# 2009 Posters

### 1. Scalable Traps for Quantum Information Processing with Ions*

Jason Amini, National Institute of Standards and Technology

**Abstract**. J. M. Amini, C. Ospelkaus, H. Uys, C. E. Langer [a], J. Britton, K. R. Brown, D. Leibfried, S. Seidelin [b], A. VanDevender, J. H. Wesenberg [c], and D. J. Wineland. Two of the key goals for the ion trap community are scaling ion traps to hold and manipulate the numbers of qubits needed for complex algorithms and improving the quality of all operations. We will cover some of the developments at NIST on microfabricated surface-electrode traps using optimized modular design components, including a new 'Y' junction design, and using novel magnetic gates. * supported by IARPA and the NIST Quantum Information Program. [a] Current address: Lockheed Martin Space Systems Company, Littleton, CO, USA. [b] Current address: University of Grenoble, France. [c] Current address: Oxford University, U.K.A.

### 2. Fault-tolerant quantum computation with color codes

Jonas Anderson, University of New Mexico

**Abstract**. Concatenated coding is a well-studied route to fault-tolerant quantum computation, but suffers from low accuracy thresholds (on the order of one part in 10,000) or high resource overheads (millions of physical qubits per logical qubit to achieve thresholds on the order of one percent). Kitaev's surface codes offer a new route to fault tolerance with more modest overheads and thresholds approaching 1%. The recently discovered color codes share many properties with surface codes, such as the ability to perform syndrome extraction locally in two dimensions. Some families of color codes admit a transversal implementation of the entire Clifford group. It is expected that color codes have a threshold near that of the surface codes, however the precise value of this threshold is not currently known. In this poster we investigate a particular class of planar color codes on the 4.8.8 lattice known as triangular codes. We develop a fault-tolerant error-correction strategy for these codes in which repeated syndrome measurements on this lattice generate a three-dimensional space-time combinatorial structure. We then develop an integer program (IP) that analyzes this structure and determines the most likely set of errors consistent with the observed syndrome values. We have implemented this IP for simulated noise on small versions of these triangular codes; our goal is to obtain an estimate on the threshold for fault-tolerant quantum memory with the 4.8.8 triangular color codes. Because the threshold for magic state distillation is likely to be higher than this value and because logical CNOT gates can be performed by code deformation in a single block instead of between pairs of blocks, the threshold for fault-tolerant quantum memory for these codes is also the threshold for fault-tolerant quantum computation with them.

### 3. Precision Metrology using Double-Pass Continuous Quantum Measurement

Ben Baragiola, University of New Mexico

**Abstract**. We summarize an ongoing study of continuously measured double-pass quantum systems relevant for quantum-limited metrology. Numerical calculations of the quantum Fisher information for the exact quantum filter indicate improved uncertainty scaling over single-pass geometry, yet quantum Kalman filters show no enhancement. We investigate other approximate filters which we hope will close this gap.

### 4. Transport and heating in an X-junction ion trap array

Brad Blakestad, National Institute of Standards and Technology

**Abstract**. Trapped ions are a useful system for studying the elements of quantum information processing. Simple algorithms have been demonstrated; but scaling to much larger tasks requires the ability to manipulate many qubits. To achieve this, ions could be distributed over separate trap zones in an array, where information would be shared between zones by moving the ions [1]. Multi-dimensional arrays incorporating junctions would allow arbitrary ions, selected from various locations, to be reliably grouped together for multi-qubit gates. Suppression of heating incurred during transport will minimize the time required for ion recooling. We report transport of Be+ ions through an ``X-junction" trap array with near unit probability and low heating (< 10 quanta). We demonstrate the preservation of qubit coherence during such transport. We also study a particular radio-frequency (RF) noise heating mechanism due to RF pseudopotential gradients, which are common in junction designs. * Supported by IARPA and the NIST Quantum Information Program [1] D. Kielpinski, C. Monroe and D.J. Wineland. Nature 417, 709 (2002)

### 5. Trapped Ion Quantum Computation with Transverse Phonon Modes

Ming-Shien Chang, University of Maryland

**Abstract**. Trapped Ion Quantum Computation with Transverse Phonon Modes

M.-S. Chang, K. Kim, S. Korenblit, K. R. Islam, L.-M. Duan†, and C. Monroe JQI and Department of Physics, University of Maryland, College Park, MD 20742

†Department of Physics, University of Michigan, Ann Arbor, MI 48109

Trapped ion systems remain as one of the most promising candidates [1] for practical quantum information processing (QIP). Recent theoretical studies suggested that using transverse collective motion as the quantum bus [2] has several potential advantages over longitudinal normal modes adopted in previous demonstrations. First, the transverse modes are more tightly bound than axial modes for any number of ions and are hence less sensitive to motional decoherence. Second, the closely-spaced spectrum of the transverse modes allows ions to couple through multiple modes simultaneously. This opens up an avenue to tailor the many-body ion coupling strengths for exploring nontrivial spin Hamiltonians [3], and enables entangling gates with arbitrary speed by applying composite laser pulses. We will report the recent experimental progress of this scheme with trapped Ytterbium ions in a linear Paul trap, and its application for quantum simulations of Heisenberg-like spin Hamiltonians. We will also discuss the scalability of this approach for trapped ion QIP.

