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Imai S, Tóth G, Gühne O. Collective Randomized Measurements in Quantum Information Processing. PHYSICAL REVIEW LETTERS 2024; 133:060203. [PMID: 39178439 DOI: 10.1103/physrevlett.133.060203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Revised: 05/08/2024] [Accepted: 07/09/2024] [Indexed: 08/25/2024]
Abstract
The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce collective randomized measurements as a tool in quantum information processing. Our idea is to perform measurements of collective angular momentum on a quantum system and actively rotate the directions using simultaneous multilateral unitaries. Based on the moments of the resulting probability distribution, we propose systematic approaches to characterize quantum entanglement in a collective-reference-frame-independent manner. First, we show that existing spin-squeezing inequalities can be accessible in this scenario. Next, we present an entanglement criterion based on three-body correlations, going beyond spin-squeezing inequalities with two-body correlations. Finally, we apply our method to characterize entanglement between spatially separated two ensembles.
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Affiliation(s)
- Satoya Imai
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
- QSTAR, INO-CNR, and LENS, Largo Enrico Fermi, 2, 50125 Firenze, Italy
| | - Géza Tóth
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spain
- EHU Quantum Center, University of the Basque Country UPV/EHU, Barrio Sarriena s/n, ES-48940 Leioa, Biscay, Spain
- Donostia International Physics Center (DIPC), P.O. Box 1072, E-20080 San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, E-48009 Bilbao, Spain
- HUN-REN Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary
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2
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Fadel M, Usui A, Huber M, Friis N, Vitagliano G. Entanglement Quantification in Atomic Ensembles. PHYSICAL REVIEW LETTERS 2021; 127:010401. [PMID: 34270307 DOI: 10.1103/physrevlett.127.010401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Accepted: 06/02/2021] [Indexed: 06/13/2023]
Abstract
Entanglement measures quantify nonclassical correlations present in a quantum system, but can be extremely difficult to calculate, even more so, when information on its state is limited. Here, we consider broad families of entanglement criteria that are based on variances of arbitrary operators and analytically derive the lower bounds these criteria provide for two relevant entanglement measures: the best separable approximation and the generalized robustness. This yields a practical method for quantifying entanglement in realistic experimental situations, in particular, when only few measurements of simple observables are available. As a concrete application of this method, we quantify bipartite and multipartite entanglement in spin-squeezed Bose-Einstein condensates of ∼500 atoms, by lower bounding the best separable approximation and the generalized robustness only from measurements of first and second moments of the collective spin operator.
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Affiliation(s)
- Matteo Fadel
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Ayaka Usui
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, 904-0495 Okinawa, Japan
| | - Marcus Huber
- Atominstitut, Technische Universität Wien, 1020 Vienna, Austria
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Nicolai Friis
- Atominstitut, Technische Universität Wien, 1020 Vienna, Austria
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Giuseppe Vitagliano
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
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3
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Leggio B, Napoli A, Nakazato H, Messina A. Bounds on Mixed State Entanglement. ENTROPY 2020; 22:e22010062. [PMID: 33285837 PMCID: PMC7516494 DOI: 10.3390/e22010062] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/28/2019] [Revised: 12/19/2019] [Accepted: 12/30/2019] [Indexed: 11/17/2022]
Abstract
In the general framework of d1×d2 mixed states, we derive an explicit bound for bipartite negative partial transpose (NPT) entanglement based on the mixedness characterization of the physical system. The derived result is very general, being based only on the assumption of finite dimensionality. In addition, it turns out to be of experimental interest since some purity-measuring protocols are known. Exploiting the bound in the particular case of thermal entanglement, a way to connect thermodynamic features to the monogamy of quantum correlations is suggested, and some recent results on the subject are given a physically clear explanation.
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Affiliation(s)
- Bruno Leggio
- Laboratoire Reproduction et Développement des Plantes, Université de Lyon, ENS de Lyon, UCB Lyon 1, CNRS, INRA, Inria, 69342 Lyon, France;
| | - Anna Napoli
- Dipartimento di Fisica e Chimica-Emilio Segrè, Università degli Studi di Palermo, Via Archirafi 36, I-90123 Palermo, Italy
- I.N.F.N. Sezione di Catania, Via Santa Sofia 64, I-95123 Catania, Italy;
- Correspondence:
| | | | - Antonino Messina
- I.N.F.N. Sezione di Catania, Via Santa Sofia 64, I-95123 Catania, Italy;
- Dipartimento di Matematica ed Informatica, Università degli Studi di Palermo, Via Archirafi, 34, I-90123 Palermo, Italy
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4
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Barghathi H, Herdman CM, Del Maestro A. Rényi Generalization of the Accessible Entanglement Entropy. PHYSICAL REVIEW LETTERS 2018; 121:150501. [PMID: 30362791 DOI: 10.1103/physrevlett.121.150501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2018] [Indexed: 06/08/2023]
Abstract
Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.097902] introduced an operational measure of the von Neumann entanglement entropy. Motivated by advances in measuring Rényi entropies in quantum many-body systems subject to conservation laws, we derive a generalization of the operationally accessible entanglement that is both computationally and experimentally measurable. Using the Widom theorem, we investigate its scaling with the size of a spatial subregion for free fermions and find a logarithmically violated area law scaling, similar to the spatial entanglement entropy, with at most a double-log leading-order correction. A modification of the correlation matrix method confirms our findings in systems of up to 10^{5} particles.
