Terahertz quantum sensing

Abstract

Quantum sensing is highly attractive for accessing spectral regions in which the detection of photons is technically challenging: Sample information is gained in the spectral region of interest and transferred via biphoton correlations into another spectral range, for which highly sensitive detectors are available. This is especially beneficial for terahertz radiation, where no semiconductor detectors are available and coherent detection schemes or cryogenically cooled bolometers have to be used. Here, we report on the first demonstration of quantum sensing in the terahertz frequency range in which the terahertz photons interact with a sample in free space and information about the sample thickness is obtained by the detection of visible photons. As a first demonstration, we show layer thickness measurements with terahertz photons based on biphoton interference. As nondestructive layer thickness measurements are of high industrial relevance, our experiments might be seen as a first step toward industrial quantum sensing applications.

Fig. 1. Scheme and nomenclature for the theoretical analysis.

In addition to a laser pump (for simplification, not drawn here), the signal (s₁) and idler (i₁) input modes enter the nonlinear crystal (NL). The interaction in the crystal leads to the generation of signal and idler photons in the output modes ${\mathrm{s}\prime }_1$ and ${\mathrm{i}\prime }_1$, respectively. They are separated by an indium tin oxide (ITO)–coated glass. Afterward, the signal radiation and the pump beam are reflected back into the crystal by the mirror M_s. The input modes for the second passage are denoted by i₂ and s_2, which is, because of the alignment, equal to ${\mathrm{s}\prime }_1$. The idler mode ${\mathrm{i}\prime }_1$ passes through the object (O), is reflected by the mirror M_i, and propagates through the object again. This acts as a beam splitter (BS) with second input mode 3 and output modes ${\mathrm{i}″}_1$ and 3^′. Aligning the idler beams, the mode ${\mathrm{i}″}_1$ corresponds to i₂. The output modes after the second passage are ${\mathrm{s}\prime }_2$ and ${\mathrm{i}″}_2$. Last, the signal radiation (in mode ${\mathrm{s}\prime }_2$) is detected by the detector. The inset shows the simulated interference signal in the Stokes (red) and anti-Stokes (blue) regions based on the detailed model (see Materials and Methods).

Fig. 2. Schematic of the experimental setup.

A continuous-wave laser with a wavelength of 659.58 nm is reflected by a VBG (VBG₁) into the interferometer part of the setup through a zero-order half-wave plate (λ/2) controlling the polarization. It is then focused by a lens f₁ into a periodically poled 1-mm-long MgO-doped LiNbO₃ (PPLN) crystal generating signal and terahertz photons that are separated by an ITO. Signal and pump radiation are reflected at M_s directly into the crystal. The terahertz radiation passes the object twice, being reflected by a moveable mirror M_i. In the second traverse of the pump through the PPLN, additional signal and idler photons are generated. Afterward, the lens f₁ collimates the pump and signal radiation for the detection starting with filtering the pump radiation by three VBGs and spatial filters (SF). To obtain the frequency-angular spectrum, the signal radiation is focused through a transmission grating (TG) by the lens f₂ onto a sCMOS camera. The inset shows a frequency-angular spectrum for the used crystal (poling period Λ = 90 μm, pumped with 450 mW). The scattering angle corresponds to the angle after the transmission from the crystal to air.

Fig. 3. Terahertz quantum interference.

In the collinear forward spot of the signal, interference is observed in the (A) Stokes and (B) anti-Stokes regions. (C and D) Corresponding FFTs peaks at about 1.26 THz. By placing an additional ITO glass in the idler path, no interference can be observed, and the peaks in the FFTs disappear.

Fig. 4. Terahertz quantum sensing.

The envelope of the interference is shifted depending on the thickness of the PTFE plate in the (A) Stokes and (B) anti-Stokes parts. (C) Thickness of the PTFE plate measured by quantum interference over PTFE thickness measured by a micrometer caliper. The solid line is the angle bisector. The horizontal error bars (hidden by the data points) take into account the uneven thicknesses of the PTFE plates and the inaccuracy of the reference measurement. The vertical error bars result from the precision of determining the shift of the envelope center of the interference.

Fig. 5. Investigation of induced emission by idler radiation generated in the first passage.

The count rates of the collinear Stokes (red, cross) and anti-Stokes (blue, plus) regions are shown for the cases of the idler beam being blocked (crosses) and unblocked (colored dots) for various pump powers. The triangles are the ratios between the unblocked and blocked cases. All values are close to a ratio of 1.00 (dashed line), which lies in the range of all error bars.

Fig. 6. Idler angular distribution.

The idler angular density Γ(θ_i) corresponding to collinear signal angles is plotted as a function of the idler angle inside the PPLN crystal θ_i for three different pump radii.