Optimal experiment design revisited: fair, precise and minimal tomography

Given an experimental set-up and a fixed number of measurements, how should one take data in order to optimally reconstruct the state of a quantum system? The problem of optimal experiment design (OED) for quantum state tomography was first broached by Kosut et al. [arXiv:quant-ph/0411093v1]. Here we provide efficient numerical algorithms for finding the optimal design, and analytic results for the case of 'minimal tomography'. We also introduce the average OED, which is independent of the state to be reconstructed, and the optimal design for tomography (ODT), which minimizes tomographic bias. We find that these two designs are generally similar. Monte-Carlo simulations confirm the utility of our results for qubits. Finally, we adapt our approach to deal with constrained techniques such as maximum likelihood estimation. We find that these are less amenable to optimization than cruder reconstruction methods, such as linear inversion.Comment: 16 pages, 7 figure

Extending electron orbital precession to the molecular case: Can orbital alignment be used to observe wavepacket dynamics?

The complexity of ultrafast molecular photoionization presents an obstacle to the modelling of pump-probe experiments. Here, a simple optimized model of atomic rubidium is combined with a molecular dynamics model to predict quantitatively the results of a pump-probe experiment in which long range rubidium dimers are first excited, then ionized after a variable delay. The method is illustrated by the outline of two proposed feasible experiments and the calculation of their outcomes. Both of these proposals use Feshbach 87Rb2 molecules. We show that long-range molecular pump-probe experiments should observe spin-orbit precession given a suitable pump-pulse, and that the associated high-frequency beat signal in the ionization probability decays after a few tens of picoseconds. If the molecule was to be excited to only a single fine structure state state, then a low-frequency oscillation in the internuclear separation would be detectable through the timedependent ionization cross section, giving a mechanism that would enable observation of coherent vibrational motion in this molecule.Comment: 9 pages, 10 figures, PRA submissio

Detection of FeO towards SgrB2

We have observed the J=5-4 ground state transition of FeO at a frequency of 153 GHz towards a selection of galactic sources. Towards the galactic center source SgrB2, we see weak absorption at approximately the velocity of other features towards this source (62 km s$^{-1}$ LSR). Towards other sources, the results were negative as they were also for MgOH(3-2) and FeC(6-5). We tentatively conclude that the absorption seen toward SgrB2 is due to FeO in the hot ($\sim$ 500 K) relatively low density absorbing gas known to be present in this line of sight. This is the first (albeit tentative) detection of FeO or any iron--containing molecule in the interstellar gas. Assuming the observed absorption to be due to FeO, we estimate [FeO]/[SiO] to be of order or less than 0.002 and [FeO]/[H$_{2}$] of order $3 10^{-11}$. This is compatible with our negative results in other sources. Our results suggest that the iron liberated from grains in the shocks associated with SgrB2 remains atomic and is not processed into molecular form.Comment: 1 postscrit figure,10 page

A Pre-Protostellar Core in L1551

Large field surveys of NH3, C2S, 13CO and C18O in the L1551 dark cloud have revealed a prolate, pre-protostellar molecular core (L1551-MC) in a relatively quiescent region to the northwest of the well-known IRS 5 source. The kinetic temperature is measured to be 9K, the total mass is ~2Msun, and the average particle density is 10^4-10^5 cm^(-3). L1551-MC is 2.25' x 1.11' in projection oriented at a position angle of 133deg. The turbulent motions are on the order of the sound speed in the medium and contain 4% of the gravitational energy, E_{grav}, of the core. The angular momentum vector is projected along the major axis of L1551-MC corresponding to a rotational energy of 2.5E-3(sin i)^(-2)|E_{grav}|. The thermal energy constitutes about a third of |E_{grav}| and the virial mass is approximately equal to the total mass. L1551-MC is gravitationally bound and in the absence of strong, ~160 microgauss, magnetic fields will likely contract on a ~0.3 Myr time scale. The line profiles of many molecular species suggest that the cold quiescent interior is surrounded by a dynamic, perhaps infalling envelope which is embedded within the ambient molecular gas of L1551.Comment: 27 pages, 7 figures, ApJ accepte

Umklapp scattering of pairs in BCS superconductivity theory

The BCS theory of superconductivity is extended to recognize pairing of electrons by both normal and umklapp scattering. Application of the variational approach shows that coexistence of normal and umklapp scattering frustrates superconductivity.Comment: 9 pages, 5 figures. to be published in Journal of Physics: Condensed Matte

