Many-body multivaluedness of particle-current variance in closed and open cold-atom systems

Metcalf, Mekena; Lai, Chen -Yen; Di Ventra, Massimiliano; Chien, Chih -Chun

doi:10.1103/PhysRevA.98.053601

Title: Many-body multivaluedness of particle-current variance in closed and open cold-atom systems

Journal Article · 31 October 2018 · Physical Review A

DOI: https://doi.org/10.1103/PhysRevA.98.053601 · OSTI ID:1482946

Metcalf, Mekena ^[1];

^[2]; Di Ventra, Massimiliano ^[3]; Chien, Chih -Chun ^[1]

Univ. of California, Merced, CA (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of California, San Diego, La Jolla, CA (United States)

The quantum variance of an observable is a fundamental quantity in quantum mechanics and provides additional information other than the average itself. By examining the relation between the particle-current variance (δJ)² and the average current J in both closed and open interacting fermionic systems, we show the emergence of a multivalued parametric curve between δJ and J due to interactions. As a closed system we consider the persistent current in a benzenelike lattice enclosing an effective magnetic flux and solve it by exact diagonalization. For the open system, the steady-state current flowing through a few lattice sites coupled to two particle reservoirs is investigated using a Lindblad equation. In both cases, interactions open a loop and change the topology of the corresponding δJ–J curve, showing that this effect is model independent. Here, we finally discuss how the predicted phenomenon can be observed in ultracold atoms, thus offering an alternative way of probing the dynamics of many-body systems.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: 89233218CNA000001; AC02-05CH11231

OSTI ID:: 1482946

Report Number(s):: LA-UR--18-23857

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 5 Vol. 98; ISSN PLRAAN; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (43)

