Many-spin System Research Articles

Dynamic quantum-enhanced sensing without entanglement in central spin systems

We propose a dynamic quantum sensing scheme by using a quantum many-spin system composed of a central spin interacting with many surrounding spins. Starting from a generalized Ising ring model, we investigate the error propagation formula of the central spin, and it indicates that Heisenberg scaling can be reached while the probe state only needs to be a product state. Particularly, we derive an analytical form of the dynamic quantum Fisher information in a limit case, which explicitly exhibits the Heisenberg scaling. By comparing with numerical results, we demonstrate that the general case can be well approximated by the analytical result when the coupling strength among the surrounding spins is much weaker than the coupling strength between the central and surrounding spins. This analytic result guides us to find the appropriate probe state and the proper measurement time to achieve the Heisenberg scaling in realistic situations. Furthermore, we investigate various effects which are important in practical quantum systems, including the central spin Zeeman term, the anisotropy of the hyperfine interaction and the inhomogeneity of the hyperfine coupling strength. Our result indicates that the dynamic quantum-enhanced sensing scheme seems feasible in realistic quantum central spin systems, like semiconductor quantum dots.

Magnon-mediated quantum battery under systematic errors

Quantum battery is one of the most prominent micro-devices in the rapid-developing quantum thermodynamics. We propose a quantum charging protocol in which both battery and charger are consisted of a many-spin system. The battery and charger are connected via the Kittle mode of the magnon system, that serves as a charging wire and then enables a long-range charging protocol. Counter-intuitively, we find that the spin-spin couplings insider both battery and charger can be used to promote the charging performance in comparison to the noninteracting condition. And a remarkable promotion is realized at a "sweet" spot in terms of the average coupling strength. Moreover, we apply the quantum-state-diffusion equation to test the robustness of our magnon-mediated charging protocol to the systematic errors about the magnon frequency.

Perturbation Independent Decay of the Loschmidt Echo in a Many-Body System.

When a qubit or spin interacts with others under a many-body Hamiltonian, the information it contains progressively scrambles. Here, nuclear spins of an adamantane crystal are used as a quantum simulator to monitor such dynamics through out-of-time-order correlators, while a Loschmidt echo (LE) asses how weak perturbations degrade the information encoded in these increasingly complex states. Both observables involve the implementation of a time-reversal procedure which, in practice, involves inverting the sign of the effective Hamiltonian. Our protocols use periodic radio frequency pulses to modulate the natural dipolar interaction implementing a Hamiltonian that can be scaled down at will. Meanwhile, experimental errors and strength of perturbative terms remain constant and can be quantified through the LE. For each scaling factor, information spreading occurs with a timescale, T_{2}, inversely proportional to the local second moment of the Hamiltonian. We find that, when the reversible interactions dominate over the perturbations, the information scrambled among up to 10^{2} spins can still be recovered. However, we find that the LE decay rate cannot become smaller than a critical value 1/T_{3}≈(0.15±0.02)/T_{2}, which only depends on the interactions themselves, and not on the perturbations. This result shows the emergence of a regime of intrinsic irreversibility in accordance to a central hypothesis of irreversibility, hinted from previous experiments.

Paramagnetic Ce3+ optical emitters in garnets: Optically detected magnetic resonance study and evidence of Gd-Ce cross-relaxation effects

Paramagnetic ${\mathrm{Ce}}^{3+}$optical emitters have been studied by means of optically detected magnetic resonance (ODMR) via ${\mathrm{Ce}}^{3+}$ spin-dependent emission in cerium-doped garnet crystals which were both gadolinium free and contain gadolinium in a concentration from the lowest (0.1%) to 100%, i.e., to the superparamagnetic state. It has been shown that the intensity of photoluminescence excited by circularly polarized light into ${\mathrm{Ce}}^{3+}$ absorption bands can be used for selective monitoring the population of the ${\mathrm{Ce}}^{3+}$ ground-state spin sublevels. Direct evidence of the cross-relaxation effects in garnet crystals containing two electron spin systems, i.e., the simplest one of ${\mathrm{Ce}}^{3+}$ ions with the effective spin $S=\frac{1}{2}$ and the system of ${\mathrm{Gd}}^{3+}$ ions with the maximum spin $S=\frac{7}{2}$, has been demonstrated. Magnetic resonance of ${\mathrm{Gd}}^{3+}$ has been found by monitoring ${\mathrm{Ce}}^{3+}$ emission in cerium-doped garnet crystals with gadolinium concentrations of 0.1 at. %, 4%--8%, and 100%, which implies the impact of the ${\mathrm{Gd}}^{3+}$ spin polarization on the optical properties of ${\mathrm{Ce}}^{3+}$. Strong internal magnetic fields in superparamagnetic crystals were shown to modify the processes of recombination between UV-radiation-induced electron and hole centers that lead to the recombination-induced ${\mathrm{Ce}}^{3+}$ emission. Observation of spikes and subsequent decay in the cross-relaxation-induced ODMR signals under pulsed microwave excitation is suggested to be an informative method to investigate transient processes in the many-spin system of ${\mathrm{Ce}}^{3+}, {\mathrm{Gd}}^{3+}$, and electron and hole radiation-induced centers.

