Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1301.5554 · Physical Review A

Classical bifurcation in a quadrupolar NMR system

A. G. Araujo-Ferreira, R. Auccaise, Roberto S. Sarthour, Ivan S. Oliveira, Tito José Bonagamba, I. Roditi

Published May 8, 2013• 31 citations
arXivHTMLPDF

Abstract

The Josephson junction model is applied to the experimental implementation of classical bifurcation in a quadrupolar nuclear magnetic resonance system. There are two regimes, one linear and one nonlinear, which are implemented by the radio-frequency and the quadrupolar terms of the Hamiltonian of a spin system, respectively. These terms provide an explanation of the symmetry breaking due to bifurcation. Bifurcation depends on the coexistence of both regimes at the same time in different proportions. The experiment is performed on a lyotropic liquid crystal sample of an ordered ensemble of ${}^{133}$Cs nuclei with spin $I=7/2$ at room temperature. Our experimental results confirm that bifurcation happens independently of the spin value and of the physical system. With this experimental spin scenario, we confirm that a quadrupolar nuclei system could be described analogously to a symmetric two-mode Bose-Einstein condensate.

DOI
10.1103/physreva.87.053605

Related papers

NMR quadrupolar system described as Bose–Einstein-condensate-like system

R. Auccaise, J. Teles, Tito José Bonagamba +3 more

This paper presents a description of nuclear magnetic resonance (NMR) of quadrupolar systems using the Holstein-Primakoff (HP) formalism and its analogy with a Bose-Einstein condensate (BEC) system. Two nuclear spin systems constituted of quadrupolar nuclei I=3/2 ((23)Na) and I=7/2 ((133)Cs) in lyotropic liquid crystals were used for experimental demonstrations. Specifically, we derived the conditions necessary for accomplishing the analogy, executed the proper experiments, and compared with quantum mechanical prediction for a Bose system. The NMR description in the HP representation could be applied in the future as a workbench for BEC-like systems, where the statistical properties may be obtained using the intermediate statistic, first established by Gentile. The description can be applied for any quadrupolar systems, including new developed solid-state NMR GaAS nanodevices.

The Journal of Chemical Physics•Apr 8, 2009•14 citations

Spin Squeezing in a Quadrupolar Nuclei NMR System

R. Auccaise, A. G. Araujo-Ferreira, Roberto S. Sarthour +3 more

We have produced and characterized spin-squeezed states at a temperature of 26 °C in a nuclear magnetic resonance quadrupolar system. The experiment was carried out on 133Cs nuclei of spin I=7/2 in a sample of lyotropic liquid crystal. The source of spin squeezing was identified as the interaction between the quadrupole moment of the nuclei and the electric field gradients present within the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing on a Hilbert space of dimension 2I+1=8. The quantitative and qualitative characterization of this spin-squeezing phenomenon is expressed by a squeezing parameter and squeezing angle developed for the two-mode Bose-Einstein condensate system, as well as by the Wigner quasiprobability distribution function. The generality of the present experimental scheme points to potential applications in solid-state physics.

arXiv:1403.2706•Physical Review Letters•Jan 29, 2015•63 citations

Nuclear magnetic resonance quantum logic gates using quadrupolar nuclei

Anatoly K. Khitrin, B. M. Fung

The use of nuclei with spin >1/2 and quadrupolar splitting of the spin energy levels has certain advantages over systems of interacting spins 1/2 for building quantum logic gates. Experimental demonstration has been made using 23Na (spin 3/2) NMR in a lyotropic liquid crystal system. The pulse sequences for establishing effective pure quantum states are given, and the resulting NMR spectra are presented.

The Journal of Chemical Physics•Apr 22, 2000•81 citations

Relaxation of coherent states in a two-qubit NMR quadrupole system

Roberto S. Sarthour, Eduardo Ribeiro DeAzevedo, Fábio Aurélio Bonk +5 more

We report a detailed study of the longitudinal relaxation of several coherent states on the nuclear-magnetic-resonance (NMR) two-qubit quadrupole system, ${}^{23}\mathrm{Na}$ (spin 3/2) in a lyotropic liquid-crystal system at room temperature. Relaxation of pseudopure states, simulated pseudo-Bell states and Hadamard states were investigated. The coherence of superposition states was verified by applying the respective quantum ``reading'' operators and comparing the recovered state with the original one. The degree of recovery varies between $\ensuremath{\approx}70%$ and $\ensuremath{\approx}100%,$ depending on the time length of the gate, as compared to relaxation times. Spin-lattice relaxation results follow a recently proposed multiexponential model that includes mixed magnetic dipolar and electric quadrupolar interactions. Relaxation curves are governed by initial conditions, and from the experimental curves individual transition rates are derived. The transverse relaxation time constant ${T}_{2}$ is found not to depend on the initial distribution of populations. This is a systematic study of relaxation in the context of NMR quantum computing.

