All evidence so far suggests that the absolute spatial orientation of an experiment never affects its outcome. This is reflected in the standard model of particle physics by requiring all particles and fields to be invariant under Lorentz transformations. The best-known tests of this important cornerstone of physics are Michelson-Morley-type experiments verifying the isotropy of the speed of light. For matter, Hughes-Drever-type experiments test whether the kinetic energy of particles is independent of the direction of their velocity, that is, whether their dispersion relations are isotropic. To provide more guidance for physics beyond the standard model, refined experimental verifications of Lorentz symmetry are desirable. Here we search for violation of Lorentz symmetry for electrons by performing an electronic analogue of a Michelson-Morley experiment. We split an electron wave packet bound inside a calcium ion into two parts with different orientations and recombine them after a time evolution of 95 milliseconds. As the Earth rotates, the absolute spatial orientation of the two parts of the wave packet changes, and anisotropies in the electron dispersion will modify the phase of the interference signal. To remove noise, we prepare a pair of calcium ions in a superposition of two decoherence-free states, thereby rejecting magnetic field fluctuations common to both ions. After a 23-hour measurement, we find a limit of h × 11 millihertz (h is Planck's constant) on the energy variations, verifying the isotropy of the electron's dispersion relation at the level of one part in 10(18), a 100-fold improvement on previous work. Alternatively, we can interpret our result as testing the rotational invariance of the Coulomb potential. Assuming that Lorentz symmetry holds for electrons and that the photon dispersion relation governs the Coulomb force, we obtain a fivefold-improved limit on anisotropies in the speed of light. Our result probes Lorentz symmetry violation at levels comparable to the ratio between the electroweak and Planck energy scales. Our experiment demonstrates the potential of quantum information techniques in the search for physics beyond the standard model.

We show that a chain of trapped ions embedded in microtraps generated by an optical lattice can be used to study oscillator models related to dry friction and energy transport. Numerical calculations with realistic experimental parameters demonstrate that both static and dynamic properties of the ion chain change significantly as the optical lattice power is varied. Finally, we lay out an experimental scheme to use the spin degree of freedom to probe the phase space structure and quantum critical behavior of the ion chain.

We use a single-ion electric-field noise sensor in combination with in situ surface treatment and analysis tools, to investigate the relationship between electric-field noise from metal surfaces in vacuum and the composition of the surface. These experiments are performed in a setup that integrates ion trapping capabilities with surface analysis tools. We find that treatment of an aluminum-copper surface with energetic argon ions significantly reduces the level of room-temperature electric-field noise, but the surface does not need to be atomically clean to show noise levels comparable to those of the best cryogenic traps. The noise levels after treatment are low enough to allow fault-tolerant trapped-ion quantum information processing on a microfabricated surface trap at room temperature.

Quantum correlations are at the heart of quantum information science 1-3 . Their detection usually requires access to all the correlated subsystems 4,5 . However, in many realistic scenarios this is not feasible, as only some of the subsystems can be controlled and measured. Such cases can be treated as open quantum systems interacting with an inaccessible environment 6 . Initial system-environment correlations play a fundamental role for the dynamics of open quantum systems 6-9 . Following a recent proposal 10,11 , we exploit the impact of the correlations on the open-system dynamics to detect system-environment quantum correlations without accessing the environment. We use two degrees of freedom of a trapped ion to model an open system and its environment. The present method does not require any assumptions about the environment, the interaction or the initial state, and therefore provides a versatile tool for the study of quantum systems.Quantum correlations are particularly important in the context of quantum simulation 12-14 , quantum phase transitions 15,16 , as well as for quantum computation 17 . In these experiments, one typically strives to study quantum many-body dynamics in high-dimensional Hilbert spaces. However, it is precisely in these complex systems where it becomes increasingly difficult to experimentally detect quantum correlations because standard methods such as full state tomography are impractical 18 . Therefore, it seems natural to restrict oneself to measurements of a smaller controllable subsystem 19 . Similarly, in quantum communication protocols, each party has access only to its part of the shared correlated state but may want to confirm the presence of quantum correlations locally 3 . All these situations can be described in the framework of a well-controlled open quantum system in contact with an inaccessible environment 6 .Initial system-environment correlations can significantly change the dynamics of open systems 6-9 . The standard master equation approach to open systems assumes an initial state with vanishing total correlations, which may not be appropriate unless a product state is explicitly prepared 20,21 . Moreover, the information flow between the system and its environment and the corresponding degree of non-Markovianity is closely related to the presence of correlations 9,22-24 .The present experiment follows a recently proposed protocol to detect nonclassical system-environment correlations of an arbitrary, unknown state by accessing only the open system 10,11 . The correlations are revealed through their effect on the open system dynamics. The protocol does not require any knowledge about the environment or the nature of the interaction, making it applicable to a wide range of scenarios where only partial access to a possibly correlated dynamical system is granted. the total system, which is connected to its accessible local subsystem in the grey box through the partial trace operation Tr E (dashed arrows). First, the accessible part ρ S of the unknown state ρ is me...

