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Conventional information processors freely convert information between different physical carriers to process, store, or transmit information. 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 kHz for transitions within the same rotational manifold, a few GHz for hyperfine transitions, up to a few THz for rotational transitions, to hundreds of THz for fundamental and overtone vibrational and electronic transitions, possibly all within the same molecule. Here, we report the first demonstration of entanglement between states of the rotation of a $\rm^{40}CaH^+$ molecular ion and internal states of a $\rm^{40}Ca^+$ atomic ion. The qubit addressed in the molecule has a frequency of either 13.4 kHz or 855 GHz, highlighting the versatility of molecular qubits. This work demonstrates how molecules can transduce quantum information between qubits with different frequencies to enable hybrid quantum systems. We anticipate that quantum control and measurement of molecules as demonstrated here will create opportunities for quantum information science, quantum sensors, fundamental and applied physics, and controlled quantum chemistry., Comment: 19 pages, 3 figures

Precision spectroscopy with single ions Spectroscopy is a powerful tool that can identify chemical species used in a wide range of settings. Usually, the samples are formed of ensembles, and this can limit the resolution with which the different species can be detected or identified. Chou et al. demonstrate an optical frequency comb technique with a single pair of trapped ions, Ca + and CaH + , to obtain the rotational spectrum of a single trapped ion, CaH + . With the ions isolated and the ensemble interactions removed, the rotational structure of the trapped molecular ion can then be obtained with high precision. As the trapping and manipulation process is general, this technique could be applied to a number of chemical species for specific purposes. Science , this issue p. 1458

Quantum logic enables state preparation, readout and spectroscopy of otherwise difficult-to-study ions. Using the coupled harmonic motion shared between co-trapped ions, information can be transferred from the "spectroscopy" ion to the easily manipulated "logic" ion. With this technique we perform high-resolution terahertz-scale rotational spectroscopy of a single CaH+ molecular ion in pure states by leveraging a Ca+ ion as our logic ion. Entangled states between a CaH+ and a Ca+ have also been demonstrated, making molecular ions possible components of hybrid systems for quantum information processing. Because all our laser operations on the molecule are driving stimulated Raman transitions with high detuning, the technique promises to be generalizable to a wide variety of molecular ion species. Additionally, we study the systematic effects of the trap RF electric field on molecular levels and use it to obtain a measurement of the dipole moment of the charged molecule.

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^{+}. By stabilizing the dominant sources of differential phase noise between the two clocks, we observe coherence between them during synchronous Ramsey interrogations as long as 8 s at a frequency of 1.12×10^{15} Hz. The observed contrast in the correlation spectroscopy signal is consistent with the 20.6 s ^{3}P_{0} state lifetime and represents a measurement instability of (1.8±0.5)×10^{-16}/sqrt[τ/s] for averaging periods longer than the probe duration when dead time is negligible.

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 $^{27}$Al$^+$ clock to enable a total fractional systematic uncertainty below $10^{-18}$. For this clock, with 38(19) nPa of room temperature H$_2$ background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order $10^{-16}$ 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 $-0.6(2.4)\times 10^{-19}$, where the shift is due to collisional heating time-dilation and the uncertainty is dominated by the worst case $\pm \pi/2$ bound used for collisional phase shift of the $^{27}$Al$^+$ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs., Comment: 13 pages, 7 figures, 3 tables

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]. A ^{25}Mg^{+} ion is simultaneously trapped with the ^{27}Al^{+} ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous ^{27}Al^{+} clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous ^{27}Al^{+} clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced.

An aluminum ion clock has a fractional-frequency uncertainty of less than one part in ${10}^{18}$, a four-decades-long goal in precision.

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 -(1.9±0.1)×10^{-18} for an ^{27}Al^{+} clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous ^{27}Al^{+} clocks.

Laboratory optical atomic clocks based on quantum-logic spectroscopy of the 1 S 0 ↔ 3 P 0 transition in 27 Al + have reached a systematic uncertainty of 8.6×10 18 [1], enabling table-top tests of fundamental physics [2] as well as measurements of gravitational potential differences [3]. New applications in geodesy and hydrology will require that such clocks be ruggedized and packaged so that they can be deployed to and operated at sites of interest outside the laboratory. Before a high-precision global optical-frequency transfer network is realized, a portable optical clock with high accuracy could also facilitate comparison between high-accuracy clocks developed around the globe.

We present and analyze four frequency measurements designed to characterize the performance of an optical frequency reference based on spectral hole burning in ${\mathrm{Eu}}^{3+}\mathrm{\text{:}}{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$. The first frequency comparison, between a single unperturbed spectral hole and a hydrogen maser, demonstrates a fractional frequency drift rate of $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. Optical frequency comparisons between a pattern of spectral holes, a Fabry-P\'erot cavity, and an ${\mathrm{Al}}^{+}$ optical atomic clock show a short-term fractional frequency stability of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ that averages down to ${2.5}_{\ensuremath{-}0.5}^{+1.1}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ at $\ensuremath{\tau}=540\text{ }\text{ }\mathrm{s}$ (with linear frequency drift removed). Finally, spectral-hole patterns in two different ${\mathrm{Eu}}^{3+}\mathrm{\text{:}}{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ crystals located in the same cryogenic vessel are compared, yielding a short-term stability of $7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ that averages down to ${5.5}_{\ensuremath{-}0.9}^{+1.8}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ at $\ensuremath{\tau}=204\text{ }\text{ }\mathrm{s}$ (with quadratic frequency drift removed).