This work is supported by the DARPA OLE Program under ARO Award W911NF-07-1-0576, IARPA under ARO contract W911NF-08-1-0355, and the NSF PIF Program under grant PHY-0601255.

[1] J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); Wineland, D. J. et al., J. Res. Natl Inst. Stand. Technol. 103, 259-328 (1998); Blatt R., Wineland D., Nature 453, 1008-1015 (2008).

[2] S.-L. Zhu, C. Monroe, and L.-M. Duan, Phys. Rev. Lett. 97, 050505 (2006).

[3] D. Porras and J. I. Cirac, Phys. Rev. Lett. 92, 207901 (2004)

### 6. The Great Hunt for Small Subsystem Codes

Gregory Crosswhite, University of Washington

**Abstract**. Thanks to the hard work of experimentalists, it is increasingly becoming practical to engineer small physical systems with arbitrary 2-local interactions. As a result, it becomes increasingly important for theorists to answer the question: what exactly can be done with such systems? Put another way, what quantum error correcting or detecting codes are there that can be built using a small number of qubits with 2-local interactions? Note that these codes will in general not be stabilizer codes -- since the interactions may not commute -- but will instead be subsystem codes, a more general case. Towards this end, in this poster we shall present the results of our own systematic search for subsystem quantum codes using small numbers of qubits and 2-local interactions.

### 7. Diagnosis of Pulsed Squeezing in Multiple Temporal Modes

Scott Glancy, National Institute of Standards and Technology, Boulder, Colorado

**Abstract**. When one makes squeezed light by downconversion of a pulsed pump laser, many temporal / spectral modes are simultaneously squeezed by different amounts. There is no guarantee that any of these modes matches the pump or the local oscillator used to measure the squeezing in homodyne detection. Therefore the state observed in homodyne detection is not pure, and many photons are present in the beam path that do not lie in the local oscillator's mode. These problems limit the fidelity of quantum information processing tasks with pulsed squeezed light. I will describe our attempts to make coherent state superpositions (sometimes called "cat states") using photon subtraction from squeezed light, the problems caused by multimode squeezing, and methods to characterize the contents of the many squeezed modes.

### 8. Controlling the Loss of Entanglement

Jon Grice, University of California, San Diego

**Abstract**. We present an open-loop discrete time control technique to slow down the loss of entanglement of a two qubit model (the X-states studied by Eberly and Yu) undergoing specific local noises. We find the optimal policy the controller must follow to maximize entanglement after N time steps in terms of the initial state.

### 9. Manipulating mixed-species ion crystals in a segmented ion trap.

Jonathan Home, National Institute of Standards and Technology

**Abstract**. Manipulating mixed-species ion crystals in a segmented ion trap* One of the main requirements for scalable quantum information processing is the ability to move information around the processor. In ion trap QIP, one possibility is to move the ions themselves, using control voltages applied to the electrodes of a segmented trap. In practice, ambient fluctuations in the electric field at the ion and imperfect control of electrode potentials mean that the ion's motion is excited, which degrades the performance of two-qubit logic gates. One solution is to trap two different ion species in the same potential. This allows re-initialization of the ground state of motion by laser cooling the refrigerator ion, while leaving quantum information stored in the internal state of the qubit ion intact. We describe experimental implementation of a range of manipulations of ion crystals containing Beryllium and Magnesium ions in a segmented ion trap, including ion re-ordering, separation, and ground state cooling. In addition, we have used the motion of these ion chains to characterize higher order terms in our trapping potential, which significantly change the normal modes of extended crystals. The precise level of control of the trap potential required for manipulating such crystals has implications for the design of small scale ion traps. * Supported by IARPA and the NIST Quantum Information Program

### 10. Upper Bounds on Fidelity Preservation with Dynamical Decoupling

Michael Hsieh, University of Southern California

**Abstract**. Dynamical decoupling (DD) continues to hold promise as a relatively simple but versatile means of mitigating the influence of a noisy and uncontrolled environment on a controlled quantum system. For a qubit coupled to a bath via an entangling Hamiltonian of the most general possible form, we calculate the range of possible joint qubit-bath dynamics (specifically, the set of permissible Kraus mappings for the total composite system) as a function of the parameters of the DD control pulses under a variety of DD pulse configurations. The upper bounds on system state fidelity preservation are obtained in terms of the minimal distance between the set of attainable Kraus mappings with the ideal set describing fully decoupled dynamics.

