Broadband Terahertz Time-domain Spectroscopy of Quantum Materials in a Dilution Refrigerator

TL;DR

The paper presents a broadband ultrafast terahertz time-domain spectroscopy system integrated with a dilution refrigerator and a 7 T split-coil magnet to study quantum materials at millikelvin temperatures. THz pulses are generated outside the cryostat via plasma-based mixing of 800 nm and 400 nm light and detected with a THz-ABCD detector after transmission through the sample, enabling free-space delivery through TPX windows. Cyclotron resonance in a GaAs quantum well is measured at $T_S = 145~\mathrm{mK}$ and fields up to $6~\mathrm{T}$, yielding an effective mass of $m^* = 0.073\,m_e$, slightly larger than the bulk value, with the line width limited by instrument response. This work demonstrates the feasibility of broadband THz spectroscopy in dilution refrigerators, opening avenues to study non-equilibrium dynamics and ground-state properties of quantum materials in the quantum limit, with potential extensions to two-dimensional THz spectroscopy and coherent control experiments.

Abstract

We have constructed a terahertz time domain spectroscopy system using a Bluefors dilution refrigerator with a 7 T split-coil magnet. Using a gallium arsenide single quantum well sample, terahertz waveforms were measured at 145 mK in a magnetic field range from 0 to 6 Tesla to measure cyclotron resonance. Effective mass is found to be $0.073 m_{e}$, which is larger than the commonly accepted bulk value of $0.068 m_{e}$.

Figures (4)

• Figure 1: We generate terahertz pulses by mixing the fundamental [$\lambda_1 = 800~\mathrm{nm}$] and second harmonic [$\lambda_2 = 400~\mathrm{nm}$, generated using $\mathrm{\beta-BaB_2 O_4}$ (BBO)] of the titanium:sapphire output in a plasma filament in airKim2008eq. Terahertz emission is separated from the residual visible light using a high-resistivity silicon filter (HR-Si). This is then collected by an off axis parabolic mirror into the Bluefors dilution refrigerator. Optical windows in and out of the sample chamber are TPX (polymethylpentene), which has adequate transmission in both the visible and over our terahertz bandwidthBichon2022. After the dilution refrigerator windows, the transmitted light is incident on a custom-constructed THz-ABCD detectorHo2010jv, which we use to recover the electric field, $\vec{E}\bigl(\tau\bigr)$, of the transmitted THz pulse.
• Figure 2: Inside the dilution refrigerator, the lowest flange has the He-3/He-4 mixing chamber along with a co-located temperature sensor ($T_{S}$). We have custom constructed a copper cold finger that is in thermal contact via an indium foil seal with the lowest flange. The cold finger has a $1~\mathrm{cm}$ transmission aperture that is aligned with the TPX optical windows. A second temperature sensor (RuOx Sensor, Model number: A01892, $T_{S}$) is attached to the copper finger at the sample position and will be the reported sample temperature in this manuscript. Samples are mounted on the transmission aperture using GE 7031 varnish, which ensures good thermal contact between the cold finger and sample Stephens1971. (Not shown) There are three internal radiation shields with a pair of windows each. This results in eight TPX windows on the full beam path.
• Figure 3: (a) A representative THz Waveform, $E\bigl(\tau\bigr)$, and the numerical window, $W(\tau)$ with a width of $\tau_{W} = 15~\mathrm{ps}$ applied to our data to remove secondary pulse reflections. (b) This is a simplified diagram of our sample (Sample ID: VA0605), consisting of the two dimensional layer ($d$) and a thick GaAs substrate ($L$). The windowed $E_W\bigl(\tau\bigr)$ is the single pass waveform through the structure and removes the multiple reflections/etalon from the calculated spectrum. (b) A schematic diagram of the sample, showing the origin of the multiple reflections in the time-domain or, equivalently, of the Fabry-Perot interference fringes in the frequency domain. (c) The FFT of numerically windowed spectrum from the first pass through the sample.
• Figure 4: (a) The change to the transmitted terahertz waveforms at $B$ when compared to the zero field transmitted THz waveform at $145~\mathrm{mK}$ for $1.5~\mathrm{T}$ to $6.0~\mathrm{T}$. For fields below $1.5~\mathrm{T}$ and above $6.0~\mathrm{T}$, the cyclotron resonance in GaAs is at a frequency outside of our experiments spectral bandwidth ($0.3~\mathrm{THz}\leq \nu\leq 7.0~\mathrm{THz}$). (b) Frequency spectra of the measured wave-forms calculated by taking the fast Fourier transform of the waveform data in (a). (c) A representative fitting of the spectrum line shape to a homogeneously broadened Lorentzian line shapeHilton2012. (d) The central frequency, $\nu_c\bigl(B\bigr)$ is shown on as a function of $B$. We determine the effective mass from the slope of this fitting, as discussed within the text and in Ref Wang2007dm. The line width, $\Delta \nu$ is instrument-response limited in our apparatus by the TPX window thickness and will be the focus of future development efforts.