Rate constants k ESR for intramolecular electron transfer between the reduced and oxidized hydrazine units of dimeric 2-tert-butyl-3−isopropyl-2,3-diazabicyclo[2.2.2]octylhydrazine radical cations which are doubly linked through the bicyclic units by four σ-bonds (aBIT + , sBIT + , and aBIH + ) were determined by simulations of their variable temperature ESR spectra in methylene chloride to be 10.5(7), 9.6(3), and 12.4(4) × 107 s-1 at 298 K, respectively. These cations show solvent sensitive charge transfer absorption bands from which the vertical electron transfer excitation energy, λ, and the electronic coupling, V J, were determined by simulation of the charge transfer bands using vibronic coupling theory (ref ). Partitioning between solvent and vibrational components of λ was made assuming that the average energy of the vibrational modes coupled to the electron transfer, hνv, is 2.29 kcal/mol (800 cm-1). The ESR rate constants at 298 K for s- and aBIT + are factors of 23 and 26, respectively, larger than k cal, calculated from λs, λv, hνv, and V J estimated using a vibronic coupling theory analysis of the charge transfer bands. The ratio k cal(350)/k cal(250) is 7.4 and 9.4(k ESR(350)/k ESR(250)) for sBIT + and aBIT + , respectively. Previously reported data for the doubly-linked four σ-bond dimeric N,N‘-bis-2,3-diazabicyclo[2.2.2]octyl hydrazine (22H + ) was also reanalyzed using vibronic coupling theory. k ESR/k cal in acetonitrile at 298 K is 20, but k cal(350)/k cal(250) is 25(k ESR(350)/k ESR(250)). Possible reasons for the rather poor agreement with theory are suggested.

We experimentally study energy transport in chains of trapped ions. We use a pulsed excitation scheme to rapidly add energy to the local motional mode of one of the ions in the chain. Subsequent energy readout allows us to determine how the excitation has propagated throughout the chain. We observe energy revivals that persist for many cycles. We study the behavior with an increasing number of ions of up to 37 in the chain, including a zig-zag configuration. The experimental results agree with the theory of normal mode evolution. The described system provides an experimental toolbox for the study of thermodynamics of closed systems and energy transport in both classical and quantum regimes.Chains of trapped ions have been proposed as a model system for the study of quantum transport of heat, equilibration in dissipative quantum systems, phase transitions in oscillator chain models, and friction in nanoscale systems [1][2][3][4]. In contrast to the current major efforts studying many body physics using the internal degree-of-freedom [5,6], these proposals focus on the motional degree of freedom of the ions. While the linear regime of the chain already exhibits interesting phenomena like violations of Fourier's law, the most intriguing physics emerges from nonlinearities in the potential. Such nonlinearities could stem from from a zig-zag configuration of the chain, an additional optical lattice, or a coupling to an internal degree-offreedom [7][8][9]. In particular, additional optical potentials allow to engineer phonon-phonon interactions realizing the Bose-Hubbard and Jaynes-Cummings-Hubbard models [10,11].

We present a method for measuring branching fractions for the decay of J = 1/2 atomic energy levels to lower-lying states based on time-resolved recording of the atom's fluorescence during a series of population transfers. We apply this method to measure the branching fractions for the decay of the 4 2 P 1/2 state of 40 Ca + to the 4 2 S 1/2 and 3 2 D 3/2 states to be 0.93565(7) and 0.06435(7), respectively. The measurement scheme requires that at least one of the lower-lying states be longlived. The method is insensitive to fluctuations in laser light intensity and magnetic field and is readily applicable to various atomic species due to its simplicity. Our result distinguishes well among existing state-of-the-art theoretical models of Ca + .

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