Dayou Yang

We propose and analyze a driven-dissipative quantum sensor that is continuously monitored close to a dissipative critical point. The sensor relies on the critical open Rabi model with the spin and phonon degrees of freedom of a single trapped ion to achieve criticality-enhanced sensitivity. Effective continuous monitoring of the sensor is realized via a co-trapped ancilla ion that switches between dark and bright internal states conditioned on a `jump' of the phonon population which, remarkably, achieves nearly perfect phonon counting despite a low photon collection efficiency. By exploiting both dissipative criticality and efficient continuous readout, the sensor device achieves highly precise sensing of oscillating electric field gradients at a criticality-enhanced precision scaling beyond the standard quantum limit, which we demonstrate is robust to the experimental imperfections in real-world applications.

In an ideal quantum measurement, the wave function of a quantum system collapses to an eigenstate of the measured observable, and the corresponding eigenvalue determines the measurement outcome. If the observable commutes with the system Hamiltonian, repeated measurements yield the same result and thus minimally disturb the system. Seminal quantum optics experiments have achieved such quantum non-demolition (QND) measurements of systems with few degrees of freedom. In contrast, here we describe how the QND measurement of a complex many-body observable, the Hamiltonian of an interacting many-body system, can be implemented in a trapped-ion analog quantum simulator. Through a single-shot measurement, the many-body system is prepared in a narrow band of (highly excited) energy eigenstates, and potentially even a single eigenstate. Our QND scheme, which can be carried over to other platforms of quantum simulation, provides a framework to investigate experimentally fundamental aspects of equilibrium and non-equilibrium statistical physics including the eigenstate thermalization hypothesis and quantum fluctuation relations.

The prospect of quantum simulating lattice gauge theories opens exciting possibilities for understanding fundamental forms of matter. Here, we show that trapped ions represent a promising platform in this context when simultaneously exploiting internal pseudo-spins and external phonon vibrations. We illustrate our ideas with two complementary proposals for simulating lattice-regularized quantum electrodynamics (QED) in (1+1) space-time dimensions. The first scheme replaces the gauge fields by local vibrations with a high occupation number. By numerical finite-size scaling, we demonstrate that this model recovers Wilson's lattice gauge theory in a controlled way. Its implementation can be scaled up to tens of ions in an array of micro-traps. The second scheme represents the gauge fields by spins 1/2, and thus simulates a quantum link model. As we show, this allows the fermionic matter to be replaced by bosonic degrees of freedom, permitting small-scale implementations in a linear Paul trap. Both schemes work on energy scales significantly larger than typical decoherence rates in experiments, thus enabling the investigation of phenomena such as string breaking, Coleman's quantum phase transition, and false-vacuum decay. The underlying ideas of the proposed analog simulation schemes may also be adapted to other platforms, such as superconducting qubits.