skip to main content


This content will become publicly available on July 22, 2025

Title: Speeding up squeezing with a periodically driven Dicke model

We present a simple and effective method to create highly entangled spin states on a faster timescale than that of the commonly employed one-axis twisting (OAT) model. We demonstrate that by periodically driving the Dicke Hamiltonian at a resonance frequency, the system effectively becomes a two-axis countertwisting Hamiltonian, which is known to quickly create Heisenberg limit scaled entangled states. For these states we show that simple quadrature measurements can saturate the ultimate precision limit for parameter estimation determined by the quantum Cramér-Rao bound. An example experimental realization of the periodically driven scheme is discussed with the potential to quickly generate momentum entanglement in a recently described experimental vertical cavity system. We analyze effects of collective dissipation in this vertical cavity system and find that our squeezing protocol can be more robust than the previous realization of OAT.

<supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </span> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> <div style="clear:both;margin-bottom:20px;"></div> <dl class="dl-horizontal small semi-colon-delimited-data"> <dt>Award ID(s):</dt> <dd> <span> <a target="_blank" rel="noopener noreferrer" href="https://par.nsf.gov/search/award_ids:1734006"> 1734006</a> </span> </dd> </dl> <dl class="dl-horizontal small"> <dt>PAR ID:</dt> <dd>10543085</dd> </dl> <dl class="dl-horizontal small"> <dt>Author(s) / Creator(s):</dt> <dd> <a target="_blank" rel="noopener noreferrer" href="https://par.nsf.gov/search/author:"Reilly, Jarrod T""><span class="author" itemprop="author">Reilly, Jarrod T</span></a><span class="sep">; </span><a target="_blank" rel="noopener noreferrer" href="https://par.nsf.gov/search/author:"Jäger, Simon B""><span class="author" itemprop="author">Jäger, Simon B</span></a><span class="sep">; </span><a target="_blank" rel="noopener noreferrer" href="https://par.nsf.gov/search/author:"Wilson, John Drew""><span class="author" itemprop="author">Wilson, John Drew</span></a><span class="sep">; </span><a target="_blank" rel="noopener noreferrer" href="https://par.nsf.gov/search/author:"Cooper, John""><span class="author" itemprop="author">Cooper, John</span></a><span class="sep">; </span><a target="_blank" rel="noopener noreferrer" href="https://par.nsf.gov/search/author:"Eggert, Sebastian""><span class="author" itemprop="author">Eggert, Sebastian</span></a><span class="sep">; </span><a target="_blank" rel="noopener noreferrer" href="https://par.nsf.gov/search/author:"Holland, Murray J""><span class="author" itemprop="author">Holland, Murray J</span></a></dd> </dl> <dl class="dl-horizontal small"> <dt>Publisher / Repository:</dt> <dd itemprop="publisher">American Physical Society</dd> </dl> <dl class="dl-horizontal small"> <dt>Date Published:</dt> <dd> <time itemprop="datePublished" datetime="2024-07-22">2024-07-22</time> </dd> </dl> <dl class="dl-horizontal small"> <dt>Journal Name:</dt> <dd>Physical Review Research</dd> </dl> <dl class="dl-horizontal small"> <dt>Volume:</dt> <dd>6</dd> </dl> <dl class="dl-horizontal small"> <dt>Issue:</dt> <dd>3</dd> </dl> <dl class="dl-horizontal small"> <dt>ISSN:</dt> <dd>2643-1564</dd> </dl> <dl class="dl-horizontal small"> <dt>Format(s):</dt> <dd>Medium: X</dd> </dl> <dl class="dl-horizontal small semi-colon-delimited-data"> <dt>Sponsoring Org:</dt> <dd itemprop="sourceOrganization"> <span>National Science Foundation</span> </dd> </dl> <div class="clearfix"></div> </div> </div> <div id="citation-addl" class="hidden-print"> <h5 id='mlt-header'>More Like this</h5> <ol class="item-list documents" id="citation-mlt" style="min-height: 80px;"> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10529385-deterministic-generation-qudit-photonic-graph-states-from-quantum-emitters" itemprop="url"> <span class='span-link' itemprop="name">Deterministic Generation of Qudit Photonic Graph States from Quantum Emitters</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PRXQuantum.5.020346" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PRXQuantum.5.020346  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Raissi, Zahra</span> <span class="sep">; </span><span class="author" itemprop="author">Barnes, Edwin</span> <span class="sep">; </span><span class="author" itemprop="author">Economou, Sophia