Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session Y33: Novel Probes of Quantum Gases and Quantum Measurement / Quantum Information |
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Sponsoring Units: DAMOP GQI Chair: Mark Coffey, Colorado School of Mines Room: E143 |
Friday, March 19, 2010 8:00AM - 8:12AM |
Y33.00001: Entropy of the Hubbard model near the N\'eel transition Matthias Troyer, Evgeni Burovski, Evgeny Kozik, Jaan Oitmaa, Lode Pollet, Vito Scarola Recent dramatic advances in experiments with ultracold lattice fermions, substantiated in particular by observations of Mott physics, promise a forthcoming realization of long-range anitiferromagnetism. The key question is how much more progress in cooling will be necessary for these systems to enter the N\'eel phase. To provide the basis for accurate thermometry and detection of the N\'eel state, we calculate the entropy of the Hubbard model near the N\'eel transition. The results are obtained using determinant diagrammatic Monte Carlo and high-temperature series expansion methods. [Preview Abstract] |
Friday, March 19, 2010 8:12AM - 8:24AM |
Y33.00002: Fermions in 2D Optical Lattices: Temperature and Entropy Scales for Observing Antiferromagnetism and Superfluidity Thereza Paiva, Richard Scalettar, Mohit Randeria, Nandini Trivedi One of the major challenges in realizing antiferromagnetic and superfluid phases in optical lattices is the ability to cool fermions. We determine constraints on the entropy for observing these phases in two-dimensional Hubbard models. We investigate antiferromagnetic correlations in the repulsive model at half filling and superfluidity of s-wave pairs in the attractive case away from half filling using determinantal quantum Monte Carlo simulations. We find that an entropy per particle ~ ln(2) is sufficient to observe the charge gap in the repulsive Hubbard model or the pairing pseudogap in the attractive case. Observing antiferromagnetic correlations or superfluidity in 2D systems requires a further reduction in entropy by a factor of three or more. In contrast to higher dimensions, we find that adiabatic cooling is not useful to achieve the required low temperatures. [Preview Abstract] |
Friday, March 19, 2010 8:24AM - 8:36AM |
Y33.00003: Mean Field Theory Calculation of Isentropic Curves of the Fermion Hubbard Model Aleksander Zujev, Richard Scalettar Recent experiments on optical lattices have focussed attention on understanding how many body correlations change when the entropy (rather than the temperature) is varied as a control parameter. Quantum Monte Carlo (QMC) simulations have addressed some of the issues involved, but, for fermions, are limited by the sign problem. In this talk, we present results for the isentropic curves of the square lattice fermion Hubbard model in mean field theory (MFT). The topology of these curves on the phase diagram is explored, and compared to what is found in QMC when the latter is available. We also compare to MFT calculations for other models. [Preview Abstract] |
Friday, March 19, 2010 8:36AM - 8:48AM |
Y33.00004: Phase sensitive measurements of order parameters for ultracold atoms through two particles interferometry Takuya Kitagawa, Alain Aspect, Marcus Greiner, Eugene Demler Nontrivial symmetry of the pair wave function is crucial to some of the most interesting states of ultracold atoms, including p-wave Feshbach molecules and d-wave paired states of fermions in optical lattices. Identifying these states in experiments requires measurements of the relative phase of different components of the pair wave function. We discuss a new method for such measurements based on two photon interference and noise correlations analysis in the time of flight experiments. Furthermore, in order to unambiguously determine the symmetry of the wave functions, we propose the method analogous to classical white fringe, which can reveal the existence of fundamental phase factors. [Preview Abstract] |
Friday, March 19, 2010 8:48AM - 9:00AM |
Y33.00005: Cooling and Thermometry for Fermionic Atoms in an Optical Lattice Jean-Sebastien Bernier, Tung-Lam Dao, Lorenzo De Leo, Corinna Kollath, Antoine Georges, Fabrice Gerbier, Christophe Salomon, Michael Koehl We propose a set of novel experimental tools to cool and measure the temperature of fermionic atoms loaded into an optical lattice. The proposed cooling method is based on spatial entropy modulation while the temperature detection scheme relies on Raman spectroscopy. [Preview Abstract] |
Friday, March 19, 2010 9:00AM - 9:12AM |
Y33.00006: Noise correlations in 1D Bose mixtures in optical lattices Anzi Hu, Ludwig Mathey, Carl Williams, Charles Clark We study the noise correlations of one-dimensional(1D) Bose mixtures, as a probe of their quantum phases. In [1], we discuss the rich structure of many-body phases, such as paired and counterflow superfluidity in such 1D mixtures. We now ask the question what is the signature of these phases in the correlations of the atomic cloud after time-of- flight at long times. Using both Luttinger liquid theory and time-evolving block decimation (TEBD) method, we find clear signatures of these phases. Within the numerical approach we also discuss the case of trapped systems.\\[4pt] [1] Anzi Hu, L. Mathey, Ippei Danshita, Eite Tiesinga, Carl J. Williams, and Charles W. Clark, \emph{Phys. Rev. A} \textbf{80}, 023619 (2009). [Preview Abstract] |
