D. B. Hume

Frequency Ratio of Al+ and Hg+ Single-Ion Optical Clocks; Metrology at the 17th Decimal Place

Time has always had a special status in physics because of its fundamental role in specifying the regularities of nature and because of the extraordinary precision with which it can be measured. This precision enables tests of fundamental physics and cosmology, as well as practical applications such as satellite navigation. Recently, a regime of operation for atomic clocks based on optical transitions has become possible, promising even higher performance. We report the frequency ratio of two optical atomic clocks with a fractional uncertainty of 5.2 × 10–17. The ratio of aluminum and mercury single-ion optical clock frequencies νAl+/νHg+ is 1.052871833148990438(55), where the uncertainty comprises a statistical measurement uncertainty of 4.3 × 10–17, and systematic uncertainties of 1.9 × 10–17 and 2.3 × 10–17 in the mercury and aluminum frequency standards, respectively. Repeated measurements during the past year yield a preliminary constraint on the temporal variation of the fine-structure constant α of batchmode documentclass[fleqn,10pt,legalpaper]{article} usepackage{amssymb} usepackage{amsfonts} usepackage{amsmath} pagestyle{empty} begin{document} ({dot{{alpha}}}{/}{alpha}=(-1.6{pm}2.3){times}10^{-17}{/}mathrm{year}) end{document}.

Frequency Comparison of Two High-Accuracy Al+ Optical Clocks

We have constructed an optical clock with a fractional frequency inaccuracy of 8.6x10{-18}, based on quantum logic spectroscopy of an Al+ ion. A simultaneously trapped Mg+ ion serves to sympathetically laser cool the Al+ ion and detect its quantum state. The frequency of the {1}S{0}<-->{3}P{0} clock transition is compared to that of a previously constructed Al+ optical clock with a statistical measurement uncertainty of 7.0x10{-18}. The two clocks exhibit a relative stability of 2.8x10{-15}tau{-1/2}, and a fractional frequency difference of -1.8x10{-17}, consistent with the accuracy limit of the older clock.

Creation of a six-atom 'Schrödinger cat' state.

Among the classes of highly entangled states of multiple quantum systems, the so-called ‘Schrödinger cat’ states are particularly useful. Cat states are equal superpositions of two maximally different quantum states. They are a fundamental resource in fault-tolerant quantum computing and quantum communication, where they can enable protocols such as open-destination teleportation and secret sharing. They play a role in fundamental tests of quantum mechanics and enable improved signal-to-noise ratios in interferometry. Cat states are very sensitive to decoherence, and as a result their preparation is challenging and can serve as a demonstration of good quantum control. Here we report the creation of cat states of up to six atomic qubits. Each qubits state space is defined by two hyperfine ground states of a beryllium ion; the cat state corresponds to an entangled equal superposition of all the atoms in one hyperfine state and all atoms in the other hyperfine state. In our experiments, the cat states are prepared in a three-step process, irrespective of the number of entangled atoms. Together with entangled states of a different class created in Innsbruck, this work represents the current state-of-the-art for large entangled states in any qubit system.

Optical Clocks and Relativity

Relativity Comes Down to Earth Over a century ago, Einstein presented the theory of relativity—where space and time are no longer fixed concepts, but are relative to an observer and their frame of reference. Tests of relativity have usually been confined to space-based measurements and/or with objects with velocities approaching the speed of light. Time-dilation and length-contraction have been confirmed and are used in satellite communication and global positioning systems. Using the precision of state-of-the-art optical clocks, Chou et al. (p. 1630) have confirmed that relativistic effects can now be measured at speeds attained by 100 meters sprinters (10 m/s) and gravitational effects due to just one meter height difference. The tiny relativistic effects of everyday life can be measured by clocks ticking at optical frequencies. Observers in relative motion or at different gravitational potentials measure disparate clock rates. These predictions of relativity have previously been observed with atomic clocks at high velocities and with large changes in elevation. We observed time dilation from relative speeds of less than 10 meters per second by comparing two optical atomic clocks connected by a 75-meter length of optical fiber. We can now also detect time dilation due to a change in height near Earth’s surface of less than 1 meter. This technique may be extended to the field of geodesy, with applications in geophysics and hydrology as well as in space-based tests of fundamental physics.

