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.

[1]  Giuliano Benenti,et al.  Principles of Quantum Computation and Information:Volume II: Basic Tools and Special Topics , 2007 .

[2]  A. Redfield,et al.  Nuclear Magnetism: Order and Disorder , 1982 .

[3]  E. B. Fel'dman,et al.  Evolution of spin entanglement and an entanglement witness in multiple-quantum NMR experiments , 2008, 0804.4406.

[4]  V. Vedral,et al.  Magnetic susceptibility as a macroscopic entanglement witness , 2005 .

[5]  W. Wootters.  Entanglement of Formation of an Arbitrary State of Two Qubits , 1997, quant-ph/9709029.

[6]  M. Goldman,et al.  Principles of nuclear magnetic ordering , 1974 .

[7]  Gregory B. Furman,et al.  Nuclear polarization and entanglement in spin systems , 2009, Quantum Inf. Process..

[8]  C. F. Roos,et al.  ‘Designer atoms’ for quantum metrology , 2006, Nature.

[9]  V. Vedral,et al.  Entanglement in many-body systems , 2007, quant-ph/0703044.

[10]  E. B. Fel'dman,et al.  Entanglement in alternating open chains of nuclear spins s = 1/2 with the XY Hamiltonian , 2007 .

[11]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[12]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.

[13]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[14]  B. Terhal.  Bell inequalities and the separability criterion , 1999, quant-ph/9911057.

[15]  D G Cory,et al.  Entanglement assisted metrology. , 2005, Physical review letters.

[16]  Gregory B. Furman,et al.  Entanglement and multiple quantum coherence dynamics in spin clusters , 2009, Quantum Inf. Process..

[17]  M. Horodecki,et al.  Separability of mixed states: necessary and sufficient conditions , 1996, quant-ph/9605038.

[18]  Vlatko Vedral,et al.  Manipulation of Entangled States for Quantum Information Processing , 2002 .

[19]  Multiple quantum NMR and entanglement dynamics in dipolar coupling spin systems , 2008, 0809.1049.