We experimentally realize a topological defect state of the quantum Rabi model in a single trapped $^{171}\mathrm{Yb}^{+}$ ion. The state is supported by a tunable interface arising from the oscillator's intrinsic number-dependent coupling in the Fock-state-lattice representation. We independently prepare the state at each sideband-phase setting and reconstruct its motional phase-space distribution using characteristic-function tomography. The resulting Wigner-centroid trajectories exhibit winding numbers of one and zero in the two coupling regimes. Changing the carrier amplitude rescales the trajectories while preserving their windings. Carrier-amplitude modulation provides a complementary dynamical probe, yielding a spin response consistent with the excitation gaps and accessible transition channels from the defect state. The experiment connects topological defect-state physics in a nonuniform synthetic lattice to the measurable phase-space geometry of a hybrid spin-boson system.
We experimentally realize a topological defect state of the quantum Rabi model in a single trapped 171Yb+ ion. The state is supported by a tunable interface arising from the oscillator's intrinsic number-dependent coupling in the Fock-state-lattice representation. We independently prepare the state at each sideband-phase setting and reconstruct its motional phase-space distribution using characteristic-function tomography. The resulting Wigner-centroid trajectories exhibit winding numbers of one and zero in the two coupling regimes. Changing the carrier amplitude rescales the trajectories while preserving their windings. Carrier-amplitude modulation provides a complementary dynamical probe, yielding a spin response consistent with the excitation gaps and accessible transition channels from the defect state. The experiment connects topological defect-state physics in a nonuniform synthetic lattice to the measurable phase-space geometry of a hybrid spin-boson system.
Abstract Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a system of two interacting qubits, by exploiting the coupling between the NV center spin and a neighboring 13C nuclear spin. Our results establish coherent dynamical responses as a versatile probe for quantum geometry, and they pave the way for the detection of novel topological phenomena in solid state.
Quantum phase transitions (QPTs) typically emerge in the thermodynamic limit, yet a single-atom QPT can arise when it is coupled to a coherently driven cavity, which provides a simple and unique platform to engineer quantum states with quantum criticality. In this driven Jaynes-Cummings (JC) model, the cavity field becomes squeezed near the critical point. However, vanishing energy gaps at the critical points lead to nonadiabaticity, hindering the practical realization of squeezing. In this work, we introduce a spin-dependent cavity drive, which induces a synthetic gauge field in the Fock-state lattice and enriches the phase diagram of the driven JC model. Remarkably, the energy spectrum can remain discrete for all driving strengths, allowing an adiabatic preparation of squeezed states with robust energy gaps. Moreover, we identify a topological phase transition characterized by projected winding numbers in the presence of broken chiral symmetry. Our results unveil topology and QPTs in a quantized light-matter system and offer a robust strategy for realizing squeezed states.
We experimentally realize a spin-momentum lattice with a homogeneously trapped Fermi gas. The lattice is created via cyclically rotated atom-laser couplings between three bare atomic spin states, and are such that they form a triangular lattice in a synthetic spin-momentum space. We demonstrate the lattice and explore its dynamics with spin- and momentum-resolved absorption imaging. This platform will provide new opportunities for synthetic spin systems and the engineering of topological bands. In particular, the use of three spin states in two spatial dimensions would allow the simulation of synthetic magnetic fields of high spatial uniformity, which would lead to ultranarrow Chern bands that support robust fractional quantum Hall states.
In addition to topological lattice defects such as dislocations and disclinations, crystals are also accompanied by unavoidable ordinary defects, devoid of any non-trivial geometry or topology, among which vacancies, Schottky defects, substitutions, interstitials, and Frenkel pairs are the most common. In this work, we demonstrate that these ubiquitous ordinary lattice defects, although geometrically trivial, can nonetheless serve as universal probes of the non-trivial topology of electronic Bloch bands, and any change in the local topological environment in an otherwise normal insulator in terms of mid-gap bound states in their vicinity. We theoretically establish these generic findings by implementing a minimal model Hamiltonian describing time-reversal symmetry breaking topological and normal insulators on a square lattice, fostering such point defects. The defect-bound mid-gap modes are also shown to be robust against sufficiently weak random point-like charge impurities. Furthermore, we showcase experimental observation of such bound states by embedding ordinary crystal defects in two-dimensional acoustic Chern lattices, where precision-controlled hopping amplitudes are implemented via active meta-atoms and Green's-function-based spectroscopy is used to reconstruct spectra and eigenstates. Our combined theory-experiment study establishes ordinary lattice defects as probes of topology that should be germane in crystals of any symmetry and dimension, raising the possibility of arresting localized Majorana modes near such defects in the bulk of topological superconductors and to emulate ordinary-defect-engineered topological devices.
Topological insulators are unique materials possessing forbidden topological gap and behaving similar to usual insulators in their bulk, but at the same time supporting localized in-gap states at their edges that demonstrate exceptional robustness, because they are protected by topology of the system and cannot be destroyed by local disorder or edge perturbations. Topological insulators discovered in different areas of physics, including optics, acoustics, and physics of Bose-Einstein and polariton condensates, usually employ potential landscapes (or lattices), designed such as to feature specific degeneracies in their linear modal spectra, that can be lifted by various physical effects or controllable deformations of the potential, leading to opening of the topological gap, where edge states appear. In this work, using binary Bose-Einstein condensate we propose a type of topological insulator that does not explicitly use specially designed potential landscape, but instead utilizes spatially inhomogeneous Rabi coupling between two components, in the form of a one- or two-dimensional Su-Schrieffer-Heeger structure, combined with Zeeman splitting. Such Rabi lattices reveal the appearance of topologically nontrivial phases (including higher-order ones) controlled by spatial shift of the domains with enhanced coupling between condensates within unit cells of the structure, where localized topological states appear at the edges or in the corners of truncated Rabi lattice. We also show that the properties of edge states, their spatial localization, and location of their chemical potential within topological gap can be controlled by interatomic interactions that lead to formation of gap topological edge solitons bifurcating from linear edge states. Such solitons in condensates with inhomogeneous Rabi coupling appear as very robust nonlinear topological objects that do not require any threshold norm for their formation even in two-dimensional geometries, and that can exist in stable form for both attractive and repulsive interactions. Our results demonstrate considerable enhancement of stability of solitons in topological Rabi lattices in comparison with trivial Rabi lattices. They open additional prospects for realization of topologically nontrivial phases by spatial engineering of coupling in multicomponent systems.
Synthetic dimensions provide a powerful approach for simulating condensed matter physics in cold atoms and photonics, whereby a set of discrete degrees of freedom are coupled together and reinterpreted as lattice sites along an artificial spatial dimension. However, atomic experimental realizations have been limited so far by the number of artificial lattice sites that can be feasibly coupled along the synthetic dimension. Here, we experimentally realize for the first time a very long and controllable synthetic dimension of atomic harmonic trap states. To create this, we couple trap states by dynamically modulating the trapping potential of the atomic cloud with patterned light. By controlling the detuning between the frequency of the driving potential and the trapping frequency, we implement a controllable force in the synthetic dimension. This induces Bloch oscillations in which atoms move periodically up and down tens of atomic trap states. We experimentally observe the key characteristics of this behavior in the real-space dynamics of the cloud, and verify our observations with numerical simulations and semiclassical theory. The Bloch oscillations thus act as a smoking-gun signature of the synthetic dimension, and allow us to characterize the effective band structure. Our methods provide an efficient approach for the manipulation and control of highly excited trap states, and set the stage for the future exploration of topological physics in higher dimensions through the use of a tunable artificial gauge field and finite-range interactions.