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We study the quantum dynamics of a non-interacting spin ensemble under the effect of a reservoir by applying the framework of the non-Hermitian Hamiltonian operators. Theoretically, the two-level model describes the quantum spin system and the Bloch vector to establish the dynamical evolution. Experimentally, phosphorous ($^{31}$P) nuclei with spin $I=1/2$ are used to represent the two-level system and the magnetization evolution is measured and used to compare with the theoretical prediction. At room temperature, the composite dynamics of the radio-frequency pulse plus field inhomogeneities (or unknown longitudinal fluctuations) along the $z$-axis transform the initial quantum state and drives it into a mixed state at the end of the dynamics. The experimental setup shows a higher accuracy when compared with the theoretical prediction (>98\%), ensuring the relevance and effectiveness of the non-Hermitian theory at a high-temperature regime., 8 pages, 4 figures

No-till (NT) cropping systems have the potential to enhance soil aggregation, providing physical protection and soil C sequestration. The existence of discrepancies in the impact of tillage on soil aggregation and soil C sequestration warrants further studies, particularly for different crop rotations. We hypothesized the following: a) NT biannual crop rotations tend to be more effective in restoring large macroaggregation and the concentrations of soil organic C (SOC), total N and permanganate oxidizable C (POXC) associated with macroaggregates than NT systems with a one-year frequency pattern and conventional tillage (CT); b) the continuous biomass-C inputs via crop residues in large macroaggregates under NT tend to increase the proportion of aliphatic C than those under CT. Therefore, the objectives of this study were: (i) to assess changes in the aggregate size distribution and levels of aggregate-associated total SOC, total N and POXC and (ii) to characterize humic acid (HA) using 13C CP-MAS nuclear magnetic resonance (NMR) spectra of 8- to 19-mm soil aggregate size class in a reference vegetation (RV) and in rice-, soybean- and cassava-based cropping systems (RcCS, SbCS and CsCS, respectively) in a clayed Oxisol after tillage and crop rotation management. We evaluated four treatments in each cropping system: 1) CT, and 2) three NT systems in a randomized complete block design with three replicates. Soil aggregate samples were collected at depths of 0–5, 5–10 and 10–20 cm. The conversion of RV to agricultural land influenced the distribution of aggregate size classes, soil aggregation indices and aggregate-associated SOC, total N and POXC in the two surface layers. The formation of large macroaggregates (8–19 mm) dominated the aggregate size distribution with a relatively higher proportion under RV and NT than under CT. Across all soil depths, the proportions of the 8- to 19-mm aggregate size fraction were 59% (NV), 43% and 47% (RcCS), 45% and 53% (SbCS) and 34% and 37% (CsCS) for the CT and NT systems, respectively. Among the three NT systems, the biannual crop rotations in the three cropping systems (NT2-Rice, NT2-Soybean, NT2-Cassava; NT3-Rice, NT3-Soybean and NT3-Cassava) indicated better performance than the one-year frequency pattern in restoring large macroaggregation and the concentrations of SOC, total N and POXC associated with large macroaggregates. Additionally, in the surface (0–5 cm) and subsurface (10–20 cm) soil layers, the SbCS with a high rate (7.32 Mg C ha−1 year−1) and diversity [Pennisetum typhoides) (Pearl millet)/maize + Brachiaria ruziziensis (Brz), Stylosanthes guianensis (St)] of biomass-C inputs reached the highest levels of lability of SOC and POXC in the macroaggregate size classes of 0.25–0.5 and 8–19 mm, respectively. The CP-MAS 13C NMR measurement suggests that the continuous and high biomass-C inputs with diverse crop residues under NT, such as millet, maize, Brz, St and Crotalaria juncea, tended to increase the proportion of aliphatic C than under CT; an opposite trend was observed for aromatic C. 13C NMR revealed an advance caused by the association between the quantity and quality of C addition via cultural residues in the discrimination of the composition of C in the macroaggregation in the tropical region.

