Spin Coherent States Research Articles

Coherent spin states and stochastic hybrid path integrals

Stochastic hybrid systems involve a coupling between a discrete Markov chain and a continuous stochastic process. If the latter evolves deterministically between jumps in the discrete state, then the system reduces to a piecewise deterministic Markov process. Well known examples include stochastic gene expression, voltage fluctuations in neurons, and motor-driven intracellular transport. In this paper we use coherent spin states to construct a new path integral representation of the probability density functional for stochastic hybrid systems, which holds outside the weak noise regime. We use the path integral to derive a system of Langevin equations in the semi-classical limit, which extends previous diffusion approximations based on a quasi-steady-state reduction. We then show how in the weak noise limit the path integral is equivalent to an alternative representation that was previously derived using Doi–Peliti operators. The action functional of the latter is related to a large deviation principle for stochastic hybrid systems.

Entanglement of General Two-Qubit States in a Realistic Framework

In the present paper, we examine the quantum entanglement for more general states of two-qubit system in the context of spin coherent states (SCSs). We consider the concurrence as a quantifier of entanglement and express it in terms of SCSs. We determine new set of maximally entangled conditions that provide the maximal amount of entanglement for certain values of the amplitudes of SCSs for the case of pure states. Finally, we examine the entanglement of a class of mixed states of the two qubits and provide the range in which the entanglement value is maximal with respect to the values of the amplitudes of SCSs.

Dynamic of the system in a periodic potential, submitted to an electromagnetic wave: Path integral approach

We introduced the formalism of path integrals to describe the dynamics of a system consisting of two particles. One is located in a periodic potential well (first subsystem), while the other particle is outside the well and subjected to a circular electromagnetic field (second subsystem). Thanks to this formalism, we are able to describe the dynamics of our system by a propagator which is the product of two subsystems of propagators. The propagator of the first subsystem is put in the standard form exp[Action] as a result of the coherent spin states. This form of propagator is possible by replacing the spin with a unit vector aligned along the polar and azimuthal directions. The second subsystem propagator come with the use of the Feynman-Vernon functional on the subsystem. Thanks to its two propagators, we have succeeded in explicitly and analytically evaluating the dynamics of our dissipative quantum system by a single propagator. Using this fundamental result, we evaluated the special case where the second subsystem bathed in a super-ohmic environment.

Creation of Greenberger-Horne-Zeilinger states with thousands of atoms by entanglement amplification

We propose an entanglement-creation scheme in a multi-atom ensemble trapped in an optical cavity, named entanglement amplification, converting unentangled states into entangled states and amplifying less-entangled ones to maximally entangled Greenberger-Horne-Zeilinger (GHZ) states whose fidelity is logarithmically dependent on the atom number and robust against common experimental noises. The scheme starts with a multi-atom ensemble initialized in a coherent spin state. By shifting the energy of a particular Dicke state, we break the Hilbert space of the ensemble into two isolated subspaces to tear the coherent spin state into two components so that entanglement is introduced. After that, we utilize the isolated subspaces to further enhance the entanglement by coherently separating the two components. By single-particle Rabi drivings on atoms in a high-finesse optical cavity illuminated by a single-frequency light, 2000-atom GHZ states can be created with a fidelity above 80% in an experimentally achievable system, making resources of ensembles at Heisenberg limit practically available for quantum metrology.

Dynamical properties of a driven dissipative dimerized S=12 chain

We consider the dynamical properties of a gapped quantum spin system coupled to the electric field of a laser, which drives the resonant excitation of specific phonon modes that modulate the magnetic interactions. We deduce the quantum master equations governing the time-evolution of both the lattice and spin sectors, by developing a Lindblad formalism with bath operators providing an explicit description of their respective phonon-mediated damping terms. We investigate the nonequilibrium steady states (NESS) of the spin system established by a continuous driving, delineating parameter regimes in driving frequency, damping, and spin-phonon coupling for the establishment of physically meaningful NESS and their related nontrivial properties. Focusing on the regime of generic weak spin-phonon coupling, we characterize the NESS by their frequency and wave-vector content, explore their transient and relaxation behavior, and discuss the energy flow, the system temperature, and the critical role of the type of bath adopted. Our study lays a foundation for the quantitative modeling of experiments currently being designed to control coherent many-body spin states in quantum magnetic materials.

