Abstract The traditional quantum adiabatic criterion based on instantaneous eigenenergy gaps becomes inadequate in certain periodically driven systems. In this work, we experimentally investigate the adiabatic mechanism in a superconducting transmon qubit driven by modulated microwave. We demonstrate that the adiabatic dynamics are governed by quasi-energy gaps between Floquet modes rather than by instantaneous eigenenergy gaps. In particular, we study the regime where the instantaneous eigenenergy gap closes and the traditional adiabatic picture fails, while the evolution nevertheless remains adiabatic due to a finite quasi-energy gap. The experimental observations reveal the role of the quasi-energy structure in the adiabatic mechanism of modulated driven systems. We further show that the flexibility of this adiabatic criterion may provide a method to shorten the duration of adiabatic evolution through adaptive parameter modulation. These results offer experimental insights into adiabatic mechanisms beyond the conventional framework and may facilitate the development of high-performance adiabatic quantum control protocols.
Abstract The traditional quantum adiabatic criterion based on instantaneous eigenenergy gaps becomes inadequate in certain periodically driven systems. In this work, we experimentally investigate the adiabatic mechanism in a superconducting transmon qubit driven by modulated microwave. We demonstrate that the adiabatic dynamics are governed by quasi-energy gaps between Floquet modes rather than by instantaneous eigenenergy gaps. In particular, we study the regime where the instantaneous eigenenergy gap closes and the traditional adiabatic picture fails, while the evolution nevertheless remains adiabatic due to a finite quasi-energy gap. The experimental observations reveal the role of the quasi-energy structure in the adiabatic mechanism of modulated driven systems. We further show that the flexibility of this adiabatic criterion may provide a method to shorten the duration of adiabatic evolution through adaptive parameter modulation. These results offer experimental insights into adiabatic mechanisms beyond the conventional framework and may facilitate the development of high-performance adiabatic quantum control protocols.
Quantum adiabaticity is the evolution of a quantum system that remains close to an instantaneous eigenstate of a time-dependent Hamiltonian. Using Floquet formalism, we derive a rigorous sufficient condition for adiabaticity in closed, finite-dimensional periodically driven systems that is valid for arbitrarily many driving periods. The condition is stroboscopic and geometric, depending only on single-cycle information: the Fubini--Study length of the instantaneous eigenray and a quasienergy-separation measure extracted from the Floquet operator. We also formulate a state-targeted refinement that reduces conservativeness when only one adiabatic branch is relevant. Rather than synthesizing control pulses, the result provides a certification criterion for a given periodic protocol. We illustrate the criterion and contrast it with conventional instantaneous-gap conditions in three representative examples.
Adiabatic time-optimal quantum controls are extensively used in quantum technologies to break the constraints imposed by short coherence times. However, practically it is crucial to consider the trade-off between the quantum evolution speed and instantaneous energy cost of process because of the constraints in the available control Hamiltonian. Here, we experimentally show that using a transmon qubit that, even in the presence of vanishing energy gaps, it is possible to reach a highly time-optimal adiabatic quantum driving at low energy cost in the whole evolution process. This validates the recently derived general solution of the quantum Zermelo navigation problem, paving the way for energy-efficient quantum control which is usually overlooked in conventional speed-up schemes, including the well-known counter-diabatic driving. By designing the control Hamiltonian based on the quantum speed limit bound quantified by the changing rate of phase in the interaction picture, we reveal the relationship between the quantum speed limit and instantaneous energy cost. Consequently, we demonstrate fast and high-fidelity quantum adiabatic processes by employing energy-efficient driving strengths, indicating a promising strategy for expanding the applications of time-optimal quantum controls in superconducting quantum circuits.
Topological Floquet energy pumps, which use periodic driving to create a topologically protected quantized energy current, have been proposed and studied theoretically, but have never been observed directly. Previous work [D. M. Long et al., Phys. Rev. Lett. 128, 183602 (2022)] proposed that such a pump could be realized with a strongly driven superconducting qubit coupled to a cavity. Here, we experimentally demonstrate that the proposed hierarchy of energy scales and drive frequencies can be realized using a transmon qubit. We develop an experimental toolkit to realize the adiabatic driving field required for energy pumping using coordinated frequency modulation of the transmon and amplitude modulation of an applied resonant microwave drive. With this toolkit, we measure adiabatic evolution of the qubit under the applied field for times comparable to T1, which far exceed the bare qubit dephasing time. This result paves the way for direct experimental observation of topological energy pumping.
Open quantum systems described by a non-Hermitian Hamiltonian exhibit rich dynamics due to the topology of their complex energy spectrum. By encircling an exceptional point degeneracy, this topology allows for topological state transport, chiral geometric phases, and eigenvalue braiding. To access these topological features, it is desirable to drive the system adiabatically. However, adiabatic transport in a system with a complex spectrum is conventionally only possible for the eigenstate whose eigenenergy has the lowest loss. Previous experiments have demonstrated such adiabatic evolution for the quantum state with relative gain, yet observed a breakdown in adiabaticity for quantum states with relative loss. In this work, we harness a shortcut to adiabaticity—counterdiabatic driving—to avoid the effects of loss while maintaining trajectories that follow the instantaneous eigenstates in significantly shorter timescales. We experimentally investigate the robustness of this control method using a superconducting transmon circuit with engineered dissipation. We observe that counterdiabatic driving stabilizes quasistatic transport and preserves the complex energy spectrum’s topology.
In quantum mechanics, adiabatic elimination is a standard tool that produces a low-lying reduced Hamiltonian for a relevant subspace of states, incorporating effects of its coupling to states with much higher energy. Suppose this powerful elimination approach is applied to quasi-energy states in periodically-driven systems, a critical question then arises that the violation of the adiabatic condition caused by driven forces challenges such a presence of spectral reduction in the non-equilibrium driven system. Here, both theoretically and experimentally, we newly reported two kinds of driven-induced eliminations universal in topologically-protected Floquet systems. We named them "quasi-adiabatic elimination" and "high-frequency-limited elimination", in terms of different driven frequencies that deny the underlying requirement for the adiabatic condition. Both two non-adiabatic eliminations are observed in our recently developed microwave Floquet simulator, a programmable test platform composed of periodically-bending ultrathin metallic coupled corrugated waveguides. Through the near-field imaging on our simulator, the mechanisms between the adiabatic and driven-induced eliminations are revealed, indicating the ubiquitous spectral decomposition for tailoring and manipulating Floquet states with quasi-energies. Finally, we hope our findings may open up profound and applicable possibilities for further developing Floquet engineering in periodically-driven systems, ranging from condensed matter physics to photonics.
The quantum adiabatic theorem, a cornerstone of quantum mechanics, asserts that a gapped quantum system remains in its instantaneous eigenstate during sufficiently slow evolution, provided no resonances occur. Here we challenge this principle and show that adiabaticity can be violated even in arbitrarily slow processes. We introduce two new parameters, Instantaneous Transition Accumulation (ITA) and Instantaneous Transition Probability (ITP), to redefine the framework of adiabatic evolution. These parameters, grounded in cross-Berry connections and eigenstate amplitudes, reveal the dynamic and geometric factors governing adiabaticity. Using a new Phase Difference Manipulation (PDM) method, we control ITP and ITA to induce adiabaticity violation in a Landau-Zener (LZ) process. We experimentally demonstrate this counterintuitive phenomenon in a photonic waveguide system, where a slow LZ process defies adiabaticity, switching energy levels despite a fivefold slower evolution speed than a conventional adiabatic process. This discovery reshapes our understanding of quantum evolution and holds potential for quantum computing, topological physics, and photonic technologies.