J. Zhang

While engineered quantum systems are a general route to the manipulation of multipartite quantum states, access in a physical system to a continuous quantum phase transition under sufficient control offers the possibility of an intrinsic source of entangled states. To this end we realize the quantum version of the linear-zigzag structural transition for arrays of up to five ground state-cooled ions held in a linear Paul trap and we demonstrate several of the control requirements towards entangled-state interferometry near the critical point. Using in-situ spectroscopy we probe the energy level structure and occupation of the soft mode associated with the structural transition, and show a stable critical point and majority ground state occupation crossing the transition. We resolve biases arising from trap electrode asymmetries that change the nature of the transition, show that they can be suppressed by varying the ion number, and demonstrate control of the transition bias using optical dipole forces.

A reproducible stationary improved confinement mode (I-mode) has been achieved recently in the Experimental Advanced Superconducting Tokamak, featuring good confinement without particle transport barrier, which could be beneficial to solving the heat flux problem caused by edge localized modes (ELM) and the helium ash problem for future fusion reactors. The microscopic mechanism of sustaining stationary I-mode, based on the coupling between turbulence transition and the edge temperature oscillation, has been discovered for the first time. A radially localized edge temperature ring oscillation (ETRO) with azimuthally symmetric structure ($n=0$,$m=0$) has been identified and it is caused by alternative turbulence transitions between ion temperature gradient modes (ITG) and trapped electron modes (TEM). The ITG-TEM transition is controlled by local electron temperature gradient and consistent with the gyrokinetic simulations. The self-organizing system consisting with ETRO, turbulence and transport transitions plays the key role in sustaining the I-mode confinement. These results provide a novel physics basis for accessing, maintaining and controlling stationary I-mode in the future.

We present a cryogenic ion trapping system designed for large scale quantum simulation of spin models. Our apparatus is based on a segmented-blade ion trap enclosed in a 4 K cryostat, which enables us to routinely trap over 100 $^{171}$Yb$^+$ ions in a linear configuration for hours due to a low background gas pressure from differential cryo-pumping. We characterize the cryogenic vacuum by using trapped ion crystals as a pressure gauge, measuring both inelastic and elastic collision rates with the molecular background gas. We demonstrate nearly equidistant ion spacing for chains of up to 44 ions using anharmonic axial potentials. This reliable production and lifetime enhancement of large linear ion chains will enable quantum simulation of spin models that are intractable with classical computer modelling.

A quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of qubits, the simulator can tackle a wider range of problems, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. We use a quantum simulator composed of up to 53 qubits to study a non-equilibrium phase transition in the transverse field Ising model of magnetism, in a regime where conventional statistical mechanics does not apply. The qubits are represented by trapped ion spins that can be prepared in a variety of initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with near 99% efficiency. This allows the single-shot measurement of arbitrary many-body correlations for the direct probing of the dynamical phase transition and the uncovering of computationally intractable features that rely on the long-range interactions and high connectivity between the qubits.

Linear arrays of trapped and laser cooled atomic ions are a versatile platform for studying emergent phenomena in strongly-interacting many-body systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatiotemporal resolution, decoupling from the external environment, and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin-models which are heralded by memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.

Due to the exponential complexity of the resources required by quantum state tomography (QST), people are interested in approaches towards identifying quantum states which require less effort and time. In this paper, we provide a tailored and efficient method for reconstructing mixed quantum states up to $12$ (or even more) qubits from an incomplete set of observables subject to noises. Our method is applicable to any pure or nearly pure state $ρ$, and can be extended to many states of interest in quantum information processing, such as multi-particle entangled $W$ state, GHZ state and cluster states that are matrix product operators of low dimensions. The method applies the quantum density matrix constraints to a quantum compressive sensing optimization problem, and exploits a modified Quantum Alternating Direction Multiplier Method (Quantum-ADMM) to accelerate the convergence. Our algorithm takes $8,35$ and $226$ seconds respectively to reconstruct superposition state density matrices of $10,11,12$ qubits with acceptable fidelity, using less than $1 \%$ of measurements of expectation. To our knowledge it is the fastest realization that people can achieve using a normal desktop. We further discuss applications of this method using experimental data of mixed states obtained in an ion trap experiment of up to $8$ qubits.

Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter. A prime example is the breaking of spatial translation symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Analogous to crystals in space, the breaking of translation symmetry in time and the emergence of a "time crystal" was recently proposed, but later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems subject to a periodic drive can exhibit persistent time-correlations at an emergent sub-harmonic frequency. This new phase of matter has been dubbed a "discrete time crystal" (DTC). Here, we present the first experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization (MBL) conditions, and observe a sub-harmonic temporal response that is robust to external perturbations. Such a time crystal opens the door for studying systems with long-range spatial-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.

Al$^+$ ions optical clock is a very promising optical frequency standard candidate due to its extremely small blackbody radiation shift. It has been successfully demonstrated with indirect cooled, quantum-logic-based spectroscopy technique. Its accuracy is limited by second-order Doppler shift, and its stability is limited by the number of ions that can be probed in quantum logic processing. We propose a direct laser cooling scheme of Al$^+$ ions optical clocks where both the stability and accuracy of the clocks are greatly improved. In the proposed scheme, two Al$^+$ ions traps are utilized. The first trap is used to trap a large number of Al$^+$ ions to improve the stability of the clock laser, while the second trap is used to trap a single Al$^+$ ions to provide the ultimate accuracy. Both traps are cooled with a continuous wave 167 nm laser. The expected clock laser stability can reach $9.0\times10^{-17}/\sqrtτ$. For the second trap, in addition to 167 nm laser Doppler cooling, a second stage pulsed 234 nm two-photon cooling laser is utilized to further improve the accuracy of the clock laser. The total systematic uncertainty can be reduced to about $1\times10^{-18}$. The proposed Al$^+$ ions optical clock has the potential to become the most accurate and stable optical clock.

We demonstrate a new technique to prepare an offline source of francium for trapping in a magneto-optical trap. Implanting a radioactive beam of $^{225}$Ac, $t_{1/2} = 9.920(3)$ days, in a foil, allows use of the decay products, i.e.$^{221}$Fr, $t_{1/2} = 288.0(4)$ s. $^{221}$Fr is ejected from the foil by the $α$ decay of $^{225}$Ac. This technique is compatible with the online accumulation of a laser-cooled atomic francium sample for a series of planned parity non-conservation measurements at TRIUMF. We obtain a 34% release efficiency for $^{221}$Fr from the recoil source based on particle detector measurements. We find that laser cooling operation with the source is $8^{+10}_{-5}$ times less efficient than from a mass-separated ion beam of $^{221}$Fr in the current geometry. While the flux of this source is two to three orders of magnitude lower than typical francium beams from ISOL facilities, the source provides a longer-term supply of francium for offline studies.

We report on the successful commissioning of the Francium Trapping Facility at TRIUMF. Large laser-cooled samples of francium are produced from a francium ion beam delivered by the ISAC radioactive ion beam facility. The ion beam is neutralized on an yttrium foil, which is subsequently heated to transfer the atoms into the magneto-optical trapping region. We have successfully trapped $^{207}$Fr, $^{209}$Fr and $^{221}$Fr, with a maximum of $2.5 \times 10^5$ $^{209}$Fr atoms. The neutral cold atoms will be used in studies of the weak interaction through measurements of atomic parity non-conservation.

We have employed the 12.6 GHz microwave transition resonance of a single trapped$^{171}$Yb+ ion to accurately measure the size and relative orientation of the magnetic and optical electric fields at the position of the ion in the trap. Accurate knowledge of these fields is required for precision experiments such as single ion PNC. As a proof of the principle we have measured the polarization dependent light-shift of the ground state hyperfine levels due to the 369 nm cooling laser to determine its electric field amplitude and polarization.