Central Spin Research Articles

Electron Induced Nanoscale Nuclear Spin Relaxation Probed by Hyperpolarization Injection.

We report on experiments that quantify the role of a central electronic spin as a relaxation source for nuclear spins in its nanoscale environment. Our strategy exploits hyperpolarization injection from the electron as a means to controllably probe an increasing number of nuclear spins in the bath and subsequently interrogate them with high fidelity. Our experiments are focused on a model system of a nitrogen vacancy center electronic spin surrounded by several hundred ^{13}C nuclear spins. We observe that the ^{13}C transverse spin relaxation times vary significantly with the extent of hyperpolarization injection, allowing the ability to measure the influence of electron-mediated relaxation extending over several nanometers. These results suggest interesting new means to spatially discriminate nuclear spins in a nanoscale environment and have direct relevance to dynamic nuclear polarization and quantum sensors and memories constructed from hyperpolarized nuclei.

Preparation of two-qubit entangled states on a spin-1/2 Ising–Heisenberg diamond spin cluster by controlling the measurement

The preparation of entangled quantum states is an inherent and indispensable step for the implementation of many quantum information algorithms. Depending on the physical system, there are different ways to control and measure them, which allow one to achieve the predefined quantum states. The diamond spin cluster is the system that can be applied for this purpose. Moreover, such a system appears in chemical compounds such as the natural mineral azurite, where the Cu2+ are arranged in a spin-1/2 diamond chain. Herein, we propose the method of preparation of pure entangled states on the Ising–Heisenberg spin-1/2 diamond cluster. We suppose that the cluster consists of two central spins which are described by an anisotropic Heisenberg model and interact with the side spins via Ising interaction. Controlling the measurement direction of the side (central) spins allows us to achieve predefined pure quantum states of the central (side) spins. We show that this directly affects the entanglement and fidelity of the prepared states. For example, we obtain conditions and fidelities for preparations of the Bell states.

Dragging of inertial frames in the composed Kerr-Newman-orbiting-ring system

The dragging of inertial frames by an orbiting object, a well known phenomenon in general relativity, implies that the horizon angular velocity ΩHBH-ring of a central black hole in a composed black-hole-orbiting-ring system is no longer related to its angular-momentum JH by the familiar vacuum functional relation ΩH(JH)=JH/Mα (here {M,α} are respectively the mass and normalized area of the central spinning black hole). Using a continuity argument, according to which the black-hole angular velocity changes smoothly during an adiabatic assimilation process of an orbiting ring, it has recently been revealed that the composed Kerr-ring system is characterized by the universal (that is, spin-independent) relation ΔΩH≡ΩHBH-ring(JH,JR,R→RH+)−ΩHKerr(JH)=JR/4M3, where {R,JR} are respectively the radius of the ring and its orbital angular momentum and RH is the horizon radius of the central Kerr black hole. This intriguing observation naturally raises the following physically interesting question: Does the physical quantity ΔΩH in a composed black-hole-orbiting-ring system is always characterized by the near-horizon functional relation ΔΩH=JR/4M3 which is independent of the spin (angular momentum) JH of the central black hole? In order to address this important question, in the present compact paper we explore the physical phenomenon of dragging of inertial frames by an orbiting ring in the composed Kerr-Newman-black-hole-orbiting-ring system. In particular, using analytical techniques, we reveal the fact that in this composed two-body (black-hole-ring) system the quantity ΔΩH has an explicit non-trivial functional dependence on the angular momentum JH of the central spinning black hole.

Near-Field Sensing of Microwave Magnetic Field Phase Difference Enabled by N - V -Center Spins

Sensing microwave (MW) fields through a quantum protocol has attracted increasing interest, and the phase of MW fields is an essential parameter in communication and quantum technologies. This work proposes a quantum-effect-based method for measuring the phase difference of MW magnetic fields under near-field conditions based on the selective transitions of nitrogen-vacancy- ($\mathrm{N}$-V) center spins in diamond. First, the relationship between the evolutions of the $\mathrm{N}$-V-center spin states and the phase difference of the MW magnetic fields, which are resonant and able to drive the transitions of the $\mathrm{N}$-V-center spins between ground-state energy levels, is deduced. Then, using a double-microstrip-line MW antenna, the variations in the Rabi frequency and maximum contrast as a function of the phase difference are experimentally revealed. Finally, the measurement of the phase difference is validated, and the sensitivity of the proof-of-principle method is estimated to be ${0.0915}^{\ensuremath{\circ}}/\sqrt{\text{Hz}}$. This method paves the way for the comprehensive quantum sensing of MW fields and has potential applications in the communication and quantum information fields.

