Direct observation of bimolecular reactions of ultracold KRb molecules.

Femtochemistry techniques have been instrumental in accessing the short time scales necessary to probe transient intermediates in chemical reactions. In this study, we took the contrasting approach of prolonging the lifetime of an intermediate by preparing reactant molecules in their lowest rovibronic quantum state at ultralow temperatures, thereby markedly reducing the number of exit channels accessible upon their mutual collision. Using ionization spectroscopy and velocity-map imaging of a trapped gas of potassium-rubidium (KRb) molecules at a temperature of 500 nanokelvin, we directly observed reactants, intermediates, and products of the reaction 40K87Rb + 40K87Rb → K2Rb2* → K2 + Rb2 Beyond observation of a long-lived, energy-rich intermediate complex, this technique opens the door to further studies of quantum-state-resolved reaction dynamics in the ultracold regime.

Building one molecule from a reservoir of two atoms.

Chemical reactions typically proceed via stochastic encounters between reactants. Going beyond this paradigm, we combined exactly two atoms in a single, controlled reaction. The experimental apparatus traps two individual laser-cooled atoms [one sodium (Na) and one cesium (Cs)] in separate optical tweezers and then merges them into one optical dipole trap. Subsequently, photoassociation forms an excited-state NaCs molecule. The discovery of previously unseen resonances near the molecular dissociation threshold and measurement of collision rates are enabled by the tightly trapped ultracold sample of atoms. As laser-cooling and trapping capabilities are extended to more elements, the technique will enable the study of more diverse, and eventually more complex, molecules in an isolated environment, as well as synthesis of designer molecules for qubits.

Quantum coherence between two atoms beyond Q=10(15).

We place two atoms in quantum superposition states and observe coherent phase evolution for 3.4×10(15) cycles. Correlation signals from the two atoms yield information about their relative phase even after the probe radiation has decohered. This technique allowed a frequency comparison of two (27)Al(+) ions with fractional uncertainty 3.7(-0.8)(+1.0)×10(-16)/√[τ/s]. Two measures of the Q factor are reported: The Q factor derived from quantum coherence is 3.4(-1.1)(+2.4)×10(16), and the spectroscopic Q factor for a Ramsey time of 3 s is 6.7×10(15). 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.

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. The first method provides a simplified way to distinguish clock states in 27Al+, 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 (1)S0 ground state of 27Al+.

Optical clocks and relativity.

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.

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.

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 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.

High-fidelity adaptive qubit detection through repetitive quantum nondemolition measurements.

Using two trapped ion species ((27)Al(+) and (9)Be(+)) as primary and ancillary quantum systems, we implement qubit measurements based on the repetitive transfer of information and quantum nondemolition detection. The repetition provides a natural mechanism for an adaptive measurement strategy, which leads to exponentially lower error rates compared to using a fixed number of detection cycles. For a single qubit we demonstrate 99.94% measurement fidelity. We also demonstrate a technique for adaptively measuring multiple qubit states using a single ancilla, and apply the technique to spectroscopy of an optical clock transition.

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 aluminum's electronic state to the beryllium's 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.

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.

Spectroscopy using quantum logic.

We present a general technique for precision spectroscopy of atoms that lack suitable transitions for efficient laser cooling, internal state preparation, and detection. In our implementation with trapped atomic ions, an auxiliary "logic" ion provides sympathetic laser cooling, state initialization, and detection for a simultaneously trapped "spectroscopy" ion. Detection is achieved by applying a mapping operation to each ion, which results in a coherent transfer of the spectroscopy ion's internal state onto the logic ion, where it is then measured with high efficiency. Experimental realization, by using 9Be+ as the logic ion and 27Al+ as the spectroscopy ion, indicates the feasibility of applying this technique to make accurate optical clocks based on single ions.

Quantum information processing with trapped ions.

Experiments directed towards the development of a quantum computer based on trapped atomic ions are described briefly. We discuss the implementation of single-qubit operations and gates between qubits. A geometric phase gate between two ion qubits is described. Limitations of the trapped-ion method such as those caused by Stark shifts and spontaneous emission are addressed. Finally, we describe a strategy to realize a large-scale device.

Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate.

Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum computation. Dynamical gates have been proposed in the context of trapped ions; however, geometric phase gates (which change only the phase of the physical qubits) offer potential practical advantages because they have higher intrinsic resistance to certain small errors and might enable faster gate implementation. Here we demonstrate a universal geometric pi-phase gate between two beryllium ion-qubits, based on coherent displacements induced by an optical dipole force. The displacements depend on the internal atomic states; the motional state of the ions is unimportant provided that they remain in the regime in which the force can be considered constant over the extent of each ion's wave packet. By combining the gate with single-qubit rotations, we have prepared ions in an entangled Bell state with 97% fidelity-about six times better than in a previous experiment demonstrating a universal gate between two ion-qubits. The particular properties of the gate make it attractive for a multiplexed trap architecture that would enable scaling to large numbers of ion-qubits.

Experimental demonstration of a technique to generate arbitrary quantum superposition states of a harmonically bound spin-1/2 particle.

Using a single, harmonically trapped 9Be(+) ion, we experimentally demonstrate a technique for generation of arbitrary states of a two-level particle confined by a harmonic potential. Rather than engineering a single Hamiltonian that evolves the system to a desired final state, we implement a technique that applies a sequence of simple operations to synthesize the state.

Experimental demonstration of a controlled-NOT wave-packet gate.

We report the experimental demonstration of a controlled-NOT (CNOT) quantum logic gate between motional and internal-state qubits of a single ion where, as opposed to previously demonstrated gates, the conditional dynamics depends on the extent of the ion's wave packet. Advantages of this CNOT gate over one demonstrated previously are its immunity from Stark shifts due to off-resonant couplings and the fact that an auxiliary internal level is not required. We characterize the gate logic through measurements of the postgate ion state populations for both logic basis and superposition input states, and we demonstrate the gate coherence via an interferometric measurement.

Trapped-ion quantum simulator: experimental application to nonlinear interferometers.

We show how an experimentally realized set of operations on a single trapped ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2 particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of two nth order nonlinear optical beam splitters comprising an interferometer sensitive to phase shift in one of the interferometer beam paths. The sensitivity in determining these phase shifts increases linearly with n, and the simulation demonstrates that the use of nonlinear beam splitters (n=2,3) enhances this sensitivity compared to the standard quantum limit imposed by a linear beam splitter (n=1).

Realization of Bose-Einstein condensates in lower dimensions.

Bose-Einstein condensates of sodium atoms have been prepared in optical and magnetic traps in which the energy-level spacing in one or two dimensions exceeds the interaction energy between atoms, realizing condensates of lower dimensionality. The crossover into two-dimensional and one-dimensional condensates was observed by a change in aspect ratio and by the release energy converging to a nonzero value when the number of trapped atoms was reduced.

Observation of vortex phase singularities in Bose-Einstein condensates.

We have observed phase singularities due to vortex excitation in Bose-Einstein condensates. Vortices were created by moving a laser beam through a condensate. They were observed as dislocations in the interference fringes formed by the stirred condensate and a second unperturbed condensate. The velocity dependence for vortex excitation and the time scale for re-establishing a uniform phase across the condensate were determined.