Introduction In Part B of this book we turn to a rigorous quantum mechanical description of NMR experiments. We explain what product operators really are, justify the way they have been used to understand the operation of NMR pulse sequences, and derive many...
We first introduce an alternative way to study the insensitive nuclei enhanced by polarization and distortionless enhancement by polarization transfer NMR experiments with the product operator descriptions for weakly coupled IS (I = 1/2, S = 1/2) spin systems as a quantum controlled not gate and a not gate, respectively.In this framework we apply the density matrix operators obtained from the analytical descriptions of the mentioned pulse sequences by using product operator formalism step by step on the NMR spin product states represented in Dirac's notation.
Genetic algorithms (GA) are stochastic global search methods based on the
mechanics of natural biological evolution, proposed by John Holland in 1975. Here
in this thesis, we have exploited possible utilities of Genetic Algorithm optimization
in Nuclear Magnetic Resonance (NMR) experiments. We have performed
(i ) Pulse sequence generation and optimization for NMR Quantum Information
Processing, (ii ) efficient creation of NOON states, (iii ) Composite operator design
and (iv ) delay optimization for refocused quantitative INEPT. We have generated
time optimal as well as robust pulse sequences for popular quantum gates. A
Matlab package is developed for basic Target unitary operator to pulse sequence
optimization and is explained with an example.
Chapter 1 contains a brief introduction to NMR, Quantum computation and Genetic
algorithm optimization. Experimental unitary operator decomposition using
Genetic Algorithm is explained in Chapter 2. Starting from a two spin homonu-
clear system (5-Bromofuroic acid), we have generated hard pulse sequences for
performing (i ) single qubit rotation, (ii ) controlled NOT gates and (iii ) pseudo
pure state creation, which demonstrates universal quantum computation in such
systems. The total length of the pulse sequence for the single qubit rotation of an
angle π/2 is less than 500µs, whereas the conventional method (using a selective
soft pulse) would need a 2ms shaped pulse. This substantial shortening in time
can lead to a significant advantage in quantum circuits. We also demonstrate the
creation of Long Lived Singlet State and other Bell states, directly from thermal
equilibrium state, with the shortest known pulse sequence. All the pulse sequences
generated here are generic i.e., independent of the system and the spectrometer.
We further generalized this unitary operator decomposition technique for a variable
operators termed as Fidelity Profile Optimization (FPO) (Chapter 3) and
performed quantum simulations of Hamiltonian such as Heisenberg XY interaction
and Dzyaloshinskii-Moriya interaction. Exact phase (φ) dependent experimental
unitary decompositions of Controlled-φ and Controlled Controlled-φ are solved
using first order FPO. Unitary operator decomposition for experimental quantum
simulation of Dzyaloshinskii-Moriya interaction in the presence of Heisenberg XY
interaction is solved using second order FPO for any relative strengths of interactions
(γ) and evolution time (τ ). Experimental gate time for this decomposition
is invariant under γ or τ , which can be used for relaxation independent studies of
the system dynamics. Using these decompositions, we have experimentally verified
the entanglement preservation mechanism suggested by Hou et al. [Annals of
Physics, 327 292 (2012)].
NOON state or Schrodinger cat state is a maximally entangled N qubit state
with superposition of all individual qubits being at |0 and being at |1 . NOON
states have received much attention recently for their high precession phase
measurements, which enables the design of high sensitivity…
We present an NMR experiment to detect the evolution of a spin system during the transient to a quasi-equilibrium state. In this way, new evidence is presented in favor of irreversible decoherence as the mechanism which leads an initial out-of-equilibrium state to quasi-equilibrium. The results are obtained using a modified Jeener-Broekaert experiment where a spin reversion pulse sequence and a decode of coherence are included. The sequence also allows visualizing the evolution of the full spectra of the different coherences during the formation of the quasi-equilibrium. We use different reversion strategies on three nematic liquid crystal samples. We conclude that the eigen-selection observed as an evidence of irreversible decoherence is an indication that the spin system in liquid-crystal NMR experiments, conform actual quantum open systems, where the quasi-equilibrium is a rigorous description of their dynamics in a time-scale far earlier than thermal equilibrium.