Parity-Engineered Light-Matter Interaction

The concept of parity describes the inversion symmetry of a system and is of fundamental relevance in the standard model, quantum information processing, and field theory. In quantum electrodynamics, parity is conserved and large field gradients are required to engineer the parity of the light-matter interaction operator. In this work, we engineer a potassiumlike artificial atom represented by a specifically designed superconducting flux qubit. We control the wave function parity of the artificial atom with an effective orbital momentum provided by a resonator. By irradiating the artificial atom with spatially shaped microwave fields, we select the interaction parity in situ. In this way, we observe dipole and quadrupole selection rules for single state transitions and induce transparency via longitudinal coupling. Our work advances the design of tunable artificial multilevel atoms to a new level, which is particularly promising with respect to quantum chemistry simulations with near-term superconducting circuits.

Figure 1

(a) Chip layout and detection scheme. (b) False-colored micrograph of the qubit architecture. Crosses indicate Josephson junctions as the one shown in the atomic force micrograph (inset). The SQUID is placed on the symmetry axis of the qubit and the center point of the two gradiometer loops (green shaded area). (c) The symmetric double well potential for flux qubits results in two eigenstates with opposite parity (blue and red wave functions). The interaction is defined by the symmetry of a drive field that can be even, odd, or without a specific symmetry, controlled by the relative phase $\phi$ between two frequency-degenerate microwave drives.

Figure 2

(a) Qubit excited state probability $p_e$ plotted versus relative phase $\phi$ at $\theta =\pi /2$. The solid line is a ${\sin }^2(\phi /2)$ fit assuming the qubit to be at zero temperature, the dashed line takes a finite qubit temperature into account and the error bars are of statistical nature. (b) Top panel: Symmetry of the drive field amplitude and the qubit potential. Lower panel: Simulated (top row) and measured (bottom row) excited state probability $p_e$ plotted versus the Bloch angle $\theta$ and the drive frequency $\omega /2\pi$. At ${\theta }^{\star }$ we observe longitudinal coupling-induced transparency. We attribute the scatter between $0.3\pi \lesssim \theta \lesssim 0.6\pi$ to variations in the signal-to-noise ratio of our measurement setup. The reduced signal strength at $\theta \simeq 0.7$ in the bottom right panel is not predicted by our model and could be due to a stray microwave mode or a two-level defect coupled to the qubit.

Figure 3

(a) Energy level diagram for ground and first three excited states for a potassium atom (top) and the qubit-resonator system (bottom). The atom follows electric SRs, which have a close analogy to sideband transitions in the qubit-resonator system. (b) Top panel: Level scheme and corresponding parity of composite qubit-resonator states for multiphoton transitions $|\mathrm{g},\delta n⟩\mapsto |e,\pm 1⟩$. Crossed out arrows denote forbidden transitions. Lower panel: Qubit excited state probability $p_e$ plotted versus Bloch angle $\theta$ and drive frequency $\omega /2\pi$. The circled areas show the red and blue sidebands (Ia–Id), the two-photon transition of the blue sideband (IIa and IIb), and the direct two-photon transition (IIIa and IIIb) for a symmetric qubit potential. Because of different power levels required to drive the transitions, the data are an overlay of different measurements. The vertical shift between the cases IIa and IIb is caused by small flux jumps between the measurements.