Subcycle measurement of intensity correlations in the terahertz frequency range

The terahertz frequency range is lacking an experimental implementation of Hanbury Brown and Twiss photon correlation measurements with sub-cycle time resolution and high sensitivity. Such a technique would be needed, for example, to observe photon pairs predicted to be released in a nonadiabatic modulation of an ultrastrongly coupled light-matter system. In this paper, we propose a room-temperature measurement of photon correlations in the THz range based on electro-optic sampling. We apply this technique to a THz quantum cascade laser and measure below and above threshold first- and second-order degree of coherence with a subcycle temporal resolution of 146 fs. The sensitivity of the proposed measurement scheme is so far limited to $\sim 1500$ photons. This technique can, in principle, be extended for ultrahigh bandwidth single-photon sensitivity in a wide range of frequencies.

Figure 1

Sketch of the setup to measure field and intensity correlations in the THz range by electro-optic sampling. (a) We exploit the electro-optic effect combined with a two-pulse probe scheme and ultrafast acquisition at the repetition rate of the sampling laser ($f_{\text{rep}}=90$ MHz). The electric field of the THz wave under investigation, here originating from a free-running THz quantum cascade laser, is sampled at two mutually delayed time points ($t$ and $t+\tau$), adjusted with a delay stage. The measured electric field values are recorded at the rate of arrival of laser pulses with an analog-to-digital converter (ADC) and further processed with a computation routine to measure $g^{\left(1\right)}\left(\tau \right)$ and $g^{\left(2\right)}\left(\tau \right)$. For increased SNR, the field and intensity correlation terms are measured via a lock-in technique (5 kHz, 50% duty cycle). (b) Comparison between electro-optic correlation scheme and Hanbury Brown and Twiss approach. Two-pulse electro-optic sampling allows for the measurement of correlations without any beam splitters for the characterized THz radiation and with subcycle temporal resolution, which is limited by the width of the fs probing pulse to 146 fs.

Figure 2

Subcycle correlation results of a THz quantum cascade laser lasing around 2.3 THz and setup sensitivity. (a) $g^{\left(1\right)}\left(\tau \right)$ and $g^{\left(2\right)}\left(\tau \right)$ in the single-mode emission regime. The few-cycle average of $g^{\left(2\right)}(\tau =0)=1.02$ corresponds to the expected theoretical value of a pure coherent state $[g^{\left(2\right)}(\tau =0)=1]$. (b) $g^{\left(1\right)}\left(\tau \right)$ and $g^{\left(2\right)}\left(\tau \right)$ in the multimode emission regime. The few-cycle average of $g^{\left(2\right)}(\tau =0)=1.3$ is due to multimode emission. (c) Fourier transformations of aforementioned $g^{\left(1\right)}\left(\tau \right)$ and $g^{\left(2\right)}\left(\tau \right)$ reveal laser operation around 2.3 THz and characteristic components of $g^{\left(2\right)}\left(\tau \right)$ at double frequency 4.6 THz because of subcycle temporal resolution. (d) Emission characteristics of the THz QCL under investigation, given in electric field or number of photons in the detection time window indicate a threshold around 495 mA. Below the limit number of photons of $\sim 1500$, the signal-to-noise ratio of the $g^{\left(2\right)}\left(\tau \right)$ measurement becomes inferior to one.

Figure 3

Comparison experimental results and theoretical prediction by Maxwell-Bloch equations. (a) Excellent agreement of the laser dynamics over full current range. (b) Theoretical (blue) and experimental (red) intensity correlation results for the full dynamical range of the THz QCL. $g^{\left(2\right)}(\tau =0)$ as a function of input current shows good agreement with theory: coherent emission at threshold, multimode emission at high input current, and onset of incoherent fluctuations at lasing threshold.

Figure 4

Sensitivity engineering: (a) Coherence properties of the nonlinear Pockels effect in ZnTe at probe wavelength of 778 nm. At a source frequency of 2.3 THz, the computed coherence length is approximately 8 mm and the effective crystal length is reduced to 0.5 mm at a geometrical length of 3 mm due to strong absorption (b) in this window. (c) Horn antenna with ZnTe crystal as core material for increased sensitivity. Confinement of the electric field in vertical direction is achieved by using a thin ZnTe crystal (500 $\mu \mathrm{m}$ height) between two copper plates. The flare of the horn antenna has an angle of 16.61 degrees, and the broadband character of this type of antenna insures usability at over a wide frequency range. Time domain simulations show the electric field profile inside the horn antenna and then inside the waveguide at a frequency of 2 THz.

Figure 5

Histogram representing the current noise of the balanced detectors used for correlation measurements. Lines indicate fitted distribution.