Cryogenic sapphire optical reference cavity with crystalline coatings at 1 × 10-16 fractional frequency instability.

The frequency stability of a laser locked to an optical reference cavity is fundamentally limited by thermal noise in the cavity length. These fluctuations are linked to material dissipation, which depends on both the temperature of the optical components and the material properties. Here, the design and experimental characterization of a sapphire optical cavity operated at 10 K with crystalline coatings at 1069 nm is presented.

Quantum state tracking and control of a single molecular ion in a thermal environment.

Understanding molecular state evolution is central to many disciplines, including molecular dynamics, precision measurement, and molecule-based quantum technology. Details of this evolution are obscured when observing a statistical ensemble of molecules. Here, we report real-time observations of thermal radiation-driven transitions between individual states ("jumps") of a single molecule.

Prospects of a thousand-ion Sn Coulomb-crystal clock with sub-10 inaccuracy.

Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn ions confined in a linear RF Paul trap with the potential to overcome this limitation.

Erratum: ^{27}Al^{+} Quantum-Logic Clock with a Systematic Uncertainty below 10^{-18} [Phys. Rev. Lett. 123, 033201 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.123.

Effects of an Oscillating Electric Field on and Dipole Moment Measurement of a Single Molecular Ion.

We characterize and model the Stark effect due to the radio-frequency (rf) electric field experienced by a molecular ion in an rf Paul trap, a leading systematic in the uncertainty of the field-free rotational transition. The ion is deliberately displaced to sample different known rf electric fields and measure the resultant shifts in transition frequencies. With this method, we determine the permanent electric dipole moment of CaH^{+}, and find close agreement with theory.

Scalable Quantum Logic Spectroscopy.

In quantum logic spectroscopy (QLS), one species of trapped ion is used as a sensor to detect the state of an otherwise inaccessible ion species. This extends precision measurements to a broader class of atomic and molecular systems for applications like atomic clocks and tests of fundamental physics. Here, we develop a new technique based on a Schrödinger cat interferometer to address the problem of scaling QLS to larger ion numbers.

Lifetime-Limited Interrogation of Two Independent ^{27}Al^{+} Clocks Using Correlation Spectroscopy.

Laser decoherence limits the stability of optical clocks by broadening the observable resonance linewidths and adding noise during the dead time between clock probes. Correlation spectroscopy avoids these limitations by measuring correlated atomic transitions between two ensembles, which provides a frequency difference measurement independent of laser noise. Here, we apply this technique to perform stability measurements between two independent clocks based on the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+}.

Quantum entanglement between an atom and a molecule.

Conventional information processors convert information between different physical carriers for processing, storage and transmission. It seems plausible that quantum information will also be held by different physical carriers in applications such as tests of fundamental physics, quantum enhanced sensors and quantum information processing. Quantum controlled molecules, in particular, could transduce quantum information across a wide range of quantum bit (qubit) frequencies-from a few kilohertz for transitions within the same rotational manifold, a few gigahertz for hyperfine transitions, a few terahertz for rotational transitions, to hundreds of terahertz for fundamental and overtone vibrational and electronic transitions-possibly all within the same molecule.

Frequency-comb spectroscopy on pure quantum states of a single molecular ion.

Spectroscopy is a powerful tool for studying molecules and is commonly performed on large thermal molecular ensembles that are perturbed by motional shifts and interactions with the environment and one another, resulting in convoluted spectra and limited resolution. Here, we use quantum-logic techniques to prepare a trapped molecular ion in a single quantum state, drive terahertz rotational transitions with an optical frequency comb, and read out the final state nondestructively, leaving the molecule ready for further manipulation. We can resolve rotational transitions to 11 significant digits and derive the rotational constant of CaH to be = 142 501 777.

Systematic uncertainty due to background-gas collisions in trapped-ion optical clocks.

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an Al clock to enable a total fractional systematic uncertainty below 10. For this clock, with 38(19) nPa of room-temperature H background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order 10 at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be -0.

^{27}Al^{+} Quantum-Logic Clock with a Systematic Uncertainty below 10^{-18}.

We describe an optical atomic clock based on quantum-logic spectroscopy of the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+} with a systematic uncertainty of 9.4×10^{-19} and a frequency stability of 1.2×10^{-15}/sqrt[τ].

Preparation and coherent manipulation of pure quantum states of a single molecular ion.

Laser cooling and trapping of atoms and atomic ions has led to advances including the observation of exotic phases of matter, the development of precision sensors and state-of-the-art atomic clocks. The same level of control in molecules could also lead to important developments such as controlled chemical reactions and sensitive probes of fundamental theories, but the vibrational and rotational degrees of freedom in molecules pose a challenge for controlling their quantum mechanical states. Here we use quantum-logic spectroscopy, which maps quantum information between two ion species, to prepare and non-destructively detect quantum mechanical states in molecular ions.

Sympathetic Ground State Cooling and Time-Dilation Shifts in an ^{27}Al^{+} Optical Clock.

We report on Raman sideband cooling of ^{25}Mg^{+} to sympathetically cool the secular modes of motion in a ^{25}Mg^{+}-^{27}Al^{+} two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of -(1.