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Affiliation(s)
- Hatem Barghathi
- Department of Physics, University of Vermont, Burlington, Vermont 05405, USA
| | - C M Herdman
- Department of Physics, Middlebury College, Middlebury, Vermont 05753, USA
| | - Adrian Del Maestro
- Department of Physics, University of Vermont, Burlington, Vermont 05405, USA
- Institut für Theoretische Physik, Universität Leipzig, D-04103 Leipzig, Germany
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5
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Pezzè L, Gabbrielli M, Lepori L, Smerzi A. Multipartite Entanglement in Topological Quantum Phases. PHYSICAL REVIEW LETTERS 2017; 119:250401. [PMID: 29303346 DOI: 10.1103/physrevlett.119.250401] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2017] [Indexed: 06/07/2023]
Abstract
We witness multipartite entanglement in the ground state of the Kitaev chain-a benchmark model of a one dimensional topological superconductor-also with variable-range pairing, using the quantum Fisher information. Phases having a finite winding number, for both short- and long-range pairing, are characterized by a power-law diverging finite-size scaling of multipartite entanglement. Moreover, the occurring quantum phase transitions are sharply marked by the divergence of the derivative of the quantum Fisher information, even in the absence of a closing energy gap.
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Affiliation(s)
- Luca Pezzè
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Marco Gabbrielli
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
- Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Luca Lepori
- Dipartimento di Scienze Fisiche e Chimiche, Università dell'Aquila, via Vetoio 42, I-67010 Coppito-L'Aquila, Italy
- INFN, Laboratori Nazionali del Gran Sasso, Via G. Acitelli 22, I-67100 Assergi (AQ), Italy
| | - Augusto Smerzi
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
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6
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Brange F, Malkoc O, Samuelsson P. Minimal Entanglement Witness from Electrical Current Correlations. PHYSICAL REVIEW LETTERS 2017; 118:036804. [PMID: 28157375 DOI: 10.1103/physrevlett.118.036804] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2016] [Indexed: 06/06/2023]
Abstract
Despite great efforts, an unambiguous demonstration of entanglement of mobile electrons in solid state conductors is still lacking. Investigating theoretically a generic entangler-detector setup, we here show that a witness of entanglement between two flying electron qubits can be constructed from only two current cross correlation measurements, for any nonzero detector efficiencies and noncollinear polarization vectors. We find that all entangled pure states, but not all mixed ones, can be detected with only two measurements, except the maximally entangled states, which require three. Moreover, detector settings for optimal entanglement witnessing are presented.
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Affiliation(s)
- F Brange
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - O Malkoc
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - P Samuelsson
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
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Sanz M, Egusquiza IL, Di Candia R, Saberi H, Lamata L, Solano E. Entanglement classification with matrix product states. Sci Rep 2016; 6:30188. [PMID: 27457273 PMCID: PMC4960485 DOI: 10.1038/srep30188] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2016] [Accepted: 06/30/2016] [Indexed: 11/23/2022] Open
Abstract
We propose an entanglement classification for symmetric quantum states based on their diagonal matrix-product-state (MPS) representation. The proposed classification, which preserves the stochastic local operation assisted with classical communication (SLOCC) criterion, relates entanglement families to the interaction length of Hamiltonians. In this manner, we establish a connection between entanglement classification and condensed matter models from a quantum information perspective. Moreover, we introduce a scalable nesting property for the proposed entanglement classification, in which the families for N parties carry over to the N + 1 case. Finally, using techniques from algebraic geometry, we prove that the minimal nontrivial interaction length n for any symmetric state is bounded by .
