Maxwell Parsons

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.

Search for the electric dipole moment of the electron with thorium monoxide

The electric dipole moment of the electron (eEDM) is a signature of CP-violating physics beyond the standard model. We describe an ongoing experiment to measure or set improved limits to the eEDM, using a cold beam of thorium monoxide (ThO) molecules. The metastable H 3 � 1 state in ThO has important advantages for such an experiment. We argue that the statistical uncertainty of an eEDM measurement could be improved by as much as three orders of magnitude compared to the current experimental limit, in a first-generation apparatus using a cold ThO beam. We describe our measurements of the H state lifetime and the production of ThO molecules in a beam, which provide crucial data for the eEDM sensitivity estimate. ThO also has ideal properties for the rejection of a number of known systematic errors; these properties and their implications are described. (Some figures in this article are in colour only in the electronic version)

A cold-atom Fermi–Hubbard antiferromagnet

Exotic phenomena in systems with strongly correlated electrons emerge from the interplay between spin and motional degrees of freedom. For example, doping an antiferromagnet is expected to give rise to pseudogap states and high-temperature superconductors. Quantum simulation using ultracold fermions in optical lattices could help to answer open questions about the doped Hubbard Hamiltonian, and has recently been advanced by quantum gas microscopy. Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a two-dimensional square lattice of about 80 sites at a temperature of 0.25 times the tunnelling energy. The antiferromagnetic long-range order manifests through the divergence of the correlation length, which reaches the size of the system, the development of a peak in the spin structure factor and a staggered magnetization that is close to the ground-state value. We hole-dope the system away from half-filling, towards a regime in which complex many-body states are expected, and find that strong magnetic correlations persist at the antiferromagnetic ordering vector up to dopings of about 15 per cent. In this regime, numerical simulations are challenging and so experiments provide a valuable benchmark. Our results demonstrate that microscopy of cold atoms in optical lattices can help us to understand the low-temperature Fermi–Hubbard model.Many exotic phenomena in strongly correlated electron systems emerge from the interplay between spin and motional degrees of freedom [1, 2]. For example, doping an antiferromagnet gives rise to interesting phases including pseudogap states and high-temperature superconductors [3]. A promising route towards achieving a complete understanding of these materials begins with analytic and computational analysis of simplified models. Quantum simulation has recently emerged as a complementary approach towards understanding these models [4–8]. Ultracold fermions in optical lattices offer the potential to answer open questions on the lowtemperature regime of the doped Hubbard model [9–11], which is thought to capture essential aspects of the cuprate superconductor phase diagram but is numerically intractable in that parameter regime. Already, Mott-insulating phases and short-range antiferromagnetic correlations have been observed, but temperatures were too high to create an antiferromagnet [12–15]. A new perspective is afforded by quantum gas microscopy [16–28], which allows readout of magnetic correlations at the site-resolved level [25–28]. Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a 2D square lattice of approximately 80 sites. Using site-resolved imaging, we detect (finite-size) antiferromagnetic long-range order (LRO) through the development of a peak in the spin structure factor and the divergence of the correlation length that reaches the size of the system. At our lowest temperature of T/t = 0.25(2) we find strong order across the entire sample, where the staggered magnetization approaches the ground-state value. Our experimental platform enables doping away from half filling, where pseudogap states and stripe ordering are expected, but theoretical methods become numerically intractable. In this regime we find that the antiferromagnetic LRO persists to hole dopings of about 15%, providing a guideline for computational methods. Our results demonstrate that quantum gas microscopy of ultracold fermions in optical lattices can now address open questions on the low-temperature Hubbard model. The Hubbard Hamiltonian is a fundamental model for spinful lattice electrons describing a competition between kinetic energy t and interaction energy U [29]. In the limiting case of half-filling (average one particle per site) and dominant interactions (U/t 1) the Hubbard model maps to the Heisenberg model [1]. There, the exchange energy J = 4t/U can give rise to antiferromagnetically ordered states at low temperatures [30]. This order persists for all finite U/t, where charge fluctuations reduce the ordering strength [31]. Away from half-filling, the coupling between motional and spin degrees of freedom is expected to give rise to a rich many-body phase diagram (see Fig. 1a), which is challenging to understand theoretically due to the fermion sign problem [32]. Even so, in the thermodynamic limit commensurate long-range order (LRO) has been conjectured to transition to incommensurate LRO infinitesimally far from half-filling, whereas for finite-size systems commensurate order is expected to extend to non-zero doping [31, 33]. The strength of global antiferromagnetic order in spin systems on bipartite lattices is quantified by the staggered magnetization m = |m|. The component along the z spin direction is

Site-resolved imaging of fermionic ^{6}Li in an optical lattice.