Quantum games have gained much popularity in the last two decades. Many of these quantum games are a redefinition of iconic classical games to fit the quantum world, and they gain many different properties and solutions in this different view. In this letter, we attempt to find a solution to an asymmetric quantum game which still troubles quantum game researchers, the quantum battle of the sexes. To achieve that, we perform an analysis using the Eisert-Wilkens-Lewenstein's protocol for this asymmetric game. The protocol highlights two solutions for the game, which solve the dilemma and satisfy the Pareto-optimal definition, unlike previous reports that rely on Nash equilibrium. We perform an experimental implementation using the NMR technique in a two-qubit system. Our results eliminate dilemmas on the quantum battle of the sexes and provide us with arguments to elucidate that the Eisert-Wilkens-Lewenstein's protocol is not restricted to symmetric games when at the quantum regime.

Recently, we reported an experimental implementation of quantum information processing (QIP) by nuclear quadrupole resonance (NQR). In this work, we present the first quantum state tomography (QST) experimental implementation in the NQR QIP context. Two approaches are proposed, employing coherence selection by temporal and spatial averaging. Conditions for reduction in the number of cycling steps are analyzed, which can be helpful for larger spin systems. The QST method was applied to the study of spin coherent states, where the alignment-to-orientation phenomenon and the evolution of squeezed spin states show the effect of the nonlinear quadrupole interaction intrinsic to the NQR system. The quantum operations were implemented using a single-crystal sample of KClO $$_{3}$$ and observing $$^{35}$$ Cl nuclei, which posses spin 3/2.

Finding the solutions of the equations that describe the dynamics of a given physical system is crucial in order to obtain important information about its evolution. However, by using estimation theory, it is possible to obtain, under certain limitations, some information on its dynamics. The quantum-speed-limit (QSL) theory was originally used to estimate the shortest time in which a Hamiltonian drives an initial state to a final one for a given fidelity. Using the QSL theory in a slightly different way, we are able to estimate the running time of a given quantum process. For that purpose, we impose the saturation of the Anandan-Aharonov bound in a rotating frame of reference where the state of the system travels slower than in the original frame (laboratory frame). Through this procedure it is possible to estimate the actual evolution time in the laboratory frame of reference with good accuracy when compared to previous methods. Our method is tested successfully to predict the time spent in the evolution of nuclear spins 1/2 and 3/2 in NMR systems. We find that the estimated time according to our method is better than previous approaches by up to four orders of magnitude. One disadvantage of our method is that we need to solve a number of transcendental equations, which increases with the system dimension and parameter discretization used to solve such equations numerically., Comment: 14 pages, 10 figures, title changed, one appendix added, partially rewritten, similar to the version published in PRA

Based on a quantum interferometric circuit, we implement a NMR quantum thermometer, in which a probe qubit measures the temperature of a nuclear spin at thermal equilibrium with a bath. The whole procedure lasts 5.5 ms, a much shorter time than the probe's spin-lattice relaxation time, which is $$T_{1}=7.0\,\hbox {s}$$T1=7.0s. The fidelity of the probe final quantum state, in respect to the ideal theoretical prediction, is above 99 %. We show that quantum coherence is essential for the high fidelity of temperature measurement. We discuss the source of errors on the temperature measurement and some possible applications of the thermometer.

In this chapter we review the contributions of Nuclear Magnetic Resonance to the study of quantum correlations, including its capabilities to prepare initial states, generate unitary transformations, and characterize the final state. These are the three main demands to implement quantum information processing in a physical system, which NMR offers, nearly to perfection, though for a small number of qubits. Our main discussion will concern liquid samples at room temperature.

We review the theoretical and the experimental aspects regarding the quantification and identification of quantum correlations in liquid-state nuclear magnetic resonance (NMR) systems at room temperature. We start by introducing a formal method to obtain the quantum discord and its classical counterpart in systems described by a deviation matrix. Next, we apply such a method to experimentally demonstrate that the peculiar dynamics, with a sudden change behaviour, of quantum discord under decoherence, theoretically predicted only for phase-noise channels, is also present even under the effect of a thermal environment. This result shows that such a phenomena are much stronger than we could think, at principle. Walking through a different path, we discuss an observable witness for the quantumness of correlations in two-qubit systems and present the first experimental implementation of such a quantity in a NMR setup. Such a witness could be very useful in situations were the knowledge of the nature of correlations (in contrast of how much correlations) presented in a given state is enough.