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Affiliation(s)
- M Sanz
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - I L Egusquiza
- Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - R Di Candia
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - H Saberi
- Department of Optics, Faculty of Science, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic.,Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), University of Paderborn, Warburger Straβe 100, 33098 Paderborn, Germany
| | - L Lamata
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - E Solano
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain.,IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
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8
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Marty O, Cramer M, Plenio MB. Practical Entanglement Estimation for Spin-System Quantum Simulators. PHYSICAL REVIEW LETTERS 2016; 116:105301. [PMID: 27015489 DOI: 10.1103/physrevlett.116.105301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Indexed: 06/05/2023]
Abstract
We present practical methods to measure entanglement for quantum simulators that can be realized with trapped ions, cold atoms, and superconducting qubits. Focusing on long- and short-range Ising-type Hamiltonians, we introduce schemes that are applicable under realistic experimental conditions including mixedness due to, e.g., noise or temperature. In particular, we identify a single observable whose expectation value serves as a lower bound to entanglement and that may be obtained by a simple quantum circuit. As such circuits are not (yet) available for every platform, we investigate the performance of routinely measured observables as quantitative entanglement witnesses. Possible applications include experimental studies of entanglement scaling in critical systems and the reliable benchmarking of quantum simulators.
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Affiliation(s)
- O Marty
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
| | - M Cramer
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
| | - M B Plenio
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
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Fukuhara T, Hild S, Zeiher J, Schauß P, Bloch I, Endres M, Gross C. Spatially Resolved Detection of a Spin-Entanglement Wave in a Bose-Hubbard Chain. PHYSICAL REVIEW LETTERS 2015; 115:035302. [PMID: 26230800 DOI: 10.1103/physrevlett.115.035302] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2015] [Indexed: 06/04/2023]
Abstract
Entanglement is an essential property of quantum many-body systems. However, its local detection is challenging and was so far limited to spin degrees of freedom in ion chains. Here we measure entanglement between the spins of atoms located on two lattice sites in a one-dimensional Bose-Hubbard chain which features both local spin- and particle-number fluctuations. Starting with an initially localized spin impurity, we observe an outwards propagating entanglement wave and show quantitatively how entanglement in the spin sector rapidly decreases with increasing particle-number fluctuations in the chain.
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Affiliation(s)
- Takeshi Fukuhara
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - Sebastian Hild
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - Johannes Zeiher
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - Peter Schauß
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - Immanuel Bloch
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Ludwig-Maximilians-Universität, Fakultät für Physik, 80799 München, Germany
| | - Manuel Endres
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Christian Gross
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
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Misra A, Biswas A, Pati AK, Sen De A, Sen U. Quantum correlation with sandwiched relative entropies: Advantageous as order parameter in quantum phase transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052125. [PMID: 26066137 DOI: 10.1103/physreve.91.052125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2014] [Indexed: 06/04/2023]
Abstract
Quantum discord is a measure of quantum correlations beyond the entanglement-separability paradigm. It is conceptualized by using the von Neumann entropy as a measure of disorder. We introduce a class of quantum correlation measures as differences between total and classical correlations, in a shared quantum state, in terms of the sandwiched relative Rényi and Tsallis entropies. We compare our results with those obtained by using the traditional relative entropies. We find that the measures satisfy all the plausible axioms for quantum correlations. We evaluate the measures for shared pure as well as paradigmatic classes of mixed states. We show that the measures can faithfully detect the quantum critical point in the transverse quantum Ising model and find that they can be used to remove an unquieting feature of nearest-neighbor quantum discord in this respect. Furthermore, the measures provide better finite-size scaling exponents of the quantum critical point than the ones for other known order parameters, including entanglement and information-theoretic measures of quantum correlations.
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Affiliation(s)
- Avijit Misra
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Anindya Biswas
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Arun K Pati
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Aditi Sen De
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Ujjwal Sen
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
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11
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Gelin MF, Bondarev IV, Meliksetyan AV. Optically promoted bipartite atomic entanglement in hybrid metallic carbon nanotube systems. J Chem Phys 2014; 140:064301. [PMID: 24527909 DOI: 10.1063/1.4863971] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study theoretically a pair of spatially separated extrinsic atomic type species (extrinsic atoms, ions, molecules, or semiconductor quantum dots) near a metallic carbon nanotube, that are coupled both directly via the inter-atomic dipole-dipole interactions and indirectly by means of the virtual exchange by resonance plasmon excitations on the nanotube surface. We analyze how the optical preparation of the system by using strong laser pulses affects the formation and evolution of the bipartite atomic entanglement. Despite a large number of possible excitation regimes and evolution pathways, we find a few generic scenarios for the bipartite entanglement evolution and formulate practical recommendations on how to optimize and control the robust bipartite atomic entanglement in hybrid carbon nanotube systems.