### 11. Multiple-unicast communication over directed Quantum Networks

Avinash Jain, University of California, San Diego

**Abstract**. We explore the possibility of network coding in multiple-unicast of quantum information over directed quantum networks. Using information-theoretic tools, we first show that over a Butterfly network, the quantum network coding does not increase the information flow over that achieved by routing. We then extend the Butterfly network to a network where quantum network coding explicitly provides gains over routing. Next we specify a criterion that any directed acyclic graph should satisfy for quantum network coding to outperform routing. We show that when this criterion is not satisfied, the quantum information flow in any 2-pair unicast communication over any directed acyclic network is bounded by sparsest multicut capacity as the fidelity of transmission approaches one.

### 12. Entangled Mechanical Oscillators*

John Jost, National Institute of Standards and Technology, Boulder

**Abstract**. J. D. Jost, J. P. Home, J. M. Amini, D. Hanneke, R. Ozeri+, C. Langer**, J. J. Bollinger, D.Leibfried & D. J. Wineland Quantum entanglement has been the subject of considerable research, in part due to its non-intuitive nature and ubiquitous presence in QIP. For this reason, it is of interest to study entanglement in a variety of systems. We demonstrate deterministic entanglement in a system pervasive in nature: mechanical oscillators. Here, the mechanical oscillators are composed of the vibrations of two Be+ - Mg+ ion pairs in spatially separate locations. In addition, we show entanglement of a spin qubit with a spatially separated mechanical oscillator. These experiments demonstrate the creation of entangled states of a mixed species chain of four trapped ions, distribution of entanglement in an ion trap array, and sympathetic recooling of logical qubits. The techniques demonstrated in this experiment form core components for large-scale trapped-ion QIP. * supported by IARPA and the NIST Quantum Information Program +Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100, Israel **Lockheed Martin Littleton, CO, U.S.A.

### 13. Status and recent progress of remote entanglement experiments with Barium-137 ions

Nathan Kurz, University of Washington

**Abstract**. Because of its visible wavelength cooling transition, relatively high natural abundance, low-lying long-lived D states for shelving readout, and stable hyperfine qubit states spaced by 8.037 GHz, barium 137 represents an excellent ionic qubit candidate. We have built the necessary apparatus and developed techniques to trap and cool this ion. To date, we have demonstrated qubit initialization into the 6S1/2|F=1, mF=0> state by optical pumping, Rabi oscillations between 6S1/2|F=1, mF=0> and 6S1/2|F=2, mF=0> states, and the ability to state-selectively shelve the qubit to the 5D3/2 state for readout. Ultrafast pulses from a mode-locked Ti:Sapphire laser on resonance with the 6P3/2 transition have been shown to excite the ion with near unit probability on a sub-picosecond time scale. When tuned on resonance with the 6P1/2 transition, these pulses will entangle the spin state of the ion with the frequency of the emitted photonic qubit to be coupled into optical fiber and mode-matched on a beam splitter with the emitted photon of an identically prepared ion to generate a remote entangled ion pair. Long-term projects include the construction of a pulse programmer to drive the 8.037 GHz hyperfine transition with phase- and envelope-controlled pulses and construction of a thulium-doped fiber amplifier to increase optical power of the shelving laser at 1762 nm to improve readout speed.

### 14. Stable Mode Sorting by Two-Dimensional Parity of Photonic Transverse Spatial States

Cody Leary, University of Oregon Dept. of Physics and Oregon Center for Optics

**Abstract**. We describe a mode sorter for two-dimensional parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. Both Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two output ports according to the two-dimensional parity of the mode in question. Our interferometer sorts HG_nm input modes depending upon whether they have even or odd order n + m; it equivalently sorts LG_lp modes depending upon whether they have an even or odd value of their orbital angular momentum l. It functions efficiently at the single-photon level, and therefore can be used to sort single-photon states. Due to the inherent phase stability of this type of interferometer as compared to those of the Mach-Zehnder type, it provides a promising tool for the manipulation and filtering of higher order transverse spatial modes for the purposes of quantum information processing. For example, several similar Sagnacs cascaded together may allow, for the first time, a stable measurement of the orbital angular momentum of a true single-photon state. Furthermore, as an alternative to well-known holographic techniques, one can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode filter, which can be used to produce spatial-mode entangled Bell states and heralded single photons in arbitrary first-order (n + m = 1) spatial states, covering the entire Poincare sphere of first-order transverse modes.