In this paper we present a series of high-resolution zero-field NMR spectra of the polycrystalline intermetallic compound GdAl2. The spectra were obtained with the sample at 4.2 K in the ordered magnetic state and in the absence of an external static magnetic field. Using a sequence composed of two RF pulses, we obtained up to five multi-quantum echoes for the 27Al nuclei, which were used to construct the zero-field NMR spectra. The spectra obtained from the FID observed after the second pulse and the even echoes exhibited higher resolution than the odd ones. In order to explain such behavior, we propose a model in which there are two regions inside the sample with different inhomogeneous spectral-line broadenings. Moreover, with the enhanced resolution from the FID signal, we were able to determine quadrupolar couplings with great precision directly from the respective spectra. These results were compared with those obtained from the quadrupolar oscillations of the echo signals, and showed good agreement. Similar data were also obtained from 155Gd and 157Gd nuclei.

In this work we applied a quantum circuit treatment to describe the nuclear spin relaxation. From the Redfield theory, we obtain a description of the quadrupolar relaxation as a computational process in a spin 3/2 system, through a model in which the environment is comprised by five qubits and three different quantum noise channels. The interaction between the environment and the spin 3/2 nuclei is described by a quantum circuit fully compatible with the Redfield theory of relaxation. Theoretical predictions are compared to experimental data, a short review of quantum channels and relaxation in NMR qubits is also present.

This article reports a relaxation study in an oriented system containing spin 3/2 nuclei using quantum state tomography (QST). The use of QST allowed evaluating the time evolution of all density matrix elements starting from several initial states. Using an appropriated treatment based on the Redfield theory, the relaxation rate of each density matrix element was measured and the reduced spectral densities that describe the system relaxation were determined. All the experimental data could be well described assuming pure quadrupolar relaxation and reduced spectral densities corresponding to a superposition of slow and fast motions. The data were also analyzed in the context of Quantum Information Processing, where the coherence loss of each qubit of the system was determined using the partial trace operation.

We have produced and characterized spin-squeezed states at a temperature of 26 °C in a nuclear magnetic resonance quadrupolar system. The experiment was carried out on 133Cs nuclei of spin I=7/2 in a sample of lyotropic liquid crystal. The source of spin squeezing was identified as the interaction between the quadrupole moment of the nuclei and the electric field gradients present within the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing on a Hilbert space of dimension 2I+1=8. The quantitative and qualitative characterization of this spin-squeezing phenomenon is expressed by a squeezing parameter and squeezing angle developed for the two-mode Bose-Einstein condensate system, as well as by the Wigner quasiprobability distribution function. The generality of the present experimental scheme points to potential applications in solid-state physics.

Working with nuclear magnetic resonance (NMR) in quadrupolar spin systems, in this paper we transfer the concept of atomic coherent state to the nuclear spin context, where it is referred to as pseudo-nuclear spin coherent state (pseudo-NSCS). Experimentally, we discuss the initialization of the pseudo-NSCSs and also their quantum control, implemented by polar and azimuthal rotations. Theoretically, we compute the geometric phases acquired by an initial pseudo-NSCS on undergoing three distinct cyclic evolutions: $ i) $ the free evolution of the NMR quadrupolar system and, by analogy with the evolution of the NMR quadrupolar system, that of $ii)$ single-mode and $ iii)$ two-mode Bose-Einstein Condensate like system. By means of these analogies, we derive, through spin angular momentum operators, results equivalent to those presented in the literature for orbital angular momentum operators. The pseudo-NSCS description is a starting point to introduce the spin squeezed state and quantum metrology into nuclear spin systems of liquid crystal or solid matter.

We review the theoretical and the experimental researches aimed at quantifying or identifying quantum correlations in liquid-state nuclear magnetic resonance (NMR) systems at room temperature. We first overview, at the formal level, a method to determine the quantum discord and its classical counterpart in systems described by a deviation matrix. Next, we describe an experimental implementation of that method. Previous theoretical analysis of quantum discord decoherence had predicted the time dependence of the discord to change suddenly under the influence of phase noise. The experiment attests to the robustness of the effect, sufficient to confirm the theoretical prediction even under the additional influence of a thermal environment. Finally, we discuss an observable witness for the quantumness of correlations in two-qubit systems and its first NMR implementation. Should the nature, not the amount, of the correlation be under scrutiny, the witness offers the most attractive alternative.

