arXiv subjects
Publications and source records attributed to W. M. Itano.
Using a single, harmonically trapped $^9$Be$^+$ 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 sate, we implement a technique that applies a sequence of simple operations to synthesize the state.
We have investigated ion dynamics associated with a dual linear ion trap where ions can be stored in and moved between two distinct locations. Such a trap is a building block for a system to engineer arbitrary quantum states of ion ensembles. Specifically, this trap is the unit cell in a strategy for scalable quantum computing using a series of interconnected ion traps. We have transferred an ion between trap locations 1.2 mm apart in 50 $μ$s with near unit efficiency ($> 10^{6}$ consecutive transfers) and negligible motional heating, while maintaining internal-state coherence. In addition, we have separated two ions held in a common trap into two distinct traps.
Frequency shifts of the ^199Hg^+ 5d^10 6s ^2S_1/2 (F=0, M_F=0) to 5d^9 6s^2 ^2D_5/2 (F=2, M_F=0) electric-quadrupole transition at 282 nm due to external fields are calculated, based on a combination of measured atomic parameters and ab initio calculations. This transition is under investigation as an optical frequency standard. The perturbations calculated are the quadratic Zeeman shift, the scalar and tensor quadratic Stark shifts, and the interaction between an external electric field gradient and the atomic quadrupole moment. The quadrupole shift is likely to be the most difficult to evaluate in a frequency standard and may have a magnitude of about 1 Hz for a single ion in a Paul trap.
We review recent experiments on entanglement, Bell's inequality, and decoherence-free subspaces in a quantum register of trapped \be ions. We have demonstrated entanglement of up to four ions using the technique of Mølmer and Sørensen. This method produces the state |down down> + |up up> for two ions and the state |down down down down> + |up up up up> for four ions. We generate the entanglement deterministically in each shot of the experiment. Measurements on the two-ion entangled state violates Bell's inequality at the $8σ$ level. Because of the high detector efficiency of our apparatus, this experiment closes the detector loophole for Bell's inequality measurements for the first time. This measurement is also the first violation of Bell's inequality by massive particles that does not implicitly assume results from quantum mechanics. Finally, we have demonstrated reversible encoding of an arbitrary qubit, originally contained in one ion, into a decoherence-free subspace (DFS) of two ions. The DFS-encoded qubit resists applied collective dephasing noise and retains coherence under ambient conditions 3.6 times longer than does an unencoded qubit. The encoding method, which uses single-ion gates and the two-ion entangling gate, demonstrates all the elements required for two-qubit universal quantum logic.
The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg^+ and Ca optical standards with respect to the SI second as realized at NIST. We find the transition frequencies to be f_Hg=1 064 721 609 899 143(10) Hz and f_Ca=455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg^+ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of |(df_Ca/dt)/f_Ca| < 8 x 10^{-14} yr^{-1}, and |(df_Hg/dt)/f_Hg|< 30 x 10^{-14} yr^{-1}.
Using a laser that is frequency-locked to a Fabry-Perot etalon of high finesse and stability, we probe the 5d10 6s 2S_1/2 (F=0) - 5d9 6s 2D_5/2 (F=2) Delta-m_F = 0 electric-quadrupole transition of a single laser-cooled 199Hg+ ion stored in a cryogenic radio-frequency ion trap. We observe Fourier-transform limited linewidths as narrow as 6.7 Hz at 282 nm (1.06 X 10^15 Hz), yielding a line Q = 1.6 X 10^14. We perform a preliminary measurement of the 5d9 6s2 2D_5/2 electric-quadrupole shift due to interaction with the static fields of the trap, and discuss the implications for future trapped-ion optical frequency standards.
We have investigated motional heating of laser-cooled 9Be+ 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.
One limit to the fidelity of quantum logic operations on trapped ions arises from heating of the ions' collective modes of motion. Sympathetic cooling of the ions during the logic operations may eliminate this source of errors. We discuss benefits and drawbacks of this proposal, and describe possible experimental implementations. We also present an overview of trapped-ion dynamics in this scheme.
We summarize efforts at NIST to implement quantum computation using trapped ions, based on a scheme proposed by J.I. Cirac and P. Zoller (Innsbruck University). The use of quantum logic to create entangled states, which can maximize the quantum-limited signal-to-noise ratio in spectroscopy, is discussed.
We report preparation in the ground state of collective modes of motion of two trapped 9Be+ 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.
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.
Methods for, and limitations to, the generation of entangled states of trapped atomic ions are examined. As much as possible, state manipulations are described in terms of quantum logic operations since the conditional dynamics implicit in quantum logic is central to the creation of entanglement. Keeping with current interest, some experimental issues in the proposal for trapped-ion quantum computation by I. Cirac and P. Zoller (University of Innsbruck) are discussed. Several possible decoherence mechanisms are examined and what may be the more important of these are identified. Some potential applications for entangled states of trapped-ions which lie outside the immediate realm of quantum computation are also discussed.
The interference pattern of the resonance fluorescence from a J=1/2 to J=1/2 transition of two identical atoms confined in a three-dimensional harmonic potential is calculated. Thermal motion of the atoms is included. Agreement is obtained with experiments [Eichmann et al., Phys. Rev. Lett. 70, 2359 (1993)]. Contrary to some theoretical predictions, but in agreement with the present calculations, a fringe visibility greater than 50% can be observed with polarization-selective detection. The dependence of the fringe visibility on polarization has a simple interpretation, based on whether or not it is possible in principle to determine which atom emitted the photon.
A single laser-cooled and trapped 9Be+ ion is used to investigate methods of coherent quantum-state synthesis and quantum logic. We create and characterize nonclassical states of motion including "Schroedinger-cat" states. A fundamental quantum logic gate is realized which uses two states of the quantized ion motion and two ion internal states as qubits. We explore some of the applications for, and problems in realizing, quantum computation based on multiple trapped ions.
Experiments are described in which a single, harmonically bound, beryllium ion in a Paul trap is put into Fock, thermal, coherent, squeezed, and Schroedinger cat states. Experimental determinations of the density matrix and the Wigner function are described. A simple calculation of the decoherence of a superposition of coherent states due to an external electric field is given.
We describe a simplified scheme for quantum logic with a collection of laser-cooled trapped atomic ions. Building on the scheme of Cirac and Zoller, we show how the fundamental controlled-NOT gate between a collective mode of ion motion and the internal states of a single ion can be reduced to a single laser pulse, and the need for a third auxiliary internal electronic state can be eliminated.