Two-spin System Research Articles

Slow relaxation of longitudinal multispin orders in weakly and strongly coupled two-spin systems.

Longitudinal multispin order (LOMO) corresponds to a nonequilibrium population distribution in spin systems that exhibit scalar (J), dipolar, or quadrupolar coupling. We investigated the relaxation of longitudinal two-spin order (2-LOMO) in systems that had either weakly or strongly J-coupled spins. Our results indicated longer relaxation times for the 2-LOMO state compared with the corresponding longitudinal single-spin state (1-LOMO). Accessing nuclear spin states that have relaxation times longer than T(1), without the use of external contrast agents, is potentially useful for in vivo imaging and also for studying systems using dynamically hyperpolarized nuclear spins where longer life times are sought to increase the time available to study (bio)chemical events.

Pulsed EPR characterization of encapsulated atomic hydrogen in octasilsesquioxane cages

Hydrogen atoms encapsulated in molecular cages are potential candidates for quantum computing applications. They provide the simplest two-spin system where the 1s electron spin, S = 1/2, is hyperfine-coupled to the proton nuclear spin, I = 1/2, with a large isotropic hyperfine coupling (A = 1420.40575 MHz for a free atom). While hydrogen atoms can be trapped in many matrices at cryogenic temperatures, it has been found that they are exceptionally stable in octasilsesquioxane cages even at room temperature [Sasamori et al., Science, 1994, 256, 1691]. Here we present a detailed spin-lattice and spin-spin relaxation study of atomic hydrogen encapsulated in Si(8)O(12)(OSiMe(2)H)(8) using X-band pulsed EPR spectroscopy. The spin-lattice relaxation times T(1) range between 1.2 s at 20 K and 41.8 μs at room temperature. The temperature dependence of the relaxation rate shows that for T < 60 K the spin-lattice relaxation is best described by a Raman process with a Debye temperature of θ(D) = 135 K, whereas for T > 100 K a thermally activated process with activation energy E(a) = 753 K (523 cm(-1)) prevails. The phase memory time T(M) = 13.9 μs remains practically constant between 200 and 300 K and is determined by nuclear spin diffusion. At lower temperatures T(M) decreases by an order of magnitude and exhibits two minima at T = 140 K and T = 60 K. The temperature dependence of T(M) between 20 and 200 K is attributed to dynamic processes that average inequivalent hyperfine couplings, e.g. rotation of the methyl groups of the cage organic substituents. The hyperfine couplings of the encapsulated proton and the cage (29)Si nuclei are obtained through numerical simulations of field-swept FID-detected EPR spectra and HYSCORE experiments, respectively. The results are discussed in terms of existing phenomenological models based on the spherical harmonic oscillator and compared to those of endohedral fullerenes.

Coupling artificial molecular spin states by photon-assisted tunnelling

Artificial molecules containing just one or two electrons provide a powerful platform for studies of orbital and spin quantum dynamics in nanoscale devices. A well-known example of these dynamics is tunnelling of electrons between two coupled quantum dots triggered by microwave irradiation. So far, these tunnelling processes have been treated as electric-dipole-allowed spin-conserving events. Here we report that microwaves can also excite tunnelling transitions between states with different spin. We show that the dominant mechanism responsible for violation of spin conservation is the spin–orbit interaction. These transitions make it possible to perform detailed microwave spectroscopy of the molecular spin states of an artificial hydrogen molecule and open up the possibility of realizing full quantum control of a two-spin system through microwave excitation.

Entanglement dynamics of two qubits coupled by Heisenberg XY interaction under a nonuniform magnetic field in a spin bath

This paper investigates the entanglement dynamics of a Heisenberg XY model for a two-spin system in the presence of a nonuniform magnetic field. The master equations and the concurrence evolution equations for the initial α state are derived and analysed. It is shown that for the symmetric initial α state, only the nonuniform field can play a role in entanglement dynamics while the uniform field and the bath will not play such a role. For the asymmetric α state, the nonuniform field leads to the beat pattern oscillation of the concurrence evolution. The inhomogeneity of the field can enhance the entanglement by suppressing the decoherence effects of both the spin—orbit interaction and the spin bath.

Decoherence and Thermalization of Quantum Spin Systems

In this review, we discuss the decoherence and thermalization of a quantum spin system interact- ing with a spin bath environment, by numerically solving the time-dependent Schrodinger equation of the whole system. The effects of the topologic structure and the initial state of the environment on the decoherence of the two-spin and many-spin system are discussed. The role of different spin-spin coupling is considered. We show under which conditions the environment drives the reduced density matrix of the system to a fully decoherent state, and how the diagonal elements of the reduced density matrix approach those expected for the system in the microcanonical or canonical ensemble, depending on the character of the additional integrals of motion. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the microcanonical distribution (in each eigenenergy subspace) and canonical ensemble are states that may result from pure quantum dynamics, suggesting that quan- tum mechanics may be regarded as the foundation of quantum statistical mechanics. Furthermore, our numerical results show that a fully decoherent quantum system prefers to stay in an equilibrium state with a maximum entropy, indicating the validity of the second law of thermodynamics in the decoherence process.

