Paul Hess

Order of Magnitude Smaller Limit on the Electric Dipole Moment of the Electron

Stubbornly Spherical The shape of the electrons charge distribution reflects the degree to which switching the direction of time impacts the basic ingredients of the universe. The Standard Model (SM) of particle physics predicts a very slight asphericity of the charge distribution, whereas SM extensions such as supersymmetry posit bigger and potentially measurable, but still tiny, deviations from a perfect sphere. Polar molecules have been identified as ideal settings for measuring this asymmetry, which should be reflected in a finite electric dipole moment (EDM) because of the extremely large effective electric fields that act on an electron inside such molecules. Using electron spin precession in the molecule ThO, Baron et al. (p. 269, published online 19 December; see the cover; see the Perspective by Brown) measured the EDM of the electron as consistent with zero. This excludes some of the extensions to the SM and sets a bound to the search for a nonzero EDM in other facilities, such as the Large Hadron Collider. Spin precession measurements in the polar molecule thorium monoxide indicate a nearly spherical charge distribution of an electron. [Also see Perspective by Brown] The Standard Model of particle physics is known to be incomplete. Extensions to the Standard Model, such as weak-scale supersymmetry, posit the existence of new particles and interactions that are asymmetric under time reversal (T) and nearly always predict a small yet potentially measurable electron electric dipole moment (EDM), de, in the range of 10−27 to 10−30 e·cm. The EDM is an asymmetric charge distribution along the electron spin (S→) that is also asymmetric under T. Using the polar molecule thorium monoxide, we measured de = (–2.1 ± 3.7stat ± 2.5syst) × 10−29 e·cm. This corresponds to an upper limit of | de | < 8.7 × 10−29 e·cm with 90% confidence, an order of magnitude improvement in sensitivity relative to the previous best limit. Our result constrains T-violating physics at the TeV energy scale.

Many-body localization in a quantum simulator with programmable random disorder

Interacting quantum systems are expected to thermalize, but in some situations in the presence of disorder they can exist in localized states instead. This many-body localization is studied experimentally in a small system with programmable disorder. When a system thermalizes it loses all memory of its initial conditions. Even within a closed quantum system, subsystems usually thermalize using the rest of the system as a heat bath. Exceptions to quantum thermalization have been observed, but typically require inherent symmetries1,2 or noninteracting particles in the presence of static disorder3,4,5,6. However, for strong interactions and high excitation energy there are cases, known as many-body localization (MBL), where disordered quantum systems can fail to thermalize7,8,9,10. We experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmable random disorder to ten spins initialized far from equilibrium. Using experimental and numerical methods we observe the essential signatures of MBL: initial-state memory retention, Poissonian distributed energy level spacings, and evidence of long-time entanglement growth. Our platform can be scaled to more spins, where a detailed modelling of MBL becomes impossible.

Observation of a discrete time crystal

Spontaneous symmetry breaking is a fundamental concept in many areas of physics, including cosmology, particle physics and condensed matter. An example is the breaking of spatial translational symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Using the analogy of crystals in space, the breaking of translational symmetry in time and the emergence of a ‘time crystal’ was recently proposed, but was later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems, which are subject to a periodic drive, can exhibit persistent time correlations at an emergent subharmonic frequency. This new phase of matter has been dubbed a ‘discrete time crystal’. Here we present the 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 conditions, and observe a subharmonic temporal response that is robust to external perturbations. The observation of such a time crystal opens the door to the study of systems with long-range spatio-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.

Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator

A quantum simulator is a type of quantum computer that controls the interactions between quantum bits (or qubits) in a way that can be mapped to certain quantum many-body problems. As it becomes possible to exert more control over larger numbers of qubits, such simulators will be able to tackle a wider range of problems, such as materials design and molecular modelling, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. Here we use a quantum simulator composed of up to 53 qubits to study non-equilibrium dynamics in the transverse-field Ising model with long-range interactions. We observe a dynamical phase transition after a sudden change of the Hamiltonian, in a regime in which conventional statistical mechanics does not apply. The qubits are represented by the spins of trapped ions, which can be prepared in various initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with an efficiency of nearly 99 per cent. Such high efficiency means that arbitrary many-body correlations between qubits can be measured in a single shot, enabling the dynamical phase transition to be probed directly and revealing computationally intractable features that rely on the long-range interactions and high connectivity between qubits.

