Nonequilibrium plasmon liquid in a Josephson junction chain

Abstract

Equilibrium quantum systems are often described by a gas of weakly-interacting normal modes. Bringing such systems far from equilibrium, however, can drastically enhance mode-to-mode interactions. Understanding the resulting liquid is a fundamental question for quantum statistical mechanics, and a practical question for engineering driven quantum devices. To tackle this question, we probe the nonequilibrium kinetics of one-dimensional plasmons in a long chain of Josephson junctions. We introduce multimode spectroscopy to controllably study the departure from equilibrium, witnessing the evolution from pairwise coupling between plasma modes at weak driving to dramatic, high-order, cascaded couplings at strong driving. Scaling to many-mode drives, we stimulate interactions between hundreds of modes, resulting in near-continuum internal dynamics. Imaging the resulting nonequilibrium plasmon populations, we then resolve the non-local redistribution of energy in the response to a weak perturbation -- an explicit verification of the emergence of a strongly interacting, non-equilibrium liquid of plasmons.

Figures (16)

• Figure 1: Microwave spectroscopy of the JJ-chain.(A) An optical micrograph of the device mounted on a sample holder, with a silicon chip measuring $7\!\times\!7$ mm. To the right, a scanning electron microscopy (SEM) image of the JJ-chain is shown. (B) Linear response transmission magnitude ($S_{21}$) of the device with background cross-talk subtracted (see Fig. S4). (C) Schematic of the three-tone measurement: two coherent tones pump modes $p$ and $q$, while a weak read-out tone near mode $k$ is used to measure $S_{21}$. (D-E)$S_{21}$ data measured around mode $k=29$ with modes $p=25$ and $q=26$ pumped at equal power $P$ at room temperature. In (D), $S_{21}$ without pumps is plotted in gray for comparison.
• Figure 2: Matrix element scaling.(A) The mode of interest $k$ couples to modes $k\pm\delta$ with the coupling strength $g$. By sweeping the detuning between two pumps, $\Delta/2\pi$, resonant coupling can be achieved. (B, C) Experimental and theoretical transmission around mode $k=29$, when modes $p=41$ and $q=44$ are pumped. The colored guides indicate energy-conserving couplings between modes $k$ with $k+\delta$ (blue) and $k$ with $k-\delta$ (red). (D) Transmission for resonant coupling between $k$ with $k-\delta$ for different pump powers. Darker lines are fits of the experimental data to the equation Eq. (S25). Pump detuning dependence for these pump powers is shown in Fig. S7. (E) Coupling strength $g$ vs product of occupations of pumped modes, $n_p n_q$, closely follows a square root law. Different markers represent decay-like coupling (modes $k$ and $k-\delta$) and excitation-like coupling (modes $k$ and $k+\delta$). (F) Coupling strength $g$, normalized by the occupations of the pumped modes, increases with the read-out mode $k$. In each dataset pumped modes are fixed and both decay-like and excitation-like couplings are measured (see legend).
• Figure 3: Cascades.(A) For sufficiently strong drives, mode $k$ couples to modes separated by integer multiples of $\delta$, $i\cdot\delta$, where $i$ takes both positive and negative integer values. (B, D) Transmission measured around mode $k=46$ with two strong drives applied. Additional features appear for both pumping configurations: $p,q < k$(B) and $p,q > k$(D). (C) Numerically calculated transmission for the same configuration as in (D). In (B-D), colored arrows indicate processes schematically depicted in (A), where blue arrows represent excitation-like processes and red arrows represent decay-like processes.
• Figure 4: Direct observation of scattered photons.(A) Schematic of the noise measurement $P_\mathrm{N}$ for cascaded scattering with orders $-1$, $-2$, and $-3$. Positive orders are measured analogously. (B) Noise power $P_\mathrm{N}$ is measured for the processes with $|i| \leq 3$. The intensity of the color represents the number of photons emitted from the cavity, on top of a background consisting of amplified input-referred added noise (of $\approx -103$ dBm). The data in each panel are measured in the same pumping configuration, with the weak tone around $k=46$ and two pump tones $p=63$ and $q=66$. Colored guides (same colors as in (A)) show when the photon from the weak tone can be resonantly scattered to the mode $k + i \cdot \delta$.
• Figure 5: Incoherent broadband drive.(A) Schematic of the experiment. The first 13 modes are pumped using an incoherent broadband source, with power controlled by a variable attenuator. Modes within the measurement band are probed with a weak tone, and the excess decay $\delta\kappa$ is extracted. (B) Under incoherent drive, the modes experience Kerr shift and an increase in linewidth. (C) Measured excess decay $\delta\kappa$ as a function of noise power (points). Solid lines represent results from simulations of kinetic equation, the dashed lines serve as a guide to the power law scaling of the decay. (D) Measurements of nonequilibrium occupations at 5 dB attenuation drive. The excess noise power spectral density, $\Delta P$, is measured with and without a weak tone applied to mode 41. Inset shows the nonequilibrium steady state distribution obtained by integrating the noise power spectral density from (D). Yellow marker indicates occupation of mode 41 calculated using cavity coupling parameters and the weak tone power.