Microfabricated surface-electrode ion trap for scalable quantum information processing.

Individual laser-cooled 24Mg+ ions are confined in a linear Paul trap with a novel geometry where gold electrodes are located in a single plane and the ions are trapped 40 microm above this plane. The relatively simple trap design and fabrication procedure are important for large-scale quantum information processing (QIP) using ions. Measured ion motional frequencies are compared to simulations. Measurements of ion recooling after cooling is temporarily suspended yield a heating rate of approximately 5 motional quanta per millisecond for a trap frequency of 2.83 MHz, sufficiently low to be useful for QIP.

Long-lived qubit memory using atomic ions

We demonstrate experimentally a robust quantum memory using a magnetic-field-independent hyperfine transition in 9Be+ atomic ion qubits at a magnetic field B approximately = 0.01194 T. We observe that the single physical qubit memory coherence time is greater than 10 s, an improvement of approximately 5 orders of magnitude from previous experiments with 9Be+. We also observe long coherence times of decoherence-free subspace logical qubits comprising two entangled physical qubits and discuss the merits of each type of qubit.

Fisher information and entanglement of non-Gaussian spin states

Subtle entanglement in an atomic cloud In the quantum world, atoms can be correlated with each other—“entangled”—which reduces the uncertainty in the knowledge of some of their properties. Physicists then use this reduced uncertainty to perform precision measurements. Strobel et al. made an unusual type of entangled state consisting of hundreds of ultracold Rb atoms. These methods may in the future be able to generate states that will be more useful in precision measurement. Science, this issue p. 424 An unconventional entangled state is created out of a mesoscopic number of ultracold rubidium atoms. Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here, we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement, which we confirm by Bayesian phase estimation with sub–shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems.

Observation of the 1S0-->3P0 clock transition in 27Al+.

We report, for the first time, laser spectroscopy of the 1S0-->3P0 clock transition in 27Al+. A single aluminum ion and a single beryllium ion are simultaneously confined in a linear Paul trap, coupled by their mutual Coulomb repulsion. This coupling allows the beryllium ion to sympathetically cool the aluminum ion and also enables transfer of the aluminums electronic state to the berylliums hyperfine state, which can be measured with high fidelity. These techniques are applied to measure the clock transition frequency nu=1,121,015,393,207,851(6) Hz. They are also used to measure the lifetime of the metastable clock state tau=20.6+/-1.4 s, the ground state 1S0 g factor gS=-0.000,792,48(14), and the excited state 3P0 g factor gP=-0.001,976,86(21), in units of the Bohr magneton.

Hyperfine Coherence in the Presence of Spontaneous Photon Scattering

The coherence of a hyperfine-state superposition of a trapped 9Be+ ion in the presence of off-resonant light is studied experimentally. It is shown that Rayleigh elastic scattering of photons that does not change state populations also does not affect coherence. We observe coherence times that exceed the average scattering time of 19 photons which is determined from measured Stark shifts. This result implies that, with sufficient control over its parameters, laser light can be used to manipulate hyperfine-state superpositions with very little decoherence.

Scalable Spin Squeezing for Quantum-Enhanced Magnetometry with Bose-Einstein Condensates

A major challenge in quantum metrology is the generation of entangled states with a macroscopic atom number. Here, we demonstrate experimentally that atomic squeezing generated via nonlinear dynamics in Bose-Einstein condensates, combined with suitable trap geometries, allows scaling to large ensemble sizes. We achieve a suppression of fluctuations by 5.3(5) dB for 12,300 particles, from which we infer that similar squeezing can be obtained for more than 10(7)u2009u2009atoms. With this resource, we demonstrate quantum-enhanced magnetometry by swapping the squeezed state to magnetically sensitive hyperfine levels that have negligible nonlinearity. We find a quantum-enhanced single-shot sensitivity of 310(47) pT for static magnetic fields in a probe volume as small as 90u2009u2009μm3.