Experimental Realization of the Rabi-Hubbard Model with Trapped Ions

Realizing Synthetic Dimensions and Artificial Magnetic Flux in a Trapped-Ion Quantum Simulator

Synthetic dimension is a potent tool in quantum simulation of topological phases of matter. Here we propose and demonstrate a scheme to simulate an anisotropic Harper-Hofstadter model with controllable magnetic flux on a two-leg ladder using the spin and motional states of a single trapped ion. We verify the successful simulation of this model by comparing the measured dynamics with theoretical predictions under various coupling strength and magnetic flux, and we observe the chiral motion of wave packets on the ladder as evidence of the topological chiral edge modes. We develop a quench path to adiabatically prepare the ground states for varying magnetic flux and coupling strength, and we measure the chiral current on the ladder for the prepared ground states, which allows us to probe the quantum phase transition between the Meissner phase and the vortex phase. Our work demonstrates the trapped ion as a powerful quantum simulation platform for topological quantum matter.

Quantum Phase Transitions in a Generalized Dicke Model

We investigate a generalized Dicke model by introducing two interacting spin ensembles coupled with a single-mode bosonic field. Apart from the normal to superradiant phase transition induced by the strong spin-boson coupling, interactions between the two spin ensembles enrich the phase diagram by introducing ferromagnetic, antiferromagnetic and paramagnetic phases. The mean-field approach reveals a phase diagram comprising three phases: paramagnetic-normal phase, ferromagnetic-superradiant phase, and antiferromagnetic-normal phase. Ferromagnetic spin-spin interaction can significantly reduce the required spin-boson coupling strength to observe the superradiant phase, where the macroscopic excitation of the bosonic field occurs. Conversely, antiferromagnetic spin-spin interaction can strongly suppress the superradiant phase. To examine higher-order quantum effects beyond the mean-field contribution, we utilize the Holstein-Primakoff transformation, which converts the generalized Dicke model into three coupled harmonic oscillators in the thermodynamic limit. Near the critical point, we observe the close of the energy gap between the ground and the first excited states, the divergence of entanglement entropy and quantum fluctuation in certain quadrature. These observations further confirm the quantum phase transition and offer additional insights into critical behaviors.

Observation of a Superradiant Phase Transition with Emergent Cat States

Superradiant phase transitions (SPTs) are important for understanding light-matter interactions at the quantum level, and play a central role in criticality-enhanced quantum sensing. So far, SPTs have been observed in driven-dissipative systems, but the emergent light fields did not show any nonclassical characteristic due to the presence of strong dissipation. Here we report an experimental demonstration of the SPT featuring the emergence of a highly nonclassical photonic field, realized with a resonator coupled to a superconducting qubit, implementing the quantum Rabi model. We fully characterize the light-matter state by Wigner matrix tomography. The measured matrix elements exhibit quantum interference intrinsic of a photonic mesoscopic superposition, and reveal light-matter entanglement.

Superpotential for Novel Symmetry in Real and Complex Space

We propose a new “superpotential” and find that neither the supersymmetric energy conditions nor the associated shape invariance conditions remain valid. On the other hand, a new energy condition En+−En(−)=2λ between the two partner Hamiltonians H(±) emerges. A mathematical proof supports the present findings, with examples being presented. It is observed that when the superpotential is associated with discontinuity or distortion, the SUSY energy conditions and the shape invariance conditions will no longer hold well. The above formalism is also valid in complex space for models involving PT-symmetry.

Nuclear magnetic resonance diffraction with subangstrom precision

Prior to the development of MRI, Mansfield and Grannell proposed NMR diffraction (NMRd) as a method to investigate the structure of crystalline materials. When realized on the atomic scale, NMRd would be a powerful tool to study the structure of materials, utilizing the spectroscopic capabilities of NMR. The main challenge to achieving this goal lies in the ability to encode large relative phase differences between neighboring nuclear spins on the atomic scale. Utilizing key advances in nanoMRI technology, we demonstrate the ability to encode and detect angstrom-scale modulation of approximately 2 million ³¹P spins in an indium-phosphide (InP) nanowire with subangstrom precision. The work represents a significant step toward the realization of atomic-scale NMRd.