Loschmidt echo in many-spin systems: contrasting time scales of local and global measurements.

A local excitation in a quantum many-spin system evolves deterministically. A time-reversal procedure, involving the inversion of the signs of every energy and interaction, should produce the excitation revival. This idea, experimentally coined in nuclear magnetic resonance, embodies the concept of the Loschmidt echo (LE). While such an implementation involves a single spin autocorrelation M(1,1), i.e. a local LE, theoretical efforts have focused on the study of the recovery probability of a complete many-body state, referred to here as global or many-body LE MMB Here, we analyse the relation between these magnitudes, with regard to their characteristic time scales and their dependence on the number of spins N We show that the global LE can be understood, to some extent, as the simultaneous occurrence of N independent local LEs, i.e. MMB∼(M(1,1))(N/4) This extensive hypothesis is exact for very short times and confirmed numerically beyond such a regime. Furthermore, we discuss a general picture of the decay of M1,1 as a consequence of the interplay between the time scale that characterizes the reversible interactions (T(2)) and that of the perturbation (τ(Σ)). Our analysis suggests that the short-time decay, characterized by the time scale τ(Σ), is greatly enhanced by the complex processes that occur beyond T(2) This would ultimately lead to the experimentally observed T(3), which was found to be roughly independent of τ(Σ) but closely tied to T(2).

Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians.

We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor |k| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates that correlate directly to the scaling factors |k|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed.

Dynamics of genuine multipartite entanglement in a quantum spin system

The time evolution of genuine multipartite entanglement is numerically studied in a model many-spin system decohered by a structured spin bath. It is found that multipartite entanglement can be more persistent than the bipartite entanglement and can even evolve into a specific constant under certain conditions. Besides, multipartite entanglement sudden death and sudden birth are observed. It is shown that the randomness of the coupling strength and connectivity between the spins in the environment will suppress these birth and death phenomena. Furthermore, the initial state of the central system plays a significant role in determining multipartite entanglement dynamics.

Berry phase of many-body system: time-dependent representation method

In this paper, we investigate the Berry phase of many-body system in the time-dependent representation. The formula of Berry phase of many-body system calculating in the time-dependent representation is derived. In this scenario, the Berry phase can be decomposed into two terms, which have different physical meanings respectively. Using these formula, we calculated the Berry phase for the many-spin system coupled by the XXZ exchange interaction. The results show that the Berry phase consists of two contributions which can be interpreted as the flux of a nonquantized monopole and the flux of a Dirac ring respectively.

Decoherence and Thermalization of Quantum Spin Systems

In this review, we discuss the decoherence and thermalization of a quantum spin system interact- ing with a spin bath environment, by numerically solving the time-dependent Schrodinger equation of the whole system. The effects of the topologic structure and the initial state of the environment on the decoherence of the two-spin and many-spin system are discussed. The role of different spin-spin coupling is considered. We show under which conditions the environment drives the reduced density matrix of the system to a fully decoherent state, and how the diagonal elements of the reduced density matrix approach those expected for the system in the microcanonical or canonical ensemble, depending on the character of the additional integrals of motion. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the microcanonical distribution (in each eigenenergy subspace) and canonical ensemble are states that may result from pure quantum dynamics, suggesting that quan- tum mechanics may be regarded as the foundation of quantum statistical mechanics. Furthermore, our numerical results show that a fully decoherent quantum system prefers to stay in an equilibrium state with a maximum entropy, indicating the validity of the second law of thermodynamics in the decoherence process.