E</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2024-05-01">May 2024</time> , PRX Quantum) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <p>We propose and analyze deterministic protocols to generate qudit photonic graph states from quantum emitters. We show that our approach can be applied to generate any qudit graph state and we exemplify it by constructing protocols to generate one- and two-dimensional qudit cluster states, absolutely maximally entangled states, and logical states of quantum error-correcting codes. Some of these protocols make use of time-delayed feedback, while others do not. The only additional resource requirement compared to the qubit case is the ability to control multilevel emitters. These results significantly broaden the range of multiphoton entangled states that can be produced deterministically from quantum emitters.</p> <sec><supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10554451-direct-observation-entangled-electronic-nuclear-wave-packets" itemprop="url"> <span class='span-link' itemprop="name">Direct observation of entangled electronic-nuclear wave packets</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevResearch.6.L022047" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevResearch.6.L022047  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Moğol, Gönenç</span> <span class="sep">; </span><span class="author" itemprop="author">Kaufman, Brian</span> <span class="sep">; </span><span class="author" itemprop="author">Weinacht, Thomas</span> <span class="sep">; </span><span class="author" itemprop="author">Cheng, Chuan</span> <span class="sep">; </span><span class="author" itemprop="author">Ben-Itzhak, Itzik</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2024-05-01">May 2024</time> , Physical Review Research) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <p>We present momentum resolved covariance measurements of entangled electronic-nuclear wave packets created and probed with octave spanning phaselocked ultrafast pulses. We launch vibrational wave packets on multiple electronic states via multiphoton absorption, and probe these wave packets via strong field double ionization using a second phaselocked pulse. Momentum resolved covariance mapping of the fragment ions highlights the nuclear motion, while measurements of the yield as a function of the relative phase between pump and probe pulses highlight the electronic coherence. The combined measurements allow us to directly visualize the entanglement between the electronic and nuclear degrees of freedom and follow the evolution of the complete wavefunction.</p> <sec><title/><supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10544883-observation-pairwise-level-degeneracies-quantum-regime-arrhenius-law-double-well-parametric-oscillator" itemprop="url"> <span class='span-link' itemprop="name">Observation of Pairwise Level Degeneracies and the Quantum Regime of the Arrhenius Law in a Double-Well Parametric Oscillator</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevX.14.031040" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevX.14.031040  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Frattini, Nicholas E</span> <span class="sep">; </span><span class="author" itemprop="author">Cortiñas, Rodrigo G</span> <span class="sep">; </span><span class="author" itemprop="author">Venkatraman, Jayameenakshi</span> <span class="sep">; </span><span class="author" itemprop="author">Xiao, Xu</span> <span class="sep">; </span><span class="author" itemprop="author">Su, Qile</span> <span class="sep">; </span><span class="author" itemprop="author">Lei, Chan U</span> <span class="sep">; </span><span class="author" itemprop="author">Chapman, Benjamin J</span> <span class="sep">; </span><span class="author" itemprop="author">Joshi, Vidul R</span> <span class="sep">; </span><span class="author" itemprop="author">Girvin, S M</span> <span class="sep">; </span><span class="author" itemprop="author">Schoelkopf, Robert J</span> <span class="sep">; </span><span class="author">et al</span></span> <span class="year">( <time itemprop="datePublished" datetime="2024-09-01">September 2024</time> , Physical Review X) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <p>By applying a microwave drive to a specially designed Josephson circuit, we have realized a double-well model system: a Kerr oscillator submitted to a squeezing force. We have observed, for the first time, the spectroscopic fingerprint of a quantum double-well Hamiltonian when its barrier height is increased: a pairwise