Counting statistics and super-Poissonian noise in a quantum dot Gustavsson, S.; Leturcq, R.; Simovic, B. arXiv https://doi.org/10.48550/arxiv.cond-mat/0605365	text	January 2006
Many-Particle Physics Mahan, Gerald D. Physics of Solids and Liquids (PSLI) https://doi.org/10.1007/978-1-4757-5714-9	book	January 2000
Zur Theorie des Diamagnetismus von Leitungselektronen Peierls, R. Zeitschrift f�r Physik, Vol. 80, Issue 11-12 https://doi.org/10.1007/BF01342591	journal	November 1933
Josephson behavior in small normal one-dimensional rings Büttiker, M.; Imry, Y.; Landauer, R. Physics Letters A, Vol. 96, Issue 7 https://doi.org/10.1016/0375-9601(83)90011-7	journal	July 1983
The one-dimensional Hubbard model: a reminiscence Lieb, Elliott H.; Wu, F. Y. Physica A: Statistical Mechanics and its Applications, Vol. 321, Issue 1-2 https://doi.org/10.1016/S0378-4371(02)01785-5	journal	April 2003
Organization of the Hilbert space for exact diagonalization of Hubbard model Sharma, Medha; Ahsan, M. A. H. Computer Physics Communications, Vol. 193 https://doi.org/10.1016/j.cpc.2015.03.014	journal	August 2015
Quantum rings for beginners: energy spectra and persistent currents Viefers, S.; Koskinen, P.; Singha Deo, P. Physica E: Low-dimensional Systems and Nanostructures, Vol. 21, Issue 1 https://doi.org/10.1016/j.physe.2003.08.076	journal	February 2004
Graphene nano-ribbon electronics Chen, Zhihong; Lin, Yu-Ming; Rooks, Michael J. Physica E: Low-dimensional Systems and Nanostructures, Vol. 40, Issue 2, p. 228-232 https://doi.org/10.1016/j.physe.2007.06.020	journal	December 2007
Quantum Transport Nazarov, Yuli V.; Blanter, Yaroslav M. https://doi.org/10.1017/CBO9780511626906	book	January 2009
Electrical Transport in Nanoscale Systems Di Ventra, Massimiliano https://doi.org/10.1017/CBO9780511755606	book	January 2008
Condensed Matter Field Theory Altland, Alexander; Simons, Ben D. https://doi.org/10.1017/CBO9780511789984	book	August 2010
Few-Layer Black Phosphorus Field-Effect Transistors with Reduced Current Fluctuation Na, Junhong; Lee, Young Tack; Lim, Jung Ah ACS Nano, Vol. 8, Issue 11 https://doi.org/10.1021/nn5052376	journal	November 2014
Synthetic magnetic fields for ultracold neutral atoms Lin, Y. -J.; Compton, R. L.; Jiménez-García, K. Nature, Vol. 462, Issue 7273 https://doi.org/10.1038/nature08609	journal	December 2009
Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms Schneider, Ulrich; Hackermüller, Lucia; Ronzheimer, Jens Philipp Nature Physics, Vol. 8, Issue 3 https://doi.org/10.1038/nphys2205	journal	January 2012
Quantum transport in ultracold atoms Chien, Chih-Chun; Peotta, Sebastiano; Di Ventra, Massimiliano Nature Physics, Vol. 11, Issue 12 https://doi.org/10.1038/nphys3531	journal	December 2015
Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport Gruss, Daniel; Velizhanin, Kirill A.; Zwolak, Michael Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep24514	journal	April 2016
Challenges and constraints of dynamically emerged source and sink in atomtronic circuits: From closed-system to open-system approaches Lai, Chen-Yen; Chien, Chih-Chun Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep37256	journal	November 2016
An Introduction to Thermal Physics Schroeder, Daniel V.; Gould, Harvey Physics Today, Vol. 53, Issue 8 https://doi.org/10.1063/1.2405696	journal	August 2000
Exact Diagonalization Methods for Quantum Systems Lin, H. Q.; Gubernatis, J. E.; Gould, Harvey Computers in Physics, Vol. 7, Issue 4 https://doi.org/10.1063/1.4823192	journal	January 1993
Light-induced gauge fields for ultracold atoms Goldman, N.; Juzeliūnas, G.; Öhberg, P. Reports on Progress in Physics, Vol. 77, Issue 12 https://doi.org/10.1088/0034-4885/77/12/126401	journal	November 2014
The origin of degeneracies and crossings in the 1d Hubbard model Yuzbashyan, Emil A.; Altshuler, Boris L.; Shastry, B. Sriram Journal of Physics A: Mathematical and General, Vol. 35, Issue 34 https://doi.org/10.1088/0305-4470/35/34/319	journal	August 2002
Two-terminal transport measurements with cold atoms Krinner, Sebastian; Esslinger, Tilman; Brantut, Jean-Philippe Journal of Physics: Condensed Matter, Vol. 29, Issue 34 https://doi.org/10.1088/1361-648X/aa74a1	journal	July 2017
Experimental demonstration of painting arbitrary and dynamic potentials for Bose–Einstein condensates Henderson, K.; Ryu, C.; MacCormick, C. New Journal of Physics, Vol. 11, Issue 4 https://doi.org/10.1088/1367-2630/11/4/043030	journal	April 2009
Continuous measurement of an atomic current Laflamme, C.; Yang, D.; Zoller, P. Physical Review A, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevA.95.043843	journal	April 2017
