Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1703.01954

Bloch-Siegert Shift and its Kramers-Kronig Pair

Arnab Chakrabarti·Rangeet Bhattacharyya
View original source ↗Read source document ↗Export metadata ↓

Abstract

We report that the Bloch-Siegert shift which appears in Nuclear Magnetic Resonance (NMR) spectroscopy can also be shown to originate as a part of a complex drive-induced second-order susceptibility term. The shift terms thus obtained are shown to have an absorptive Kramers-Kronig pair. The theoretical treatment involves a finite time-propagation of a nuclear spin-$1/2$ system and the spin-bearing molecule under the action of thermal fluctuations acting on the latter. The finite propagator is constructed to account for many instances of thermal fluctuations occurring in a time-scale during which the spin density matrix changes infinitesimally. Following an ensemble average, the resulting quantum master equation directly yields a finite time-nonlocal complex susceptibility term from the external drive, which is extremely small but measurable in solution-state NMR spectroscopy. The dispersive part of this susceptibility term originating from the non-resonant component of the external drive results in the Bloch-Siegert shift. We have verified experimentally the existence of the absorptive Kramers-Kronig pair of the second-order shift term, by using a novel refocussed nutation experiment. Our method provides a single approach to explain both relaxation phenomena as well as Bloch-Siegert effect, which have been treated using non-concurrent techniques in the past.

Explore related subjects

quant-phcond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Arnab Chakrabarti, Rangeet Bhattacharyya. 2018-03-20. Bloch-Siegert Shift and its Kramers-Kronig Pair. https://arxiv.org/abs/1703.01954

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fermionic magic resources in disordered quantum spin chains

Fermionic non-Gaussianity quantifies a quantum state's deviation from a classically tractable free-fermionic description, constituting a necessary resource for computational quantum advantage. Here we use fermionic antiflatness (FAF) to measure this deviation across ergodic and many-body localized (MBL) regimes. We focus on the paradigmatic disordered spin-$1\!/2$ XXZ chain and its impurity variant with local interactions. Across highly excited eigenstates, FAF evolves from typical-state behavior at weak disorder to strongly suppressed values deep in the MBL regime, with volume-law scaling in the XXZ chain and an area-law bound in the impurity setting. Rare long-range cat-like eigenstates exhibit a pronounced enhancement of FAF, making it a sensitive diagnostic of mechanisms proposed to destabilize MBL. Starting from product states, we find that in the MBL regime FAF grows slowly in time, approaching saturation via a power-law relaxation. Overall, our results show that MBL suppresses fermionic non-Gaussianity, and the associated complexity beyond free fermions, while ergodicity restores it, motivating explorations of fermionic non-Gaussianity in other ergodicity-breaking phenomena.

quant-ph↗
arXiv2026

Progressive Binarization - Pauli Correlation Encoding: a Continuation Method for Constrained Optimization

Pauli Correlation Encoding (PCE) reduces the qubit requirements of quantum optimization by embedding the problem variables into the expectation values of Pauli observables, so that the number of qubits can be much smaller than the number of variables. PCE has not yet been studied for constrained optimization. We extend it to constrained combinatorial problems, using the budget-constrained MinCut as a case study, and show that the standard formulation fails to reliably enforce the constraint: feasibility hinges on the binarization of the encoded variables, which depends sensitively on hyperparameters that are hard to tune and do not transfer across instances. To address this, we introduce Progressive-Binarization PCE (PB-PCE), an adaptive continuation scheme that progressively increases the binarization parameter while re-optimizing the circuit from the previous solution, driving the variables towards the binary domain. PB-PCE attains near-complete constraint satisfaction (88--100\%) and smaller cut sizes than standard PCE, with a number of stages (10--20) essentially independent of problem size, solving instances of up to 300 variables with only 9-qubit circuits.

quant-ph↗
arXiv2026

A quantum model for synchronizing finite state transition systems

We propose a quantum model for finding a resetting input sequence (RS) which can take a finite state transition system (FA), to particular state independent of its current state. The complexity of finding such sequences for various types of FA can be NP-Hard or even PSPACE-Complete. To this end, we represent the FA states, inputs, and transition function in quantum space. Accordingly, we propose a model to represent the execution of an input sequence of a particular length $l$ starting form an initial FA state. The model is extended considering the application in superposition of all input sequences of length $l$ to an initial state of the FA. The model is further extended considering the application of all input sequences to all initial states of the FA capturing for every input sequence the collection (ordered list) of states reached by applying the sequence to all states of the FA. The amplitude amplification algorithm is then used as it combines similar collections of reached states while preserving all input sequences that reach these collections. A Grover search for a reached collection where its elements correspond to the same FA state provides a RS for the FA. Our approach offers a quadratic gain over the exponential complexity of traditional brute-force method, which is the only method that can be applied to a general FA class.

quant-ph↗