The Role of Electrolytes in the Relaxation of Near-Surface Spin Defects in Diamond.

Quantum sensing with spin defects in diamond, such as the nitrogen vacancy (NV) center, enables the detection of various chemical species on the nanoscale. Molecules or ions with unpaired electronic spins are typically probed by their influence on the NV center's spin relaxation. Whereas it is well-known that paramagnetic ions reduce the NV center's relaxation time (T1), here we report on the opposite effect for diamagnetic ions. We demonstrate that millimolar concentrations of aqueous diamagnetic electrolyte solutions increase the T1 time of near-surface NV center ensembles compared to pure water. To elucidate the underlying mechanism of this surprising effect, single and double quantum NV experiments are performed, which indicate a reduction of magnetic and electric noise in the presence of diamagnetic electrolytes. In combination with ab initio simulations, we propose that a change in the interfacial band bending due to the formation of an electric double layer leads to a stabilization of fluctuating charges at the interface of an oxidized diamond. This work not only helps to understand noise sources in quantum systems but could also broaden the application space of quantum sensors toward electrolyte sensing in cell biology, neuroscience, and electrochemistry.

Distribution of Bipartite and Tripartite Entanglement within a Spin-1/2 Heisenberg Star in a Magnetic Field.

The spatial distribution of entanglement within a spin-1/2 Heisenberg star composed from a single central spin and three peripheral spins is examined in the presence of an external magnetic field using the Kambe projection method, which allows an exact calculation of the bipartite and tripartite negativity serving as a measure of the bipartite and tripartite entanglement. Apart from a fully separable polarized ground state emergent at high-enough magnetic fields, the spin-1/2 Heisenberg star exhibits at lower magnetic fields three outstanding nonseparable ground states. The first quantum ground state exhibits the bipartite and tripartite entanglement over all possible decompositions of the spin star into any pair or triad of spins, whereby the bipartite and tripartite entanglement between the central and peripheral spins dominates over that between the peripheral spins. The second quantum ground state has a remarkably strong tripartite entanglement between any triad of spins in spite of the lack of bipartite entanglement. The central spin of the spin star is separable from the remaining three peripheral spins within the third quantum ground state, where the peripheral spins are subject to the strongest tripartite entanglement arising from a two-fold degenerate W-state.

Nuclear spin diffusion in the central spin system of a GaAs/AlGaAs quantum dot

The spin diffusion concept provides a classical description of a purely quantum-mechanical evolution in inhomogeneously polarized many-body systems such as nuclear spin lattices. The central spin of a localized electron alters nuclear spin diffusion in a way that is still poorly understood. Here, spin diffusion in a single GaAs/AlGaAs quantum dot is witnessed in the most direct manner from oscillatory spin relaxation dynamics. Electron spin is found to accelerate nuclear spin relaxation, from which we conclude that the long-discussed concept of a Knight-field-gradient diffusion barrier does not apply to GaAs epitaxial quantum dots. Our experiments distinguish between non-diffusion relaxation and spin diffusion, allowing us to conclude that diffusion is accelerated by the central electron spin. Such acceleration is observed up to unexpectedly high magnetic fields – we propose electron spin-flip fluctuations as an explanation. Diffusion-limited nuclear spin lifetimes range between 1 and 10 s, which is sufficiently long for quantum information storage and processing.

Waveguide-integrated silicon T centres.

