In a paper published in the journal Nature Physics, researchers used a superconducting quantum simulator to emulate the dynamics of charged particles in an electromagnetic field. By applying continuous modulation tones to qubits, they generated a synthetic magnetic vector potential that successfully adhered to the principles of electromagnetism.
Study: A synthetic magnetic vector potential in a 2D superconducting qubit array. Image Credit: ArtemisDiana/Shutterstock.com
The simulator produced an artificial magnetic field breaking time-reversal symmetry and a synthetic electric field from temporal variations. They also observed the Hall effect under the synthetic electromagnetic field.
Related Work
Past work has shown that using arrays of coupled superconducting qubits, analogue quantum simulators can emulate the Harper–Hofstadter model to study charged particles in magnetic fields.
Researchers broke time-reversal symmetry by detuning qubits and applying modulation tones, generating synthetic electromagnetic fields. It allowed for the emulation of spatially varying magnetic and electric fields, demonstrating effects like Bloch oscillations and the Hall effect. These capabilities provide insights into complex condensed matter phenomena.
Synthetic Quantum Field Emulation
The experiment was conducted on a superconducting quantum processor of 16 flux-tunable transmission-line shunted plasma oscillation qubit (transmon) qubits arranged in a 4x4 grid. Each qubit had an individual flux control line and readout resonator on a separate chip, positioned in a flip-chip configuration.
Nearest-neighbor qubits were transversely coupled through a fixed mutual capacitance, implementing the Bose-Hubbard model. The on-site energies were tunable through flux control, and the system’s bare particle exchange interactions had an average strength of 5.9 MHz.
The researchers used a synthetic vector potential to emulate charged particle dynamics in electromagnetic fields. By employing a parametric coupling scheme, they modulated the on-site energy of qubits at specific detuning frequencies.
This modulation induced complex coupling between adjacent qubits, with Peierls phases derived from the modulation tones. The parametric modulation enabled the emulation of the Harper-Hofstadter model, breaking time-reversal symmetry and creating synthetic magnetic fields in the lattice.
The team observed Aharonov-Bohm interference in various configurations, such as 2x2 plaquettes and larger rings. They demonstrated that the interference patterns depended only on the net flux through the rings, confirming the gauge invariance of the synthetic magnetic field.
This result illustrated that the emulator effectively captured key features of 2D electronic systems in the presence of magnetic fields. The dynamics were verified against simulations of the superconducting processor and the idealized Harper-Hofstadter model.
Additionally, the researchers emulated a synthetic electric field by varying modulation phases linearly over time, simulating a linear potential along a one-dimensional chain of sites.
They observed Bloch oscillations, where the particle remained confined rather than spreading, reflecting the behavior expected in the presence of a linear potential. The experiments agreed with the actual device simulations and theoretical models, achieving effective coupling strengths of approximately 2.0 MHz.
Quantum Dynamics and Synthetic Fields
The researchers investigated particle dynamics using a superconducting quantum processor, studying the impact of synthetic magnetic flux. They discovered that the particle's movement between two sites did not depend on the Peierls phase unless arranged in a closed path, where the magnetic flux became significant.
By placing four qubits in a 2x2 plaquette and modulating the connections, they observed the Aharonov–Bohm effect, where a particle's two trajectories interfered constructively at zero flux but destructively at a flux of π, preventing propagation. Extending the experiment to larger rings confirmed these interference patterns and matched numerical simulations, proving the system's accuracy.
They then explored gauge invariance by rearranging the Peierls phases while keeping the magnetic flux constant. Using an 8-site ring, they demonstrated that the interference patterns remained consistent under different phase configurations, affirming gauge freedom.
To simulate synthetic electric fields, they varied the Peierls phases over time, generating confinement effects in an 11-site chain. It created Wannier-Stark localization, where the particle remained near its initial site, replicating Bloch oscillations. These observations aligned well with simulations of a tight-binding model, showing effective energy localization.
Next, the Hall effect was emulated using a 16-site array with a uniform synthetic magnetic field. By applying an artificial electric field, they observed particle deflection transverse to the initial velocity, mimicking the Hall effect. The particle's motion required breaking both time-reversal and spatial inversion symmetry.
Simulations demonstrated that the deflection depended on the magnetic and electric fields but not longitudinal velocity, diverging from classical Lorentz force predictions. Experimental data, though skewed by coupling-strength inhomogeneities, followed trends predicted by the semi-classical model.
Lastly, they quantified the Hall coefficient by measuring how the transverse deflection changed with variations in the electric field. The ballistic nature of the particle transport necessitated a wavepacket-based description, as the deflection was independent of longitudinal drift velocity, unlike in classical conductors.
Simulations confirmed this unique behavior, which aligned with semi-classical predictions, highlighting differences between quantum ballistic systems and classical electrical conductors. These results offered more profound insights into the dynamics of synthetic quantum systems.
Conclusion
To sum up, the study successfully emulated a tight-binding lattice with adjustable synthetic magnetic vector potentials using a 2D array of superconducting qubits. It verified the presence of artificial magnetic fields through Aharonov–Bohm interference and demonstrated their consistency with Maxwell's equations.
The research also showcased a particle's transverse deflection in synthetic electromagnetic fields, highlighting differences between quantum and classical particle motion. The approach provided a platform for exploring artificial matter in high magnetic fields and complex magnetic environments.
Journal Reference
Rosen, I. T., et al. (2024). A synthetic magnetic vector potential in a 2D superconducting qubit array. Nature Physics. doi: 10.1038/s41567-024-02661-3. https://www.nature.com/articles/s41567-024-02661-3
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