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arXiv:1403.2706 · Physical Review Letters

Spin Squeezing in a Quadrupolar Nuclei NMR System

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

Published Jan 29, 2015• 63 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.114.043604

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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.
This study investigates spin squeezed states in nuclear magnetic resonance (NMR) quadrupolar systems with spins I=3/2I=3/2I=3/2 and I=7/2I=7/2I=7/2 at room temperature, taking into account the effects of relaxation on the dynamics. The origin of spin squeezing is attributed to the interaction between the nuclear quadrupole moment and the electric field gradients in the molecular environment. The formal description of the nonlinear operators responsible for spin squeezing is achieved using the spin angular momentum representation via the one-axis twisting mechanism. This approach provides a framework for quantum control and metrology over the spin squeezing process while accounting for the influence of relaxation phenomena. Non-Cartesian angular momentum operators are proposed, with their variances products catching the quantum effects during the dynamics. An upper bound for the squeezing parameter and the Heisenberg uncertainty at thermal equilibrium are also predicted for any spin quantum number.
Control over nuclear-spin fluctuations is essential for processes that rely on preserving the quantum state of an embedded system. For this purpose, squeezing is a viable alternative, so far that has not been properly exploited for the nuclear spins. Of particular relevance in solids is the electric quadrupole interaction (QI), which operates on nuclei having spin higher than 1/2. In its general form, QI involves an electric-field gradient (EFG) biaxiality term. Here, we show that as this EFG biaxiality increases, it enables continuous tuning of single-particle squeezing from the one-axis twisting to the two-axis countertwisting limits. A detailed analysis of QI squeezing is provided, exhibiting the intricate consequences of EFG biaxiality. The initial states over the Bloch sphere are mapped out to identify those favorable for fast initial squeezing, or for prolonged squeezings. Furthermore, the evolution of squeezing in the presence of a phase-damping channel and an external magnetic field are investigated. We observe that dephasing drives toward an antisqueezed terminal state, the degree of which increases with the spin angular momentum. Finally, QI squeezing in the limiting case of a two-dimensional EFG with a perpendicular magnetic field is discussed, which is of importance for two-dimensional materials, and the associated beat patterns in squeezing are revealed.
Nuclear magnetic resonance (NMR) experiments can reveal local properties in materials, but are often limited by the low signal-to-noise ratio.Spin squeezed states have an improved resolution below the Heisenberg limit in one of the spin components, and have been extensively used to improve the sensitivity of atomic clocks, for example [1].Interacting and entangled spin ensembles with non-linear coupling are a natural candidate for implementing squeezing.Here, we propose measurement of the spin-squeezing parameter that itself can act as a local probe of emergent orders in quantum materials.In particular, we demonstrate how to investigate an anisotropic electric field gradient via its coupling to the nuclear quadrupole moment.While squeezed spin states are pure, the squeezing parameter can be estimated for both pure and mixed states.We evaluate the range of fields and temperatures for which a thermal-equilibrium state is sufficient to improve the resolution in an NMR experiment and probe relevant parameters of the quadrupole Hamiltonian, including its anisotropy.
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 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.