Assaf Hamo

Quantum control protocols are typically devised in the time domain, leaving their spectral behavior to emerge only a posteriori. Here, we invert this paradigm. Starting from a target frequency-domain filter, we employ the dynamical-invariant framework to derive the continuous driving fields that enact the chosen spectral response on a qubit. This approach, Quantum Invariant Filtering (QIF), maps arbitrary finite-impulse responses, including multi-band and phase-sensitive profiles, into experimentally feasible Hamiltonian modulations. Implemented on a single nitrogen-vacancy center in diamond, the method realizes the prescribed passbands with high fidelity, suppresses noise, and preserves coherence for milliseconds, two orders of magnitude longer than Carr-Purcell-Meiboom-Gill sequences, while remaining robust to 50% drive-amplitude errors. Our results establish QIF as a broadly applicable framework for enhanced quantum control and sensing across diverse physical platforms, including superconducting qubits, trapped ions, and nuclear magnetic resonance systems.

Recent years have seen the development of several experimental systems capable of tuning local parameters of quantum Hamiltonians. Examples include ultracold atoms, trapped ions, superconducting circuits, and photonic crystals. By design, these systems possess negligible disorder, granting them a high level of tunability. Conversely, electrons in conventional condensed matter systems exist inside an imperfect host material, subjecting them to uncontrollable, random disorder, which often destroys delicate correlated phases and precludes local tunability. The realization of a condensed matter system that is disorder-free and locally-tunable thus remains an outstanding challenge. Here, we demonstrate a new technique for deterministic creation of locally-tunable, ultra-low-disorder electron systems in carbon nanotubes suspended over circuits of unprecedented complexity. Using transport experiments we show that electrons can be localized at any position along the nanotube and that the confinement potential can be smoothly moved from location to location. Nearly perfect mirror symmetry of transport characteristics about the centre of the nanotube establishes the negligible effects of electronic disorder, thus allowing experiments in precision engineered one-dimensional potentials. We further demonstrate the ability to position multiple nanotubes at chosen separations, generalizing these devices to coupled one-dimensional systems. These new capabilities open the door to a broad spectrum of new experiments on electronics, mechanics, and spins in one dimension.