Physical Review A•Aug 22, 2003•24 citations

Classical resonance interactions and Josephson junction in macroscopic quantum dynamics

Valery N. Pilipchuk

It is shown that the classical dynamics of 1:1 resonance interaction between two identical linearly coupled Duffing oscillators is equivalent to the symmetric (non-biased) case of `macroscopic' quantum dynamics of two weakly coupled Bose-Einstein condensates. The analogy develops through the boson Josephson junction equations, however, reduced to a single conservative energy partition (EP) oscillator. The derived oscillator is solvable in quadratures, furthermore it admits asymptotic solution in terms of elementary functions after transition to the action-angle variables. Energy partition and coherency indexes are introduced to provide a complete characterization of the system dynamic states through the state variables of the EP oscillator. In particular, nonlinear normal and local mode dynamics of the original system associate with equilibrium points of such oscillator. Additional equilibrium points - the local modes - may occur on high energy level as a result of the symmetry breaking bifurcation, which is equivalent to the macroscopic quantum self-trapping effect in boson Josephson junction. Finally, since the Hamiltonian of EP oscillator is always quadratic with respect its linear momentum, the idea of second quantization can be explored without usual transition to the rigid pendulum approximation.

arXiv:1205.4842•May 22, 2012•1 citation

Use of quadrupolar nuclei for quantum-information processing by nuclear magnetic resonance: Implementation of a quantum algorithm

Ranabir Das, Anil Kumar

Physical implementation of quantum-information processing by liquid-state nuclear magnetic resonance, using weakly coupled spin-$\frac{1}{2}$ nuclei of a molecule, is well established. Nuclei with $\mathrm{spin}>1/2$ oriented in liquid-crystalline matrices is another possibility. Such systems have multiple qubits per nuclei and large quadrupolar couplings resulting in well separated lines in the spectrum. So far, creation of pseudopure states and logic gates has been demonstrated in such systems using transition selective radio-frequency pulses. In this paper we report two developments. First, we implement a quantum algorithm that needs coherent superposition of states. Second, we use evolution under quadrupolar coupling to implement multiqubit gates. We implement the Deutsch-Jozsa algorithm on a spin-$\frac{3}{2}$ (2 qubit) system. The controlled-NOT operation needed to implement this algorithm has been implemented here by evolution under the quadrupolar Hamiltonian. To the best of our knowledge, this method has been implemented for the first time in quadrupolar systems. Since the quadrupolar coupling is several orders of magnitude greater than the coupling in weakly coupled spin-$\frac{1}{2}$ nuclei, the gate time decreases, increasing the clock speed of the quantum computer.