### 15. Resolved sideband cavity cooling of 88Sr+

David Leibrandt, MIT

**Abstract**. Cavity cooling is a method of laser cooling which uses coherent scattering into an optical cavity to cool particles [PRL 84, 3787 (2000)]. The particle to be cooled is placed in an optical cavity and excited with a laser tuned to the red of the cavity resonance. On average, scattering events which remove a photon from the laser and put it into the optical cavity cool the particle. The cooling limit is determined by the linewidth and cooperativity of the cavity, which can be designed to allow sub-Doppler cooling. Furthermore, because the cooling limit is independent of the energy level structure of the particle, cavity cooling is in principle applicable to particles without closed optical transitions [PRL 99, 073001 (2007); PRA 77, 023402 (2008)]. In this work we describe an experiment to study cavity cooling of a single 88Sr+ ion in the previously unexplored resolved sideband regime. The ion is confined in a linear RF Paul trap with motional frequencies of 0.86, 1.2, and 1.5 MHz. Large cavity cooling rates are attained by cooling near the 422 nm S1/2 to P1/2 optical dipole transition. We use a 5 cm long, near-confocal Fabry-Perot cavity with a linewidth of 164 kHz and a cooperativity of 0.25. The theoretical cavity cooling limit is 3 motional quanta, which is slightly lower than the Doppler cooling limit for 88Sr+ on the S1/2 to P1/2 transition. Experimental results demonstrate resolved sideband cavity cooling, but with a cavity cooling rate which is several times smaller than predicted by the theory.

### 16. Quantum limited metrology with (β0〉 + 0β〉)/√2 states

Vaibhav Madhok, University Of New Mexico

**Abstract**. We show how to achieve Heisenberg-limited sensitivity using states of the form (β0〉 + 0β〉)/√2 where | β〉 is a coherent state, in a two-arm interferometer. We describe appropriate measurements to achieve the above limit and discuss a scheme for making such states and measurements. We compare these states with "NOON" states and with other methods for achieving the Heisenberg-limited sensitivity.

### 17. Creation of Pure-State Photon Pairs and Single Photon Wavelength Translation in Photonic Crystal Fibers

Hayden McGuinness, University of Oregon

**Abstract**. H. J. McGuinness and M. G. Raymer Oregon Center for Optics University of Oregon Tailor-made photonic crystal fibers (PCFs) allow for unprecedented control over important properties such as fiber dispersion, while also producing tight light confinement and nearly endlessly single mode behavior. It is possible to engineer a PCF which, with judicious choice of pumping scheme, spontaneously produces two-photon states with spectral correlations (“entanglement”) ranging from almost complete correlation to almost no correlation, without the need for spectral post filtering. Of special interest are pure, uncorrelated states, which could be a resource in quantum information processing. Under a different pumping scheme it is possible to translate photon states from one wavelength to another with theoretically one hundred percent efficiency and with no additional noise. The translation can occur over a few up to several hundred nanometers, for example, from telecom to visible wavelengths, and visa versa. We study these types of photon state creation and translation theoretically and experimentally.

### 18. Comparing quantum codes with a Clifford-circuit simulator

Adam Meier, University of Colorado at Boulder

**Abstract**. The stabilizer formalism used in the proof of the Gottesman-Knill theorem allows classical computers to simulate efficiently a class of quantum circuits known as Clifford circuits. Within this class, the circuits needed to encode and decode additive quantum codes are of particular interest due to the large portion of time most designs for quantum computers spend on encoding and decoding. By modeling these processes on a classical computer under different error models, we can compare different quantum codes in a very practical and pertinent way. We present progress on our design of a fast Clifford-circuit simulator and some results for codes based on Galois fields of prime-power order. This work is in collaboration with K. Costello, B. Eastin, S. Glancy and E. Knill.

### 19. Quantum Control of Hyperfine Spins with Coherent Electromagnetic Fields

Seth Merkel, University of New Mexico

**Abstract**. With long coherence times and well characterized control fields from the "quantum optics toolbox", cold neutral atoms provide a useful platform in which to explore methods and techniques for quantum information processing and quantum control. In this poster we study the use of coherent electromagnetic fields to control ultracold neutral alkali atoms in their electronic ground state. In cesium-133, the two hyperfine manifolds comprise a 16 dimensional state space that we can manipulate with rf/microwave magnetic fields. These fields lead to evolutions that are controllable in the Lie algebraic sense and have a relatively simple geometric structure. We look at three protocols for quantum control in this poster: state preparation (mapping a fiducial state to an arbitrary target state), generating unitary maps from state preparations, and robust state preparations using composite pulse techniques from NMR.

### 20. Control of Atomic Wave Functions in Optical Lattices

Brian Mischuck, University of New Mexico

**Abstract**. The coherent transport of atoms in optical lattices is essential for quantum computation and quantum simulations involving controlled collisions between the atoms. Such coherence is typically limited by inhomogeneities and background fields. By applying the techniques of quantum control, we study protocols for robustly evolving the motional wave function in the ground band using applied external fields, and well-designed lattices. We examine explicit constructions for synthesizing specific unitary maps.

