Quantum Thermometry with Single Molecules in Nanoprobes

An understanding of heat transport is relevant to developing efficient strategies for thermal management in areas of study such as microelectronics, as well as for fundamental science purposes. However, the measurement of temperatures in nanostructured environments and in cryogenic conditions remains a challenging task, requiring both high sensitivity and noninvasive approaches. Here, we present a portable nanothermometer based on a molecular two-level quantum system that operates in the (3–20)-K temperature range, with temperatures and spatial resolutions on the order of millikelvins and micrometers, respectively. We validate the performance of this molecular thermometer by estimating the thermal conductivity of a nanopatterned silicon membrane, where we find a quadratic temperature dependence. In addition, we demonstrate two-dimensional temperature mapping via the simultaneous spectroscopy of multiple probes deposited onto such a suspended membrane. Overall, these results demonstrate the unique potential of the proposed molecular thermometer to explore thermal properties with submicron accuracy and unveil related phenomena manifested at cryogenic temperatures.

Popular Summary

Temperature is one of the main parameters to be controlled and measured in most physical experiments. As the size of a sample decreases, thermometers themselves begin to perturb the system to be measured, and minimizing its invasivity becomes an important consideration. A similar problem occurs at low temperatures, where the thermal capacities of materials decrease, meaning that small amounts of heat significantly change the material temperature. These challenges are cumulative when incorporating thermometers at cryogenic temperatures with small dimensions. In this work, we show how the exploitation of the emission properties of a quantum emitter consisting of a single organic molecule inserted as an impurity into an anthracene crystal allows for the measurement of temperatures between 3 and 20 K with submicrometer spatial resolutions.

At low temperature, dibenzoterrylene (DBT) behaves as a two-level quantum system whose transition width is strongly dependent on temperature. Utilizing this fact allows for DBT to act as a low-temperature nanoscale thermometer upon appropriate calibration. We validate the performance of our nanothermometer by estimating the thermal conductance of a suspended silicon membrane. Finally, we measure the temperature profile on the membrane induced by a heating laser by simultaneously probing many DBT molecules distributed at different positions on the surface.

We show that the sensitivity obtained is unprecedented in our size and temperature range. These characteristics are promising for future investigations concerning thermal-conduction regimes beyond Fourier diffusion and for accurately monitoring temperature in micrometer-scale structures.

Figure 1

An illustration of the experimental setup and working principle. A sketch of the experimental setup is shown on the left, in which an excitation laser (red beam) interrogates the molecular thermometers (red disks on a patterned silicon membrane) consisting of dibenzoterrylene (DBT) molecules in anthracene (Ac) nanocrystals (NCx) emitting single photons (red spots), while the heating laser (yellow beam) acts as a controllable heating source. The Stokes-shifted fluorescence intensity ($I_S$) is collected as a function of ${\omega }_L$, giving rise to Lorentzian peaks with temperature-dependent line widths. The relevant energy levels (center) of DBT-Ac NCx, where $|S_0⟩$ and $|S_1⟩$ represent the singlet ground and excited states, respectively. As the temperature increases, the energy levels, and in consequence the transition lines, broaden in a reproducible way, providing an ideal optical transduction (see the graph on the right).

Figure 2

The performance of a DBT-Ac nanocyrstal as a thermometer. (a) The intensity of the Stokes-shifted emission of a DBT-Ac nanocrystal on a silicon substrate as a function of the frequency detuning ($\mathrm{\Delta }\omega$) between the excitation laser and the molecule ZPL for different sample temperatures. The dashed line displays a representative fit of the measurement to a Lorentzian peak. (b) Calibration curves, i.e., line width versus sample temperature, on gold (yellow), silicon (blue), and a patterned silicon membrane (green). The scattered points show the experimental measurements with error bars and the dashed and solid lines display the best fits to ${\mathrm{\Gamma }}_2(T)={\mathrm{\Gamma }}_1/2+{\mathrm{\Gamma }}_2^{\ast }(T)$ with ${\mathrm{\Gamma }}_2^{\ast }(T)$ given by Eq. (1). (c) The power dependence of the line width at $T=2.8$ K. (d) The thermometer relative sensitivity ($S_r$, scattered points) and temperature resolution ($\mathrm{\Delta }T$, dashed lines) as a function of the temperature [colors as in (b)].

Figure 3

The temperature profile on a silicon-patterned membrane. (a) A sketch of the sample cross section with the heating and probe laser (yellow and red beam, respectively). The insets at the foot show scanning-electron-microscope (SEM) images of the sample: the complete membrane (shown in the left inset) depicts the surrounding frame, while the shamrock-shaped pattern is visible in the right inset. (b) The line width versus the relative distance between the moving heating laser and the DBT-Ac nanocrystal. The error bars correspond to repeated laser scans as explained in Sec. 3a. The inset shows a schematic of the measurement configuration, with the fixed probe laser on the NCx (the red disk on the surface of the sample) and the displacing heat source. The dashed vertical line indicates the frame position. (c) The temperature profile as a function of the relative distance. The black squares denote temperatures estimated from experimental measurements in (b), considering a calibration curve as described in Sec. 3a. The solid lines represent the calculated temperature profiles assuming different power laws ($\nu$) for the dependence of the thermal conductivity on the temperature [see Eq. (F4)].