level kissing (coalescence) corresponding to the exponential reduction of tunnel splitting in the excited states as they sink under the barrier. The discrete levels in the wells also manifest themselves in the activation time across the barrier which, instead of increasing smoothly as a function of the barrier height, presents steps each time a pair of excited states is captured by the wells. This experiment illustrates the quantum regime of Arrhenius’s law, whose observation is made possible here by the unprecedented combination of low dissipation, time-resolved state control, 98.5% quantum nondemolition single shot measurement fidelity, and complete microwave control over all Hamiltonian parameters in the quantum regime. Direct applications to quantum computation and simulation are discussed.</p> <sec><title/><supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10566777-quantum-many-body-scars-few-body-dipole-dipole-interactions" itemprop="url"> <span class='span-link' itemprop="name">Quantum many-body scars in few-body dipole-dipole interactions</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevResearch.6.043086" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevResearch.6.043086  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Spielman, Sarah E</span> <span class="sep">; </span><span class="author" itemprop="author">Handian, Alicia</span> <span class="sep">; </span><span class="author" itemprop="author">Inman, Nina P</span> <span class="sep">; </span><span class="author" itemprop="author">Carroll, Thomas J</span> <span class="sep">; </span><span class="author" itemprop="author">Noel, Michael W</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2024-11-01">November 2024</time> , Physical Review Research) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <p>We simulate the dynamics of Rydberg atoms resonantly exchanging energy via two-, three-, and four-body dipole-dipole interactions in a one-dimensional array. Using simplified models of a realistic experimental system, we study the initial-state survival probability, mean level spacing, spread of entanglement, and properties of the energy eigenstates. By exploring a range of disorders and interaction strengths, we find regions in parameter space where the three- and four-body dynamics either fail to thermalize or do so slowly. The interplay between the stronger hopping and weaker field-tuned interactions gives rise to quantum many-body scar states, which play a critical role in slowing the dynamics of the three- and four-body interactions.</p> <sec><supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10541374-boundary-measurement-tomography-bose-hubbard-model-general-graphs" itemprop="url"> <span class='span-link' itemprop="name">Boundary measurement tomography of the Bose Hubbard model on general graphs</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevResearch.6.033058" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevResearch.6.033058  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Saxena, Abhi</span> <span class="sep">; </span><span class="author" itemprop="author">Abbasgholinejad, Erfan</span> <span class="sep">; </span><span class="author" itemprop="author">Majumdar, Arka</span> <span class="sep">; </span><span class="author" itemprop="author">Trivedi, Rahul</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2024-07-01">July 2024</time> , Physical Review Research) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <p>Correlated quantum many-body phenomena in lattice models have been identified as a set of physically interesting problems that cannot be solved classically. Analog quantum simulators, in photonics and microwave superconducting circuits, have emerged as near-term platforms to address these problems. An important ingredient in practical quantum simulation experiments is the tomography of the implemented Hamiltonians—while this can easily be performed if we have individual measurement access to each qubit in the simulator, this could be challenging to implement in many hardware platforms. In this paper, we present a scheme for tomography of quantum simulators which can be described by a Bose-Hubbard Hamiltonian while having measurement access to only some sites on the boundary of the lattice. We present an algorithm that uses the experimentally routine transmission and two-photon correlation functions, measured at the boundary, to extract the Hamiltonian parameters at the standard quantum limit. Furthermore, by building on quantum enhanced spectroscopy protocols that, we show that with the additional ability to switch on and off the on-site repulsion in the simulator, we can sense the Hamiltonian parameters beyond the standard quantum limit.