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 x 10(-17). The ratio of aluminum and mercury single-ion optical clock frequencies nuAl+/nuHg+ is 1.052871833148990438(55), where the uncertainty comprises a statistical measurement uncertainty of 4.3 x 10(-17), and systematic uncertainties of 1.9 x 10(-17) and 2.3 x 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 alpha of alpha/alpha = (-1.6+/-2.3) x 10(-17)/year.

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.

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 qubit's 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.

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. [14,15]. The production of these fragile states in large systems remains a challenge and efficient methods for characterization are necessary because full state reconstruction becomes intractable. Here, we generate a class of non-Gaussian many-particle entangled states and reveal their quantum properties by studying the distinguishability of experimental probability distributions.A measure of the distinguishability with respect to small phase changes of the state is provided by the Fisher information F [16]. It is related to the highest attainable interferometric phase sensitivity by the Cramer-Rao bound ∆θ CR = 1/ √ F [17]. This limit follows from general statistical arguments for a measurement device with fluctuating output [18]. The Fisher information is limited by quantum fluctuations of the input state as well as the performance of the device. Even in the absence of technical noise, the Fisher information of a classical input state is F ≤ N because of the intrinsic granularity of N independent particles which translates into the shot-noise limit ∆θ ≥ 1/ √ N for phase estimation. This classical bound can be surpassed with a reduction of the input fluctuations by introducing entanglement between the N particles [5]. These states, known as squeezed states, are fully characterized by mean and variance of the observable and already employed in precision measurements [19][20][21]. In contrast, non-Gaussian quantum states can have increased fluctuations of the observable but nevertheless allow surpassing shot-noise limited performance. A textbook example is the Schrödinger cat state characterized by macroscopic fluctuations but achieving the best interferometric performance allowed by quantum mechanics, i.e. at the fundamental Heisenberg limit F = N . The initial coherent spin state (green) ideally evolves into a squeezed state (orange) followed by non-Gaussian states at later evolution times (violet). Edges of shaded areas are contours of the Husimi distribution for N = 380 at 1/e 2 of its maximum. (C) Experimental absorption picture, showing the site-and state-resolved optical lattice after a Stern-Gerlach separation. Shaded boxes indicate the sites with a total atom number in the range 380 ± 15, which are sele...

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.

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.

We describe an optical atomic clock based on quantum-logic spectroscopy of the 1 S0 ↔ 3 P0 transition in 27 Al + with a systematic uncertainty of 9.4 × 10 −19 and a frequency stability of 1.2 × 10 −15 / √ 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.

We demonstrate experimentally a robust quantum memory using a magnetic-field-independent hyperfine transition in 9 Be + atomic ion qubits at a magnetic field B ≃ 0.01194 T. We observe that the single physical qubit memory coherence time is greater than 10 seconds, an improvement of approximately five orders of magnitude from previous experiments with 9 Be + . 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.PACS numbers: 03.67. Pp, 32.60.+i, 03.65.Yz, 03.67.Mn Scalable quantum information processing (QIP) requires physical systems capable of reliably storing coherent superpositions for periods over which quantum error correction can be implemented [1]. Moreover, suppressing memory error rates to very low levels allows for simpler error-correcting algorithms [2,3]. In many current atomic ion QIP experiments, a dominant source of memory error is decoherence induced by fluctuating ambient magnetic fields [4,5]. To address this problem, we investigate creating long-lived qubit memories using a first-order magnetic-field-independent hyperfine transition and logical qubits of a decoherence-free subspace [6].Atomic systems have proven themselves as good candidates for quantum information storage through their use in highly stable atomic clocks [7]. Here, the principle of using first-order magnetic-field-independent transitions is well established. A typical clock transition |F, m F = 0 ↔ |F ′ , m F ′ = 0 between hyperfine states of angular momentum F and F ′ in alkali atoms has no linear Zeeman shift at zero magnetic field, and coherence times exceeding 10 minutes have been observed [8]. Unfortunately, magnetic sublevels in each hyperfine manifold are degenerate at zero magnetic field. This makes it more advantageous to operate at a nonzero field in order to spectrally resolve the levels, thereby inducing a linear field dependence of the transition frequency. However, field-independent transitions between hyperfine states also exist at nonzero magnetic field. In the context of atomic clocks, coherence times exceeding 10 minutes have been observed in 9 Be + ions at a magnetic field B = 0.8194 T [9].In neutral-atom systems suitable for QIP, fieldindependent transitions at nonzero magnetic field have been investigated in rubidium [10,11]. The radio-frequency (RF)/microwave two-photon stimulatedRaman hyperfine transition |F = 1, m F = −1 ↔ |F ′ = 2, m F ′ = 1 is field-independent at approximately 3.23 × 10 −4 T , and coherence times of 2.8 s have been observed [11]. In these and the clock experiments, transitions were driven by microwave fields on large numbers of atoms. Using microwaves, it may be difficult to localize the fields well enough to drive individual qubits unless a means (e.g., a magnetic-field gradient or Stark-shift gradient) is employed to provide spectral selection [12,13], a technique that has the additional overhead of keeping track of the phases induced by these shifts. With transitio...