A cryogenic beam of refractory, chemically reactive molecules with expansion cooling

Cryogenically cooled buffer gas beam sources of the molecule thorium monoxide (ThO) are optimized and characterized. Both helium and neon buffer gas sources are shown to produce ThO beams with high flux, low divergence, low forward velocity, and cold internal temperature for a variety of stagnation densities and nozzle diameters. The beam operates with a buffer gas stagnation density of ∼10(15)-10(16) cm(-3) (Reynolds number ∼1-100), resulting in expansion cooling of the internal temperature of the ThO to as low as 2 K. For the neon (helium) based source, this represents cooling by a factor of about 10 (2) from the initial nozzle temperature of about 20 K (4 K). These sources deliver ∼10(11) ThO molecules in a single quantum state within a 1-3 ms long pulse at 10 Hz repetition rate. Under conditions optimized for a future precision spectroscopy application [A. C. Vutha et al., J. Phys. B: At., Mol. Opt. Phys., 2010, 43, 074007], the neon-based beam has the following characteristics: forward velocity of 170 m s(-1), internal temperature of 3.4 K, and brightness of 3 × 10(11) ground state molecules per steradian per pulse. Compared to typical supersonic sources, the relatively low stagnation density of this source and the fact that the cooling mechanism relies only on collisions with an inert buffer gas make it widely applicable to many atomic and molecular species, including those which are chemically reactive, such as ThO.

Observation of prethermalization in long-range interacting spin chains

Many-body interactions could lead to quantum thermalization, but long-range interactions provide an alternative. Although statistical mechanics describes thermal equilibrium states, these states may or may not emerge dynamically for a subsystem of an isolated quantum many-body system. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale, and instead relax to quasi-stationary prethermal states that can be described by statistical mechanics, when approximately conserved quantities are included in a generalized Gibbs ensemble (GGE). We experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse-field Ising Hamiltonian following a sudden quench. For sufficiently long-range interactions, the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. However, the prethermal state in this case cannot be described by a standard GGE; it rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.

Non-thermalization in trapped atomic ion spin chains

Linear arrays of trapped and laser-cooled atomic ions are a versatile platform for studying strongly interacting many-body quantum 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 spatio-temporal 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, effects that are heralded by the 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. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

Engineering large Stark shifts for control of individual clock state qubits

In quantum information science, the external control of qubits must be balanced with the extreme isolation of the qubits from the environment. Atomic qubit systems typically mitigate this balance through the use of gated laser fields that can create superpositions and entanglement between qubits. Here we propose the use of high-order optical Stark shifts from optical fields to manipulate the splitting of atomic qubits that are insensitive to other types of fields. We demonstrate a fourth-order AC Stark shift in a trapped atomic ion system that does not require extra laser power beyond that needed for other control fields. We individually address a chain of tightly-spaced trapped ions and show how these controlled shifts can produce an arbitrary product state of ten ions as well as generate site-specific magnetic field terms in a simulated spin Hamiltonian.

Shot-noise-limited spin measurements in a pulsed molecular beam

Heavy diatomic molecules have been identified as good candidates for use in electron electric dipole moment (eEDM) searches. Suitable molecular species can be produced in pulsed beams, but with a total flux and/or temporal evolution that varies significantly from pulse to pulse. These variations can degrade the experimental sensitivity to changes in the spin precession phase of an electrically polarized state, which is the observable of interest for an eEDM measurement. We present two methods for measurement of the phase that provide immunity to beam temporal variations, and make it possible to reach shot-noise-limited sensitivity. Each method employs rapid projection of the spin state onto both components of an orthonormal basis. We demonstrate both methods using the eEDM-sensitive H3Δ1 state of thorium monoxide, and use one of them to measure the magnetic moment of this state with increased accuracy relative to previous determinations.

STIRAP preparation of a coherent superposition of ThO

Experimental searches for the electron electric dipole moment (EDM) probe new physics beyond the Standard Model. The current best EDM limit was set by the ACME Collaboration [Science \textbf{343}, 269 (2014)], constraining time reversal symmetry (