Deterministic Entanglement of Two Trapped Ions

Abstract

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...

An efficient single-step scheme for manipulating quantum information of two trapped ions beyond the Lamb–Dicke limit

“…According to the experiment reported in [10], two 9 Be + ions spaced 2µm apart can be confined along the axis of a linear Paul trap with an axial center-of mass frequency of ν = ω z ≈ 7 MHz ≪ ω x, y . The collective mode of motion of the ions has been successfully cooled to the ground state by Doppler cooling (see, e.g., [19] ).…”

“…for the processes (10). Especially, for the commonly considered case, m = 0, the above equation becomes…”

“…The entangled state of two trapped ions realized experimentally in [10] is not the maximally entangled state. Its degree of entanglement E is 0.94.…”

“…Recently, the quantum entanglement of two and four trapped ions have been generated experimentally (see, e.g., [5,10]), although the operations are limited to the weakcoupling LD regime. We now show that the entangled states of two trapped ions can also be produced outside the LD limit.…”

“…The collective normal modes of oscillation shared by all of the ions form the information bus, through which all gate operations can be performed. In the past few years, several key features of the proposal in [6], including the production of entangled states and the implementation of quantum controlled operations between a pair of trapped ions, have already been experimentally demonstrated * lfwei@riken.jp † fnori@riken.jp ‡ Permanent address [5,8,9,10]. Also, several alternative theoretical schemes (see, e.g., [11,12,13,14,15,16,17]) have been developed for overcoming various difficulties in realizing a practical iontrap quantum information processor.…”