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Affiliation(s)
- M F Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
| | - I V Bondarev
- Department of Physics, North Carolina Central University, Durham, North Carolina 27707, USA
| | - A V Meliksetyan
- Department of Physics, North Carolina Central University, Durham, North Carolina 27707, USA
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12
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Spatial entanglement of bosons in optical lattices. Nat Commun 2014; 4:2161. [PMID: 23864124 DOI: 10.1038/ncomms3161] [Citation(s) in RCA: 59] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2013] [Accepted: 06/18/2013] [Indexed: 11/08/2022] Open
Abstract
Entanglement is a fundamental resource for quantum information processing, occurring naturally in many-body systems at low temperatures. The presence of entanglement and, in particular, its scaling with the size of system partitions underlies the complexity of quantum many-body states. The quantitative estimation of entanglement in many-body systems represents a major challenge, as it requires either full-state tomography, scaling exponentially in the system size, or the assumption of unverified system characteristics such as its Hamiltonian or temperature. Here we adopt recently developed approaches for the determination of rigorous lower entanglement bounds from readily accessible measurements and apply them in an experiment of ultracold interacting bosons in optical lattices of ~10(5) sites. We then study the behaviour of spatial entanglement between the sites when crossing the superfluid-Mott insulator transition and when varying temperature. This constitutes the first rigorous experimental large-scale entanglement quantification in a scalable quantum simulator.
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Moroder T, Bancal JD, Liang YC, Hofmann M, Gühne O. Device-independent entanglement quantification and related applications. PHYSICAL REVIEW LETTERS 2013; 111:030501. [PMID: 23909300 DOI: 10.1103/physrevlett.111.030501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2013] [Indexed: 06/02/2023]
Abstract
We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on the observed data only but independent of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device-independent entanglement witnesses involving an arbitrary number of parties.
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Affiliation(s)
- Tobias Moroder
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Strasse 3, D-57068 Siegen, Germany
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Dijkstra AG, Tanimura Y. Non-Markovianity: initial correlations and nonlinear optical measurements. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2012; 370:3658-71. [PMID: 22753819 PMCID: PMC3385673 DOI: 10.1098/rsta.2011.0203] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
By extending the response function approach developed in nonlinear optics, we analytically derive an expression for the non-Markovianity in the time evolution of a system in contact with a quantum mechanical bath, and find a close connection with the directly observable nonlinear optical response. The result indicates that memory in the bath-induced fluctuations rather than in the dissipation causes non-Markovianity. Initial correlations between states of the system and the bath are shown to be essential for a correct understanding of the non-Markovianity. These correlations are included in our treatment through a preparation function.
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Popkov V, Salerno M, Schütz GM. Behavior of magnetic currents in anisotropic Heisenberg spin chains out of equilibrium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031137. [PMID: 22587068 DOI: 10.1103/physreve.85.031137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2012] [Revised: 03/04/2012] [Indexed: 05/31/2023]
Abstract
The behavior of the magnetic currents in one-dimensional Heisenberg XXZ spin chains kept out of equilibrium by boundary driving fields is investigated. In particular, the dependence of the spin currents on the anisotropy parameter Δ and on the boundary fields is studied both analytically and numerically in the framework of the Lindblad master equation formalism. We show that the spin current can be maximized with appropriate choices of the boundary fields, and for odd system sizes, N, we demonstrate the existence of additional symmetries that cause the current to be an odd function of Δ. From direct numerical integrations of the quantum master equation, we find that for an arbitrary N the current J(z)(N) vanishes for Δ=0, while for Δ negative it alternates its sign with the system size. In the gapless critical region |Δ|<1, the scaling of the current is shown to be J(z)(N)∼1/N while in the gapped region |Δ|>1 we find that J(z)(N)∼exp(-αN). A simple mean-field approach, which predicts rather well the values of J(z)(N) for the gapped region and the values of the absolute current maxima in the critical region, is developed. The existence of two different stationary solutions for the mean-field density matrix in the whole parameter range is also demonstrated.
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Affiliation(s)
- V Popkov
- Dipartimento di Fisica ER Caianiello, Università di Salerno, Fisciano (SA), Italy
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Bermudez A, Almeida J, Schmidt-Kaler F, Retzker A, Plenio MB. Frustrated quantum spin models with cold Coulomb crystals. PHYSICAL REVIEW LETTERS 2011; 107:207209. [PMID: 22181770 DOI: 10.1103/physrevlett.107.207209] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2011] [Indexed: 05/31/2023]
Abstract
We exploit the geometry of a zigzag cold-ion crystal in a linear trap to propose the quantum simulation of a paradigmatic model of long-ranged magnetic frustration. Such a quantum simulation would clarify the complex features of a rich phase diagram that presents ferromagnetic, dimerized-antiferromagnetic, paramagnetic, and floating phases, together with previously unnoticed features that are hard to assess by numerics. We analyze in detail its experimental feasibility, and provide supporting numerical evidence on the basis of realistic parameters in current ion-trap technology.
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Affiliation(s)
- A Bermudez
- Institut für Theoretische Physik, Universität Ulm, Germany
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