Non-adiabatic Response and Counterdiabatic Driving of Coherent States

Quantum state preparation has drawn great attention to physical community. In order to solve this challenge, the protocol of counterdiabatic driving was put forward. In this paper, the idea was applied to two important models, Coherent states and Spin coherent states, which had played important roles in the development of quantum optic and atomic physics. If their parameters vary slowly, the evolution can be studied by the adiabatic perturbation theory. Furthermore, their non-adiabatic response are investigated respectively. Specifically, we build the relationship between the generalized force and Berry curvature of coherent states and spin coherent states. And the leading corrections to energy are also been researched, which lead to the mass and moment of inertia renormalization respectively. In addition, we also calculate the broadening of the energy distribution (energy variance), which determined by the metric tensor. Finally, in order to suppress transition and speed up the evolution, the counterdiabatic Hamiltonians are designed, which would have potential use in the field of quantum manipulation.

Quantum Features of Atom–Field Systems in the Framework of Deformed Fields

We propose a new kind of Schrödinger cat state introduced as a superposition of spin coherent states in the framework of noncommutative spaces. We analyze the nonclassical features for these noncommutative deformed states in terms of the main physical parameters. The physical importance of deformed states is that they provide a convenient description of a large set of laser systems. As an application, we develop the Jaynes–Cummings model by considering the interaction among atoms and cat state fields associated to deformed spin algebras. In this context, we show the dynamical behavior of the nonlocal correlation and nonclassical properties in these quantum systems.

Phase space theory for open quantum systems with local and collective dissipative processes

In this article we investigate driven dissipative quantum dynamics of an ensemble of two-level systems given by a Markovian master equation with collective and local dissipators. Exploiting the permutation symmetry in our model, we employ a phase space approach for the solution of this equation in terms of a diagonal representation with respect to certain generalized spin coherent states. Remarkably, this allows to interpolate between mean field theory and finite system size in a formalism independent of Hilbert-space dimension. Moreover, in certain parameter regimes, the evolution equation for the corresponding quasiprobability distribution resembles a Fokker–Planck equation, which can be efficiently solved by stochastic calculus. Then, the dynamics can be seen as classical in the sense that no entanglement between the two-level systems is generated. Our results expose, utilize and promote techniques pioneered in the context of laser theory, which can be powerful tools to investigate problems of current theoretical and experimental interest.

Colloidal Quantum Dots as Platforms for Quantum Information Science.

Colloidal quantum dots (QDs) are nanoscale semiconductor crystals with surface ligands that enable their dispersion in solvents. Quantum confinement effects facilitate wave function engineering to sculpt the spatial distribution of charge and spin states and thus the energy and dynamics of QD optical transitions. Colloidal QDs can be integrated in devices using solution-based assembly methods to position single QDs and to create ordered QD arrays. Here, we describe the synthesis, assembly, and photophysical properties of colloidal QDs that have captured scientific imagination and have been harnessed in optical applications. We focus especially on the current understanding of their quantum coherent effects and opportunities to exploit QDs as platforms for quantum information science. Freedom in QD design to isolate and control the quantum mechanical properties of charge, spin, and light presents various approaches to create systems with robust, addressable quantum states. We consider the attributes of QDs for optically addressable qubits in emerging quantum computation, sensing, simulation, and communication technologies, e.g., as robust sources of indistinguishable, single photons that can be integrated into photonic structures to amplify, direct, and tune their emission or as hosts for isolated, coherent spin states that can be coupled to light or to other spins in QD arrays.

Heisenberg-Limited Noisy Atomic Clock Using a Hybrid Coherent and Squeezed State Protocol.