</p> <sec><title/><supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> </ol> <div class="push_top"></div> </div> </div> <div class="col-md-3"> <div id="citation-sidebar"> <ul class="nav nav-list" id="citation-fulltext-sidebar" style="font-size: 14px; font-family: Georgia Regular;"> <li style="font-weight: bold; margin-bottom: 5px; font-size:13px;">Free Publicly Accessible Full Text</li> <li class="small"> This content will become publicly available on July 22, 2025</li> <li class="divider"></li> <li style="font-weight: bold;font-size:13px;">Journal Article:</li> <li style="word-break:break-all" class="small"> <a href="https://doi.org/10.1103/PhysRevResearch.6.033090" target="_blank" rel="noopener noreferrer" title="Document DOI URL" class="external-link" data-ostiid="10543085" style="word-wrap: break-word;">https://doi.org/10.1103/PhysRevResearch.6.033090  <span class="fas fa-external-link-alt"></span></a></li> </ul> <div class="hidden-print"> <ul class="nav nav-list clearfix" id="sidebar-feedback" style="margin-top: 20px; margin-bottom: 20px; clear: both;"> <li style="position: relative;"> <div class="feedback-container"> <div style="font-family: Georgia Regular; font-size: 14px; color: #313b52; padding:20px;"> Have feedback or suggestions for a way to improve these results?<br/> <span style="text-decoration: underline;"> <script type="text/javascript" defer>/* <![CDATA[ */ user = "feedback"; site = "research.gov"; subject = "?subject=Comments or Suggestions"; content = "<span class='fa fa-envelope'></span><span class='span-link' style='padding-left:5px'>Let us know</span>"; id = ""; document.write('<a itemprop="'+ id +'" href="mailto:' + user + '@' + site + subject + '">' + (content != '' ? content : (user + '@' + site)) + '</a>'); /* ]]> */</script> <noscript></noscript>!</span> </div> </li> </ul> <ul class="nav nav-list" style="font-size: 14px; font-family: Arial Regular;"> <li class="nav-header header-format">Citation Formats</li> <li class="links-format"><a href="#cite-mla" data-toggle="modal">MLA</a> <div id="cite-mla" class="modal" tabindex="-1" role="dialog" aria-labelledby="cite-mla_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="cite-mla_label">Cite: MLA Format</strong> </div> <div class="modal-body" >Reilly, Jarrod T, Jäger, Simon B, Wilson, John Drew, Cooper, John, Eggert, Sebastian, and Holland, Murray J. <em>Speeding up squeezing with a periodically driven Dicke model</em>. Retrieved from https://par.nsf.gov/biblio/10543085. <em>Physical Review Research</em> 6.3 Web. doi:10.1103/PhysRevResearch.6.033090. </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="links-format"><a href="#cite-apa" data-toggle="modal">APA</a> <div id="cite-apa" class="modal" tabindex="-1" role="dialog" aria-labelledby="cite-apa_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="cite-apa_label">Cite: APA Format</strong> </div> <div class="modal-body">Reilly, Jarrod T, Jäger, Simon B, Wilson, John Drew, Cooper, John, Eggert, Sebastian, & Holland, Murray J. <em>Speeding up squeezing with a periodically driven Dicke model</em>. <em>Physical Review Research</em>, <em>6</em> (3). Retrieved from https://par.nsf.gov/biblio/10543085. <a href="https://doi.org/10.1103/PhysRevResearch.6.033090">https://doi.org/10.1103/PhysRevResearch.6.033090</a> </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="links-format"><a href="#cite-chi" data-toggle="modal">Chicago</a> <div id="cite-chi" class="modal" tabindex="-1" role="dialog" aria-labelledby="cite-chi_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="cite-chi_label">Cite: Chicago Format</strong> </div> <div class="modal-body">Reilly, Jarrod T, Jäger, Simon B, Wilson, John Drew, Cooper, John, Eggert, Sebastian, and Holland, Murray J. "Speeding up squeezing with a periodically driven Dicke model". <em>Physical Review Research</em> 6 (3). Country unknown/Code not available: American Physical Society. <a href="https://doi.org/10.1103/PhysRevResearch.6.033090">https://doi.org/10.1103/PhysRevResearch.6.033090.