The performance of modular, networked quantum technologies will be strongly dependent upon the quality of their quantum light-matter interconnects. Solid-state colour centres, and in particular T centres in silicon, offer competitive technological and commercial advantages as the basis for quantum networking technologies and distributed quantum computing. These newly rediscovered silicon defects offer direct telecommunications-band photonic emission, long-lived electron and nuclear spin qubits, and proven native integration into industry-standard, CMOS-compatible, silicon-on-insulator (SOI) photonic chips at scale. Here we demonstrate further levels of integration by characterizing T centre spin ensembles in single-mode waveguides in SOI. In addition to measuring long spin T1 times, we report on the integrated centres' optical properties. We find that the narrow homogeneous linewidth of these waveguide-integrated emitters is already sufficiently low to predict the future success of remote spin-entangling protocols with only modest cavity Purcell enhancements. We show that further improvements may still be possible by measuring nearly lifetime-limited homogeneous linewidths in isotopically pure bulk crystals. In each case the measured linewidths are more than an order of magnitude lower than previously reported and further support the view that high-performance, large-scale distributed quantum technologies based upon T centres in silicon may be attainable in the near term.

Memory and Transduction Prospects for Silicon T Center Devices

The T center, a silicon-native spin-photon interface with telecommunication-band optical transitions and long-lived microwave qubits, offers an appealing new platform for both optical quantum memory and microwave-to-optical telecommunication-band transduction. A wide range of quantum memory and transduction schemes could be implemented withT center ensembles with sufficient optical depth, with advantages and disadvantages that depend sensitively on the ensemble properties. In this work we characterize T center spin ensembles to inform device design. We perform the first T ensemble optical depth measurement and calculate the improvement in center density or resonant optical enhancement required for efficient optical quantum memory. We further demonstrate a coherent microwave interface by coherent population trapping and Autler-Townes splitting. We then determine the most promising microwave and optical quantum memory protocol for such ensembles. By estimating the memory efficiency both in free space and in the presence of a cavity, we show that efficient optical memory is possible with reasonable optical density forecasts. Finally, we formulate a transduction proposal and discuss the achievable efficiency and fidelity.Received 13 September 2022Accepted 13 March 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020308Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCoherent population trappingElectromagnetically induced transparencyQuantum information with hybrid systemsQuantum information with solid state qubitsQuantum interconnectsQuantum memoriesQuantum networksQuantum repeatersQuantum InformationAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Measurement-Induced Continuous Time Crystals.

Strong measurements usually restrict the dynamics of measured finite dimensional systems to the Zeno subspace, where subsequent evolution is unitary due to the suppression of dissipative terms. Here, we show qualitatively different behavior induced by the competition between strong measurements and the thermodynamic limit, inducing a time-translation symmetry breaking phase transition resulting in a continuous time crystal. We consider an undriven spin star model, where the central spin is subject to a strong continuous measurement, and qualify the dynamic behavior of the system in various parameter regimes. We show that above a critical value of measurement strength, the magnetization of the thermodynamically large ancilla spins, along with the central spin, develops limit-cycle oscillations.

Partially disordered Heisenberg antiferromagnet with short-range stripe correlations

Zero-point quantum fluctuations of a N\'eel order can produce effective interactions between quasi-orphan spins weakly coupled to the lattice. On the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$-distorted triangular lattice, this phenomenon leads to a correlated partially disordered phase. In this article, we use matrix product state methods to study a similar model: the $S=1/2$ stuffed square lattice. Tuning the exchange amplitudes we go from a square lattice plus orphan central spins at ${J}^{\ensuremath{'}}/J=0$, to the union jack lattice at ${J}^{\ensuremath{'}}/J=1$, and a square lattice including all spins at $J/{J}^{\ensuremath{'}}=0$. We calculate the complete antiferromagnetic phase diagram, dominated by ferrimagnetic and N\'eel orders, and compare it with existing results. Most importantly, we find a partially disordered phase in the weakly frustrated regime. In this phase, the N\'eel order from the square lattice is unaffected, while the central spins form a collective state with exponentially decaying double-striped correlations. We also study the role of quantum fluctuations by introducing an ordering staggered magnetic field on the square sublattice and find that the central spins order ferromagnetically when fluctuations from the N\'eel order are suppressed.

