Phase-stable free-space optical lattices for trapped ions

We demonstrate control of the absolute phase of an optical lattice with respect to a single trapped ion. The lattice is generated by off-resonant free-space laser beams, we actively stabilize its phase by measuring its ac-Stark shift on a trapped ion. The ion is localized within the standing wave to better than 2% of its period. The locked lattice allows us to apply displacement operations via resonant optical forces with a controlled direction in phase space. Moreover, we observe the lattice-induced phase evolution of spin superposition states in order to analyze the relevant decoherence mechanisms. Finally, we employ lattice-induced phase shifts for inferring the variation of the ion position over 157~$mu$m range along the trap axis at accuracies of better than 6~nm.

Manipulating Transverse Modes of Photons for Quantum Cryptography

Several schemes have been proposed to extend Quantum Key Distribution protocols aiming at improving their security or at providing new physical substrates for qubit implementation. We present a toolbox to jointly create, manipulate and measure qubits stored in polarization and transverse-modes degrees of freedom of single photons. The toolbox includes local operations on single qubits, controlled operations between the two qubits and projective measurements over a wide variety of non-local bases in the four dimensional space of states. We describe how to implement the toolbox to perform an extended version of the BB84 protocol for this Hilbert space (ideally transmitting two key bits per photon). We present the experimental implementation of the measurement scheme both in the regimes of intense light beams and with single photons. Thus, we show the feasibility of implementing the protocol providing an interesting example of a new method for quantum information processing using the polarization and transverse modes of light as qubits.

Light with orbital angular momentum interacting with trapped ions

We study the interaction of a light beams carrying angular momentum with a single, trapped and well localized ion. We provide a detailed calculation of selection rules and excitation probabilities for quadrupole transitions. The results show the dependencies on the angular momentum and polarization of the laser beam as well as the direction of the quantization magnetic field. In order to observe optimally the specific effects, focusing the angular momentum beam close to the diffraction limit is required. We discuss a protocol for examining experimentally the effects on the S$_{1/2}$ to D$_{5/2}$ transition using a $^{40}$Ca$^+$ ion. Various applications and advantages are expected when using light carrying angular momentum: In quantum information processing, where qubit states of ion crystals are controlled, parasitic light shifts could be avoided as the ion is excited in the dark zone of the beam at zero electric field amplitude. Such interactions also open the door to high dimensional entanglement between light and matter. In spectroscopy one might access transitions which have escaped excitation so far due to vanishing transition dipole moments.

Ancilla-less selective and efficient quantum process tomography

Several methods, known as Quantum Process Tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we present the theory describing a new type of method for quantum process tomography. We describe an algorithm that can be used to selectively estimate any parameter characterizing a quantum process. Unlike any of its predecessors this new quantum tomographer combines two main virtues: it requires investing a number of physical resources scaling polynomially with the number of qubits and at the same time it does not require any ancillary resources. We present the results of the first photonic implementation of this quantum device, characterizing quantum processes affecting two qubits encoded in heralded single photons. Even for this small system our method displays clear advantages over the other existing ones.

Selective and efficient quantum process tomography with single photons

We present the results of the first photonic implementation of a new method for quantum process tomography. The method (originally presented by A. Bendersky et al, Phys. Rev. Lett 100, 190403 (2008)) enables the estimation of any element of the chi-matrix that characterizes a quantum process using resources that scale polynomially with the number of qubits. It is based on the idea of mapping the estimation of any chi-matrix element onto the average fidelity of a quantum channel and estimating the latter by sampling randomly over a special set of states called a 2-design. With a heralded single photon source we fully implement such algorithm and perform process tomography on a number of channels affecting the polarization qubit. The method is compared with other existing ones and its advantages are discussed.