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NMR Quantum Information Processing: Indian Contributions and Perspectives. J Indian Inst Sci 2023. [DOI: 10.1007/s41745-022-00353-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/18/2023]
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Sánchez CM, Buljubasich L, Pastawski HM, Chattah AK. Evolution of multiple quantum coherences with scaled dipolar Hamiltonian. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 281:75-81. [PMID: 28558273 DOI: 10.1016/j.jmr.2017.05.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Revised: 05/10/2017] [Accepted: 05/16/2017] [Indexed: 06/07/2023]
Abstract
In this article, we introduce a pulse sequence which allows the monitoring of multiple quantum coherences distribution of correlated spin states developed with scaled dipolar Hamiltonian. The pulse sequence is a modification of our previous Proportionally Refocused Loschmidt echo (PRL echo) with phase increment, in order to verify the accuracy of the weighted coherent quantum dynamics. The experiments were carried out with different scaling factors to analyze the evolution of the total magnetization, the time dependence of the multiple quantum coherence orders, and the development of correlated spins clusters. In all cases, a strong dependence between the evolution rate and the weighting factor is observed. Remarkably, all the curves appeared overlapped in a single trend when plotted against the self-time, a new time scale that includes the scaling factor into the evolution time. In other words, the spin system displayed always the same quantum evolution, slowed down as the scaling factor decreases, confirming the high performance of the new pulse sequence.
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Affiliation(s)
- Claudia M Sánchez
- Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, X5016LAE Córdoba, Argentina
| | - Lisandro Buljubasich
- Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, X5016LAE Córdoba, Argentina; IFEG - CONICET, X5016LAE Córdoba, Argentina
| | - Horacio M Pastawski
- Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, X5016LAE Córdoba, Argentina; IFEG - CONICET, X5016LAE Córdoba, Argentina
| | - Ana K Chattah
- Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, X5016LAE Córdoba, Argentina; IFEG - CONICET, X5016LAE Córdoba, Argentina.
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Sánchez CM, Levstein PR, Buljubasich L, Pastawski HM, Chattah AK. Quantum dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2016; 374:rsta.2015.0155. [PMID: 27140972 PMCID: PMC4855398 DOI: 10.1098/rsta.2015.0155] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/23/2016] [Indexed: 05/25/2023]
Abstract
In this work, we overview time-reversal nuclear magnetic resonance (NMR) experiments in many-spin systems evolving under the dipolar Hamiltonian. The Loschmidt echo (LE) in NMR is the signal of excitations which, after evolving with a forward Hamiltonian, is recovered by means of a backward evolution. The presence of non-diagonal terms in the non-equilibrium density matrix of the many-body state is directly monitored experimentally by encoding the multiple quantum coherences. This enables a spin counting procedure, giving information on the spreading of an excitation through the Hilbert space and the formation of clusters of correlated spins. Two samples representing different spin systems with coupled networks were used in the experiments. Protons in polycrystalline ferrocene correspond to an 'infinite' network. By contrast, the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline in the nematic mesophase represents a finite proton system with a hierarchical set of couplings. A close connection was established between the LE decay and the spin counting measurements, confirming the hypothesis that the complexity of the system is driven by the coherent dynamics.
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Affiliation(s)
- C M Sánchez
- Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina
| | - P R Levstein
- Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina Instituto de Física Enrique Gaviola (IFEG-CONICET), Ciudad Universitaria, Córdoba 5000, Argentina
| | - L Buljubasich
- Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina Instituto de Física Enrique Gaviola (IFEG-CONICET), Ciudad Universitaria, Córdoba 5000, Argentina
| | - H M Pastawski
- Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina Instituto de Física Enrique Gaviola (IFEG-CONICET), Ciudad Universitaria, Córdoba 5000, Argentina
| | - A K Chattah
- Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina Instituto de Física Enrique Gaviola (IFEG-CONICET), Ciudad Universitaria, Córdoba 5000, Argentina
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Buljubasich L, Sánchez CM, Dente AD, Levstein PR, Chattah AK, Pastawski HM. Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians. J Chem Phys 2015; 143:164308. [PMID: 26520514 DOI: 10.1063/1.4934221] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor |k| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates that correlate directly to the scaling factors |k|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed.
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Affiliation(s)
| | - Claudia M Sánchez
- Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina
| | - Axel D Dente
- Instituto de Física Enrique Gaviola (IFEG-CONICET), Córdoba 5000, Argentina
| | | | - Ana K Chattah
- Instituto de Física Enrique Gaviola (IFEG-CONICET), Córdoba 5000, Argentina
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Maximov II, Vinding MS, Tse DHY, Nielsen NC, Shah NJ. Real-time 2D spatially selective MRI experiments: Comparative analysis of optimal control design methods. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2015; 254:110-120. [PMID: 25863895 DOI: 10.1016/j.jmr.2015.03.003] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2014] [Revised: 03/12/2015] [Accepted: 03/13/2015] [Indexed: 06/04/2023]
Abstract
There is an increasing need for development of advanced radio-frequency (RF) pulse techniques in modern magnetic resonance imaging (MRI) systems driven by recent advancements in ultra-high magnetic field systems, new parallel transmit/receive coil designs, and accessible powerful computational facilities. 2D spatially selective RF pulses are an example of advanced pulses that have many applications of clinical relevance, e.g., reduced field of view imaging, and MR spectroscopy. The 2D spatially selective RF pulses are mostly generated and optimised with numerical methods that can handle vast controls and multiple constraints. With this study we aim at demonstrating that numerical, optimal control (OC) algorithms are efficient for the design of 2D spatially selective MRI experiments, when robustness towards e.g. field inhomogeneity is in focus. We have chosen three popular OC algorithms; two which are gradient-based, concurrent methods using first- and second-order derivatives, respectively; and a third that belongs to the sequential, monotonically convergent family. We used two experimental models: a water phantom, and an in vivo human head. Taking into consideration the challenging experimental setup, our analysis suggests the use of the sequential, monotonic approach and the second-order gradient-based approach as computational speed, experimental robustness, and image quality is key. All algorithms used in this work were implemented in the MATLAB environment and are freely available to the MRI community.
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Affiliation(s)
- Ivan I Maximov
- Institute of Neuroscience and Medicine 4, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany.
| | - Mads S Vinding
- Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, DK-8000 Aarhus, Denmark.
| | - Desmond H Y Tse
- Institute of Neuroscience and Medicine 4, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Niels Chr Nielsen
- Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, DK-8000 Aarhus, Denmark
| | - N Jon Shah
- Institute of Neuroscience and Medicine 4, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany; Department of Neurology, Faculty of Medicine, RWTH Aachen University, JARA, 52074 Aachen, Germany
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