### 21. Dynamical Control of Cs Atoms in an Optical Lattice using Microwave Manipulation

Enrique Montano, University of Arizona

**Abstract**. Enrique Montaño, Jae Hoon Lee, Poul Jessen College of Optical Sciences, University of Arizona, Tucson, AZ Brian Mischuck, Ivan Deutch Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM Many schemes for quantum information processing in optical lattices require quantum coherent transport of the atomic qubits. Such transport usually relies on tunneling or dynamical changes in the lattice potential. We are developing a new, more controllable and potentially far more robust approach based on µw transitions between the sites of a spinor lattice. As a first step, we have demonstrated the ability to coherently transfer a qubit between well-defined vibrational states at neighboring lattice sites. We will explore the types of dynamical control this can lead to in our spinor lattice system. In a lattice composed of counter propagating beams with orthogonal, linear polarizations (the lin-90˚-lin configuration) a µw field will couple each site equally to its neighbors, and the spatial wavefunction of an atom will spread out over the sites in a continuous-time random walk. In a lin-theta≠90˚-lin lattice the symmetry is broken and each site is coupled to a single neighboring site either to the left or to the right, depending on the choice of theta. With this configuration, controlled transport over the entire lattice can be constructed from a series of pairwise couplings.

### 22. Induced Nonlinear Interactions and Parameter Estimation in Cold Atoms

Heather Partner, University of New Mexico

**Abstract**. Recent progress in both theory and experiment have suggested that nonlinear interactions could provide improved uncertainty scaling for quantum precision measurements. It is our goal to translate these ideas into a functional experimental design, specifically in atomic magnetometry. We discuss our plans to perform double-passed continuous measurements on the collective spin of cooled atoms in a fountain configuration, with the aim of investigating improvements over single-pass geometries.

### 23. Magnetic Resonance Force Microscopy with spin noise

Shesha Raghunathan, University of Southern California

**Abstract**. A promising technique for measuring single electron spins is magnetic resonance force microscopy (MRFM), in which a micro-cantilever with a permanent magnetic tip is resonantly driven by a single oscillating spin. If the quality factor of the cantilever is high enough, this signal will be amplified over time to the point that it can be detected by optical or other techniques. An important requirement, however, is that this measurement process occur on a time scale short compared to any noise which disturbs the orientation of the measured spin. We describe a model of spin noise for the MRFM system, and show how this noise is transformed to become time-dependent by going to the usual rotating frame. We simplify the description of the spin-cantilever system by approximating the cantilever wavefunction as a gaussian wavepacket, and show that the resulting approximation closely matches the full quantum behavior. We then examine the problem of detecting the signal for a cantilever with thermal noise and spin with spin noise, deriving a condition for this to be a useful measurement.

### 24. Source and Detector Technologies for Optical Quantum Information

Radhika Rangarajan, University of Illinois Urbana Champaign

**Abstract**. Scalable quantum computation and quantum communication require the ability to create and detect multiple qubits with high fidelity. We report on our progress in developing both source and detector technologies high-brightness high-fidelity polarization entangled sources and high-efficiency photon-number resolving detectors. High-fidelity pulsed entanglement sources are essential for various quantum communication protocols, including quantum teleportation. By using temporal and spatial compensation, we can generate high-fidelity entanglement from pulsed and diode laser sources. We have demonstrated for the first time a robust, high quality, large aperture source of degenerate and non-degenerate Type-I entangled photons using BiBO, a highly nonlinear non-hygroscopic biaxial crystal, with a diode laser source. We also report on our progress in developing a high-fidelity Type-I source using an ultrafast pulsed source. On the detector front, we report on our current status in developing Visible Light Photon Counters (VLPCs) and Solid State Photo-Multipliers (SSPMs). VLPCs and SSPMs are photon number resolving detectors that have high quantum efficiency. Past measured efficiency for both the detectors were limited to less than 88% due to in-coupling losses. We are currently working to improve the overall performance of these detectors by a) reducing coupling losses and blocking infrared background, b) using improved low-noise electronics, and c) incorporating novel cryogenic designs.

### 25. Quantum Information as Complementary Classical Information

Joseph Renes, Technical University of Darmstadt

**Abstract**. Since the breakthrough by Calderbank, Shor, and Steane on the existence of quantum error-correcting codes, an oft-used notion in quantum information theory is that we can treat quantum information essentially as a strange combination of two types of classical information, pertaining to two complementary observables "amplitude" and "phase". Correcting errors afflicting either of these observables is sufficient to restore the quantum information to its original state. This approach is also appealing on a more fundamental level, as it suggests that the important differences between classical and quantum information processing originate from the phenomenon of complementarity, which is at the heart of the difference between classical and quantum mechanics. However, the central results of quantum information theory established recently, such as the achieveable rate of quantum communication over a noisy channel, follow a different approach termed *decoupling* which has a natural origin in the study of quantum cryptography. We show that the decoupling-based results can be concretely established in the complementary classical information picture. By adopting an information-theoretic approach to complementarity, we are able to construct entanglement distillation protocols which straightforwardly seek to distill amplitude and phase correlations without venturing into decoupling. This gives new and intuitive proofs of both the noisy channel coding theorem and the asymptotic rates of both secret-key distillation and state merging. Joint work with J.-C. Boileau.