Monte Carlo simulation of the topological quantities in fractional quantum Hall systems

Generally speaking, for a fractional quantum Hall (FQH) state, the electronic occupation number for each Landau orbit could be obtained from numerical methods such as exact diagonalization, density matrix renormalization group or algebraic recursive schemes (Jack polynomial). In this work, we apply a Metroplis Monte Carlo method to calculate the occupation numbers of several FQH states in cylinder geometry. The convergent occupation numbers for more than 40 particles are used to verify the chiral bosonic edge theory and determine the topological quantities via momentum polarization or dipole moment. The guiding center spin, central charge and topological spin of different topological sectors are consistent with theoretical values and other numerical studies. Especially, we obtain the topological spin of $e/4$ quasihole in Moore-Read and 331 states. At last, we calculate the electron edge Green's functions and analysis position dependence of the non-Fermi liquid behavior.

Entanglement of the Ising–Heisenberg diamond spin- cluster in evolution

In the last two decades, magnetic, thermodynamic properties and bipartite thermal entanglement in diamond spin clusters and chains have been studied. Such spin structures are presented in various compounds. The ions of Cu2+ in the natural mineral azurite are arranged in a diamond spin chain. There are no studies of the entanglement behaviour during the quantum evolution of such systems. Herein, we consider the evolution of entanglement in the diamond spin-1/2 cluster. This cluster consists of two central spins described by the anisotropic Heisenberg model, which interact with two side spins via Ising interaction. The influence of the interaction coupling with side spins on the entanglement of central spins is investigated. It is shown that choosing the value of this coupling allows us to control the behaviour of entanglement between central spins. As a result, we find conditions for achieving the maximal values of entanglement. In addition, the entanglement behaviour between the side spins, central and side spins, and between a certain spin and the rest of the system is studied. In these cases, the conditions for achieving maximal entanglement are also obtained.

Truncated Wigner approximation for the bosonic model of large spin baths

The central spin model has a wide applicability. It is ideally suited to describe a small quantum system, for instance a quantum bit, in contact to a bath of spins, e.g., nuclear spins or other small quantum systems in general. According to previous work [R. R\"ohrig et al., Phys. Rev. B 97, 165431 (2018)], a large bath of quantum spins can be described as a bath of quantum harmonic oscillators. But the resulting quantum model is still far from being straightforwardly solvable. Hence we consider a chain representation for the bosonic degrees of freedom to study how well a semi-classical truncated Wigner approximation of the effective model of harmonic oscillators (bTWA) works in comparison with other approximate and exact methods. We find that the bTWA works well for short times, but deviates from the results of other methods for long times. The general message is that the applicability of semi-classical approaches strongly depends on the variables in terms of which the model is formulated. Numerically, we examine the effect of the number of bath spins and of the truncation level, i.e., the chain length.

Algorithms and radiation dynamics for the vicinity of black holes

We present the results of our studies on accretion disks in the proximity of astrophysical black holes. These disks can be of varying degrees of opacity, geometrical shapes, sizes, and volumes. The central compact object is a Schwarzschild or a Kerr black hole of various spin parameters. We describe the environment and the physics of the systems under examination and the disk models considered. We first investigate the effects of the spacetime rotation on photon trajectories. We then examine the radiation forces recorded at various points of the arrangement inside and outside the disk material, and in the inner, outer, and off-equatorial material orbits. We document and explore the radiation effects, which are revealed to be significant and positively consequential. Afterward, we inspect the possible imaging outcome of various types of black hole and accretion disk configurations, and we show our results for plots that could be used to estimate the central black hole spin in a system. Finally, we show results regarding the disk material orbit degradation due to its thermal radiation.

Thermodynamics of Quantum Spin-Bath Depolarization.

We analyze here through exact calculations the thermodynamical effects in depolarizing a quantum spin-bath initially at zero temperature through a quantum probe coupled to an infinite temperature bath by evaluating the heat and entropy changes. We show that the correlations induced in the bath during the depolarizing process does not allow for the entropy of the bath to increase towards its maximal limit. On the contrary, the energy deposited in the bath can be completely extracted in a finite time. We explore these findings through an exactly solvable central spin model, wherein a central spin-1/2 system is homogeneously coupled to a bath of identical spins. Further, we show that, upon destroying these unwanted correlations, we boost the rate of both energy extraction and entropy towards their limiting values. We envisage that these studies are relevant for quantum battery research wherein both charging and discharging processes are key to characterizing the battery performance.

