Single-Atom Gating of Quantum State Superpositions

The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric interpretation: this state space--or Hilbert space--is spanned by mutually orthogonal state vectors corresponding to the quantized degrees of freedom of the real-space system. Measurement of superpositions is akin to accessing the direction of a vector in Hilbert space, determining an angle of rotation equivalent to quantum phase. Here we show that an individual atom inside a designed quantum corral can control this angle, producing arbitrary coherent superpositions of spatial quantum states. Using scanning tunnelling microscopy and nanostructures assembled atom-by-atom we demonstrate how single spins and quantum mirages can be harnessed to image the superposition of two electronic states. We also present a straightforward method to determine the atom path enacting phase rotations between any desired state vectors. A single atom thus becomes a real space handle for an abstract Hilbert space, providing a simple technique for coherent quantum state manipulation at the spatial limit of condensed matter.Comment: Published online 6 April 2008 in Nature Physics; 17 page manuscript (including 4 figures) + 3 page supplement (including 2 figures); supplementary movies available at http://mota.stanford.ed

Ghost imaging with engineered quantum states by Hong-Ou-Mandel interference

Traditional ghost imaging experiments exploit position correlations between correlated states of light. These correlations occur directly in spontaneous parametric down-conversion (SPDC), and in such a scenario, the two-photon state used for ghost imaging is symmetric. Here we perform ghost imaging using an anti-symmetric state, engineering the two-photon state symmetry by means of Hong-Ou-Mandel interference. We use both symmetric and anti-symmetric states and show that the ghost imaging setup configuration results in object-image rotations depending on the state selected. Further, the object and imaging arms employ spatial light modulators for the all-digital control of the projections, being able to dynamically change the measuring technique and the spatial properties of the states under study. Finally, we provide a detailed theory that explains the reported observations.Comment: Published version. 19 pages, 5 figure

Integrated optical waveplates for arbitrary operations on polarization-encoded single-qubits

Integrated photonic technologies applied to quantum optics have recently enabled a wealth of breakthrough experiments in several quantum information areas. Path encoding was initially used to demonstrate operations on single or multiple qubits. However, a polarization encoding approach is often simpler and more effective. Two-qubits integrated logic gates as well as complex interferometric structures have been successfully demonstrated exploiting polarization encoding in femtosecond-laser-written photonic circuits. Still, integrated devices performing single-qubit rotations are missing. Here we demonstrate waveguide-based waveplates, fabricated by femtosecond laser pulses, capable to effectively produce arbitrary single-qubit operations in the polarization encoding. By exploiting these novel components we fabricate and test a compact device for the quantum state tomography of two polarization-entangled photons. The integrated optical waveplates complete the toolbox required for a full manipulation of polarization-encoded qubits on-chip, disclosing new scenarios for integrated quantum computation, sensing and simulation, and possibly finding application also in standard photonic devices

Classical and quantum properties of cylindrically polarized states of light

We investigate theoretical properties of beams of light with non-uniform polarization patterns. Specifically, we determine all possible configurations of cylindrically polarized modes (CPMs) of the electro-magnetic field, calculate their total angular momentum and highlight the subtleties of their structure. Furthermore, a hybrid spatio-polarization description for such modes is introduced and developed. In particular, two independent Poincar\'e spheres have been introduced to represent simultaneously the polarization and spatial degree of freedom of CPMs. Possible mode-to-mode transformations accomplishable with the help of conventional polarization and spatial phase retarders are shown within this representation. Moreover, the importance of these CPMs in the quantum optics domain due to their classical features is highlighted.Comment: 22 pages, 8 figure