A. K. Khitrin

Phase-modulated heteronuclear decoupling in NMR of solids.

A theoretical description of heteronuclear decoupling in solids, which takes into account homonuclear dipole-dipole interactions and spinning of the sample, is presented. Based on this analysis, a simple and efficient decoupling sequence nPPM is introduced. It consists of n/4 TPPM subcycles, followed by another n/4 subcycles with reversed phases.

Pseudopure state of a twelve-spin system

Pseudopure states of a system of twelve interacting spins are experimentally demonstrated. The system is a cluster of dipolar-coupled nuclear spins of fully labeled (13)C(6)-benzene in a liquid crystalline matrix. At present, this is the largest and the most complex composite system where individual quantum states have been addressed.

Uniform saturation of a strongly coupled spin system by two-frequency irradiation

The theoretical basis of two-frequency saturation is given here in the framework of Provotorov theory. The parameters influencing the saturation efficiency are discussed and studied experimentally using a liquid-crystalline test system. It is shown that double-frequency irradiation can be extremely efficient when the irradiation frequencies are placed at opposite sides of the characteristic frequency of the spin system, and that the frequency separation in the double-frequency irradiation can be varied over a large range. Provotorov theory is also shown to provide good insights into the experimental findings, which would otherwise be difficult to obtain from simulations.

Thermodynamics of adiabatic cross polarization

Using a spin-temperature approach, we describe a scheme of adiabatic cross polarization, based on demagnetization/remagnetization, when the Zeeman order of abundant nuclei in the laboratory frame is first adiabatically converted into the dipolar order, and then, into the Zeeman order of rare nuclei. The scheme, implemented with two low-power frequency-sweeping pulses, is very efficient for static samples and can significantly increase polarization of rare nuclei, compared to the conventional Hartmann-Hahn cross polarization. The experimental examples are presented for a solid, liquid crystal, and small molecules in a liquid-crystalline solvent.

Preparation of pseudopure states in a cluster of dipolar-coupled spins using multiple-quantum dynamics

A method of creating pseudopure spin states in large clusters of coupled spins is described. It is based on filtering multiple-quantum coherence of the highest order, followed by a time-reversal period and partial saturation. Experimental demonstration is presented for a cluster of six dipolar-coupled proton spins of a benzene molecule in a liquid crystalline matrix, and the details of spin dynamics are studied numerically.

Experimental demonstration of quantum state expansion in a cluster of dipolar-coupled nuclear spins.

It is experimentally demonstrated that an arbitrary quantum state of a single spin 1/2: ↓ + ↑ b a can be converted into a superposition of the two ferromagnetic states of a spin cluster: ↓↓ ↓↓ + ↑↑ ↑↑ b a . The physical system is a cluster of seven dipolar-coupled nuclear spins of single-labeled C-benzene molecules in a liquidcrystalline matrix. In this complex system, the pseudopure ground state and the required controlled unitary transformations have been implemented. The experimental scheme can be considered as an explicit model of quantum measurement. PACS: 03.65.-w, 03.67.Mn, 42.50.Dv, 76.60.-k Theory of quantum measurements, which describes a boundary between quantum and classical worlds [1,2], is the least established part of quantum theory. Different approaches to this problem lead to different interpretations of quantum mechanics. A serious difficulty in exploring this subject is that practical measuring devices are too complex to allow a detail analysis of their dynamics. It may be helpful to consider some simple and explicit models of quantum measurement, using systems with controllable quantum dynamics. One of possible experimental models is proposed and studied in this work. Let us consider a system of 1 + N spins 1/2 (qubits) in the initial state N N b a 0 0 0 0 ) 1 0 ( ψ 1 2 1 0 0 in − + = ... , 1 2 2 = + b a , (1) where the qubit notations k k ↑ ≡ 0 and k k ↓ ≡ 1 are used. In this state, the 0-th qubit is in some arbitrary state, defined by two complex coefficients a and b , while the qubits 1 to are in the ground state. Quantum logic circuit [3] N 1 , 0 2 , 1 1 , 2 , 1 CNOT CNOT CNOT CNOT U N N N N ... − − − = (2) is a chain of unitary controlled-not gates , which flip the target qubit n when the control qubit m is in the state n m CNOT , m 1 and do not change the qubit n when the qubit m is in the state m 0 . If the 0-th qubit is in the state 0 1 , it flips the qubit 1, the qubit 1 flips the qubit 2, and so on. A wave of flipped qubits, triggered by the 0-th qubit, propagates until it covers the entire system. As a result, the circuit (2) converts the initial state (1) into the final state N N N N b a U 1 1 1 1 0 0 0 0 ψ ψ 1 1 0 1 1 0 in out − − + = = ... ... . (3)

Projective measurement in nuclear magnetic resonance

It is demonstrated that nuclear magnetic resonance experiments using pseudopure spin states can give possible outcomes of projective quantum measurement and probabilities of such outcomes. The physical system is a cluster of six dipolar-coupled nuclear spins of benzene in a liquid-crystalline matrix. For this system with the maximum total spin S=3, the results of measuring SX are presented for the cases when the state of the system is one of the eigenstates of SZ.

Twelve-spin “Schrödinger cat”

Pseudopure “cat” state, a superposition of quantum states with all spins up and all spins down, is experimentally demonstrated for a system of 12 dipolar-coupled nuclear spins of fully C13-labeled benzene molecule oriented in a liquid-crystalline matrix.

Selective excitation of homogeneous spectral lines

It is possible, by selective excitation of homogeneously broadened lines, to produce response signals, which are orders of magnitude narrower than the original lines. The new type of echo, which allows detecting such signals, and the formalism, useful for understanding the phenomenon, as well as the experimental examples from NMR spectroscopy are presented. Long-lived partial NMR echo in solids can be excited by a simple two-pulse Hahn sequence.

Stimulated wave of polarization in a one-dimensional Ising chain

It is demonstrated that in a one-dimensional Ising chain with nearest-neighbor interactions, irradiated by a weak resonant transverse field, a stimulated wave of flipped spins can be triggered by a flip of a single spin. This analytically solvable model illustrates mechanisms of quantum amplification and quantum measurement.