The Josephson Junction model is applied to the experimental implementation of classical bifurcation in a quadrupolar Nuclear Magnetic Resonance system. There are two regimes, one linear and one nonlinear which are implemented by the radio-frequency term and the quadrupolar term of the Hamiltonian of a spin system respectively. Those terms provide an explanation of the symmetry breaking due to bifurcation. Bifurcation depends on the coexistence of both regimes at the same time in different proportions. The experiment is performed on a lyotropic liquid crystal sample of an ordered ensemble of $^{133}$Cs nuclei with spin $I=7/2$ at room temperature. Our experimental results confirm that bifurcation happens independently of the spin value and of the physical system. With this experimental spin scenario, we confirm that a quadrupolar nuclei system could be described analogously to a symmetric two--mode Bose--Einstein condensate., 5 pages, 3 figures

We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance (NMR) setup and employing geometric discord, we evaluate the quantum correlations of a state without resorting to prior knowledge of its density matrix. The method is applicable to any (2 x d) system and provides, in terms of number of measurements required, an advantage over full state tomography scaling with the dimension d of the unmeasured subsystem. The negativity of quantumness is measured as well for reference. We also observe the phenomenon of sudden transition of quantum correlations when local phase and amplitude damping channels are applied to the state., 5+2 pages, 3+1 figures. Published in PRL

Recent results in biochar research show that it is not only composed of stable carbon, since a portion of these materials is degraded relatively easily once applied to soil, and this condition is most dependent on pyrolysis conditions, especially the final temperature. Thus, the aim of this study was to evaluate pyrolysis final temperature effects on the stability of biochar produced from forest residues using solid-state 13C NMR. Pyrolysis was performed at a heating rate of 10°C·min−1 up to the final temperature of interest (350, 450 and 550°C), maintaining this temperature for 60 min. Solid-state 13C NMR spectra were obtained on a Varian 500-MHz spectrometer for fresh wood and biochars produced at 350, 450 and 550°C for Eucalyptus dunnii (DUN) and Pinus caribaea (CAR). Comparing fresh samples with their respective biochars, regardless of the botanical group, after pyrolysis, carbohydrates are degraded, and there is a change in the structure of the materials, with a predominance of aromatic structures, which are more resistant to degradation, therefore reflecting in the increased stability of these materials. For 350°C, it is still possible to observe signals related to lignin indicating that up to this temperature it has not been completely degraded. The spectra of biochars produced at 450 and 550°C are very similar, indicating that there is no need to produce biochars at very high final temperatures, since the structure of these materials obtained at 550°C slightly altered as of 450°C, keeping the predominance of aromatic structures.

The high fertility and resilience of Terras Pretas de Indios are attributed to the high contents of polycondensed aromatic structures with carboxylic functionality originating from the natural alterations of carbonised biomass added to the soil by the pre-Columbian indigenous populations. There are several proposals to reproduce the positive characteristics of these special soils, including the use of charred biomass (biochar); however, the time necessary to modify this material in the peculiar organic matter of Terras Pretas de Indios is still undetermined. The 13C NMR analysis of the humic acids extracted at pH 10.6 from soils treated with fines of charcoal indicates that after 3 years a small portion of the added charcoal is already partially oxidised to a compound similar to the ones found in Terras Pretas de Indios; however, the large fraction still looks like unaltered charcoal. Additionally, the proposed method of selective extraction of the characteristic humic fraction from Terras Pretas de Indios, combined with multivariate data analysis tools, can be used as a method to evaluate the proposals to reproduce these special soils.

Nuclear magnetic resonance (NMR) was successfully employed to test several protocols and ideas in quantum information science. In most of these implementations, the existence of entanglement was ruled out. This fact introduced concerns and questions about the quantum nature of such bench tests. In this paper, we address some issues related to the non-classical aspects of NMR systems. We discuss some experiments where the quantum aspects of this system are supported by quantum correlations of separable states. Such quantumness, beyond the entanglement–separability paradigm, is revealed via a departure between the quantum and the classical versions of information theory. In this scenario, the concept of quantum discord seems to play an important role. We also present an experimental implementation of an analogue of the single-photon Mach–Zehnder interferometer employing two nuclear spins to encode the interferometric paths. This experiment illustrates how non-classical correlations of separable states may be used to simulate quantum dynamics. The results obtained are completely equivalent to the optical scenario, where entanglement (between two field modes) may be present.