### 26. Quantum State Reconstruction and Random Evolution

Carlos Riofrio, University of New Mexico

**Abstract**. In order to perform quantum state reconstruction, the set of measured observables must be informationally complete. In this poster, we explore the performance of the reconstruction algorithm developed by Silberfarb et al. (PRL 95, 030402 (2005)) under the asumption that the quantum system undergoes random evolution. We show that in that case, although the measurements do not span the space of all density matrices, we are able to reconstruct the set of all pure states and almost-all mixed states with very high fidelities. We find that this is only possible after the inclusion of the physical constraint of positivity. Using as an example the quantum states stored in the ground-electronic hyperfine manifold (F=3) of an ensemble of Cs 133 atoms controlled by radio-frequency magnetic fields, we give a possible physical realization of this protocol provided that the dynamics exhibits a classically chaotic phase space. For this purpose, we chose the well studied quantum kicked top dynamics.

### 27. Practical entanglement swapping with imperfect parametric down conversion sources and inaccurate detectors

Artur Scherer, Institute for Quantum Information Science at the University of Calgary in Alberta, Canada

**Abstract**. Entanglement swapping between photon pairs is a fundamental building block in schemes using quantum relays and quantum memories to overcome the range limits of long distance quantum key distribution. Its practical realization, however, suffers from experimental deficiencies due to imperfect entangled-pairs parametric down conversion (PDC) sources and inaccurate detectors. We provide a model for practical entanglement swapping that takes into account the multi-pair nature of all PDC sources as well as detector inefficiencies and dark count events. In particular, we calculate the resultant mixed entangled quantum state given two imperfect PDC sources and the result of a Bell measurement with faulty detectors. We investigate how the entanglement present in the final state of the remaining modes is affected by the practical deficiencies. This allows us to suggest the implications of the imperfections on schemes using entanglement swapping as a fundamental tool. To test the predictions of our model, comparison with experiments on entanglement swapping is provided. We gratefully acknowledge the support of General Dynamics Canada, iCORE, CIFAR, MITACS, NSERC and Quantum Works in preparing this work.

### 28. Towards an optimal algorithm for the hidden subgroup problem of dihedral group of order 2p (p: prime greater than 2)

Asif Shakeel, University of California at San Diego

**Abstract**. Pretty Good Measurement is optimal for the problem of determining order two subgroups of dihedral group consisting of the identity and a reflection. Importantly, the work of Moore and Russell provides a representation theoretic proof of that. The main result of this paper is development of a multi-query algorithm that exploits the representation of dihedral group. Bacon, Van Dam and Childs and prior to them Regev show that the solution of the subset sum problem may be central to an algorithm implementing the Pretty Good Measurement. In our work, subset sum problem surfaces in the identification of irreducible sub-representations. Rest of the computations are explicitly shown in terms of Fourier transform on dihedral group, which is implemented by abelian transforms.

### 29. Optical Systems for Trapped Ion Fluorescence Collection

Gang Shu, University of Washington

**Abstract**. Efficient and controllable ion fluorescence collection scheme is crucial for trapped ion qubit detection and single photon sources. We designed a non-imaging optical system to work directly with photon multiplier tubes (PMTs) for our new trap with a spherical mirror. We studied the possibility of collimating the diverging beam from the in-chamber spherical mirror by an external aspherical correlator, which may even enable efficient single-mode optical fiber coupling. In order to achieve efficient and reliable detections of fluorescence from two or more adjacent ions, we carefully characterized our Andor Luca EMCCD camera and developed a LabView program to reduce the image noise and count photons from customized sensor areas, with which we get satisfactory quiet images and fast accurate counts.

### 30. Experimental Quantum Control of the 133Cs Hyperfine Ground Manifold

Aaron Smith, University of Arizona

**Abstract**. Aaron Smith, Brian Anderson, and Poul Jessen College of Optical Sciences, University of Arizona, Tucson, AZ In recent work our group has demonstrated complete quantum control and quantum state reconstruction for the F = 3 irreducible subspace within the electronic ground hyperfine manifold of 133Cs. The control Hamiltonian for this system was generated by a time dependent magnetic field and a laser induced AC Stark shift, where the latter necessarily brings a penalty in terms of decoherence from spontaneous photon scattering. We are currently working to extend control and measurement to the full ground hyperfine manifold, by driving the atom solely with DC, radiofrequency and microwave magnetic fields [S. Merkel et al, PRA 78, 023404 (2008)]. We will report on experimental progress towards this goal.