arXiv:quant-ph/0306100•Physical Review A•Sep 10, 2003•54 citations
The Josephson junction model is applied to the experimental implementation of classical bifurcation in a quadrupolar nuclear magnetic resonance system. There are two regimes, one linear and one nonlinear, which are implemented by the radio-frequency and the quadrupolar terms of the Hamiltonian of a spin system, respectively. These terms provide an explanation of the symmetry breaking due to bifurcation. Bifurcation depends on the coexistence of both regimes at the same time in different proportions. The experiment is performed on a lyotropic liquid crystal sample of an ordered ensemble of 133{}^{133}133Cs nuclei with spin I=7/2I=7/2I=7/2 at room temperature. Our experimental results confirm that bifurcation happens independently of the spin value and of the physical system. With this experimental spin scenario, we confirm that a quadrupolar nuclei system could be described analogously to a symmetric two-mode Bose-Einstein condensate.
This paper presents a description of nuclear magnetic resonance (NMR) of quadrupolar systems using the Holstein-Primakoff (HP) formalism and its analogy with a Bose-Einstein condensate (BEC) system. Two nuclear spin systems constituted of quadrupolar nuclei I=3/2 ((23)Na) and I=7/2 ((133)Cs) in lyotropic liquid crystals were used for experimental demonstrations. Specifically, we derived the conditions necessary for accomplishing the analogy, executed the proper experiments, and compared with quantum mechanical prediction for a Bose system. The NMR description in the HP representation could be applied in the future as a workbench for BEC-like systems, where the statistical properties may be obtained using the intermediate statistic, first established by Gentile. The description can be applied for any quadrupolar systems, including new developed solid-state NMR GaAS nanodevices.
We have produced and characterized spin-squeezed states at a temperature of 26 °C in a nuclear magnetic resonance quadrupolar system. The experiment was carried out on 133Cs nuclei of spin I=7/2 in a sample of lyotropic liquid crystal. The source of spin squeezing was identified as the interaction between the quadrupole moment of the nuclei and the electric field gradients present within the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing on a Hilbert space of dimension 2I+1=8. The quantitative and qualitative characterization of this spin-squeezing phenomenon is expressed by a squeezing parameter and squeezing angle developed for the two-mode Bose-Einstein condensate system, as well as by the Wigner quasiprobability distribution function. The generality of the present experimental scheme points to potential applications in solid-state physics.
We report a detailed study of the longitudinal relaxation of several coherent states on the nuclear-magnetic-resonance (NMR) two-qubit quadrupole system, 23Na{}^{23}\mathrm{Na}23Na (spin 3/2) in a lyotropic liquid-crystal system at room temperature. Relaxation of pseudopure states, simulated pseudo-Bell states and Hadamard states were investigated. The coherence of superposition states was verified by applying the respective quantum ``reading'' operators and comparing the recovered state with the original one. The degree of recovery varies between $\ensuremath{\approx}70%$ and $\ensuremath{\approx}100%,$ depending on the time length of the gate, as compared to relaxation times. Spin-lattice relaxation results follow a recently proposed multiexponential model that includes mixed magnetic dipolar and electric quadrupolar interactions. Relaxation curves are governed by initial conditions, and from the experimental curves individual transition rates are derived. The transverse relaxation time constant T2{T}_{2}T2​ is found not to depend on the initial distribution of populations. This is a systematic study of relaxation in the context of NMR quantum computing.
It is shown that the classical dynamics of 1:1 resonance interaction between two identical linearly coupled Duffing oscillators is equivalent to the symmetric (non-biased) case of `macroscopic' quantum dynamics of two weakly coupled Bose-Einstein condensates. The analogy develops through the boson Josephson junction equations, however, reduced to a single conservative energy partition (EP) oscillator. The derived oscillator is solvable in quadratures, furthermore it admits asymptotic solution in terms of elementary functions after transition to the action-angle variables. Energy partition and coherency indexes are introduced to provide a complete characterization of the system dynamic states through the state variables of the EP oscillator. In particular, nonlinear normal and local mode dynamics of the original system associate with equilibrium points of such oscillator. Additional equilibrium points - the local modes - may occur on high energy level as a result of the symmetry breaking bifurcation, which is equivalent to the macroscopic quantum self-trapping effect in boson Josephson junction. Finally, since the Hamiltonian of EP oscillator is always quadratic with respect its linear momentum, the idea of second quantization can be explored without usual transition to the rigid pendulum approximation.
Physical implementation of quantum-information processing by liquid-state nuclear magnetic resonance, using weakly coupled spin-12\frac{1}{2}21​ nuclei of a molecule, is well established. Nuclei with spin>1/2\mathrm{spin}>1/2spin>1/2 oriented in liquid-crystalline matrices is another possibility. Such systems have multiple qubits per nuclei and large quadrupolar couplings resulting in well separated lines in the spectrum. So far, creation of pseudopure states and logic gates has been demonstrated in such systems using transition selective radio-frequency pulses. In this paper we report two developments. First, we implement a quantum algorithm that needs coherent superposition of states. Second, we use evolution under quadrupolar coupling to implement multiqubit gates. We implement the Deutsch-Jozsa algorithm on a spin-32\frac{3}{2}23​ (2 qubit) system. The controlled-NOT operation needed to implement this algorithm has been implemented here by evolution under the quadrupolar Hamiltonian. To the best of our knowledge, this method has been implemented for the first time in quadrupolar systems. Since the quadrupolar coupling is several orders of magnitude greater than the coupling in weakly coupled spin-12\frac{1}{2}21​ nuclei, the gate time decreases, increasing the clock speed of the quantum computer.