Active control of a plasmonic metamaterial for quantum state engineering

We experimentally demonstrate the active control of a plasmonic metamaterial operating in the quantum regime. A two-dimensional metamaterial consisting of unit cells made from gold nanorods is investigated. Using an external laser, we control the temperature of the metamaterial and carry out quantum process tomography on single-photon polarization-encoded qubits sent through, characterizing the metamaterial as a variable quantum channel. The overall polarization response can be tuned by up to 33% for particular nanorod dimensions. To explain the results, we develop a theoretical model and find that the experimental results match the predicted behavior well. This work goes beyond the use of simple passive quantum plasmonic systems and shows that external control of plasmonic elements enables a flexible device that can be used for quantum state engineering.

Figure 1

Overview and experimental setup for demonstrating active control of a metamaterial in the quantum regime. (a) Pictorial representation of one of the metamaterials used with a single photon (red) and an active control laser beam (white) sent through. The spot size of the control and single-photon beams are the same in the experiment; however, the control beam is shown smaller for pictorial purposes. The inset shows a three-dimensional figure of the nanorods in each unit cell (dimensions considered are given in the main text). (b) Experimental setup, where a nonlinear BiBO crystal is pumped at 405 nm, producing pairs of photons at 810 nm via spontaneous parametric down-conversion. One photon is detected at detector ${\text{D}}_A$ and heralds the presence of a single photon in the other arm. Here H is a half-wave plate, Q is a quarter-wave plate, L is a plano-convex lens ($f=25$ mm), PBS is a polarizing beam splitter, IF is an interference filter ($\lambda =810$ nm and $\mathrm{\Delta }\lambda =10$ nm), and ${\text{D}}_A$ and ${\text{D}}_B$ are single-photon detectors. (c) Temperature dependence of the permittivity ${\epsilon }_d$ of (i) the silica substrate and that of the gold used for the nanorods (ii) $\mathrm{Re}\left[{\epsilon }_m\right]$ and (iii) $\mathrm{Im}\left[{\epsilon }_m\right]$.

Figure 2

Temperature-dependent transmission response of metamaterials with different nanorod dimensions (theory). In (a)–(f) the period is fixed at $d_x=d_y=200$ nm and the thickness is $t=30$ nm. In (a)–(c) the lower solid resonance curve is for vertical transmission at $T=300$ K and the lower dotted resonance curve is for vertical transmission at $T=340$ K. The horizontal solid line is for horizontal transmission. The dimensions of the nanorods used are (a) width $w=46$ nm and length $l=130$ nm, (b) $w=47$ nm and $l=140$ nm, and (c) $w=48$ nm and $l=144$ nm. (d)–(f) Corresponding temperature dependence over a range of $50\mathrm{K}$ at $\lambda =810$ nm with the nanorod dimensions chosen as those used in (a)–(c), respectively. (g) Transmission response of a metamaterial with nanorod dimensions corresponding to (a) in the middle and with $\pm 2$ nm added to the length, width, and thickness.

Figure 3

Temperature-dependent transmission response of metamaterials with different nanorod dimensions (experiment). (a)–(c) Atomic force microscope images of three metamaterials used in the experiment. The period and thickness of the nanorods are approximately equal, whereas the width and length increase from (a) to (c). See the main text for dimensions. (d)–(f) Classical transmission spectra of the metamaterials at $T_0$ for horizontal (squares) and vertical (circles) polarized light. (g)–(i) Transmission probabilities in the quantum regime for single qubits encoded into the vertical polarization of single photons as $|V\rangle$ and sent through the metamaterials as the temperature is changed. The five different temperature settings are $T_0=295\mathrm{K}$, $T_1=303\mathrm{K}$, $T_2=319\mathrm{K}$, $T_3=331\mathrm{K}$, and $T_4=347\mathrm{K}$, corresponding to values consistent with the range used in the theoretical model. The values are determined by the laser power used and are spaced apart by approximately $10\mathrm{K}$.

Figure 4

Quantum process tomography $\chi$ matrices for the first metamaterial at two different temperatures $T_0$ and $T_4$. (a) and (c) Real and imaginary parts of the experimental $\chi$ matrix at $T_0$. (b) and (d) Real and imaginary parts of an ideal partial polarizer $\chi$ matrix with $T_V=0.476$. (e) and (g) Real and imaginary parts of the experimental $\chi$ matrix at $T_4$. (f) and (h) Real and imaginary parts of an ideal partial polarizer $\chi$ matrix with $T_V=0.324$.