Quantum Correlations from the Conditional Statistics of Incomplete Data

We study, in theory and experiment, the quantum properties of correlated light fields measured with click-counting detectors providing incomplete information on the photon statistics. We establish a correlation parameter for the conditional statistics, and we derive the corresponding nonclassicality criteria for detecting conditional quantum correlations. Classical bounds for Pearson's correlation parameter are formulated that allow us, once they are violated, to determine nonclassical correlations via the joint statistics. On the one hand, we demonstrate nonclassical correlations in terms of the joint click statistics of light produced by a parametric down conversion source. On the other hand, we verify quantum correlations of a heralded, split single-photon state via the conditional click statistics together with a generalization to higher-order moments. We discuss the performance of the presented nonclassicality criteria to successfully discern joint and conditional quantum correlations. Remarkably, our results are obtained without making any assumptions on the response function, quantum efficiency, and dark-count rate of the photodetectors

The slowly expanding envelope of CRL618 probed with HC3N rotational ladders

Lines from HC3N and isotopic substituted species in ground and vibrationally excited states produce crowded millimeter and submillimeter wave spectra in the C-rich protoplanetary nebula CRL618. The complete sequence of HC3N rotational lines from J=9-8 to J=30-29 has been observed with the IRAM 30m telescope toward this object. Lines from a total of 15 different vibrational states (including the fundamental), with energies up to 1100 cm^-1, have been detected for the main HC3N isotopomer. In addition, the CSO telescope has been used to complement this study in the range J=31-30 to J=39-38, with detections in five of these states, all of them below 700 cm^-1. Vibrationally excited HC3N rotational lines exhibit P-Cygni profiles at 3 mm, evolving to pure emission lineshapes at shorter wavelengths. This evolution of the line profile shows little dependence on the vibrational state from which they rotational lines arise. The absorption features are formed against the continuum emission, which has been successfully characterized in this work due to the large frequency coverage. The HC3N column density in front of the the continuum source has been determined by comparing the output of an array of models to the data. The best fits are obtained for column densities in the range 2.0-3.5 10$^17 cm^-2, consistent with previous estimates from ISO data, and TK in the range 250 to 275 K, in very good agreement with estimates made from the same ISO data.Comment: 24 pages, 7 figures, accepted in ApJ part I (Jul. 8, 2004

The Nature of the Molecular Environment within 5 pc of the Galactic Center

We present a detailed study of molecular gas in the central 10pc of the Galaxy through spectral line observations of four rotation inversion transitions of NH3 made with the VLA. Updated line widths and NH3(1,1) opacities are presented, and temperatures, column densities, and masses are derived. We examine the impact of Sgr A East on molecular material at the Galactic center and find that there is no evidence that the expansion of this shell has moved a significant amount of the 50 km/s GMC. The western streamer, however, shows strong indications that it is composed of material swept-up by the expansion of Sgr A East. Using the mass and kinematics of the western streamer, we calculate an energy of E=(2-9)x10^{51} ergs for the progenitor explosion and conclude that Sgr A East was most likely produced by a single supernova. The temperature structure of molecular gas in the central ~20pc is also analyzed in detail. We find that molecular gas has a ``two-temperature'' structure similar to that measured by Huttemeister et al. (2003a) on larger scales. The largest observed line ratios, however, cannot be understood in terms of a two-temperature model, and most likely result from absorption of NH3(3,3) emission by cool surface layers of clouds. By comparing the observed NH3 (6,6)-to-(3,3) line ratios, we disentangle three distinct molecular features within a projected distance of 2pc from Sgr A*. Gas associated with the highest line ratios shows kinematic signatures of both rotation and expansion. The southern streamer shows no significant velocity gradients and does not appear to be directly associated with either the circumnuclear disk or the nucleus. The paper concludes with a discussion of the line-of-sight arrangement of the main features in the central 10pc.Comment: 51 pages, 16 figures, accepted for publication in ApJ. Due to size limitations, some of the images have been cut from this version. A complete, color PS or PDF version can be downloaded from http://www.astro.columbia.edu/~herrnstein/NH3/paper

Modematching an optical quantum memory

We analyse the off-resonant Raman interaction of a single broadband photon, copropagating with a classical `control' pulse, with an atomic ensemble. It is shown that the classical electrodynamical structure of the interaction guarantees canonical evolution of the quantum mechanical field operators. This allows the interaction to be decomposed as a beamsplitter transformation between optical and material excitations on a mode-by-mode basis. A single, dominant modefunction describes the dynamics for arbitrary control pulse shapes. Complete transfer of the quantum state of the incident photon to a collective dark state within the ensemble can be achieved by shaping the control pulse so as to match the dominant mode to the temporal mode of the photon. Readout of the material excitation, back to the optical field, is considered in the context of the symmetry connecting the input and output modes. Finally, we show that the transverse spatial structure of the interaction is characterised by the same mode decomposition.Comment: 17 pages, 4 figures. Brief section added treating the transverse spatial structure of the memory interaction. Some references added. A few typos fixe