We propose a hybrid quantum-classical atomic clock where the interrogation of atoms prepared in a spin-coherent (or weakly squeezed) state is used to feed back one or more highly spin-squeezed atomic states toward their optimal phase-sensitivity point. The hybrid clock overcomes the stability of a single Ramsey clock using coherent or optimal spin-squeezed states and reaches a Heisenberg-limited stability while avoiding nondestructive measurements. When optimized with respect to the total number of particles, the protocol surpasses the state-of-the-art proposals that use Greenberger-Horne-Zeilinger or NOON states. We compare analytical predictions with numerical simulations of clock operations, including correlated 1/f local oscillator noise.

Noisy Quantum Metrology Enhanced by Continuous Nondemolition Measurement.

We show that continuous quantum nondemolition (QND) measurement of an atomic ensemble is able to improve the precision of frequency estimation even in the presence of independent dephasing acting on each atom. We numerically simulate the dynamics of an ensemble with up to N=150 atoms initially prepared in a (classical) spin coherent state, and we show that, thanks to the spin squeezing dynamically generated by the measurement, the information obtainable from the continuous photocurrent scales superclassically with respect to the number of atoms N. We provide evidence that such superclassical scaling holds for different values of dephasing and monitoring efficiency. We moreover calculate the extra information obtainable via a final strong measurement on the conditional states generated during the dynamics and show that the corresponding ultimate limit is nearly achieved via a projective measurement of the spin-squeezed collective spin operator. We also briefly discuss the difference between our protocol and standard estimation schemes, where the state preparation time is neglected.

Entanglement of formation and quantum discord in multipartite j-spin coherent states

We study the entanglement of formation and the quantum discord contained in even and odd multipartite [Formula: see text]-spin coherent states. The key element of this investigation is the fact that a single [Formula: see text]-spin coherent state is viewed as comprising [Formula: see text] qubit states. We compute the quantum correlations present in the n even and odd [Formula: see text]-spin coherent states by considering all possible bipartite splits of the multipartite system. We discuss the different bi-partition schemes of quantum systems and we examine in detail the conservation rules governing the distribution of quantum correlations between the different qubits of the multipartite system. Finally, we derive the explicit expressions of quantum correlations present in even and odd spin coherent states decomposed in four spin sub-systems. We also analyze the properties of monogamy and we show in particular that the entanglement of the formation and the quantum discord obey the relation of monogamy only for even multipartite [Formula: see text]-spin coherent states.

Dynamics of the homogeneous two-qubit XXZ central spin model with the spin bath prepared in superpositions of symmetric Dicke states

We obtain exact dynamics of a two-qubit central spin model (CSM) consisting of two interacting qubits homogeneously coupled to a spin bath via the $XXZ$-type coupling, with the bath initially prepared in linear superpositions of the symmetric Dicke states. Using the interaction picture Hamiltonian with respect to the non-spin-flipping part of the model, we derive a sequence of equations of motion within each magnetization sector satisfied by the probability amplitudes of the time-evolved state. These equations of motion admit analytical solutions for the single-qubit CSM in which one of the two central qubits decouples from the rest of the system. Based on this, we provide a quantitative interpretation to the observed collapse-revival phenomena in the single-qubit Rabi oscillations when the bath is prepared in the spin coherent state. We then study the disentanglement and coherence dynamics of two initially entangled noninteracting qubits when the two qubits interact with individual baths or with a common bath. For individual baths the coherent dynamics is found to positively correlated to the single-qubit purity dynamics, and entanglement sudden disappearance and revivals are observed in both cases. The entanglement creation of two initially separable qubits coupled to a common bath is also studied and collapse and revival behaviors in the entanglement dynamics are observed. Choosing the equally weighted state and the $W$-class states as the bath initial states, we finally study the dynamics of entanglement between two individual bath spins and demonstrate the entanglement sharing mechanism in such a system.

Universal computation with quantum fields

We explore a way of universal quantum computation with particles which cannot occupy the same position simultaneously and are symmetric under exchange of particle labels. Therefore the associated creation and annihilation operators are neither bosonic nor fermionic. In this work we first show universality of our method and numerically address several examples. We demonstrate dynamics of a Bloch electron system from a viewpoint of adiabatic quantum computation. In addition we provide a novel Majorana fermion system and analyze phase transitions with spin-coherent states and the time average of the out-of-time-order correlator (OTOC). We report that a first-order phase transition is avoided when it evolves in a non-stoquastic manner and the time average of the OTOC diagnoses the phase transitions successfully.