ChemInform Abstract: Quantum Computing with NMR

AbstractReview: 534 refs.

A convenient method for the measurements of transverse relaxation rates in homonuclear scalar coupled spin systems

A new solution-state NMR method is proposed to determine apparent transverse NMR relaxation rates in both weakly and strongly scalar coupled two-spin systems.

Maximal entanglement of bipartite spin states in the context of quantum algebra

In the framework of the Uq (su(2)) quantum algebra, we investigate the entanglement properties of two-spin systems, of arbitrary spins j1 and j2, defined in an entanglement of deformed spin coherent states of each of the spins. We derive the amount of entanglement and we give conditions under which bipartite entangled states become maximally entangled. Using these conditions, we construct a large class of Bell states for any choices of the parameters that specify the spin coherent states.

Simultaneous time-optimal control of the inversion of two spin-12particles

We analyze the simultaneous time-optimal control of two-spin systems. The two noncoupled spins, which differ in the value of their chemical offsets, are controlled by the same magnetic fields. Using an appropriate rotating frame, we restrict the study to the case of opposite shifts. We then show that the optimal solution of the inversion problem in a rotating frame is composed of a pulse sequence of maximum intensity and is similar to the optimal solution for inverting only one spin by using a nonresonant control field in the laboratory frame. An example is implemented experimentally using nuclear magnetic resonance techniques.

Life-times of long-lived coherences under different motional regimes

The transverse relaxation rate R 2 of single quantum coherences, the relaxation rate R LLC of long-lived coherences (LLC), and the ratio R 2/ R LLC have been studied by experiment, simulation and theory in the two-spin system formed by the Glycine aliphatic protons of the dipeptide Alanine–Glycine as a function of the correlation time of rotational diffusion.

Separable states and geometric phases of an interacting two-spin system

It is known that an interacting bipartite system evolves as an entangled state in general, even if it is initially in a separable state. Due to the entanglement of the state, the geometric phase of the system is not equal to the sum of the geometric phases of its two subsystems. However, there may exist a set of states in which the nonlocal interaction does not affect the separability of the states, and the geometric phase of the bipartite system is then always equal to the sum of the geometric phases of its subsystems. In this article, we illustrate this point by investigating a well-known physical model. We give a necessary and sufficient condition in which a separable state remains separable so that the geometric phase of the system is always equal to the sum of the geometric phases of its subsystems.

Ferromagnetic Fractional Quantum Hall States in a Valley-Degenerate Two-Dimensional Electron System

We study a two-dimensional electron system where the electrons occupy two conduction band valleys with anisotropic Fermi contours and strain-tunable occupation. We observe persistent quantum Hall states at filling factors nu=1/3 and 5/3 even at zero strain when the two valleys are degenerate. This is reminiscent of the quantum Hall ferromagnet formed at nu=1 in the same system at zero strain. In the absence of a theory for a system with anisotropic valleys, we compare the energy gaps measured at nu=1/3 and 5/3 to the available theory developed for single-valley, two-spin systems, and find that the gaps and their rates of rise with strain are much smaller than predicted.

Guidelines for the use of band-selective radiofrequency pulses in hetero-nuclear NMR: Example of longitudinal-relaxation-enhanced BEST-type 1H– 15N correlation experiments

Band-selective radiofrequency (rf) pulses provide powerful spectroscopic tools for many biomolecular NMR applications. Band-selectivity is commonly achieved by pulse shaping where the rf amplitude and phase are modulated according to a numerically optimized function. This results in complex spin evolution trajectories during the pulse duration. Here we introduce simplified representations of a number of shaped pulses, commonly used in biomolecular NMR spectroscopy. These simple schemes, consisting in a suite of free evolution delays and ideal rf pulses, reproduce astonishingly well the effect on a scalar-coupled hetero-nuclear two-spin system. As a consequence, optimal use of such pulse shapes in complex multi-pulse sequences becomes straightforward, as demonstrated here for the example of longitudinal-relaxation-enhanced BEST-HSQC and BEST-TROSY experiments. Applications of these optimized pulse sequences to several proteins in the size range of 8–21 kDa are shown.

Master equation approach to line shape in dissipative systems

We propose a formulation to obtain the line shape of a magnetic response with dissipative effects that directly reflects the nature of the environment. Making use of the fact that the time evolution of a response function is described by the same equation as the reduced density operator, we formulate a full description of the complex susceptibility. We describe the dynamics using the equation of motion for the reduced density operator, including the term for the initial correlation between the system and a thermal bath. In this formalism, we treat the full description of non-Markovian dynamics including the initial correlation. We present an explicit and compact formula up to the second order of cumulants, which can be applied in a straightforward way to multiple-spin systems. We also take into account the frequency shift by the system-bath interaction. We study the dependence of the line shape on the type of interaction between the system and the thermal bath. We demonstrate that the present formalism is a powerful tool for investigating various kinds of systems and we show how it is applied to spin systems, including those with up to three spins. We distinguish the contributions of the initial correlation and the frequency shift and make clear the role of each contribution in the Ohmic coupling spectral function. As examples of applications to multispin systems, we obtain the dependence of the line shape on the spatial orientation in relation to the direction of the static field (Nagata-Tazuke effect), including the effects of the thermal environment, in a two-spin system, along with the dependence on the arrangement of a triangle in a three-spin system.

