Implementing an electronic sideband offset lock for isotope shift spectroscopy in radium.

We demonstrate laser frequency stabilization with at least 6 GHz of offset tunability using an in-phase/quadrature (IQ) modulator to generate electronic sidebands (ESB) on a titanium sapphire laser at 714 nm and we apply this technique to perform isotope shift spectroscopy of 226Ra and 225Ra. By locking the laser to a single resonance of a high finesse optical cavity and adjusting the lock offset, we determine the frequency difference between the magneto-optical trap (MOT) transitions in the two isotopes to be 2630.0 ± 0.3 MHz, a factor of 29 more precise than the previously available data. Using the known value of the hyperfine splitting of the 3P1 level, we calculate the isotope shift for the 1S0 to 3P1 transition to be 2267.0 ± 2.2 MHz, a factor of 8 more precise than the best available value. Our technique could be applied to countless other atomic systems to provide unprecedented precision in isotope shift spectroscopy and other relative frequency comparisons.

Collective atomic scattering and motional effects in a dense coherent medium.

We investigate collective emission from coherently driven ultracold (88)Sr atoms. We perform two sets of experiments using a strong and weak transition that are insensitive and sensitive, respectively, to atomic motion at 1 µK. We observe highly directional forward emission with a peak intensity that is enhanced, for the strong transition, by >10(3) compared with that in the transverse direction. This is accompanied by substantial broadening of spectral lines. For the weak transition, the forward enhancement is substantially reduced due to motion. Meanwhile, a density-dependent frequency shift of the weak transition (∼10% of the natural linewidth) is observed. In contrast, this shift is suppressed to <1% of the natural linewidth for the strong transition. Along the transverse direction, we observe strong polarization dependences of the fluorescence intensity and line broadening for both transitions. The measurements are reproduced with a theoretical model treating the atoms as coherent, interacting radiating dipoles.

First Measurement of the Atomic Electric Dipole Moment of (225)Ra.

The radioactive radium-225 ((225)Ra) atom is a favorable case to search for a permanent electric dipole moment. Because of its strong nuclear octupole deformation and large atomic mass, (225)Ra is particularly sensitive to interactions in the nuclear medium that violate both time-reversal symmetry and parity. We have developed a cold-atom technique to study the spin precession of (225)Ra atoms held in an optical dipole trap, and demonstrated the principle of this method by completing the first measurement of its atomic electric dipole moment, reaching an upper limit of |d((225)Ra)|<5.0×10(-22) e cm (95% confidence).

Quantum simulation. Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism.

SU(N) symmetry can emerge in a quantum system with N single-particle spin states when spin is decoupled from interparticle interactions. Taking advantage of the high measurement precision offered by an ultrastable laser, we report a spectroscopic observation of SU(N ≤ 10) symmetry in (87)Sr. By encoding the electronic orbital degree of freedom in two clock states while keeping the system open to as many as 10 nuclear spin sublevels, we probed the non-equilibrium two-orbital SU(N) magnetism via Ramsey spectroscopy of atoms confined in an array of two-dimensional optical traps; we studied the spin-orbital quantum dynamics and determined the relevant interaction parameters. This study lays the groundwork for using alkaline-earth atoms as testbeds for important orbital models.

Heisenberg-limited atom clocks based on entangled qubits.

We present a quantum-enhanced atomic clock protocol based on groups of sequentially larger Greenberger-Horne-Zeilinger (GHZ) states that achieves the best clock stability allowed by quantum theory up to a logarithmic correction. Importantly the protocol is designed to work under realistic conditions where the drift of the phase of the laser interrogating the atoms is the main source of decoherence. The simultaneous interrogation of the laser phase with a cascade of GHZ states realizes an incoherent version of the phase estimation algorithm that enables Heisenberg-limited operation while extending the coherent interrogation time beyond the laser noise limit. We compare and merge the new protocol with existing state of the art interrogation schemes, and identify the precise conditions under which entanglement provides an advantage for clock stabilization: it allows a significant gain in the stability for short averaging time.

An optical lattice clock with accuracy and stability at the 10(-18) level.

Progress in atomic, optical and quantum science has led to rapid improvements in atomic clocks. At the same time, atomic clock research has helped to advance the frontiers of science, affecting both fundamental and applied research. The ability to control quantum states of individual atoms and photons is central to quantum information science and precision measurement, and optical clocks based on single ions have achieved the lowest systematic uncertainty of any frequency standard. Although many-atom lattice clocks have shown advantages in measurement precision over trapped-ion clocks, their accuracy has remained 16 times worse. Here we demonstrate a many-atom system that achieves an accuracy of 6.4 × 10(-18), which is not only better than a single-ion-based clock, but also reduces the required measurement time by two orders of magnitude. By systematically evaluating all known sources of uncertainty, including in situ monitoring of the blackbody radiation environment, we improve the accuracy of optical lattice clocks by a factor of 22. This single clock has simultaneously achieved the best known performance in the key characteristics necessary for consideration as a primary standard-stability and accuracy. More stable and accurate atomic clocks will benefit a wide range of fields, such as the realization and distribution of SI units, the search for time variation of fundamental constants, clock-based geodesy and other precision tests of the fundamental laws of nature. This work also connects to the development of quantum sensors and many-body quantum state engineering (such as spin squeezing) to advance measurement precision beyond the standard quantum limit.