### 31. Optical One-Way Barrier for Atoms

Daniel Steck, University of Oregon

**Abstract**. We demonstrate an asymmetric optical potential barrier for ultracold ^{87}Rb atoms using laser light tuned near the D_{2} transition. Such a one-way barrier, where atoms impinging on one side are transmitted but reflected from the other, is a literal realization of Maxwell's demon and has important implications for cooling atomic species not amenable to standard laser-cooling techniques. In our experiment, atoms are confined to a far-detuned dipole trap consisting of a single focused Gaussian beam, which is divided near the focus by the barrier. The one-way barrier consists of two focused laser beams oriented normal to the dipole trap. The first barrier beam is tuned between the *F = 1 → F'* and the *F = 2 → F'* families of hyperfine transitions, and presents a barrier only for atoms in the *F = 2* ground state, while letting *F = 1* atoms pass. The second beam pumps the atoms to *F = 2* on the reflecting side of the barrier, thus producing the asymmetry. We study experimentally the reflection and transmission dynamics of atoms in the presence of the one-way barrier.

### 32. A scalable, high-speed measurement-based quantum computer using trapped ions

Rene Stock, University of Toronto

**Abstract**. A scalable, high-speed measurement-based quantum computer using trapped ions R. Stock, D. F. V. James Department of Physics, University of Toronto, Canada The tremendous progress achieved in the control of trapped ions has recently led to the creation of an entangled state of eight ions. The entanglement of many more ions for large-scale quantum computer seems very feasible. However, the slow entangling gate and slow readout of ions hinder fast operations and will limit the practical use of a future ion-trap quantum computer. One-way (i.e. measurement-based) quantum computing architectures offer a way out by parallelizing the slow entangling operations to create a many-body entangled state and by processing quantum information via fast readout and measurement of qubits. In this work, we investigate the challenges involved in developing a high-speed one-way quantum-computing scheme for ions. We devise an architecture for the creation of many-body entangled states and show how a 3D cluster state suitable for error correction can be efficiently mapped to 2D ion-trap architectures. We propose the projective measurement of ions via multi-photon photoionization for nanosecond measurement and operation, and discuss the viability of such a scheme for Ca ions.

### 33. Practical quantum metrology with Bose-Einstein condensates

Alexandre Tacla, University of New Mexico

**Abstract**. We analyze in detail the recently proposed experiment [Boixo et al., Phys. Rev. Lett. **101**, 040403 (2008)] for achieving better than 1/n scaling in a quantum metrology protocol using a two-mode Bose-Einstein condensate of n atoms. There were several simplifying assumptions in the original proposal that made it easy to see how a scaling approaching 1/n^{3/2} may be obtained. We look at these assumptions in detail to see when they may be justified. We present numerical results that confirm our theoretical predictions for the effect of the spreading of the BEC wave function with increasing n on the scaling. Numerical integration of the coupled Gross-Pitaevskii equations for the two mode BEC also shows that the assumption that the two modes share the same spatial wave function is justified for a length of time that is sufficient to run the metrology scheme.

### 34. Spin squeezing in a double-pass optical-feedback geometry

Collin Trail, University of New Mexico

**Abstract**. Squeezed collective atomic spin states can be generated using the Faraday effect, by passing light through an atomic sample twice, imprinting the spin component along the direction of the propagation of light on to the light on the first pass, and rotating the atoms proportionally to this spin component on the second pass, thus creating an effective nonlinearity (M. Takeuchi et al., 2005, Phys. Rev. Lett. 94, 023003). The squeezing produced is reduced by loss of light still entangled to the atoms. We show how this scheme can be improved by a quantum eraser effect, where measuring the light properly reduces it's entanglement to our atomic sample. Furthermore, we present estimates for the reduction in squeezing due to spontaneous emission, by approximating the distribution of the collective variables by a Gaussian.