We demonstrate site-resolved imaging of individual fermionic ^{6}Li atoms in a single layer of a 3D optical lattice. To preserve the density distribution during fluorescence imaging, we simultaneously cool the atoms with 3D Raman sideband cooling. This laser cooling technique, demonstrated here for the first time for ^{6}Li atoms, also provides a pathway to rapid low-entropy filling of an optical lattice. We are able to determine the occupation of individual lattice sites with a fidelity >95%, enabling direct, local measurement of particle correlations in Fermi lattice systems. This ability will be instrumental for creating and investigating low-temperature phases of the Fermi-Hubbard model, including antiferromagnets and d-wave superfluidity.

Site-resolved measurement of the spin-correlation function in the Fermi-Hubbard model

Quantum many-body systems exhibiting magnetic correlations underlie a wide variety of phenomena. High-temperature superconductivity, for example, can arise from the correlated motion of holes on an antiferromagnetic (AFM) Mott insulator. Ultracold fermionic atoms in optical lattices provide realizations of strongly correlated many-body systems with a tunability that is unparalleled in conventional solid-state systems. Recent experiments exploring the Hubbard model with cold atoms are accessing temperatures where AFM correlations form, but have only observed these correlations via measurements that were averages over inhomogeneous systems. With the advance of quantum gas microscopy we can now take a snapshot of the real-space correlations in a single quantum many-body state at the atomic scale. Here we report site-resolved observations of AFM correlations in a Hubbard-regime optical lattice. The ability to locally measure spin correlations for a many-body state allows us to make unprecedented comparisons to theoretical predictions. We measure the in-situ distributions of the particle density and magnetic correlations, extract thermodynamic quantities from comparisons to theory, directly measure the correlation length, and study how lattice loading dynamics affect our ability to prepare samples in thermal equilibrium. The largest nearest-neighbor spin correlator that we observe is 53 % of the value predicted by quantum Monte Carlo calculations in the zero-temperature limit. Our results demonstrate that quantum gas microscopy is a powerful tool for studying fermionic quantum magnetism. Direct access to many-body physics at the single-particle level and the microscopic study of quantum dynamics will further our understanding of how new states of matter emerge from the interplay of motion and magnetism in quantum many-body systems.Exotic phases of matter can emerge from strong correlations in quantum many-body systems. Quantum gas microscopy affords the opportunity to study these correlations with unprecedented detail. Here, we report site-resolved observations of antiferromagnetic correlations in a two-dimensional, Hubbard-regime optical lattice and demonstrate the ability to measure the spin-correlation function over any distance. We measure the in situ distributions of the particle density and magnetic correlations, extract thermodynamic quantities from comparisons to theory, and observe statistically significant correlations over three lattice sites. The temperatures that we reach approach the limits of available numerical simulations. The direct access to many-body physics at the single-particle level demonstrated by our results will further our understanding of how the interplay of motion and magnetism gives rise to new states of matter.

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.

A traveling wave decelerator for neutral polar molecules

Recently, a decelerator for neutral polar molecules has been presented that operates on the basis of macroscopic, three-dimensional, traveling electrostatic traps [A. Osterwalder, S. A. Meek, G. Hammer, H. Haak, and G. Meijer, Phys. Rev. A 81, 051401 (2010)]. In the present paper, a complete description of this decelerator is given, with emphasis on the electronics and the mechanical design. Experimental results showing the transverse velocity distributions of guided molecules are shown and compared to trajectory simulations. An assessment of non-adiabatic losses is made by comparing the deceleration signals from (13)CO with those from (12)CO and with simulated signals.

Methods, Analysis, and the Treatment of Systematic Errors for the Electron Electric Dipole Moment Search in Thorium Monoxide

We recently set a new limit on the electric dipole moment of the electron (eEDM) (J Baron et al and ACME collaboration 2014 Science 343 269–272), which represented an order-of-magnitude improvement on the previous limit and placed more stringent constraints on many charge-parity-violating extensions to the standard model. In this paper we discuss the measurement in detail. The experimental method and associated apparatus are described, together with the techniques used to isolate the eEDM signal. In particular, we detail the way experimental switches were used to suppress effects that can mimic the signal of interest. The methods used to search for systematic errors, and models explaining observed systematic errors, are also described. We briefly discuss possible improvements to the experiment.