</a> <a href="https://par.nsf.gov/biblio/10543085">https://par.nsf.gov/biblio/10543085</a>. </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="links-format"><a href="#cite-bib" data-toggle="modal">BibTeX</a> <div id="cite-bib" class="modal" tabindex="-1" role="dialog" aria-labelledby="cite-bib_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="cite-bib_label">Cite: BibTeX Format</strong> </div> <div class="modal-body"> @article{osti_10543085,<br/> place = {Country unknown/Code not available}, title = {Speeding up squeezing with a periodically driven Dicke model}, url = {https://par.nsf.gov/biblio/10543085}, DOI = {10.1103/PhysRevResearch.6.033090}, abstractNote = {We present a simple and effective method to create highly entangled spin states on a faster timescale than that of the commonly employed one-axis twisting (OAT) model. We demonstrate that by periodically driving the Dicke Hamiltonian at a resonance frequency, the system effectively becomes a two-axis countertwisting Hamiltonian, which is known to quickly create Heisenberg limit scaled entangled states. For these states we show that simple quadrature measurements can saturate the ultimate precision limit for parameter estimation determined by the quantum Cramér-Rao bound. An example experimental realization of the periodically driven scheme is discussed with the potential to quickly generate momentum entanglement in a recently described experimental vertical cavity system. We analyze effects of collective dissipation in this vertical cavity system and find that our squeezing protocol can be more robust than the previous realization of OAT. Published by the American Physical Society2024}, journal = {Physical Review Research}, volume = {6}, number = {3}, publisher = {American Physical Society}, author = {Reilly, Jarrod T and Jäger, Simon B and Wilson, John Drew and Cooper, John and Eggert, Sebastian and Holland, Murray J}, }</div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="divider"></li> </ul> <ul class="nav nav-list" style="font-size: 14px; font-family: Arial Regular;"> <li class="nav-header header-format">Export Metadata</li> <li class="links-format"><a href="https://par.nsf.gov/endnote?osti_id=10543085">EndNote</a></li> <li class="links-format"><a href="https://par.nsf.gov/export/format:excel/osti-id:10543085">Excel</a></li> <li class="links-format"><a href="https://par.nsf.gov/export/format:csv/osti-id:10543085">CSV</a></li> <li class="links-format"><a href="https://par.nsf.gov/export/format:xml/osti-id:10543085">XML</a></li> <li class="divider"></li> </ul> <ul class="nav nav-list" style="font-size: 14px; font-family: Arial Regular;"> <li class="nav-header header-format">Save / Share this Record</li> <li class="links-format"><a href="#shareemail" data-toggle="modal">Send to Email</a> <div id="shareemail" class="modal" tabindex="-1" role="dialog" aria-labelledby="shareemail_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="shareemail_label" style="margin: 0px;">Send to Email</strong> </div> <form id="sendtoemail-form" style="margin-bottom: 0px;"> <div class="modal-body" id="shareemail_body"> <div class="modal-body-default"> <label for="sendtoemail-email">Email address:</label><br/> <input type="text" name="email" value="" class="col-md-5 input-sm form-control" id="sendtoemail-email"/> <input type="hidden" name="osti_id" id="sendtoemail-osti_id" value="10543085" /> <input type="hidden" name="subject" id="sendtoemail-subject" /> <div class="clearfix"></div> <div class="hide"><label for="sendtoemail-body">Content:</label></div> <textarea name="body" id="sendtoemail-body" style="display:none;"></textarea> </div> <div class="modal-body-submitted hide"> </div> </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="submit" id="shareemail_submit"> <span class="fa fa-envelope"></span> Send </button> </div> </form> </div> </div> </div> </li> </ul> </div> <div class="push_top"></div> </div> </div> </div> </div> </div> </div> <input type="hidden" id="host_url" value="https://par.nsf.gov"/> <input type="hidden" id="base_url" value="/"/> <input type="hidden" id="param_osti_id" value="10543085"/> <span id="highlight-data"> </span> </div> </div> <footer class="row" id="footer-wrapper"> <div class="footer-content"> <div id="footerOSTI" class=" hidden-print"> <ul> <li><a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/">Website Policies</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/about/performance/">Budget and Performance</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/oig/">Inspector General</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/privacy.jsp">Privacy</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/foia.jsp">FOIA</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/od/odi/notice.jsp">No FEAR Act</a> | <a