Quantum mechanics allows for many-particle wavefunctions that cannot be factorized into a product of single-particle wavefunctions, even when the constituent particles are entirely distinct. Such 'entangled' states explicitly demonstrate the non-local character of quantum theory, having potential applications in high-precision spectroscopy, quantum communication, cryptography and computation. In general, the more particles that can be entangled, the more clearly nonclassical effects are exhibited--and the more useful the states are for quantum applications. Here we implement a recently proposed entanglement technique to generate entangled states of two and four trapped ions. Coupling between the ions is provided through their collective motional degrees of freedom, but actual motional excitation is minimized. Entanglement is achieved using a single laser pulse, and the method can in principle be applied to any number of ions.

We have investigated motional heating of laser-cooled 9 Be + ions held in radio-frequency (Paul) traps. We have measured heating rates in a variety of traps with different geometries, electrode materials, and characteristic sizes.The results show that heating is due to electric-field noise from the trap electrodes which exerts a stochastic fluctuating force on the ion. The scaling of the heating rate with trap size is much stronger than that expected from a spatially uniform noise source on the electrodes (such as Johnson noise from external circuits), indicating that a microscopic uncorrelated noise source on the electrodes (such as fluctuating patch-potential fields) is a more likely candidate for the source of heating.

The theory of quantum mechanics applies to closed systems. In such ideal situations, a single atom can, for example, exist simultaneously in a superposition of two different spatial locations. In contrast, real systems always interact with their environment, with the consequence that macroscopic quantum superpositions (as illustrated by the 'Schrodinger's cat' thought-experiment) are not observed. Moreover, macroscopic superpositions decay so quickly that even the dynamics of decoherence cannot be observed. However, mesoscopic systems offer the possibility of observing the decoherence of such quantum superpositions. Here we present measurements of the decoherence of superposed motional states of a single trapped atom. Decoherence is induced by coupling the atom to engineered reservoirs, in which the coupling and state of the environment are controllable. We perform three experiments, finding that the decoherence rate scales with the square of a quantity describing the amplitude of the superposition state.

We have prepared the internal states of two trapped ions in both the Bell-like singlet and triplet entangled states. In contrast to all other experiments with entangled states of either massive particles or photons, we do this in a deterministic fashion, producing entangled states on demand without selection. The deterministic production of entangled states is a crucial prerequisite for large-scale quantum computation.Since the seminal discussions of Einstein, Podolsky, and Rosen, two-particle quantum entanglement has been used to magnify and confirm the peculiarities of quantum mechanics [1]. More recently, quantum entanglement has been shown to be not purely of pedagogical interest, but also relevant to computation [2], information transfer [3], cryptography [4] and spectroscopy [5,6]. Quantum computation (QC) exploits the inherent parallelism of quantum superposition and entanglement to perform certain tasks more efficiently than can be achieved classically [7].Relatively few physical systems are able to approach the severe requirements of QC: controllable coherent interaction between the quantum information carriers (quantum bits or qubits), isolation from the environment, and high-efficiency interrogation of individual qubits. Cirac and Zoller have proposed a scalable scheme utilizing trapped ions for QC [8]. In it, the qubits are two internal states of an ion; entanglement and computation are achieved by quantum logic operations on pairs of ions involving shared quantized motion. Previously, quantum logic operations were demonstrated between a single ion's motion and its spin [9]; the requirements of QC have been explored experimentally in related cavity QED systems [10]. In this Letter, we use conditional quantum logic transformations to entangle and manipulate the qubits of two trapped ions.Previous experiments have studied entangled states of photons [11,12] and of massive particles [13][14][15]. These experiments rely in some way on random processes, either in creation of the entanglement, as in photon cascades [11], photon down-conversion [12] and proton scattering [13], or in the random arrival times of atoms in a cavity [14]. Recent results in NMR of bulk samples have shown entanglement of particle spins [15,16] but because pseudo-pure states are selected through averaging over a thermal distribution, the signal is exponentially degraded as the number of qubits is increased. All the above processes are selectable but are not deterministic generators of entanglement. By deterministic, we mean that a known and controllable quantum state of (all of) a given set of particles is generated at a specified time [17]. Deterministic entanglement coupled with the ability to store entangled states for future use is crucial for the realization of large-scale quantum computation. Ion-trap QC has no fundamental scaling limits; moreover, even the simple two-ion manipulations described here can, in principle, be incorporated into large-scale computing, either by coupling two-ion subsystems via cavities [18], or by u...

We report preparation in the ground state of collective modes of motion of two trapped 9 Be + ions. This is a crucial step towards realizing quantum logic gates which can entangle the ions' internal electronic states. We find that heating of the modes of relative ion motion is substantially suppressed relative to that of the center-of-mass modes, suggesting the importance of these modes in future experiments.03.67. Lx,32.80.Pj In physics, quantum computation [1] provides a general framework for fundamental investigations into subjects such as entanglement, quantum measurement, and quantum information theory. Since quantum computation relies on entanglement between qubits, any implementation of a quantum computer must offer isolation from the effects of decoherence, but also allow controllable and coherent interaction between the qubits. Cirac and Zoller [2] have proposed an attractive scheme for realizing a quantum computer, which is scalable to an arbitrary number of qubits. Their scheme is based on a collection of trapped atomic ions, where each qubit (one per ion) is comprised of a pair of the ions' internal states, while quantum information is transferred between different ions using a particular quantized mode of the ions' collective motion. This "quantum data bus" must first be initialized in a pure quantum state [2]: for example, its ground state [3]. The basics of this scheme have been demonstrated experimentally in a fundamental logic gate (a Controlled-NOT) operating between a motional mode of a single trapped ion and two of the ion's internal states [4]. In that work, the motional state was initialized in the ground state by laser cooling [5]. The next step towards implementing the Cirac-Zoller scheme is to cool at least one mode of collective motion of multiple ions to the ground state. In this Letter, we describe the first experiments to realize this goal. We also report significant difference between the decoherence rates of the center-of-mass and non-center-of-mass modes of motion.We confine 9 Be + ions in a coaxial-resonator-based rf (Paul) trap, similar to that described in Ref. [6]. The electrodes in this trap are made from 125 µm-thick sheets of Be metal, as shown in Fig. 1. We apply a potential φ(t) = V 0 cos(Ω T t) + U 0 to the (elliptical) ring electrode relative to the endcap electrodes. If several ions are trapped and cooled, they will naturally align themselves along the major axis of the ring electrode. The electrode's elliptical shape, in combination with U 0 > 0, allows a linear crystal to be maintained while suppressing rf-micromotion of the ions along this direction [7]. With V 0 ≈ 520 V, Ω T /2π ≈ 238 MHz, and U 0 =0 V, the pseudopotential oscillation frequencies are (ω x , ω y , ω z )/2π ≈ (4.6,12.7,17.0) MHz. With U 0 = 18.2 V, the frequencies become (8.6,17.6,9.3) MHz. Fig. 1 shows two ions confined in the trap and imaged with an f /3 lens system onto a position-sensitive photomultiplier tube.The ions are cooled and probed with laser beams whose geometry is indicated in Fig. ...

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