Collapse and revival structure of information backflow for a central spin coupled to a finite spin bath

The Markovianity of quantum dynamics is an important property of open quantum systems determined by various ingredients of the system and bath. Apart from the system-bath interaction, the initial state of the bath, etc., the dimension of the bath plays a critical role in determining the Markovianity of quantum dynamics, as a strict decay of the bath correlations requires an infinite dimension for the bath. In this work, we investigate the role of finite bath dimension in the Markovianity of quantum dynamics by considering a simple but nontrivial model in which a central spin is isotropically coupled to a finite number of bath spins, and show how the dynamics of the central spin transits from non-Markovian to Markovian as the number of the bath spins increases. The non-Markovianity is characterized by the information backflow from the bath to the system in terms of the trace distance of the system states. We derive the time evolution of the trace distance analytically, and find periodic collapse-revival patterns in the information flow. The mechanism underlying this phenomenon is investigated in detail, and it shows that the period of the collapse-revival pattern is determined by the competition between the number of the bath spins, the system-bath coupling strength, and the frequency detuning. When the number of bath spins is sufficiently large, the period of the collapse-revival structure as well as the respective collapse and revival times increase in proportion to the number of the bath spins, which characterizes how the information backflow decays with a large dimension of the bath. We also analyze the effect of the system-bath interaction strength and frequency detuning on the collapse-revival patterns of the information flow, and obtain the condition for the existence of the collapse-revival structure. The results are illustrated by numerical computation.

Visualization of bulk and edge photocurrent flow in anisotropic Weyl semimetals

Materials that rectify light into current in their bulk are desired for optoelectronic applications. In inversion-breaking Weyl semimetals, bulk photocurrents may arise due to nonlinear optical processes that are enhanced near the Weyl nodes. However, the photoresponse of these materials is commonly studied by scanning photocurrent microscopy (SPCM), which convolves the effects of photocurrent generation and collection. Here, we directly image the photocurrent flow inside the type-II Weyl semimetals WTe2 and TaIrTe4 using high-sensitivity quantum magnetometry with nitrogen-vacancy center spins. We elucidate an unknown mechanism for bulk photocurrent generation termed the anisotropic photothermoelectric effect (APTE), where unequal thermopowers along different crystal axes drive intricate circulations of photocurrent around the photoexcitation. Using simultaneous SPCM and magnetic imaging at the sample's interior and edges, we visualize how the APTE stimulates the long-range photocurrent collected in our Weyl semimetal devices through the Shockley-Ramo theorem. Our results highlight an overlooked, but widely relevant source of current flow and inspire novel photodetectors using homogeneous materials with anisotropy.

Quantum phase transition in the XXZ central spin model

We investigate the quantum phase transition (QPT) in the XXZ central spin model, which can be described as a spin-$\frac{1}{2}$ particle coupled to $N$ bath spins. In general, the QPT is supposed to occur only in the thermodynamical limit. In contrast, we present that the central spin model exhibits a normal-to-superradiant phase transition in the limit where the ratio of the transition frequency of the central spin to that of the bath spins and the number of bath spins tend to infinity. We give the low-energy effective Hamiltonian analytically in the normal phase and the superradiant phase, and we find that the longitudinal interaction $\mathrm{\ensuremath{\Delta}}$ can significantly influence the excitation number and the coherence of the ground state. These two quantities are remarkably enhanced for the negative longitudinal interaction while suppressed for the positive longitudinal interaction. In addition, the finite-size effect on the central spin model is also illustrated through the mean-field analysis. We further exploit the quantum Fisher information to characterize the QPT and propose a measurement scheme that can be applied in practice. This work builds a connection between the qubit-spin systems and the qubit-field systems, which provides a possibility for the realization of criticality-enhanced quantum sensing in central spin systems.

Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

The U(1) symmetry of the XXZ central spin model with an arbitrary central magnetic field B is broken, since its total spin in the z-direction is not conserved. We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method. The thermodynamic limit is investigated based on the solutions. We find that the contribution of the inhomogeneous term in the associated T–Q relation to the ground state energy satisfies an N −1 scaling law, where N is the total number of spins. This result makes it possible to investigate the properties of the system in the thermodynamic limit. By assuming the structural form of the Bethe roots in the thermodynamic limit, we obtain the contribution of the direction of B to the ground state energy. It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit. This is the phenomenon caused by the U(1) symmetry breaking of the system.