target="_blank" rel="noreferrer" href="http://usa.gov">USA.gov</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/access.jsp">Accessibility</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/nsf_plain_language.jsp">Plain Language</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/help/contact.jsp">Contact</a> | <a target="_blank" rel="noreferrer" href="https://nsf.gov/help/">Help</a> </li> </ul> The National Science Foundation, 2415 Eisenhower Avenue, Alexandria, Virginia 22314, USA Tel: (703) 292-5111, FIRS: (800) 877-8339 | TDD: (800) 281-8749 </div> </div> </footer> </div> <div id="authorselect" class="modal" tabindex="-1" role="dialog" aria-labelledby="authorselect_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <div id="authorselect_label">Author Select</div> </div> <form id="authorselect-form" style="margin-bottom: 0px;"> <input type="hidden" name="pg" id="authorselect-pg" value="1" /> <div class="modal-body" id="authorselect_body"> <div class="row"> <div class="col-md-4"> <label for="authorselect-lname">Last Name:</label><br /> <input type="text" name="lname" class="input-sm form-control" id="authorselect-lname" placeholder="Last name" /><br /> </div> <div class="col-md-4"> <label for="authorselect-fname">First Name:</label><br /> <input type="text" name="fname" class="input-sm form-control" id="authorselect-fname" placeholder="First name" /> </div> <div class="col-md-2">  <br /> <a href="#" onclick="$('#authorselect-form').submit(); return false;" class="btn btn-sm btn-default"><span class="fa fa-search"></span><span class="sr-only">Search</span></a> </div> </div> <div class="push_top"></div> <div class="row"> <div class="col-md-12"> <ul class="nav nav-tabs"> <li class="active"><a href="#authorselect-tab-res" id="authorselect-tab-res-btn" data-toggle="tab">Search Results</a></li> <li><a href="#authorselect-tab-sel" id="authorselect-tab-sel-btn" data-toggle="tab">Selected Authors</a></li> </ul> <div class="tab-content"> <div class="tab-pane active" id="authorselect-tab-res" style="max-height: 450px;"> <div class="padding text-muted" id="authorselect-tab-res-content">Type in a name, or the first few letters of a name, in one or both of appropriate search boxes above and select the search button. An attempt will be made to match authors that most closely relate to the text you typed.</div> </div> <div class="tab-pane" id="authorselect-tab-sel" style="max-height: 450px;"> <div class="padding text-muted" id="authorselect-tab-sel-content">No authors are currently selected. Choosing "Select These Authors" will enter a blank value for author search in the parent form.</div> </div> </div> </div> </div> </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="authorselect_review" onclick="$('#authorselect-tab-sel-btn').click();" style="display: none;">Review Selections</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="authorselect_submit" onclick="authorSelectAddToForm(); $('#authorselect').modal('hide');">Add Selections</button> </div> </form> </div> </div> </div> <div id="editorselect" class="modal" tabindex="-1" role="dialog" aria-labelledby="editorselect_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <div id="editorselect_label">Editor Select</div> </div> <form id="editorselect-form" style="margin-bottom: 0px;"> <input type="hidden" name="pg" id="editorselect-pg" value="1" /> <div class="modal-body" id="editorselect_body"> <div class="row"> <div class="col-md-4"> <label for="editorselect-lname">Last Name:</label><br /> <input type="text" name="lname" class="input-sm form-control" id="editorselect-lname" placeholder="Last name" /><br /> </div> <div class="col-md-4"> <label for="editorselect-fname">First Name:</label><br /> <input type="text" name="fname" class="input-sm form-control" id="editorselect-fname" placeholder="First name" /> </div> <div class="col-md-2">  <br /> <a href="#" onclick="$('#editorselect-form').submit(); return false;" class="btn btn-sm btn-default"><span class="fa fa-search"></span><span class="sr-only">Search</span></a> </div> </div> <div class="push_top"></div> <div class="row"> <div class="col-md-12"> <ul class="nav nav-tabs"> <li class="active"><a href="#editorselect-tab-res" id="editorselect-tab-res-btn" data-toggle="tab">Search Results</a></li> <li><a href="#editorselect-tab-sel" id="editorselect-tab-sel-btn" data-toggle="tab">Selected Editors</a></li> </ul> <div class="tab-content"> <div class="tab-pane active" id="editorselect-tab-res" style="max-height: 450px;"> <div class="padding text-muted" id="editorselect-tab-res-content">Type in a name, or the first few letters of a name, in one or both of appropriate search boxes above and select the search button. An attempt will be made to match editors that most closely relate to the text you typed.