One of the milestones of quantum mechanics is Bohr's complementarity principle. It states that a single quantum can exhibit a particle-like \emph{or} a wave-like behaviour, but never both at the same time. These are mutually exclusive and complementary aspects of the quantum system. This means that we need distinct experimental arrangements in order to measure the particle or the wave nature of a physical system. One of the most known representations of this principle is the single-photon Mach-Zehnder interferometer. When the interferometer is closed an interference pattern is observed (wave aspect of the quantum) while if it is open, the quantum behaves like a particle. Here, using a molecular quantum information processor and employing nuclear magnetic resonant (NMR) techniques, we analyze the quantum version of this principle by means of an interferometer that is in a quantum superposition of being closed and open, and confirm that we can indeed measure both aspects of the system with the same experimental apparatus. More specifically, we observe with a single apparatus the interference between the particle and the wave aspects of a quantum system.

Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance (NMR) experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW's are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance.

The quantification of quantum correlations (other than entanglement) usually entails labored numerical optimization procedures also demanding quantum state tomographic methods. Thus it is interesting to have a laboratory friendly witness for the nature of correlations. In this Letter we report a direct experimental implementation of such a witness in a room temperature nuclear magnetic resonance system. In our experiment the nature of correlations is revealed by performing only few local magnetization measurements. We also compared the witness results with those for the symmetric quantum discord and we obtained a fairly good agreement.

Nonclassical correlations play a crucial role in the development of quantum information science. The recent discovery that nonclassical correlations can be present even in separable (nonentangled) states has broadened this scenario. This generalized quantum correlation has been increasing in relevance in several fields, among them quantum communication, quantum computation, quantum phase transitions, and biological systems. We demonstrate here the occurrence of the sudden-change phenomenon and immunity against some sources of noise for the quantum discord and its classical counterpart, in a room temperature nuclear magnetic resonance setup. The experiment is performed in a decohering environment causing loss of phase relations among the energy eigenstates and exchange of energy between system and environment, resulting in relaxation to the Gibbs ensemble.

The existence of quantum correlation (as revealed by quantum discord), other than entanglement and its role in quantum-information processing (QIP), is a current subject for discussion. In particular, it has been suggested that this nonclassical correlation may provide computational speedup for some quantum algorithms. In this regard, bulk nuclear magnetic resonance (NMR) has been successfully used as a test bench for many QIP implementations, although it has also been continuously criticized for not presenting entanglement in most of the systems used so far. In this paper, we report a theoretical and experimental study on the dynamics of quantum and classical correlations in an NMR quadrupolar system. We present a method for computing the correlations from experimental NMR deviation-density matrices and show that, given the action of the nuclear-spin environment, the relaxation produces a monotonic time decay in the correlations. Although the experimental realizations were performed in a specific quadrupolar system, the main results presented here can be applied to whichever system uses a deviation-density matrix formalism., Comment: Published version

This paper presents a description of nuclear magnetic resonance (NMR) of quadrupolar systems using the Holstein-Primakoff (HP) formalism and its analogy with a Bose-Einstein condensate (BEC) system. Two nuclear spin systems constituted of quadrupolar nuclei I=3/2 ((23)Na) and I=7/2 ((133)Cs) in lyotropic liquid crystals were used for experimental demonstrations. Specifically, we derived the conditions necessary for accomplishing the analogy, executed the proper experiments, and compared with quantum mechanical prediction for a Bose system. The NMR description in the HP representation could be applied in the future as a workbench for BEC-like systems, where the statistical properties may be obtained using the intermediate statistic, first established by Gentile. The description can be applied for any quadrupolar systems, including new developed solid-state NMR GaAS nanodevices.

In this paper, we describe a quantum state tomography method based on global rotations of the spin system which, together with a coherence selection scheme, enables the complete density matrix reconstruction. The main advantage of this technique, in respect to previous proposals, is the use of much shorter rf pulses, which decreases significantly the time necessary for algorithm quantum state tomography. In this case, under adequate experimental conditions, the rf pulses correspond to simple spatial rotations of the spin states, and its analytical description is conveniently given in the irreducible tensor formalism. Simulated results show the feasibility of the method for a single spin 72 nucleus. As an experimental result, we exemplify the application of this method by tomographing the steps during the implementation of the Deutsch algorithm. The algorithm was implemented in a (23)Na quadrupole nucleus using the strongly modulated pulses technique. We also extended the tomography method for a 3-coupled homonuclear spin 12 system, where an additional evolution under the internal Hamiltonian is necessary for zero order coherences evaluation.