Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase damping and amplitud
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Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase damping and amplitude damping noise channels HARPREET SINGH1,2 , ARVIND1 and KAVITA DORAI1
,∗
1 Department
of Physical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81 Knowledge City, P.O. Manauli, Mohali 140 306, India 2 Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany ∗ Corresponding author. E-mail: [email protected] MS received 18 April 2020; revised 25 July 2020; accepted 18 August 2020 Abstract. In this work, we studied the relaxation dynamics of coherences of different orders present in a system of two coupled nuclear spins. We used a previously designed model for intrinsic noise present in such systems which considers the Lindblad master equation for Markovian relaxation. We experimentally created zero-, singleand double-quantum coherences in several two-spin systems and performed a complete state tomography and computed state fidelity. We experimentally measured the decay of zero- and double-quantum coherences in these systems. The experimental data fitted well to a model that considers the main noise channels to be a correlated phase damping (CPD) channel acting simultaneously on both spins in conjunction with a generalised amplitude damping channel acting independently on both spins. The differential relaxation of multiple-quantum coherences can be ascribed to the action of a CPD channel acting simultaneously on both the spins. Keywords. Nuclear magnetic resonance relaxation theory; Multiple quantum coherences; Lindblad master equation; Markovian noisy channels. PACS Nos
03.65.Yz; 76.60.−k; 03.67.a
1. Introduction Quantum coherence is associated with a transition between the eigenstates of a quantum system and most spectroscopic signals crucially rely on the manipulation, transfer and detection of such coherences [1]. In nuclear magnetic resonance (NMR), spin coherence resides in the off-diagonal elements of the density operator of the system and a system of coupled spin1/2 nuclei can have coherences of different orders n (n = 0, 1, 2, . . .) [2]. NMR can directly access only those off-diagonal elements of the density matrix whose difference in magnetic quantum number is ±1 (the single quantum transitions). The direct observation of multiple quantum transitions (m = ±1) is forbidden by quantum-mechanical selection rules (in the dipole approximation). Multiple quantum coherences have found several useful applications in NMR including spectral simplification, spin-locking and crosspolarisation experiments [3].
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The interaction with the environment of a quantum system causes loss of coherence and forces the system to relax back towards a time-invariant equilibrium state. This limits the time over which coherences live and leads to poor signal sensitivity [4]. In solution state NMR the problem is exaggerated when dealing with larger spin systems such as those encountered in proteins,
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