arXiv subjects

G. B. Furman

Publications and source records attributed to G. B. Furman.

15 recordsLinked to original sources

arXiv2017

Single-spin entanglement

We show that the operators and the quadrupole and Zeeman Hamiltonians for a spin (3/2) can be represented in terms for a system of two coupling fictitious spins (1/2) using the Kronecker product of Pauli matrices. Particularly, the quadrupole Hamiltonian which describes the interaction of the nuclear quadrupole moment with an electric field gradient is represented as the Hamiltonian of Ising model in a transverse selective magnetic field. The Zeeman Hamiltonian, which describes interaction of the nuclear spin with the external magnetic field, can be considered as the Hamiltonian of the Heisenberg model in a selective magnetic field. The total Hamiltonian can be interpreted as the Hamiltonian of 3D Heisenberg model in an inhomogeneous magnetic field applied along the x-axis. The representation of a single spin (3/2) as two-spin (1/2) system allows us to study entanglement in the spin system. One of the features of the fictitious spin system is that, in both the pure and the mixed states, the concurrence tends to 0.5 with increase of applied magnetic field. The representation of a spin (3/2) as a system of two coupling fictitious spins (1/2) and possibility of formation of the entangled states in this system open a way to the application of a single spin (3/2) in quantum computation.

quant-ph↗

arXiv2013

Low temperature MQ NMR dynamics in dipolar ordered state

We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in dipolar ordered spin systems of nuclear spins 1/2 at a low temperatures. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar energy. The other method uses an additional resonance (π/4)_{y}-pulse after the preparation period of the standard MQ NMR experiment in solids and allows one to measure the Zeeman energy. The both considered methods are sensitive to the contribution of remote spins in the interaction and to the spin system structure. The QS method is sensitive to the spin number in the molecule while the PS method gives very similar time dependencies of the intensities of MQ coherences for different spin numbers. It is shown that the use of the dipolar ordered initial state has the advantage of exciting the highest order MQ coherences in clusters of 4m identical spins, where m=1,2,3..., that is impossible to do with the standard MQ method. MQ NMR methods based on the dipolar ordered initial states at low temperatures complement the standard NMR spectroscopy for better studying structures and dynamic processes in solids.

cond-mat.mes-hall↗

arXiv2013

Quantum entanglement at negative temperature

An isolated spin system that is in internal thermodynamic equilibrium and that has an upper limit to its allowed energy states can possess a negative temperature. We calculate the thermodynamic characteristics and the concurrence in this system over the entire range of positive and negative temperatures. Our calculation was performed for different real structures, which can be used in experiments. It is found that the temperature dependence of the concurrence is substantially asymmetrical similarly other thermodynamic characteristics. At a negative temperature the maximum concurrence and the absolute temperature of the entanglement appearance are sufficiently larger than those at a positive temperature. The concurrence can be characterized by two dimensionless parameters: by the ratio between the Zeeman and dipolar energies and by the ratio of the thermal and dipolar energies. It was shown that for all considered structures the dimensionless temperatures of the transition between entanglement and separability of the first and second spins are independent of spin structure and number of spins.

quant-ph↗

arXiv2010

Entanglement between states of single quadrupole nuclear spin

We study entanglement between quantum states of multi level spin system of a single particle considering a nucleus with spin 3/2 in both the internal electric field gradient and the external magnetic field. It was shown that entanglement is achieved by applying a magnetic field to a single particle at low temperature (~ 5 mK). In this temperature range, the numerical calculation revealed the coincidence between magnetization and concurrence. As a result, the magnetization can be used as an entanglement witness for such systems.

quant-ph↗

arXiv2010

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.

quant-ph↗

arXiv2009

Multiple Quantum Coherence and Entanglement 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.

quant-ph↗

arXiv2008

Multiple Quantum NMR Dynamics in Pseudopure States

We investigate 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 pseudopure initial state. Simulations of the MQ NMR with the real molecular structures such as six dipolar-coupled proton spins of a benzene, hydroxyl proton chains in calcium hydroxyapatite and fluorine chains in calcium fluorapatite open the way to experimental NMR testing of the obtained results. It was found that multiple-spin 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

cond-mat.other↗

arXiv2008

Polarization and entanglement in spin systems

We established important relationships between entanglement measures and the order parameter (spin 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.

quant-ph↗

arXiv2008

Multiple Quantum NMR and Entanglement Dynamics in Dipolar Coupling Spin

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.

quant-ph↗

arXiv2008

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 the 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 investigated model 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 the direct interactions between the nearest neighbors, the entanglement between remote spins is generated.

quant-ph↗

arXiv2007

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.

cond-mat.other↗

arXiv2006

Stimulated wave of polarization in spin chains

Stimulated wave of polarization, triggered by a flip of a single spin, presents a simple model of quantum amplification. Previously, it has been found that such wave can be excited in a 1D Ising chain with nearest-neighbor interactions, irradiated by a weak resonant transverse field. Here we explore models with more realistic Hamiltonians, in particular, with natural dipole-dipole interactions. Results of simulations for 1D spin chains and rings with up to nine spins are presented.

quant-ph↗

arXiv2004

Perturbation approach to dipolar coupling spin dynamics

A perturbation method is presented which can be applied to the description of a wide range of physical problems that deal with dynamics of dipolar coupled spins in solids. The method is based on expansion of the operator exponent in a perturbation series. As example of application the method, the multile-quantum coherence dynamics in three and four spin cluster are considered. The calculated 0Q- and 2Q intensities vs the duration of the preparation period give closed agreement with exact results and simulations data. The exact solutions for J0Q and J2Q coherences in four spin system are obtained.

cond-mat.other↗

arXiv2004

Multi-photon resonances in pure multiple-pulse NQR

We have observed multi-photon resonances in a system with a spin 3/2 irradiated simultaneously by a multiple pulse radiofrequency sequence and a low frequency field swept in the range 0-80 kHz. The used excitation scheme allowed us to measure the effective field of the radiofrequency sequence. A peculiarity of this scheme is that the intensity of the resonance lines decreases slowly with the mode number. The theoretical description of the effect is presented using both the rotating frame approximation and the Floquet theory. Both approaches give indentical results at the calculation of the resonance frequencies, transition probabilities and shifts of resonance frequency. The calculated magnetization vs. the frequency of the low-frequency field agrees well with the obtained experimental data. The multi-frequency spectra give a way for studying slow atomic motion in solids.

cond-mat.mtrl-sci↗

arXiv2004

Multiple quantum dynamics in a system of dipole-coupling spins in solid

A perturbation method deals with dipolar coupling spins in solids is presented. As examples of the application the method, the multile-quantum coherence dynamics in clusters of a linear chain of four nuclear spins and a ring of six spins coupled by dipole-dipole interaction are considered. The calculated 0Q- and 2Q intensities in a linear chain of four nuclear spins and 6Q intensity in a ring of six spins vs the duration of the preparation period agree well with the exact solutions (for linear chain of four nuclear spins) and simulation data (for linear chain of four nuclear spins and a ring of six spin).

cond-mat.mtrl-sci↗