We have combined ultrasensitive force-based spin detection with high-fidelity spin control to achieve NMR diffraction (NMRd) measurement of ~2 million 31P spins in a (50 nm)3 volume of an indium-phosphide (InP) nanowire. NMRd is a technique originally proposed for studying the structure of periodic arrangements of spins, with complete access to the spectroscopic capabilities of NMR. We describe two experiments that realize NMRd detection with subangstrom precision. In the first experiment, we encode a nanometer-scale spatial modulation of the z-axis magnetization of 31P spins and detect the period and position of the modulation with a precision of <0.8 Å. In the second experiment, we demonstrate an interferometric technique, utilizing NMRd, to detect an angstrom-scale displacement of the InP sample with a precision of 0.07 Å. The diffraction-based techniques developed in this work extend the Fourier-encoding capabilities of NMR to the angstrom scale and demonstrate the potential of NMRd as a tool for probing the structure and dynamics of nanocrystalline materials.

Observation of Non-Markovian Spin Dynamics in a Jaynes-Cummings-Hubbard Model Using a Trapped-Ion Quantum Simulator

The Jaynes-Cummings-Hubbard (JCH) model is a fundamental many-body model for light-matter interaction. As a leading platform for quantum simulation, the trapped ion system has realized the JCH model for two to three ions. Here, we report the quantum simulation of the JCH model using up to 32 ions. We verify the simulation results even for large ion numbers by engineering low excitations and thus low effective dimensions; then we extend to 32 excitations for an effective dimension of 2^{77}, which is difficult for classical computers. By regarding the phonon modes as baths, we explore Markovian or non-Markovian spin dynamics in different parameter regimes of the JCH model, similar to quantum emitters in a structured photonic environment. We further examine the dependence of the non-Markovian dynamics on the effective Hilbert space dimension. Our Letter demonstrates the trapped ion system as a powerful quantum simulator for many-body physics and open quantum systems.

Determination of Multimode Motional Quantum States in a Trapped Ion System

Trapped atomic ions are a versatile platform for studying interactions between spins and bosons by coupling the internal states of the ions to their motion. Measurement of complex motional states with multiple modes is challenging, because all motional state populations can only be measured indirectly through the spin state of ions. Here we present a general method to determine the Fock state distributions and to reconstruct the density matrix of an arbitrary multimode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a five-ion chain. This method can be extended to any system with Jaynes-Cummings-type interactions.

Observation of supersymmetry and its spontaneous breaking in a trapped ion quantum simulator

Supersymmetry (SUSY) helps solve the hierarchy problem in high-energy physics and provides a natural groundwork for unifying gravity with other fundamental interactions. While being one of the most promising frameworks for theories beyond the Standard Model, its direct experimental evidence in nature still remains to be discovered. Here we report experimental realization of a supersymmetric quantum mechanics (SUSY QM) model, a reduction of the SUSY quantum field theory for studying its fundamental properties, using a trapped ion quantum simulator. We demonstrate the energy degeneracy caused by SUSY in this model and the spontaneous SUSY breaking. By a partial quantum state tomography of the spin-phonon coupled system, we explicitly measure the supercharge of the degenerate ground states, which are superpositions of the bosonic and the fermionic states. Our work demonstrates the trapped-ion quantum simulator as an economic yet powerful platform to study versatile physics in a single well-controlled system.

Quantum Simulation of the Two-Dimensional Weyl Equation in a Magnetic Field

Quantum simulation of 1D relativistic quantum mechanics has been achieved in well-controlled systems like trapped ions, but properties like spin dynamics and response to external magnetic fields that appear only in higher dimensions remain unexplored. Here we simulate the dynamics of a 2D Weyl particle. We show the linear dispersion relation of the free particle and the discrete Landau levels in a magnetic field, and we explicitly measure the spatial and spin dynamics from which the conservation of helicity and properties of antiparticles can be verified. Our work extends the application of an ion trap quantum simulator in particle physics with the additional spatial and spin degrees of freedom.