</div> </div> <div class="tab-pane" id="editorselect-tab-sel" style="max-height: 450px;"> <div class="padding text-muted" id="editorselect-tab-sel-content">No editors are currently selected. Choosing "Select These Editors" will enter a blank value for editor search in the parent form.</div> </div> </div> </div> </div> </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="editorselect_review" onclick="$('#editorselect-tab-sel-btn').click();" style="display: none;">Review Selections</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="editorselect_submit" onclick="editorSelectAddToForm();$('#editorselect').modal('hide');">Add Selections</button> </div> </form> </div> </div> </div> <div class="push_top"></div> <!-- External Link Modal --> <div class="modal fade" id="external-link-modal" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close nsf-close" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> <h4 class="modal-title"><strong>Warning: Leaving National Science Foundation Website</strong></h4> </div> <div class="modal-body"> <div> <img src="https://par.nsf.gov/img/nsf/nsf_logo.png" width="292" height="53" alt="National Science Foundation Logo" border="0" /> </div> <br> <span>You are now leaving the National Science Foundation website to go to a non-government website.</span> <br> <br> Website: <a id="external-link-url" rel='noopener noreferrer' target='_blank'></a> <br> <br> <span> NSF takes no responsibility for and exercises no control over the views expressed or the accuracy of the information contained on this site. Also be aware that NSF's privacy policy does not apply to this site. </span> <br> <br> </div> <div class="modal-footer"> <div class="pull-right"> <button id="external-link-continue" type="button" data-extlink="" class="btn btn-primary" data-dismiss="modal"><u>Continue to Site</u></button> <button type="button" class="btn btn-default" data-dismiss="modal"><u>Cancel</u></button> </div> </div> </div> </div> </div> <!-- /content --> <input type='hidden' id='webtrend-id' value='dcsngbilzcxafpc7vw2qgbbij_3j2v'/> <input type='hidden' id='js-context-path' value='https://par.nsf.gov/'/> <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/latest.js?config=TeX-MML-AM_CHTML" defer></script> <script type="text/x-mathjax-config" defer> MathJax.Hub.Config({ tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]} }); </script> <noscript></noscript> <script src="https://par.nsf.gov/js/context.js" type="text/javascript" defer></script> <noscript>You must have javascript enabled</noscript> <script src="https://par.nsf.gov/js/libraries/jquery.min.js" type="text/javascript" defer></script> <noscript></noscript> <script src="https://par.nsf.gov/chosen/chosen.jquery.min.js" type="text/javascript" defer></script> <noscript></noscript> <script src="https://par.nsf.gov/js/nsf_pages.extras.min.js" type="text/javascript" defer></script> <noscript></noscript> <script src="https://par.nsf.gov/js/nsf_pages.min.js" type="text/javascript" defer></script> <noscript></noscript> <!--$$$$$$$$$ the following blocks are for WebTrends $$$$$$$$--> <!-- START OF SmartSource Data Collector TAG --> <!-- Copyright (c) 1996-2009 WebTrends Inc. All rights reserved. --> <!-- Version: 8.6.2 --> <!-- Tag Builder Version: 3.0 --> <!-- Created: 5/7/2009 8:32:37 PM --> <script src="https://par.nsf.gov/js/webtrends.min.js" type="text/javascript" defer></script> <noscript></noscript> <!-- ----------------------------------------------------------------------------------- --> <!-- Warning: The two script blocks below must remain inline. Moving them to an external --> <!-- JavaScript include file can cause serious problems with cross-domain tracking. --> <!-- ----------------------------------------------------------------------------------- --> <script src="https://par.nsf.gov/js/webtrend-script.min.js" type="text/javascript" defer></script> <noscript> <div><img alt="" id="DCSIMG" width="1" height="1" src="http://wt.research.gov/dcsngbilzcxafpc7vw2qgbbij_3j2v/njs.gif?dcsuri=/nojavascript&WT.js=No&DCS.dcscfg=1&WT.tv=8.6.2"/></div> </noscript> <script src="https://par.nsf.gov/js/webtrendsactions.min.js" type="text/javascript" defer></script> <noscript></noscript> <!-- $$$$$$$$ End WebTrends $$$$$ --> <!-- /scripts --> </body> <!-- NSF PAGES v.@project.version@ --> </html>