Tony E. Lee

There is currently intensive research into creating a large-scale quantum computer with trapped ions. It is well known that for a linear ion crystal in a harmonic potential, the ions near the center are more closely spaced compared to the ions near the ends. This is problematic as the number of ions increases. Here, we consider a linear ion crystal in an anharmonic potential that is purely quartic in position. We find that the ions are more evenly spaced compared to the harmonic case. We develop a variational approach to calculate the properties of the ground state. We also characterize the zigzag transition in an anharmonic potential.

Quantum simulators based on atoms or molecules often have long-range interactions due to dipolar or Coulomb interactions. We present a method based on Floquet engineering to turn a long-range interaction into a short-range one. By modulating a magnetic-field gradient with one or a few frequencies, one reshapes the interaction profile, such that the system behaves as if it only had nearest-neighbor interactions. Our approach works in both one and two dimensions and for both spin-1/2 and spin-1 systems. It does not require individual addressing, and is applicable to all experimental systems with long-range interactions: trapped ions, polar molecules, Rydberg atoms, nitrogen-vacancy centers, and cavity QED. Our approach allows one achieve a short-range interaction without relying on Hubbard superexchange.

We study the transverse-field Ising model with interactions that are modulated in time. In a rotating frame, the system is described by a time-independent Hamiltonian with many-body interactions, similar to the cluster Hamiltonians of measurement-based quantum computing. In one dimension, there is a three-body interaction, which leads to string order instead of conventional magnetic order. We show that the string order is robust to power-law interactions that decay with the cube of distance. In two and three dimensions, there are five- and seven-body interactions. We discuss adiabatic preparation of the ground state as well as experimental implementation with trapped ions, Rydberg atoms, and polar molecules.

It has been predicted that particles with imaginary mass, called tachyons, would be able to travel faster than the speed of light. There has not been any experimental evidence for tachyons occurring naturally. Here, we propose how to experimentally simulate Dirac tachyons with trapped ions. Quantum measurement on a Dirac particle simulated by a trapped ion causes it to have an imaginary mass so that it may travel faster than the effective speed of light. We show that a Dirac tachyon must have spinor-motion correlation in order to be superluminal. We also show that it exhibits significantly more Klein tunneling than a normal Dirac particle. We provide numerical simulations of realistic ion systems and show that our scheme is feasible with current technology.

We show that non-Hermitian dynamics generate substantial entanglement in many-body systems. We consider the non-Hermitian Lipkin-Meshkov-Glick model and show that its phase transition occurs with maximum multiparticle entanglement: there is full N-particle entanglement at the transition, in contrast to the Hermitian case. The non-Hermitian model also exhibits more spin squeezing than the Hermitian model, showing that non-Hermitian dynamics are useful for quantum metrology. Experimental implementations with trapped ions and cavity QED are discussed.

We study the XY model with infinite-range interactions (Lipkin-Meshkov-Glick model) in the presence of dissipation from spontaneous decay. We show that independent and collective decay lead to qualitatively different phase transitions of the steady state, even though the phase boundary is the same. Independent decay leads to a second-order phase transition to a ferromagnet, while collective decay leads to a first-order transition to a time-dependent oscillatory phase. Then we show that the addition of a drive leads to infinite spin squeezing for collective decay in the thermodynamic limit. Our results can be experimentally seen in trapped-ion and cavity-QED experiments.

Quantum phase transitions are usually studied in terms of Hermitian Hamiltonians. However, cold-atom experiments are intrinsically non-Hermitian due to spontaneous decay. Here, we show that non-Hermitian systems exhibit quantum phase transitions that are beyond the paradigm of Hermitian physics. We consider the non-Hermitian XY model, which can be implemented using three-level atoms with spontaneous decay. We exactly solve the model in one dimension and show that there is a quantum phase transition from short-range order to quasi-long-range order despite the absence of a continuous symmetry in the Hamiltonian. The ordered phase has a frustrated spin pattern. The critical exponent $ν$ can be 1 or 1/2. Our results can be seen experimentally with trapped ions, cavity QED, and atoms in optical lattices.

We study the synchronization of dissipatively-coupled van der Pol oscillators in the quantum limit, when each oscillator is near its quantum ground state. Two quantum oscillators with different frequencies exhibit an entanglement tongue, which is the quantum analogue of an Arnold tongue. It means that the oscillators are entangled in steady state when the coupling strength is greater than a critical value, and the critical coupling increases with detuning. An ensemble of many oscillators with random frequencies still exhibits a synchronization phase transition in the quantum limit, and we analytically calculate how the critical coupling depends on the frequency disorder. Our results can be experimentally observed with trapped ions or neutral atoms.

We study the transverse-field Ising model with infinite-range coupling and spontaneous emission on every site. We find that there is spin squeezing in steady state due to the presence of the transverse field. This means that there is still entanglement, despite the decoherence from spontaneous emission. We analytically calculate fluctuations beyond mean-field theory using a phase-space approach, which involves converting the master equation into a Fokker-Planck equation for the Wigner function. Our calculations are relevant to current experiments with trapped ions.

Van der Pol oscillators are prototypical self-sustaining oscillators which have been used to model nonlinear processes in biological and other classical processes. In this work, we investigate how quantum fluctuations affect phase-locking in one or many van der Pol oscillators. We find that phase-locking is much more robust in the quantum model than in the equivalent classical model. Trapped-ion experiments are ideally suited to simulate van der Pol oscillators in the quantum regime via sideband heating and cooling of motional modes. We provide realistic experimental parameters for ${}^{171}\text{Yb}^+$ achievable with current technology.

We consider strongly interacting systems of effective spins, subject to dissipative spin-flip processes associated with optical pumping. We predict the existence of novel magnetic phases in the steady-state of this system, which emerge due to the competition between coherent and dissipative processes. Specifically, for strongly anisotropic spin-spin interactions, we find ferromagnetic, antiferromagnetic, spin-density-wave, and staggered-XY steady states, which are separated by nonequilibrium phase transitions meeting at a Lifshitz point. These transitions are accompanied by quantum correlations, resulting in spin squeezing. Experimental implementations in ultracold atoms and trapped ions are discussed.

Ion traps are a versatile tool to study nonequilibrium statistical physics, due to the tunability of dissipation and nonlinearity. We propose an experiment with a chain of trapped ions, where dissipation is provided by laser heating and cooling, while nonlinearity is provided by trap anharmonicity and beam shaping. The collective dynamics are governed by an equation similar to the complex Ginzburg-Landau equation, except that the reactive nature of the coupling leads to qualitatively different behavior. The system has the unusual feature of being both oscillatory and excitable at the same time. We account for noise from spontaneous emission and find that the patterns are observable for realistic experimental parameters. Our scheme also allows controllable experiments with noise and quenched disorder.