Suppression of decoherence in a generalization of the spin-bath model

The works on decoherence due to spin baths usually agree in studying a one-spin system in interaction with a large spin bath. In this paper we generalize those models by analyzing a many-spin system and by studying decoherence or its suppression in function of the relation between the numbers of spins of the system and the bath. This model may help to identify clusters of particles unaffected by decoherence, which, as a consequence, can be used to store quantum information.

Zero-quantum frequency-selective recoupling of homonuclear dipole-dipole interactions in solid state nuclear magnetic resonance

We describe a method for measuring magnetic dipole-dipole interactions, and hence distances, between pairs of like nuclear spins in a many-spin system under magic-angle spinning (MAS). This method employs a homonuclear dipolar recoupling sequence that creates an average dipole-dipole coupling Hamiltonian under MAS with full zero-quantum symmetry, including both secular and flip-flop terms. Flip-flop terms are then attenuated by inserting rotor-synchronized periods of chemical shift evolution between recoupling blocks, leaving an effective Hamiltonian that contains only secular terms to a good approximation. Couplings between specific pairs of nuclear spins can then be selected with frequency-selective pi pulses. We demonstrate this technique, which we call zero-quantum shift evolution assisted homonuclear recoupling, in a series of one-dimensional and two-dimensional (13)C NMR experiments at 17.6 T and 40.00 kHz MAS frequency on uniformly (13)C-labeled L-threonine powder and on the helix-forming peptide MB(i+4)EK, synthesized with a pair of uniformly (13)C-labeled L-alanine residues. Experimental demonstrations include measurements of distances between (13)C sites that are separated by three bonds, placing quantitative constraints on both sidechain and backbone torsion angles in polypeptides.

Semiclassical coherent-state propagator for many spins

We obtain the semiclassical coherent-state propagator for a many-spin system with an arbitrary Hamiltonian.

Importance of the Internal Shape Mode in Magnetic Vortex Dynamics

We investigate the motion of a nonplanar vortex in a circular easy-plane magnet with a rotating in-plane magnetic field. Our numerical simulations of the Landau-Lifshitz equations show that the vortex tends to a circular limit trajectory, with an orbit frequency which is lower than the driving field frequency. To describe this we develop a new collective variable theory by introducing additional variables which account for the internal degrees of freedom of the vortex core, strongly coupled to the translational motion. We derive the evolution equations for these collective variables and find limit-cycle solutions whose characteristics are in qualitative agreement with the simulations of the many-spin system.

Berry phase for many-spin system with the uniaxial anisotropic exchange interaction in a time-dependent magnetic field

The amplitude structure of the instantaneous eigenstate for the many-spin system possessing the uniaxial anisotropic exchange interaction in a time-dependent magnetic field is analyzed. Based on the result, the Berry phase for this system is worked out. Furthermore, the effect of the anisotropic exchange interaction on the Berry phase of the state for the many-spin system is studied.

Measurement of dipole-coupled lineshapes in a many-spin system by constant-time two-dimensional solid state NMR with high-speed magic-angle spinning

A two-dimensional solid state NMR technique for measurements of dipole–dipole couplings in many-spin systems under high-speed magic-angle spinning (MAS) is described. The technique, called constant-time finite-pulse radio-frequency-driven recoupling (fpRFDR-CT), uses the fpRFDR pulse sequence to generate non-zero effective homonuclear dipole–dipole couplings under high-speed MAS that have the same operator symmetry as static dipole–dipole couplings. By incorporating fpRFDR into a multiple-pulse cycle based on the Waugh–Huber–Haeberlen (WAHUHA) homonuclear decoupling cycle, a constant-time t 1 evolution period is created. The constant-time t 1 period minimizes distortions of the experimental data due to various pulse sequence imperfections. The fpRFDR-CT technique is demonstrated experimentally in 13C NMR spectroscopy of carboxylate-labeled, polycrystalline l-alanine. 2D fpRFDR-CT spectra correlate the dipole-coupled lineshape of the 13C carboxylate groups with their isotropic chemical shift. Good agreement is obtained between the experimental second and fourth moments of the dipole-coupled lineshapes and calculated moments based on the l-alanine crystal structure and an average Hamiltonian analysis of the fpRFDR sequence. Applications in structural investigations of biologically relevant systems are anticipated. This technique illustrates many of the important concepts in modern multi-dimensional solid state NMR.