### 35. Cryogenic surface electrode ion traps for quantum computation

Shannon Wang, Massachusetts Institute of Technology

**Abstract**. Dense arrays of trapped ions provide one way of scaling up ion trap quantum information processing. However, miniaturization of ion traps is currently limited by sharply increasing motional state decoherence at sub-100μm ion-electrode distances. The ability to address individual ions and perform quantum operations in such dense, small ion traps is another important challenge. We present a cryogenic ion trap system using microfabricated traps, which addresses the heating and addressing issues. In these traps, a single trapped Sr+ ion is characterized using the temperature dependence between 10-100 K to elucidate the heating mechanism. At 6 K, heating rates are observed to be as low as two quanta per second with the ion located 100 μm above the surface; this heating rate is more than two orders of magnitude lower than the best results obtained in a comparable trap at room temperature. The cryogenic system enable novel use of superconductors as flux shields to stabilize the magnetic field, and the low heating rates enable high fidelity quantum operations. We performed coherent operations on the internal and motional state and found the classical fidelity of a Controlled-NOT gate to be 95%. We also performed some initial experiments on full process tomography of the CNOT gate. Finally, we have developed a scheme to create a local magnetic field gradient by integrating current sources onto a microfabricated surface-electrode trap, and obtained some initial experimental results on individual addressing of ions. The low heating rates and individual addressing in a cryogenic surface-electrode ion trap makes it a viable candidate system for realizing scalable quantum computation.

### 36. Correlated photon pairs from a warm atomic ensemble of Rubidium

Tommy Willis, Joint Quantum Institute, University of Maryland

**Abstract**. We produce polarization-entangled correlated photon pairs from a warm atomic vapor of Rubidium using a spontaneous four-wave mixing interaction. In the experiment we apply two pump lasers (795 nm, 1324 nm) to the atomic ensemble and observe the cross-correlation function of two photons (780 nm, 1367 nm) emitted into the phase-matched direction. We see that the pairs have non-classical polarization correlation. The temporal and spectral character of the photon pairs can be modified by changing the absorption/dispersion of the atomic vapor at the wavelength of the generated pairs.

### 37. Raman Optical Comb Generation in Hydrogen-filled Hollow Core Fiber

Chunbai Wu, Oregon Center for Optics, University of Oregon

**Abstract**. Title: Raman Optical Comb Generation in Hydrogen-filled Hollow Core Fiber Chunbai Wu, Erin Mondloch, Cade Gledhill and M. G. Raymer Oregon Center for Optics, University of Oregon Abstract: Frequency comb generation has attracted many research efforts in recent years, with applications such as optical atomic clocks and attosecond pulse synthesis. In addition, super-continuum generation of light has been demonstrated in specially structured photonic crystal fibers. Recently, researchers at the University of Bath developed a large hollow-core (single-defect) fiber with Kagome- or square-lattice pattern cladding. [1] These fibers show high transmission spectra spanning from ultra-violet to infrared. High pressure hydrogen gas is filled in the fiber's hollow core throughout the length of the fiber, and up to 45 vibrational and rotational Raman transition lines of molecular hydrogen are observed following a high-power 10-ns IR laser pulse being coupled into the fiber. [2] The question outstanding is to what extent are the phases of these optical comb lines correlated. Perfect correlation would in principle allow deterministic phase tailoring to create attosecond pulses. A preliminary simplified model calculation indicated a high degree of correlation would exist. [2] To understand better this cascaded, coherent stimulated Raman scattering (SRS), we solve the quantum mechanical model of SRS [2,3] for the temporal evolution of first-order Stokes and anti-Stokes fields at the end of the fiber, as well as the spatial evolution of molecular polarization (collective vibrational state) stored in the hydrogen gas. (Higher order Raman lines are neglected from the equations because they are much weaker.) In the high-gain transient regime, the degree of anti-correlation between complex Stokes and anti-Stokes fields is calculated and found to equal unity throughout the duration of the pulses, even at large phase mismatch of wave vectors induced by the dispersion of the fiber. This result indicates that the generated first-order Stokes and anti-Stokes fields are nearly perfectly phase anti-correlated, although the absolute value of the phase is random due to the spontaneous initiation of the SRS process. Stokes and anti-Stokes fields are generated with opposite spectral phase. Further analysis on higher order Stokes and anti-Stokes fields is needed. In experiment, we collaborate with researchers at University of Bath (who produce the fiber). We designed a high-pressure gas chamber for filling the fiber at its ends, by using commercially-available "Swagelok" fittings. We have observed multiple Raman scattering lines from hydrogen and the team is now attempting to verify the phase coherence between them. Reference: [1] F. Couny, F. Benabid, P. S. Light, Opt. Lett. 31, 3574 (2006) [2] F. Couny, F. Benabid, P. J. Roberts, P. S. Light, M. G. Raymer, Science 318, 1118 (2007) [3] S. Ya. Kilin, Europhys. Lett. 5, 419 (1988)

### 38. Entanglement verification based on SIC-POVM measurement

Jun Yin, University of Oregon

**Abstract**. Maximum likelihood estimation and Bayesian methods are applied and compared to acquire certain properties (e.g., purity and entanglement) of a four-qubit system from finite measurement records. In particular, we assume a SIC-POVM is measured on each qubit. We tentatively propose a criterion for the number of SIC-POVM measurements needed to obtain reliable estimates of purity, the amount of multi-partite entanglement, and whether the state is entangled or not.