Tunable frequency conversion and comb generation with a superconducting artificial atom

Abstract

We investigate the power spectral density emitted by a superconducting artificial atom coupled to the end of a semi-infinite transmission line and driven by two continuous radio-frequency fields. In this setup, we observe the generation of multiple frequency peaks and the formation of frequency combs with equal detuning between those peaks. The frequency peaks originate from wave mixing of the drive fields, mediated by the artificial atom, highlighting the potential of this system as both a frequency converter and a frequency-comb generator. We demonstrate precise control and tunability in generating these frequency features, aligning well with theoretical predictions, across a relatively wide frequency range (tens of MHz, exceeding the linewidth of the artificial atom). The extensive and simple tunability of this frequency converter and comb generator, combined with its small physical footprint, makes it promising for quantum optics on chips and other applications in quantum technology.

Figures (4)

• Figure 1: Experimental scheme, sample, and theoretical model. (a) Simplified schematic of the experimental setup, featuring two input fields, with carrier frequencies $\omega_1$ and $\omega_2$, combined via an RF combiner in adding mode at room temperature. The sample (red dashed box) is placed at the bottom of a dilution refrigerator at [10]mK. The input and output fields are separated by a cryogenic circulator, with the output field amplified and measured by a spectrum analyzer (SA; see the Supplementary Material Supp Section S1 for details). (b) Device used in this experiment. A single artificial atom (transmon), a superconducting circuit, is capacitively coupled to the end of a semi-infinite transmission line wen2018reflectivePhysRevA.109.023705. The vertical line is a local flux line that is not utilized in this work. We employ only a single input-output port, as indicated by the incident (red and green) and reflected (black) fields. The small green square marks the position of the superconducting quantum interference device (SQUID); the inset is a scanning electron microscope (SEM) image of the SQUID, which has two Josephson junctions. (c) An $M$-level transmon, with $M = 5$, serving as a nonlinear medium, is pumped by the two continuous RF fields with carrier frequencies $\omega_1$ and $\omega_2$, respectively, with frequency difference $\Delta \omega = \omega_2 - \omega_1$. The detailed theoretical model is presented in Section S4 of the Supplementary Material Supp.
• Figure 2: Frequency up- and down-conversion. Two continuous fields at frequencies $\omega_1$ and $\omega_2$ are applied with a fixed power of $P_2 = \unit[-125]{dBm}$, and the normalized power spectral density is measured under three distinct input powers $P_1$: (a) $\unit[-129]{dBm}$, (b) $\unit[-125]{dBm}$, and (c) $\unit[-121]{dBm}$. Three notable features emerge. In (a), where $P_1 < P_2$, a new spectral peak appears at $2 \omega_2 - \omega_1$. In (b), where $P_1 = P_2$, two symmetrical peaks form on both sides of the carrier frequencies $\omega_1$ and $\omega_2$, each at equal detuning. In (c), where $P_1 > P_2$, a new peak arises at $2 \omega_1 - \omega_2$. Red dots represent experimental data, and solid black curves depict theoretical predictions, showing good agreement.
• Figure 3: Tunable frequency conversion. (a) Measured PSD$_n$ as a function of spectrum analyzer frequency (x axis) and input frequency $\omega_2$ (y axis). The carrier frequency $\omega_1$ is fixed at $\omega_{10}$ with an input power of $P_1 = \unit[-130]{dBm}$, while the carrier frequency $\omega_2$ is swept at a constant input power $P_2 = \unit[-130]{dBm}$. (b) Theoretical prediction for (a). The spectrum reveals four new frequency peaks at $3 \omega_2 - 2 \omega_1$, $2 \omega_2 - \omega_1$, $2 \omega_1 - \omega_2$, and $3 \omega_1 - 2 \omega_2$. (c) Line cut at $\omega_2 / 2\pi = \unit[4.86]{GHz}$ [red arrow in (a), black arrow in (b)], displaying a new peak at $2 \omega_1 - \omega_2$. The other peaks are not seen here due to the limited frequency span. The conversion frequency is tunable by selecting an appropriate $\omega_2$ frequency as needed. Red dots represent experimental data and the solid black curve is the theoretical prediction; the two agree well.
• Figure 4: Generation of frequency combs. (a) Measured PSD$_n$ as a function of spectrum analyzer frequency (x axis) and detuning $\Delta \omega = \omega_2 - \omega_1$ (y axis). The detuning varies at a fixed input power of $P_1 = P_2 = \unit[-123]{dBm}$. The artificial atom is biased at its resonant frequency, $\omega_{10} / 2\pi = \unit[4.82]{MHz}$, halfway between $\omega_1$ and $\omega_2$. Four new frequencies are generated symmetrically around the carrier frequencies $\omega_1$ and $\omega_2$. (b) Line cut from at $\unit[52]{MHz}$, indicated by the red arrow in (a), where all four new peaks are observed. (c) With input powers increased to $P_1 = P_2 = \unit[-120]{dBm}$ and detuning set to $\unit[10]{MHz}$, eight new peaks emerge at equidistant intervals, though some exhibit small amplitudes. Each peak is labeled by its mixing frequency. This demonstrates frequency-comb generation through appropriate detuning and input power selection. Red dots are experimental data and the solid black curves are theoretical predictions; the two agree well.