Friday, March 19, 2010 9:12AM - 9:24AM |
Y33.00007: Phase Identification and Thermometry of Condensates in 2D Optical Lattices Eric Duchon, Yasuyuki Kato, Naoki Kawashima, Nandini Trivedi Definitive identification of the phases in a periodic optical lattice and an overall confining potential continues to present difficulties. By direct comparison of density images from experiments\footnote{N. Gemelke, et al., \emph{Nature} \textbf{460}, 995-998 (2009).} of bosons on 2D optical lattices to QMC density profile calculations,\footnote{Y. Kato, et al., \emph{Nature Physics} \textbf{4}, 617 (2008).} we differentiate between Mott insulator, superfluid and normal phases. Kinks in the compressibility spatially locate the emergence of superfluid order.\footnote{Q. Zhou, et al., \emph{Phys. Rev. Lett.} \textbf{103}, 085701 (2009).} The temperature is estimated by examining the deviations from integer density of the Mott plateaus as well as from the tails of the density profiles. [Preview Abstract] |
Friday, March 19, 2010 9:24AM - 9:36AM |
Y33.00008: Density Matrix Reconstruction from a Time-Independent Continuous Measurement Seth Merkel, Carlos Riofrio, Steve Flammia, Ivan Deutsch In this paper we examine measurement records that are derived from a continuous probe of a quantum system undergoing time-independent dynamics. We show that this type of measurement is insufficient to perfectly reconstruct every quantum state, but that for very generic conditions the unmeasurable observables occupy only a vanishingly small fraction of operator space. We present numerical simulations that show that tomography based on these incomplete measurement records yield estimates with very high average fidelity for states drawn from ensembles of pure or mixed states. We also look at using the Floquet operator of the quantum delta kicked top as a means of generating a this type of measurement record in an atomic spin system. [Preview Abstract] |
Friday, March 19, 2010 9:36AM - 9:48AM |
Y33.00009: Optimal Estimation of Single Qubit Quantum Evolution Parameters David Collins, Michael Frey The evolution of a quantum system can depends on one or more parameters. The process for determining these requires subjecting a quantum system to the evolution, performing a measurement and attempting to infer the parameter from the measurement outcome. Quantum estimation deals with this task where a finite number of copies of the quantum system are available. We consider rotations of a spin-1/2 particle about a fixed axis and which are parameterized by a rotation angle, which is to be estimated. We use the quantum Fisher information to establish optimal bounds on the variance in any estimator of this parameter in scenarios involving one use of the rotation upon each of a collection of spin-1/2 particles. We show that optimal estimation occurs when all spin-1/2 particles are entangled and present exact analytical results for the bound that is generated and the required input state. We show that this offers a significant advantage over the use of unentangled states and describe the accuracy of estimation for various possible entangled input states. [Preview Abstract] |
Friday, March 19, 2010 9:48AM - 10:00AM |
Y33.00010: Symmetric Informationally-Complete States Are Minimum Uncertainty States in Prime Dimensions Hoan Bui Dang, Marcus Appleby, Christopher Fuchs Symmetric informationally-complete (SIC) sets of quantum states have received growing attention due to their many nice properties. For prime dimensions, we add another property to the list: Weyl-Heisenberg covariant SIC states achieve minimum uncertainty (in a sense defined independently by the authors [1] and Wootters and Sussman [2]) with respect to a complete set of mutually unbiased bases. In this way, SIC states can be considered as finite-dimensional analogues to coherent states. Because of an observation in [2], measurements based on these states are particularly important for quantum eavesdropping in generalized BB84 quantum key distribution schemes. References: [1] D. M. Appleby, H. B. Dang, and C. A. Fuchs, ``Symmetric Informationally-Complete Quantum States as Analogues to Orthonormal Bases and Minimum-Uncertainty States,'' arXiv:0707.2071v1 [quant-ph]. \newline [2] D. Sussman and W. K. Wootters, ``Discrete Phase Space and Minimum-Uncertainty States,'' arXiv:0704.1277v1 [quant-ph]. [Preview Abstract] |
Friday, March 19, 2010 10:00AM - 10:12AM |