An open source digital servo for atomic, molecular, and optical physics experiments.

We describe a general purpose digital servo optimized for feedback control of lasers in atomic, molecular, and optical physics experiments. The servo is capable of feedback bandwidths up to roughly 1 MHz (limited by the 320 ns total latency); loop filter shapes up to fifth order; multiple-input, multiple-output control; and automatic lock acquisition. The configuration of the servo is controlled via a graphical user interface, which also provides a rudimentary software oscilloscope and tools for measurement of system transfer functions.

Laser-Frequency Stabilization Based on Steady-State Spectral-Hole Burning in Eu(3+)∶Y(2)SiO(5).

We present and analyze a method of laser-frequency stabilization via steady-state patterns of spectral holes in Eu(3+)∶Y(2)SiO(5). Three regions of spectral holes are created, spaced in frequency by the ground-state hyperfine splittings of (151)Eu(3+). The absorption pattern is shown not to degrade after days of laser-frequency stabilization.

Absolute and relative stability of an optical frequency reference based on spectral hole burning in Eu3+:Y2SiO5.

We present and analyze four frequency measurements designed to characterize the performance of an optical frequency reference based on spectral hole burning in Eu3+:Y2SiO5. The first frequency comparison, between a single unperturbed spectral hole and a hydrogen maser, demonstrates a fractional frequency drift rate of 5×10(-18)  s(-1). Optical frequency comparisons between a pattern of spectral holes, a Fabry-Pérot cavity, and an Al(+) optical atomic clock show a short-term fractional frequency stability of 1×10(-15)τ(-1/2) that averages down to 2.

Trapped-ion state detection through coherent motion.

We demonstrate a general method for state detection of trapped ions that can be applied to a large class of atomic and molecular species. We couple a spectroscopy ion (27Al+) to a control ion (25Mg+) in the same trap and perform state detection through off-resonant laser excitation of the spectroscopy ion that induces coherent motion. The motional amplitude, dependent on the spectroscopy ion state, is measured either by time-resolved photon counting or by resolved sideband excitations on the control ion.

Ion crystal transducer for strong coupling between single ions and single photons.

A new approach for the realization of a quantum interface between single photons and single ions in an ion crystal is proposed and analyzed. In our approach the coupling between a single photon and a single ion is enhanced via the collective degrees of freedom of the ion crystal. Applications including single-photon generation, a memory for a quantum repeater, and a deterministic photon-photon, photon-phonon, or photon-ion entangler are discussed.

Field-test of a robust, portable, frequency-stable laser.

We operate a frequency-stable laser in a non-laboratory environment where the test platform is a passenger vehicle. We measure the acceleration experienced by the laser and actively correct for it to achieve a system acceleration sensitivity of Δf / f = 11(2) × 10(−12)/g, 6(2) × 10(−12)/g, and 4(1) × 10(−12)/g for accelerations in three orthogonal directions at 1 Hz. The acceleration spectrum and laser performance are evaluated with the vehicle both stationary and moving.

Spherical reference cavities for frequency stabilization of lasers in non-laboratory environments.

We present an optical cavity design that is insensitive to both vibrations and orientation. The design is based on a spherical cavity spacer that is held rigidly at two points on a diameter of the sphere. Coupling of the support forces to the cavity length is reduced by holding the sphere at a "squeeze insensitive angle" with respect to the optical axis.

Measurement and real-time cancellation of vibration-induced phase noise in a cavity-stabilized laser.

We demonstrate a method to measure and actively reduce the coupling of vibrations to the phase noise of a cavity-stabilized laser. This method uses the vibration noise of the laboratory environment rather than active drive to perturb the optical cavity. The laser phase noise is measured via a beat note with a second unperturbed ultra-stable laser while the vibrations are measured by accelerometers positioned around the cavity.

Cavity sideband cooling of a single trapped ion.

We report a demonstration and quantitative characterization of one-dimensional cavity cooling of a single trapped (88)Sr(+) ion in the resolved-sideband regime. We measure the spectrum of cavity transitions, the rates of cavity heating and cooling, and the steady-state cooling limit. The cavity cooling dynamics and cooling limit of 22.

Temperature dependence of electric field noise above gold surfaces.

Electric field noise from fluctuating patch potentials is a significant problem for a broad range of precision experiments, including trapped ion quantum computation and single spin detection. Recent results demonstrated strong suppression of this noise by cryogenic cooling, suggesting an underlying thermal process. We present measurements characterizing the temperature and frequency dependence of the noise from 7 to 100 K, using a single Sr+ ion trapped 75 mum above the surface of a gold plated surface electrode ion trap.

Suppression of heating rates in cryogenic surface-electrode ion traps.

Dense arrays of trapped ions provide one way of scaling up ion trap quantum information processing. However, miniaturization of ion traps is currently limited by sharply increasing motional state decoherence at sub-100 mum ion-electrode distances. We characterize heating rates in cryogenically cooled surface-electrode traps, with characteristic sizes in the 75 to 150 mum range.