Figure 4

2D temperature mapping on a patterned silicon surface. (a) The measured and calculated temperature profiles (color scale) for the suspended membrane also analyzed in Fig. 3. The experimental points are highlighted with circles. The position of the heating laser is indicated with a white $x$. The inset shows a schematic of the measurement configuration, in which the heating laser (yellow beam) remains static while the excitation laser (expanded red beam) allows for the collection of fluorescence (red dots) from several molecular thermometers (red disks on the surface of the sample) simultaneously, providing a temperature map of the sample. (b) The dependence of the temperature on the heating-laser power for four DBT-Ac nanocrystals, labeled as $A$, $B$, $C$, and $D$, positioned as highlighted in (a) [see Eq. (F4)]. (c) The temperature as a function of the DBT-Ac nanocrystal distance with respect to the heating source at 4-$\text{μ}\mathrm{W}$ heating-laser power. The black squares correspond to experimental data, whereas the red circles denote the calculated temperature, assuming $\nu =2$.

Figure 5

A histogram of the relative arrival time between the two SPADs in the Hanbury Brown–Twiss configuration. The solid red line is a single exponential fit to the data, yielding $g^{(2)}(0)=0.02\pm 0.04$ and ${\tau }_1=3.5\pm 0.2$ ns.

Figure 6

The temperature profile on a broken patterned silicon membrane. (a) A cross section of the sample indicating the thickness of the membrane, the substrate, and the space between them, together with a representative placement of the position of the lasers (red and yellow beams). An SEM image of the complete membrane reveals the frame surrounding the membrane in the inset on the left. The inset on the right shows the shamrock-shaped pattern of the membrane. (b) The line width versus the relative distance between the moving heating laser and the DBT-Ac nanocrystal. The error bars correspond to repeated laser scans, as explained in Sec. 3a. The inset shows a schematic of the configuration in which the measurements are taken, interrogating only one nanocrystal while displacing the heat source. In addition, the dashed vertical lines indicate the location of the frame and the tear with respect to the position of the nanocrystal. (c) The temperature profile as a function of the relative distance between the moving heating laser and the DBT-Ac nanocrystal. The red circles denote temperatures estimated from experimental measurements in (b) considering a calibration curve as described in Sec. 3a. The solid lines represent simulated temperature profiles assuming different power laws of dependence of the thermal conductivity on the temperature, as well as the presence or lack thereof of the tear, as described in the text.

Figure 7

2D temperature mapping on a nonsuspended patterned silicon surface. (a) A schematic of the measurement configuration, in which the heating laser (yellow beam) remains static while the excitation laser (expanded red beam) allows collection of the photoluminescence (red spots of light) of several molecular thermometers (red hexagonal crystals on the sample) simultaneously, providing a temperature map of the sample. The sample consists of a SOI substrate with a 250-nm-thick silicon device layer with the pattern shown in the inset in a SEM image, a 3-$\text{μ}\text{m}$ silicon dioxide buried oxide middle layer, and a 600-$\text{μ}\text{m}$ silicon substrate. (b),(c) Optical microscope (b) and SEM (c) images before and after performing measurements in the cryostat, respectively. (d) A top view of a corner of the patterned silicon surface. The heating laser and DBT-Ac nanocrystals are represented by a yellow circle and small squares, respectively. The color scale denotes the temperature measured by each molecular thermometer on the sample surface. (e) The dependence of the line width on the heating-laser power for four DBT-Ac nanocrystals, labeled as A, B, C, and D, highlighted in white in (d). (f) The temperature as a function of the DBT-Ac nanocrystal distance with respect to the heating source at a given heating power of $180\text{μ}\mathrm{W}$. The colored squares correspond to labeled nanocrystals in (e) with the same color code. The inset shows the speckle pattern of the heating laser on the sample surface.

Figure 8

Examples of calibration curves of different molecules on a silicon substrate. The scattered points represent the experimental data, whereas the solid lines correspond to fitting curves according to ${\mathrm{\Gamma }}_2(T)={\mathrm{\Gamma }}_1/2+{\mathrm{\Gamma }}_2^{\ast }(T)$ and Eq. (1). The fixed values of parameters $\mu$ and $\xi$ are $6.3\times {10}^{-6}{\mathrm{ps}}^5$ and $6.1{\mathrm{ps}}^{-1}$, respectively, which are the same values as in the main text.

Figure 9

The temperature as a function of the distance from the heater is shown for different values of the thermal conductivity exponent $\nu$. The solid lines are the results of the simulations using Eq. (F5) and the squares and dashed lines represent the results of the theory evaluating Eq. (F4) for a square and a circular membrane, respectively. The parameters used are ${\kappa }_0=0.0084$ and ${\kappa }_0=0.00155$ for $\nu =0$ and $\nu =2$, respectively. We have further assumed a Gaussian heating profile at the center of power $1\mathrm{\%}\times 4\text{μ}\mathrm{W}$ and radius $1.5\text{μ}\mathrm{m}$. The membrane thickness has been assumed to be 250 nm.