Fluxonium-Based Artificial Molecule with a Tunable Magnetic Moment

Engineered quantum systems allow us to observe phenomena that are not easily accessible naturally. The LEGO®-like nature of superconducting circuits makes them particularly suited for building and coupling artificial atoms. Here, we introduce an artificial molecule, composed of two strongly coupled fluxonium atoms, which possesses a tunable magnetic moment. Using an applied external flux, one can tune the molecule between two regimes: one in which the ground-excited state manifold has a magnetic dipole moment and one in which the ground-excited state manifold has only a magnetic quadrupole moment. By varying the applied external flux, we find the coherence of the molecule to be limited by local flux noise. The ability to engineer and control artificial molecules paves the way for building more complex circuits for quantum simulation and protected qubits.

Popular Summary

Nature provides us with a limited set of atoms for constructing useful materials. For detection and characterization of external fields—such as electric or magnetic fields—one would like to have a molecule whose response to the field could change depending on the strength and spatial distribution of the field. Achieving such flexibility, however, is extremely challenging in a molecule synthesized from natural atoms. Superconducting circuits that mimic atoms are a solution to this problem. Such artificial atoms are much less limited in the types of interactions that can be generated between them and their environment. Here, we introduce an artificial molecule whose intrinsic magnetic properties can be changed by an external magnetic field.

Our artificial molecule is composed of two fluxonium atoms (artificial atoms built from Josephson junctions, which are composed of an oxide sandwiched between two layers of superconducting material) coupled via a shared inductance. By applying an external flux, the magnetic moment of the molecule can be tuned in situ from being dipolar to only quadrupolar. We used this tunability to determine that local flux noise is the major source of decoherence in the artificial molecule. In addition, spectroscopic observations of our molecule reveal remarkable agreement between data and a theoretical model with a small number of parameters. This demonstrates that complex superconducting circuits can obey simple Hamiltonians with a few engineerable parameters.

We expect that our experiment will stimulate the creation of novel artificial molecules and materials built using superconducting circuits. Further work on the origins of local flux noise in superconducting circuits is needed, however, before we can harness their full potential.

Figure 1

(a) Electrical circuit diagram of the artificial molecule. (b,c) Magnetic dipole regime: Ground- and excited-state wave functions ($\mathrm{\Psi }$), and potential ($U$) at ${\mathrm{\Phi }}_{\mathrm{ext}}=\overline{({\mathrm{\Phi }}_1+{\mathrm{\Phi }}_2)}/2=0.1{\mathrm{\Phi }}_0$. The direction of persistent current flow in the ground state is indicated with green arrows. The ground state is a product state of the two fluxonium atoms and is localized in the potential well near ${\phi }_1$, ${\phi }_2=0$. The excited state corresponds to persistent currents flowing in opposite directions and is delocalized in multiple potential wells. (d,e) Magnetic quadrupole regime: Approximate kets for the ground and excited states at ${\mathrm{\Phi }}_{\mathrm{ext}}=0.5{\mathrm{\Phi }}_0$. Ground-state and excited-state wave functions ($\mathrm{\Psi }$) are shown above the potential ($U$) of the artificial molecule. The ground and excited states are symmetric and antisymmetric superpositions of persistent currents flowing in opposite directions. The wave functions are localized in the two lowest potential wells, which are degenerate. Higher-energy excited states tend to be localized in the shallower potential wells.

Figure 2

(a) Scanning electron micrograph of device A. Small junctions are indicated in the yellow circles. The artificial molecule is coupled via Josephson junctions to the readout antenna whose optical image is shown in (b). (c) The molecule and antenna are fabricated on a sapphire chip, which is then placed inside a copper waveguide.

Figure 3

(a,b) Transition frequency from $|g⟩$ to excited states $|e⟩$, $|f⟩$, $|h⟩$, $|d⟩$ in device A and device C. Measured data are indicated with open circles. The solid lines were fit to the data using the Hamiltonian in Eq. (1) and the definition of ${\mathrm{\Phi }}_{\mathrm{ext}}$ (see text). Grey shaded areas indicate where the $|g⟩-|e⟩$ transition is only quadrupolar. Device C has a higher asymmetry between the two loops, which leads to a larger difference between the $|g⟩$ to $|e⟩$ transition frequency at ${\mathrm{\Phi }}_{\mathrm{ext}}=0.5{\mathrm{\Phi }}_0$ and the $|g⟩$ to $|e⟩$ transition frequency at ${\mathrm{\Phi }}_{\mathrm{ext}}=1.5{\mathrm{\Phi }}_0$ when compared with device A.

Figure 4

(a)–(c) Ramsey dephasing rates as a function of flux in devices A, B, and C. The data are shown in open blue circles. Fit curves are the calculated Ramsey dephasing rates resulting from power spectral density values of differential-mode flux noise (green dashed), common-mode flux noise (red dashed), and their sum (black solid). We note that slight asymmetries in the two fluxonium loops cause the curves to be asymmetric around ${\mathrm{\Phi }}_{\mathrm{ext}}=0.5{\mathrm{\Phi }}_0$. This asymmetry also affects the amplitudes necessary to drive transitions and the visibility of the transitions between $|g⟩$ and $|e⟩$, resulting in the asymmetry in data of about ${\mathrm{\Phi }}_{\mathrm{ext}}=0.5{\mathrm{\Phi }}_0$ in these plots. Ramsey dephasing rate measurements could not be taken for the full range in ${\mathrm{\Phi }}_{\mathrm{ext}}$ for every sample because of the changing coupling between the molecule and readout antenna.