Quantification of the memory effect of steady-state currents from interaction-induced transport in quantum systems Lai, Chen-Yen; Chien, Chih-Chun Physical Review A, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevA.96.033628	journal	September 2017
Persistent current of a Hubbard ring threaded with a magnetic flux Yu, Naichang; Fowler, Michael Physical Review B, Vol. 45, Issue 20 https://doi.org/10.1103/PhysRevB.45.11795	journal	May 1992
Stochastic memory: Memory enhancement due to noise Stotland, Alexander; Di Ventra, Massimiliano Physical Review E, Vol. 85, Issue 1 https://doi.org/10.1103/PhysRevE.85.011116	journal	January 2012
Peierls Substitution in an Engineered Lattice Potential Jiménez-García, K.; LeBlanc, L. J.; Williams, R. A. Physical Review Letters, Vol. 108, Issue 22 https://doi.org/10.1103/PhysRevLett.108.225303	journal	May 2012
Observation of Quantum Periodicity in the Transition Temperature of a Superconducting Cylinder Little, W. A.; Parks, R. D. Physical Review Letters, Vol. 9, Issue 1 https://doi.org/10.1103/PhysRevLett.9.9	journal	July 1962
Counting Statistics of Single Electron Transport in a Quantum Dot Gustavsson, S.; Leturcq, R.; Simovič, B. Physical Review Letters, Vol. 96, Issue 7 https://doi.org/10.1103/PhysRevLett.96.076605	journal	February 2006
Observations of Density Fluctuations in an Elongated Bose Gas: Ideal Gas and Quasicondensate Regimes Esteve, J.; Trebbia, J. -B.; Schumm, T. Physical Review Letters, Vol. 96, Issue 13 https://doi.org/10.1103/PhysRevLett.96.130403	journal	April 2006
Band and Correlated Insulators of Cold Fermions in a Mesoscopic Lattice Lebrat, Martin; Grišins, Pjotrs; Husmann, Dominik Physical Review X, Vol. 8, Issue 1 https://doi.org/10.1103/PhysRevX.8.011053	journal	March 2018
Introduction to quantum noise, measurement, and amplification Clerk, A. A.; Devoret, M. H.; Girvin, S. M. Reviews of Modern Physics, Vol. 82, Issue 2 https://doi.org/10.1103/RevModPhys.82.1155	journal	April 2010
Violation of the Noncrossing Rule: the Hubbard Hamiltonian for Benzene* Heilmann, Ole J.; Lieb, Elliott H. Annals of the New York Academy of Sciences, Vol. 172, Issue 15 https://doi.org/10.1111/j.1749-6632.1971.tb34956.x	journal	October 1971
Atom-by-atom assembly of defect-free one-dimensional cold atom arrays Endres, Manuel; Bernien, Hannes; Keesling, Alexander Science, Vol. 354, Issue 6315 https://doi.org/10.1126/science.aah3752	journal	November 2016
An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays Barredo, Daniel; de Léséleuc, Sylvain; Lienhard, Vincent Science, Vol. 354, Issue 6315 https://doi.org/10.1126/science.aah3778	journal	November 2016
Bringing order to neutral atom arrays Regal, Cindy Science, Vol. 354, Issue 6315 https://doi.org/10.1126/science.aaj2145	journal	November 2016
Fundamentals and New Frontiers of Bose-Einstein Condensation Ueda, Masahito https://doi.org/10.1142/7216	book	January 2010
Quantum Dissipative Systems Weiss, Ulrich https://doi.org/10.1142/8334	book	March 2012
Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction Landauer, R. IBM Journal of Research and Development, Vol. 1, Issue 3 https://doi.org/10.1147/rd.13.0223	journal	July 1957
Tunable current circulation in triangular quantum-dot metastructures Lai, Chen-Yen; Di Ventra, Massimiliano; Scheibner, Michael EPL (Europhysics Letters), Vol. 123, Issue 4 https://doi.org/10.1209/0295-5075/123/47002	journal	August 2018
Condensed Matter in a Nutshell Mahan, Gerald D. https://doi.org/10.1515/9781400837021	book	December 2011
Geometrical and Graphical Representations Analysis of Lissajous Figures in Rotor Dynamic System Al-Khazali, Hisham A. H. IOSR Journal of Engineering, Vol. 02, Issue 05 https://doi.org/10.9790/3021-0205971978	journal	May 2012

Cited By (1)

Study of counterintuitive transport properties in the Aubry-André-Harper model via entanglement entropy and persistent current Roy, Nilanjan; Sharma, Auditya Physical Review B, Vol. 100, Issue 19 https://doi.org/10.1103/physrevb.100.195143	journal	November 2019

Similar Records

Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems

Journal Article · 2022 · Physical Review Letters · OSTI ID:1980320

Zhang, Yikang; Barthel, Thomas

Creating exotic condensates via quantum-phase-revival dynamics in engineered lattice potentials

Journal Article · 2011 · Physical Review. A · OSTI ID:22068535

Buchhold, Michael; Bissbort, Ulf; Hofstetter, Walter; +1 more

Boundary driven open quantum many-body systems

Journal Article · 2014 · AIP Conference Proceedings · OSTI ID:22264081

Prosen, Tomaž

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Material Science

Title: Many-body multivaluedness of particle-current variance in closed and open cold-atom systems

Citation Formats

References (43)

Cited By (1)

Similar Records

Related Subjects