Correcting the effects of spontaneous emission on cold trapped ions

We propose two quantum error correction schemes which increase the maximum storage time for qubits in a system of cold trapped ions, using a minimal number of ancillary qubits. Both schemes consider only the errors introduced by the decoherence due to spontaneous emission from the upper levels of the ions. Continuous monitoring of the ion fluorescence is used in conjunction with selective coherent feedback to eliminate these errors immediately following spontaneous emission events, and the conditional time evolution between quantum jumps is removed by symmetrizing the quantum codewords.Comment: 19 pages; 2 figures; RevTex; The quantum codewords are extended to achieve invariance under the conditional time evolution between jump

Generation of eigenstates using the phase-estimation algorithm

The phase estimation algorithm is so named because it allows the estimation of the eigenvalues associated with an operator. However it has been proposed that the algorithm can also be used to generate eigenstates. Here we extend this proposal for small quantum systems, identifying the conditions under which the phase estimation algorithm can successfully generate eigenstates. We then propose an implementation scheme based on an ion trap quantum computer. This scheme allows us to illustrate two simple examples, one in which the algorithm effectively generates eigenstates, and one in which it does not.Comment: 5 pages, 3 Figures, RevTeX4 Introduction expanded, typos correcte

Stability, Gain, and Robustness in Quantum Feedback Networks

This paper concerns the problem of stability for quantum feedback networks. We demonstrate in the context of quantum optics how stability of quantum feedback networks can be guaranteed using only simple gain inequalities for network components and algebraic relationships determined by the network. Quantum feedback networks are shown to be stable if the loop gain is less than one-this is an extension of the famous small gain theorem of classical control theory. We illustrate the simplicity and power of the small gain approach with applications to important problems of robust stability and robust stabilization.Comment: 16 page

Implementing the Quantum Random Walk

Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the variance on the line, and the mixing time on the circle increase quadratically faster in the quantum versions as compared to the classical versions. Here, we propose a scheme to implement the quantum random walk on a line and on a circle in an ion trap quantum computer. With current ion trap technology, the number of steps that could be experimentally implemented will be relatively small. However, we show how the enhanced features of these walks could be observed experimentally. In the limit of strong decoherence, the quantum random walk tends to the classical random walk. By measuring the degree to which the walk remains `quantum', this algorithm could serve as an important benchmarking protocol for ion trap quantum computers

A quantum phase gate implementation for trapped ions in thermal motion

We propose a novel scheme to implement a quantum controlled phase gate for trapped ions in thermal motion with one standing wave laser pulse. Instead of applying the rotating wave approximation this scheme makes use of the counter-rotating terms of operators. We also demonstrate that the same scheme can be used to generate maximally entangled states of $N$ trapped ions by a single laser pulse

Measurements on trapped laser-cooled ions using quantum computations

We show that a series of quantum computations involving an isolated N-quantum-bit ion register can be used to make an approximate quantum nondemolition measurement of the number state distribution of a collective vibrational mode. A unitary transformation is applied to the Fourier transformed state of the ion register to copy the vibrational statistics to the electronic mode, and the number state distribution is then measured in the electronic number state basis using the quantum jumps technique

Synthesis and characterization of entangled mesoscopic superpositions for a trapped electron

We propose a scheme for the generation and reconstruction of entangled states between the internal and external (motional) degrees of freedom of a trapped electron. Such states also exhibit quantum coherence at a mesoscopic level.Comment: 4 pages, 1 figure, RevTeX (twocolumn

Measuring the vibrational energy of a trapped ion

We show that an approximate quantum-nondemolition measurement of the vibrational energy of a trapped ion in a standing wave may be made by monitoring the fluorescent intensity from a probe transition. The ac component of the mean photocurrent signal is directly proportional to the average vibrational quantum number. The power spectrum of the photocurrent also contains information on the vibrational energy. We show that the phase of the vibrational motion undergoes diffusion as expected for a quantum-limited measurement of the energy of oscillation

Nonlinear Decoherence in Quantum State Preparation of a Trapped Ion

We present a nonlinear decoherence model which models decoherence effect caused by various decohereing sources in a quantum system through a nonlinear coupling between the system and its environment, and apply it to investigating decoherence in nonclassical motional states of a single trapped ion. We obtain an exactly analytic solution of the model and find very good agreement with experimental results for the population decay rate of a single trapped ion observed in the NIST experiments by Meekhof and coworkers (D. M. Meekhof, {\it et al.}, Phys. Rev. Lett. {\bf 76}, 1796 (1996)).Comment: 5 pages, Revte

The Haroche-Ramsey experiment as a generalized measurement

A number of atomic beam experiments, related to the Ramsey experiment and a recent experiment by Brune et al., are studied with respect to the question of complementarity. Three different procedures for obtaining information on the state of the incoming atom are compared. Positive operator-valued measures are explicitly calculated. It is demonstrated that, in principle, it is possible to choose the experimental arrangement so as to admit an interpretation as a joint non-ideal measurement yielding interference and ``which-way'' information. Comparison of the different measurements gives insight into the question of which information is provided by a (generalized) quantum mechanical measurement. For this purpose the subspaces of Hilbert-Schmidt space, spanned by the operators of the POVM, are determined for different measurement arrangements and different values of the parameters.Comment: REVTeX, 22 pages, 5 figure