Entanglement enhancement for two spins assisted by two phase kicks

We study the entanglement dynamics in a two-spin system governed by a bilinear Hamiltonian and assisted by phase kicks. It is found that the application of instant kicks to both spins at some specific moments leads to enhancement of entanglement. This procedure also improves the transient character of entanglement leading, for large spins, to a formation of a plateau for the I-concurrence. We have numerically investigated the spin-spin dynamics for several values of spins and observed a substantial enhancement of entanglement in comparison to the evolution without kicks.

Quantitative analysis of Earth’s field NMR spectra of strongly-coupled heteronuclear systems

In the Earth’s magnetic field, it is possible to observe spin systems consisting of unlike spins that exhibit strongly coupled second-order NMR spectra. Such spectra result when the J-coupling between two unlike spins is of the same order of magnitude as the difference in their Larmor precession frequencies. Although the analysis of second-order spectra involving only spin-½ nuclei has been discussed since the early days of NMR spectroscopy, NMR spectra involving spin-½ nuclei and quadrupolar (I>½) nuclei have rarely been treated. Two examples are presented here, the tetrahydroborate anion, BH4-, and the ammonium cation, NH4+. For the tetrahydroborate anion, 1J(11B,1H)=80.9Hz, and in an Earth’s field of 53.3μT, ν(1H)=2269Hz and ν(11B)=728Hz. The 1H NMR spectra exhibit features that both first- and second-order perturbation theory are unable to reproduce. On the other hand, second-order perturbation theory adequately describes 1H NMR spectra of the ammonium anion, 14NH4+, where 1J(14N,1H)=52.75Hz when ν(1H)=2269Hz and ν(14N)=164Hz. Contrary to an early report, we find that the 1H NMR spectra are independent of the sign of 1J(14N,1H). Exact analysis of two-spin systems consisting of quadrupolar nuclei and spin-½ nuclei are also discussed.

Maximal violations of a Bell inequality by entangled spin-coherent states

We study the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality for two-spin systems, of arbitrary spins ${j}_{1}$ and ${j}_{2}$, prepared in an entanglement of spin-coherent states of each of the spins. We show that the Bell-CHSH inequality is quite robustly violated for a wide range of values of the parameters that specify the spin-coherent states, and, for a particular choice of these parameters, maximal violations are obtained. That is, the violations can reach the Tsirelson bound, $2\sqrt{2}$, for any choices of the spins.

Dynamic nuclear polarization of water by a nitroxide radical: rigorous treatment of the electron spin saturation and comparison with experiments at 9.2 Tesla

The interaction between nuclear and electronic spins is of interest for structural characterization of biomolecules and biomedical imaging based on nuclear magnetic resonance. The polarization of the nuclear spins can be increased significantly if the electron spin polarization is kept out of equilibrium. We employ semiclassical relaxation theory to analyze the electronic polarization of the two-spin system characteristic of nitroxide radicals. Atomistic molecular dynamics simulations of the nitroxide TEMPOL in water are performed to account for the effects of tumbling and spin-rotation coupling on the spin-spin and spin-lattice relaxation times. Concentration effects on the electron saturation are introduced by allowing for Heisenberg spin exchange between two nitroxides. Polarization enhancement profiles, calculated from the computed saturation, are directly compared with liquid-state dynamic nuclear polarization experiments conducted at 260 GHz/400 MHz. The contribution of the separate hyperfine lines to the saturation can be easily disentangled using the developed formalism.

Naimark-DilatedPT-Symmetric Brachistochrone

The quantum mechanical brachistochrone system with a PT-symmetric Hamiltonian is Naimark-dilated and reinterpreted as a subsystem of a Hermitian system in a higher-dimensional Hilbert space. This opens a way to a direct experimental implementation of the recently hypothesized PT-symmetric ultrafast brachistochrone regime of Bender et al. [Phys. Rev. Lett. 98, 040403 (2007)] in an entangled two-spin system.

Clear Evasion of the Uncertainty Relation with Very Small Probability

We entertain the idea that the uncertainty relation is not a principle, but rather it is a consequence of quantum mechanics. The uncertainty relation is then a probabilistic statement and can be clearly evaded in processes which occur with a very small probability in a tiny sector of the phase space. This clear evasion is typically realized when one utilizes indirect measurements, and some examples of the clear evasion appear in the system with entanglement though the entanglement by itself is not essential for the evasion. The standard Kennard's relation and its interpretation remain intact in our analysis. As an explicit example, we show that the clear evasion of the uncertainty relation for coordinate and momentum in the diffraction process discussed by Ballentine is realized in a tiny sector of the phase space with a very small probability. We also examine the uncertainty relation for a two-spin system with the EPR entanglement and show that no clear evasion takes place in this system with the finite discrete degrees of freedom.