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 (Al+) to a "control" ion (Mg+) 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. The first method provides a simplified way to distinguish "clock" states in Al+, which avoids ground state cooling and sideband transitions. The second method reduces spontaneous emission and optical pumping on the spectroscopy ion, which we demonstrate by nondestructively distinguishing Zeeman sublevels in the 1S0 ground state of Al+., Comment: 5 pages, 3 figures. Replaced with published version

We place two atoms in quantum superposition states and observe coherent phase evolution for 3.4x10^15 cycles. Correlation signals from the two atoms yield information about their relative phase even after the probe radiation has decohered. This technique was applied to a frequency comparison of two Al+ ions, where a fractional uncertainty of 3.7+1.0-0.8x10^-16/\sqrt{\tau/s} was observed. Two measures of the Q-factor are reported: The Q-factor derived from quantum coherence is 3.4+2.4-1.1x10^16, and the spectroscopic Q-factor for a Ramsey time of 3 s is 6.7x10^15. As part of this experiment, we demonstrate a method to detect the individual quantum states of two Al+ ions in a Mg+-Al+-Al+ linear ion chain without spatially resolving the ions., Comment: 4 pages, 4 figures

We have constructed an optical clock with a fractional frequency inaccuracy of 8.6e-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 1S0->3P0 clock transition is compared to that of a previously constructed Al+ optical clock with a statistical measurement uncertainty of 7.0e-18. The two clocks exhibit a relative stability of 2.8e-15/ sqrt(tau), and a fractional frequency difference of -1.8e-17, consistent with the accuracy limit of the older clock., 4 pages, 2 tables, 3 figures

We compare the rates of two Al+ optical clocks. Despite many differences, their rates agree to 1.8 +/− 0.7 × 10−17, within the accuracy limit of the older clock. The newer clock has an accuracy of 8.6 × 10−18 and stability near 10−15 (τ/s)−1/2.

We have investigated theoretically and experimentally a method for preparing Dicke states in trapped atomic ions. We consider a linear chain of $N$ ion qubits that is prepared in a particular Fock state of motion, $|m>$. The $m$ phonons are removed by applying a laser pulse globally to the $N$ qubits, and converting the motional excitation to $m$ flipped spins. The global nature of this pulse ensures that the $m$ flipped spins are shared by all the target ions in a state that is a close approximation to the Dicke state $\D{N}{m}$. We calculate numerically the fidelity limits of the protocol and find small deviations from the ideal state for $m = 1$ and $m = 2$. We have demonstrated the basic features of this protocol by preparing the state $\D{2}{1}$ in two $^{25}$Mg$^+$ target ions trapped simultaneously with an $^{27}$Al$^+$ ancillary ion., 5 pages, 2 figures

Repeated measurements of the frequency ratio of 199Hg + and 27A1+ singleatom optical clocks over the course of a year yield a constraint on the possible present-era temporal variation of the fine-structure constant a. The time variation of the measured ratio corresponds to a time variation in the fine structure constant of ά/α = (-1.6 ± 2.3) × 10-17/year, consistent with no change. The frequency ratio of these clocks was measured with a fractional uncertainty of 5.2 × 10-17. Stability simulations for optical clocks whose probe period is limited by 1/f-noise in the laser local oscillator provide an estimate of the optimal probe period, as well as a modified expression for the theoretical clock stability.

We demonstrate entanglement distribution between two remote quantum nodes located 3 meters apart. This distribution involves the asynchronous preparation of two pairs of atomic memories and the coherent mapping of stored atomic states into light fields in an effective state of near maximum polarization entanglement. Entanglement is verified by way of the measured violation of a Bell inequality, and can be used for communication protocols such as quantum cryptography. The demonstrated quantum nodes and channels can be used as segments of a quantum repeater, providing an essential tool for robust long-distance quantum communication., 10 pages, 7 figures. Text revised, additional information included in Appendix. Published online in Science Express, 5 April, 2007

We report significant improvements in the retrieval efficiency of a single excitation stored in an atomic ensemble and in the subsequent generation of strongly correlated pairs of photons. A 50% probability of transforming the stored excitation into one photon in a well-defined spatio-temporal mode at the output of the ensemble is demonstrated. These improvements are illustrated by the generation of high-quality heralded single photons with a suppression of the two-photon component below 1% of the value for a coherent state. A broad characterization of our system is performed for different parameters in order to provide input for the future design of realistic quantum networks.

Conditioned upon a photoelectric event, entanglement is created between two atomic ensembles separated by 2.8 m. The joint atomic state is transferred to two light modes and entanglement verified by quantum state tomography.