Roberto Leoni

SPIE Digital Library Proceedings

DOI: https://doi.org/10.1103/PhysRevB.98.119901

We design a hybrid-dipole antenna split-ring resonator based cavities with extremely small effective mode volumes to probe ultra-strong coupling on less than 100 electrons, showing an effective mass heavier than the uncoupled cyclotron mass.

Ultrastrong light-matter coupling allows the exploration of new states of matter through the interaction of strong vacuum fields with huge electronic dipoles. By using hybrid dipole antenna-split ring resonator-based cavities with extremely small effective mode volumes V_eff/λ₀³ ≃ 6 × 10^–10 and surfaces S_eff/λ₀² ≃ 3.5 × 10^–7, we probe the ultrastrong light-matter coupling at 300 GHz to less than 100 electrons located in the last occupied Landau level of a high mobility two-dimensional electron gas, measuring a normalized coupling ratio of Ω_R/ω_c = 0.36. Effects of the extremely reduced cavity dimensions are observed as the light-matter coupled system is better described by an effective mass heavier than the uncoupled one. These results open the way to ultrastrong coupling at the single-electron level in two-dimensional electron systems.

We report on the design, fabrication and electro-optical characterization at T = 2.9 K of a photon number resolving detector designed to obtain a pulse-position resolution. This pulse-position-resolving detector (PPRD) is based on the spatial multiplexing of four superconducting nanowire avalanche photodiodes (SNAPs) [8, 9] connected in series. We choose to exploit the 2-SNAP configuration (i.e., 2 connected in parallel nanowires) to improve the signal-to-noise ratio (SNR) of the PPRD. Each pixel (i.e., a 2-SNAP) has in parallel AuPd resistor Ri (with i = 1, 4) of different value. As a result of a detection event, each pixel produces a pulse with peak voltage I_bR_i, allowing in this way position resolution of the detection event.

We measure the maximal distance at which two absorbed photons can jointly trigger a detection event in NbN nanowire superconducting single photon detector microbridges by comparing the one-photon and two-photon efficiencies of bridges of different overall lengths, from 0 to 400 nm. We find a length of 23 ± 2 nm. This value is in good agreement with the size of the quasiparticle cloud at the time of the detection event.

We show the fabrication and the electro-optical characterization at 2.9 K of a photon number resolving detector modified to obtain a pulse position resolution. The detector exploits the spatial multiplexing of four SNSPDs connected in series: each pixel has in parallel an on-chip resistor of different value Ri. To improve the signal to noise ratio (SNR) of the pulse-position- resolving detector (PPRD), two parallel wires arranged in the so-called SNAP configuration has been used in each pixel.

Summary form only given. Strong light-matter coupling has been recently successfully explored in the GHz and THz [1] range with on-chip platforms. New and intriguing quantum optical phenomena have been predicted in the ultrastrong coupling regime [2], when the coupling strength Ω becomes comparable to the unperturbed frequency of the system ω. We recently proposed a new experimental platform where we couple the inter-Landau level transition of an high-mobility 2DEG to the highly subwavelength photonic mode of an LC meta-atom [3] showing very large Ω/ω _c = 0.87. Our system benefits from the collective enhancement of the light-matter coupling which comes from the scaling of the coupling Ω ∝ √n, were n is the number of optically active electrons. In our previous experiments [3] and in literature [4] this number varies from 10 ⁴ -10 ³ electrons per meta-atom. We now engineer a new cavity, resonant at 290 GHz, with an extremely reduced effective mode surface S _eff = 4 × 10 ^-14 m ² (FE simulations, CST), yielding large field enhancements above 1500 and allowing to enter the few (<;100) electron regime. It consist of a complementary metasurface with two very sharp metallic tips separated by a 60 nm gap (Fig.1(a, b)) on top of a single triangular quantum well. THz-TDS transmission experiments as a function of the applied magnetic field reveal strong anticrossing of the cavity mode with linear cyclotron dispersion. Measurements for arrays of only 12 cavities are reported in Fig.1(c). On the top horizontal axis we report the number of electrons occupying the topmost Landau level as a function of the magnetic field. At the anticrossing field of B=0.73 T we measure approximately 60 electrons ultra strongly coupled (Ω/ω _c = 0.3) to the cavity mode. We also performed measurements of single resonators at 280 GHz (data not shown) where we measure a normalized ratio Ω/ω _c = 0.08 for 100 electrons and Ω/ω _c = 0.05 for 60 electrons. These experiments open up the possibility of single-object ultrastrong coupling experiments on few electrons.

Strong light-matter coupling lies at the heart of quantum optics and recently has been successfully explored also in the GHz and THz range. New, intriguing quantum optical phenomena have been predicted in the ultrastrong coupling regime, when the coupling strength Omega becomes comparable to the unperturbed frequency of the system omega_c. We recently proposed a new experimental platform where the physics of the ultrastrong coupling can be investigated at GHz-THz frequencies. We couple the inter-Landau level transition of an high-mobility 2 dimensional electron gas (2DEG) to the subwavelength photonic mode of an LC meta-atom. Our system benefits from the collective enhancement of the light-matter coupling which comes from the scaling of the coupling constant Omega with the square root of the number of electrons in the last Landau level. In our previous experiments and in literature this number varies from 10000-1000 electrons per resonator. Here we present ultrastrong coupling between a high-mobility 2DEG (mu=2.3X 10^6 cm^2/Vs) and an extremely subwavelength hybrid-LC resonator ensemble (11 resonators) with an highly reduced effective mode volume V_eff=4 x 10^-19 m^3=4 x 10^(-10) lambda^3 at a frequency of 300 GHz. The number of optically active electrons is given by the flux quantum multiplied by the effective resonator area and is proportional to the magnetic field. At the anticrossing field of B=0.73 T we measure less than 80 electrons ultrastrongly coupled to the resonator with a normalized coupling ratio Omega/omega_c=0.35. This experiment paves the way towards the study of ultrastrong coupling physics in the regime of quantum non-linearities.