Optical spectrum analyzer with quantum-limited noise floor.

Interactions between atoms and lasers provide the potential for unprecedented control of quantum states. Fulfilling this potential requires detailed knowledge of frequency noise in optical oscillators with state-of-the-art stability. We demonstrate a technique that precisely measures the noise spectrum of an ultrastable laser using optical lattice-trapped 87Sr atoms as a quantum projection noise-limited reference. We determine the laser noise spectrum from near dc to 100 Hz via the measured fluctuations in atomic excitation, guided by a simple and robust theory model. The noise spectrum yields a 26(4) mHz linewidth at a central frequency of 429 THz, corresponding to an optical quality factor of 1.6×10(16). This approach improves upon optical heterodyne beats between two similar laser systems by providing information unique to a single laser and complements the traditionally used Allan deviation which evaluates laser performance at relatively long time scales. We use this technique to verify the reduction of resonant noise in our ultrastable laser via feedback from an optical heterodyne beat. Finally, we show that knowledge of our laser's spectrum allows us to accurately predict the laser-limited stability for optical atomic clocks.

A quantum many-body spin system in an optical lattice clock.

Strongly interacting quantum many-body systems arise in many areas of physics, but their complexity generally precludes exact solutions to their dynamics. We explored a strongly interacting two-level system formed by the clock states in (87)Sr as a laboratory for the study of quantum many-body effects. Our collective spin measurements reveal signatures of the development of many-body correlations during the dynamical evolution. We derived a many-body Hamiltonian that describes the experimental observation of atomic spin coherence decay, density-dependent frequency shifts, severely distorted lineshapes, and correlated spin noise. These investigations open the door to further explorations of quantum many-body effects and entanglement through use of highly coherent and precisely controlled optical lattice clocks.

Comparison of two independent Sr optical clocks with 1×10(-17) stability at 10(3) s.

Many-particle optical lattice clocks have the potential for unprecedented measurement precision and stability due to their low quantum projection noise. However, this potential has so far never been realized because clock stability has been limited by frequency noise of optical local oscillators. By synchronously probing two ^{87}Sr lattice systems using a laser with a thermal noise floor of 1×10(-15), we remove classically correlated laser noise from the intercomparison, but this does not demonstrate independent clock performance. With an improved optical oscillator that has a 1×10(-16) thermal noise floor, we demonstrate an order of magnitude improvement over the best reported stability of any independent clock, achieving a fractional instability of 1×10(-17) in 1000 s of averaging time for synchronous or asynchronous comparisons. This result is within a factor of 2 of the combined quantum projection noise limit for a 160 ms probe time with ~10(3) atoms in each clock. We further demonstrate that even at this high precision, the overall systematic uncertainty of our clock is not limited by atomic interactions. For the second Sr clock, which has a cavity-enhanced lattice, the atomic-density-dependent frequency shift is evaluated to be -3.11×10(-17) with an uncertainty of 8.2×10(-19).

Resolved atomic interaction sidebands in an optical clock transition.

We report the observation of resolved atomic interaction sidebands (ISB) in the (87)Sr optical clock transition when atoms at microkelvin temperatures are confined in a two-dimensional optical lattice. The ISB are a manifestation of the strong interactions that occur between atoms confined in a quasi-one-dimensional geometry and disappear when the confinement is relaxed along one dimension. The emergence of ISB is linked to the recently observed suppression of collisional frequency shifts. At the current temperatures, the ISB can be resolved but are broad. At lower temperatures, ISB are predicted to be substantially narrower and useful spectroscopic tools in strongly interacting alkaline-earth gases.

Hyperfine suppression of 2 3 S 1--3 3 P J transitions in 3He.

Two anomalously weak transitions within the 2(3)S_(1)--3(3)P_(J) manifolds in 3He have been identified. Their transition strengths are measured to be 1000 times weaker than that of the strongest transition in the same group. This dramatic suppression of transition strengths is due to the dominance of the hyperfine interaction over the fine-structure interaction. An alternative selection rule based on IS coupling (where the nuclear spin is first coupled to the total electron spin) is proposed. This provides qualitative understanding of the transition strengths. It is shown that the small deviations from the IS coupling model are fully accounted for by an exact diagonalization of the strongly interacting states.

Diffusion-weighted MRI in cortical ischaemia.

We carried out MRI on 16 male and three female comatose patients, aged 2 days to 79 years, with suspected cortical ischaemia referred from our intensive care units. Using a head coil, and following standard imaging, including coronal fluid-attenuated inversion-recovery images, we performed diffusion-weighted imaging (DWI) using a whole-brain multislice single-shot echo-planar sequence with b 0 and 1000 s/mm2: 5-mm slices covering the whole brain, TR 7000 TE 106 ms, 128 x 128 pixels, field of view 250 mm, one excitation. Maps of apparent diffusion coefficients (ADC) were generated automatically. DWI showed cortical, basal ganglia and watershed-area high signal in all cases, associated with a decrease in ADC to 60- 80% of normal. DWI showed lesions not seen (40%) or underestimated (40%) on conventional T2-weighted imaging. Within 24 h of the onset of symptoms, DWI showed changes not readily detectable on T2-weighted images. The cortical high signal on DWI and the ADC changes, suggesting severe ischaemia rather than oedema, was found in areas known to be affected by cortical laminar necrosis. Extension to the brain stem and white matter was associated with a higher likelihood of death.