Y33.00011: The Uncertainty Principle in the Presence of Quantum Memory Joseph M. Renes, Mario Berta, Matthias Christandl, Roger Colbeck, Renato Renner One consequence of Heisenberg's uncertainty principle is that no observer can predict the outcomes of two incompatible measurements performed on a system to arbitrary precision. However, this implication is invalid if the the observer possesses a quantum memory, a distinct possibility in light of recent technological advances. Entanglement between the system and the memory is responsible for the breakdown of the uncertainty principle, as illustrated by the EPR paradox. In this work we present an improved uncertainty principle which takes this entanglement into account. By quantifying uncertainty using entropy, we show that the sum of the entropies associated with incompatible measurements must exceed a quantity which depends on the degree of incompatibility and the amount of entanglement between system and memory. Apart from its foundational significance, the uncertainty principle motivated the first proposals for quantum cryptography, though the possibility of an eavesdropper having a quantum memory rules out using the original version to argue that these proposals are secure. The uncertainty relation introduced here alleviates this problem and paves the way for its widespread use in quantum cryptography. [Preview Abstract] |
Friday, March 19, 2010 10:12AM - 10:24AM |
Y33.00012: Quantum channel convexity and Birkhoff's theorem Ian Durham Birkhoff's Theorem states that doubly stochastic matrices are convex combinations of permutation matrices. Quantum mechanically these matrices are doubly stochastic channels, i.e. they are completely positive maps preserving both the trace and the identity. We expect these channels to be convex combinations of unitary channels and yet it is known that some channels cannot be written that way. Recent work has suggested that $n$ copies of a single channel might approximate a mixture (convex combination) of unitaries. It turns out that when approached from a mixture of category and group theory, one can show that unital quantum channels and the associated algebra of their Hilbert space, possess category- and group-like properties. From this it can be shown that $n(n+1)/2$ copies of an invertible unital quantum channel may be approximated by a mixture (convex combination) of unitarily implemented channels. This is a stronger result since it means that the asymptotic limit may be approached in fewer steps. It can also be shown that the properties of the channel are preserved in the asymptotic limit. [Preview Abstract] |
Friday, March 19, 2010 10:24AM - 10:36AM |
Y33.00013: Two-party information splitting Patrick Coles, Li Yu, Vlad Gheorghiu, Robert Griffiths Consider the very general process where the state of a quantum system is encoded into a (possibly larger) quantum system, which is then physically split into pieces A and B. One can ask: how much information does A have (about the original state), how much does B have, and how are they related? We find a deterministic trade-off between the quantum information in A and that in B. One can go a step further and consider different types of information (e.g. the X, Y, and Z components of angular momentum), asking how much each party has of each information type. While classical information can be copied to both A and B, we find a trade-off inequality for an information type in A and a mutually-unbiased type in B, e.g. $I(X,A)+I(Z,B)\leq 1$ for X-information in A and Z-information in B. Even more intriguing is our finding that, for certain information measures, the information splitting between A and B, $I(W,A)-I(W,B)$, is invariant to the information type W. The fundamental phenomena of measurement and decoherence can be viewed as information splitting processes between the system and the apparatus (or environment), so our results are applicable to these phenomena. [Preview Abstract] |
Friday, March 19, 2010 10:36AM - 10:48AM |
Y33.00014: Exploring Qutrits through Symmetric Informationally Complete Measurements Gelo Noel Tabia By representing quantum states as probability distributions induced by symmetric, informationally complete measurements (or SICs), we uncover some fundamental properties of the qutrit state space that are not immediately recognizable in the usual Hilbert space picture. In addition, we present a detailed study of all eight (non-unitarily equivalent) one-parameter families of SICs in dimension three, the relationships among the various probability distributions they generate, and the structure coefficients for gl(3,C) they give rise to. An experimental realization of a qutrit SIC-POVM via weak measurements by the Steinberg group at the University of Toronto [1] provides an excellent venue for highlighting the practical significance of some of our theoretical results. \\[4pt] [1] Z.E.D. Medendorp, et al., ``Simulating a Qutrit SIC-POVM using Weak Measurements,'' poster presented at Quantum Works -- 2009. [Preview Abstract] |
Friday, March 19, 2010 10:48AM - 11:00AM |
Y33.00015: Fidelity susceptibility as a seeker for quantum phase transitions Wing Chi Yu, Ho Man Kwok, Junpeng Cao, Shi-Jian Gu Fidelity, a concept emerging from the quantum information theory, has recently become an attractive approach towards the study of quantum phase transitions (QPT). Being the leading response of the fidelity to the external driving parameter, people believed that the fidelity susceptibility (FS) can be used as a seeker for QPT. In this presentation, a brief review on the formulism of FS and its scaling behavior would be given. Also, the analytical result of FS in the one-dimensional transverse-field Ising model and its numerical result in the two-dimensional XXZ and Ising models would be presented. [Preview Abstract] |
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