p-polarized), consisting of photon number correlated signal (purple) and idler (cyan) pulses. The idler polarization is rotated to s-polarization using a half-wave plate (HWP). The signal pulse is used for the electro-optical (EO) detection of the THz electric field while the idler is delayed to not interact with the THz pulse and serves as a reference. The EO modulation is analyzed by a polarimetric arrangement comprising an HWP, a Wollaston polarizer, and a low-noise, high–quantum-efficiency balanced detector. The temporal resolution is achieved by delaying the THz with respect to the signal and idler pulses using a linear translation stage. Note that the idler polarization impinging on the EO crystal is orthogonal (s-polarized) to that of the signal, and both are rotated by 45° with an HWP before interacting with the linearly polarized THz field in the EO crystal, and then are rotated back to almost the same initial condition before reaching the Wollaston prism.

Fig. 2.. Noise analysis.

(A) Spectral noise density of the differential signal recorded by our balanced detector illuminated by two coherent sources of equal amplitude as a function of the total power impinging on the two photodiodes (input power). The red line is the expected shot noise. The experimental data match well with the theoretical prediction, confirming that the detection is shot-noise limited. The inset shows a far-field image of the radiation generated by parametric down-conversion in the BBO crystal. The faint ring is the spontaneous PDC (SPDC) radiation while the two spots are the amplified seed (signal) and the idler beams. (B) Left axis: noise reduction factor (NRF) in the decibel scale for the squeezed source and detector used in our experiment and recorded using the setup shown in Fig. 1 in the absence of the THz signal. Note that the NRF is computed without subtraction of the electronic noise. The red curve is a fit of the data that serves as a guide for the eye. Right axis: ratio of the total measured noise to the electronic noise.

Fig. 3.. Noise analysis for the THz-TDS measurement.

(A) Time-resolved THz electric field amplitude measured with the approach described in the text. The error bars on both curves (classical in blue and quantum enhanced in red) are obtained from the experimental data calculating the SD of the spectral noise density within a selected frequency band. (B) Standard deviation of the electric field resolved in time for the classical (blue) and quantum (red) acquisitions. The dashed lines are the averages in both cases (with values reported in the figure panel). (C) and (D) are the normalized electric field value acquired over 1 min for the classical and quantum measurements, respectively. Values within 1 SD are shown in both cases with a shaded area.

Fig. 4.. Spectral analysis.

Normalized power spectral density (PSD, solid colors, right axis) for the classical (light green) and quantum (light purple) measurements, computed as explained in the text. Note the smaller error bars in the quantum case. The red and blue crosses show the values of the sensitivity improvement in the estimation of the spectral phase and power spectral density, respectively (left axis, see the main text for details). The solid blue and red curves are interpolants that serve as a guide for the eye.