G. B. Furman

NMR multiple-quantum dynamics with various initial conditions

An approach to creating the highest-order multiple-quantum coherences is developed. The method is based on using the multiple-quantum NMR technique and various initial conditions and can be considered as supplemental to earlier developed methods. Using the dipolar ordered state as the initial one, it is demonstrated that in a cluster of four and eight dipolar-coupled nuclear spins the highest-order multiple-quantum coherences can be created.

Dynamics of entanglement in a one-dimensional Ising chain

The evolution of entanglement in a one-dimensional Ising chain is numerically studied under various initial conditions. We analyze two problems concerning the dynamics of entanglement: (i) generation of the entanglement from the pseudopure separable state and (ii) transportation of the entanglement from one end of the chain to the other. The model investigated is a one-dimensional Ising spin-1/2 chain with nearest-neighbor interactions placed in an external magnetic field and irradiated by a weak resonant transverse field. The possibility of selective initialization of partially entangled states is considered. It was shown that, in spite of the use of a model with direct interactions between the nearest neighbors, entanglement between remote spins is generated.

Entanglement of dipolar coupling spins

Entanglement of dipole-dipole interacting spins 1/2 is usually investigated when the energy of interaction with an external magnetic field (the Zeeman energy) is greater than the energy of dipole interactions by three orders. Under this condition only a non-equilibrium state of the spin system, realized by pulse radiofrequence irradiations, results in entanglement. The present paper deals with the opposite case: the dipolar interaction energy is the order of magnitude or even larger than the Zeeman one. It was shown that entanglement appears under the thermodynamic equilibrium conditions and the concurrence reaches the maximum when the external field is directed perpendicular to the vector connecting the nuclei. For this direction of the field and a system of two spins with the Hamiltonian accounting the realistic dipole-dipole interactions in low external magnetic field, the exact analytical expression for concurrence was also obtained. The condition of the entanglement appearance and the dependence of concurrence on the external magnetic field, temperature, and dipolar coupling constant were studied.

Nuclear polarization and entanglement in spin systems

We investigated relationships between entanglement measures and the order parameter (nuclear polarization) in nuclear spin systems controlled by the nuclear magnetic resonance (NMR) technique. Since spin polarization can be easily manipulated by the NMR technique, experimentalists are presented with an opportunity to study the dynamic properties of entanglement, i.e., the creation and evolution of entangled states. Our approach may constitute the basis for researching the relations between the entanglement measures and measurable parameters of order in other quantum systems.

Multiple quantum NMR and entanglement dynamics in dipolar coupling spin systems

We investigate numerically the time dependence of the multiple quantum coherences and entanglement in linear chains up to nine nuclear spins of 1/2 coupled by the dipole-dipole interactions. Two models are considered: (1) a spin chain with nearest-neighbor dipole -dipole interactions; (2) a more realistic model with interactions between all spins. It is shown that the entangled states appear between remote particles which do not interact directly (model 1), while the interaction between all spins (model 2) not always results in entanglement between remote spins.

Multiple quantum NMR dynamics in dipolar ordered spin systems

We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by the dipole-dipole interactions in the case of the dipolar ordered initial state. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar temperature in the quasi-equilibrium state which establishes after the time of order T2 after the MQ NMR experiment. The other method uses an additional resonance 45^0 -pulse after the preparation period of the standard MQ NMR experiment in solids. Many-spin clusters and correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids.

Entanglement in dipolar coupling spin system in equilibrium state

We study the appearance of the entangled states in a one-dimensional finite chain of dipolar-coupling nuclear spins of 1/2 in the conditions of thermodynamic equilibrium. It is shown that entanglement is achieved by the application of a low external magnetic field in which the Zeeman interaction energy is the order of or even less than the dipolar interaction one. When these energies are equal, the critical temperature, i. e. the temperature of the entanglement appearance, coincides with the temperature at which the heat capacity of the spin chain achieves its maximum. The obtained relationship between the critical temperature and the magnetic field can be considered as an entanglement witness. The dependences of the heat capacity on temperature and magnetic field have different character for entangled and separable states and can be served for experimental detection of entangled states.

Dipolar temperature and multiple-quantum NMR dynamics in dipolar ordered-spin systems

We investigate analytically and numerically the multiple-quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by dipole-dipole interactions in the case of the dipolar-ordered initial state. We suggest a new method of MQ NMR based on the measurement of the dipolar temperature in the quasi-equilibrium state, which establishes after the time of order ωloc−1 (ωloc is the dipolar local field) after the MQ NMR experiment. Manyspin clusters and correlations are created faster in such an experiment than in usual MQ NMR experiments and can be used for the investigation of the many-spin dynamics of nuclear spins in solids.

Entanglement and multiple quantum coherence dynamics in spin clusters

With the purpose to reveal consistency between multiple quantum (MQ) coherences and entanglement, we investigate numerically the dynamics of these phenomena in one-dimensional linear chains and ring of nuclear spins 1/2 coupled by dipole–dipole interactions. As opposed to the calculation of the MQ coherence intensity based on the density matrix describing the spin system as a whole, we consider the “differentiated” intensity related only to the chosen spin pair based on the reduced density matrix. It is shown that the entanglement and the MQ coherence have similar dynamics only for nearest neighbors while we did not obtained any consistency for remote spins.

Two qubits in pure nuclear quadrupole resonance

It is shown theoretically that by the use of two radio-frequency fields of the same resonance frequency but with the different phases and directions the degeneracy of the energy spectrum of a spin system with I = 3/2 is removed. This leads to four non-degenerate spin states which can be used as a platform for quantum computing. The feasibility of quantum computing based on a pure (without DC magnetic fields) nuclear quadrupole resonance technique is investigated in detail. Various quantum logic gates can be constructed by using different excitation techniques allowing different manipulations with the spin system states. Three realizations of quantum logic gates are considered: the application of an additional magnetic field with the resonance frequency, the amplitude modulation of one of the applied RF fields by the resonance frequency field, and the level-crossing method. It is shown that the probabilities of the resonance transitions depend on the method of excitation and on the direction of the excitation field. Feasibility of quantum computing is demonstrated with the examples of constructing a controlled-NOT logic gate using the resonance excitation technique and SWAP and NOT2 logic gates using the level-crossing method.