Time-reversal of the evolution of a dipole-coupled, many-spin system under continuous resonant irradiation

Time-reversal of the evolution of a dipole-coupled, many-spin system under continuous resonant excitation with a radio-frequency (rf) field of arbitrary amplitude is demonstrated in solid-state H1 nuclear magnetic resonance (NMR) experiments on polycrystalline adamantane. Time-reversed evolution is accomplished with an rf pulse sequence that generates an effective nuclear spin Hamiltonian that includes both dipole–dipole coupling and rf interaction terms, with signs opposite to those in forward evolution. The amplitude of the effective continuous rf field is varied by varying the phases of rf pulses in the sequence. Experiments show echo-like NMR signals under time-reversed evolution after forward evolution to an apparent quasiequilibrium state under continuous rf excitation. Such echolike signals are inconsistent with the hypothesis of spin temperature in the rotating frame, according to which the approach to quasiequilibrium under continuous rf excitation is an irreversible process. The use of this time-reversed evolution in multiple quantum (MQ) NMR spectroscopy is also demonstrated. MQ NMR spectra obtained with increasing excitation times exhibit a partial confinement of nuclear spin order to zero- and one-quantum operators. This novel behavior is shown to be a consequence of energy conservation.

Berry Phases for Many-Spin Systems with Anisotropy Exchange Interaction in a Strong Magnetic Field

An approximate instantaneous eigenstate is presented for the many-spin system possessing the anisotropy exchange interaction in a strong magnetic field by the perturbation method. Based on the instantaneous eigenstate, the Berry phase of this state is worked out. Furthermore, the effect of the anisotropy exchange interaction on the Berry phase of the state for the many-spin system is studied.

Simulation of many-spin system dynamics via sparse matrix methodology

A sparse-matrix-based numerical method is constructed to simulate NMR spectra of many-spin systems, including the effects of chemical exchange and/or relaxation. The associated computational demands are predicted to scale like O(22n), as the number of spins n increases. This is vastly superior to the inevitable O(26n) scaling of conventional Householder-based methodology. The improved scaling is verified via numerical computations of simple isomerization systems with four to nine spins. The new method is based on splitting the propagator and use of Chebyshev polynomial expansion of the exponential function.

Equations of Motion of Nuclear Magnetism

A general formalism from a previous paper is applied to derive an exact equation of motion for the total magnetic moment M of a system containing a single species of nuclear spins in an arbitrarily time-dependent external magnetic field H. Then, the equation is simplified for $\mathrm{kT}$ large compared with $\ensuremath{\gamma}H$ and compared with microscopic anisotropic spin energies but not necessarily compared with microscopic exchange energies. Only this high-temperature approximation is needed for the equation to reduce to $\frac{d\mathbf{M}}{\mathrm{dt}}=\ensuremath{\gamma}\mathbf{M}\ifmmode\times\else\texttimes\fi{}\mathbf{H}\ensuremath{-}\ensuremath{\int}{0}^{t}\mathbf{K}(t,{t}^{\ensuremath{'}})\ifmmode\cdot\else\textperiodcentered\fi{}[\mathbf{M}({t}^{\ensuremath{'}})\ensuremath{-}{\ensuremath{\chi}}_{0}\mathbf{H}({t}^{\ensuremath{'}})]d{t}^{\ensuremath{'}},$ which is valid for systems with arbitrarily long correlations times. The system is assumed to be in equilibrium for $tl0$, but it may deviate arbitrarily far from equilibrium for $tg0$. The kernel K is a dyad that depends upon $T$ and upon H but not upon M. The equation is capable of describing nonexponential relaxation and therefore non-Lorentzian resonance line shapes. For arbitrarily large times $t$, it is valid for, but not restricted to, a many-spin system with strong dipole-dipole interactions between spins in a rigid lattice and with spin \ensuremath{\ge}\textonehalf{}. For a nonrigid lattice, no assumption is made that the lattice is or is not in equilibrium, that it is a thermal bath, or that the density matrix may be factored. Instead, in order to simplify the formal expression for K and thus the solution of the equation, slowly-varying-temperature, high-temperature, and high-frequency approximations are made so that $\mathbf{K}(t,{t}^{\ensuremath{'}})$ becomes a function of $t\ensuremath{-}{t}^{\ensuremath{'}}$ only. Finally, the approximation of neglecting the dependence of K on ${H}_{1}$ is made, so that K becomes diagonal and equal to a sum of terms each consisting of a simple oscillatory factor times a function that may be interpreted as the correlation function of a stationary random process. The corresponding correlation times need not be short, but for comparison with previous formalisms a short-correlation-time approximation is also made.