Entanglement dynamics of two coupled spins interacting with an adjustable spin bath: effect of an exponential variable magnetic field

The present work is devoted to studying the entanglement dynamics of two central spins coupled in a spin environment and subjected, simultaneously, to an external magnetic field changing with time t as an exponential function $${\mathfrak {B}}\left( 1-\mathrm{e}^{-\lambda t}\right) $$ . We want to determine whether interaction among central spins with an external magnetic field as well as preparation of bath in an appropriate spin coherent state, $$|\beta \rangle _\mathrm{{bath}}$$ , is shown to affect the decoherence process in a qualitatively significant manner. We show that the dynamics of the entanglement depends on the initial state of the central spins as well as the bath, the coupling constants and the strength of a magnetic field, $${\mathfrak {B}}, \lambda $$ . Compared with some cases already discussed in the literature as magnetic fields of periodic $$\sin (\lambda t)$$ and $$\cos (\lambda t)$$ functions, we can see that a magnetic field of exponential function $$\mathrm{e}^{-\lambda t}$$ plays a very crucial role in the entanglement generation between the two-spin qubits and its protection. To do this, we use an operator technique of the Holstein–Primakoff transformation, and the dynamics of the reduced density matrix of two coupled spin qubits is obtained in both finite and infinite numbers of bath spins. We also derive the concurrence measure to quantify the entanglement of the reduced density matrix of the two coupled central spins and look for conditions that provide information on whether this becomes robust against decoherence. It has been shown that the entanglement distribution can be both amplified, stabilized and protected with $${\mathfrak {B}}, \lambda $$ and $$\beta $$ . These results motivate developments toward the implementation or simulation of the purely theoretical model employing exponential fields.

Geometrical analysis and entanglement measure of symmetric multiqubit states

We geometrically examine the entanglement in symmetric multiquibt states using the spin coherent states properties. We employ the Majorana representation to examine how coherent (polarized) and unpolarized states can be represented in the Bloch sphere and subsequently to quantify entanglement in multipartite systems. Entanglement can be viewed as a distance separate two points in Bloch sphere and how this notion can be extended for multipartite states in W class. This provides us with an entanglement measure for [Formula: see text]-states analogue to the notion of Concurrence.

Entanglement of bipartite partly non-orthogonal -spin coherent states

We investigate the entanglement of a bipartite partly non-orthogonal state of the form through -spin coherent states by adopting the concurrence as a measure to quantify the degree of entanglement of the two-qubit system. After, we study the amount of entanglement of mixed states represented by a statistical mixture of partly non-orthogonal bipartite pure states. We also express the lower and upper bounds of the squared concurrence of mixed states in terms of the amplitudes of spin coherent states.

Strict deformation quantization of the state space of Mk(ℂ) with applications to the Curie–Weiss model

Increasing tensor powers of the [Formula: see text] matrices [Formula: see text] are known to give rise to a continuous bundle of [Formula: see text]-algebras over [Formula: see text] with fibers [Formula: see text] and [Formula: see text], where [Formula: see text], the state space of [Formula: see text], which is canonically a compact Poisson manifold (with stratified boundary). Our first result is the existence of a strict deformation quantization of [Formula: see text] à la Rieffel, defined by perfectly natural quantization maps [Formula: see text] (where [Formula: see text] is an equally natural dense Poisson subalgebra of [Formula: see text]). We apply this quantization formalism to the Curie–Weiss model (an exemplary quantum spin with long-range forces) in the parameter domain where its [Formula: see text] symmetry is spontaneously broken in the thermodynamic limit [Formula: see text]. If this limit is taken with respect to the macroscopic observables of the model (as opposed to the quasi-local observables), it yields a classical theory with phase space [Formula: see text] (i.e. the unit three-ball in [Formula: see text]). Our quantization map then enables us to take the classical limit of the sequence of (unique) algebraic vector states induced by the ground state eigenvectors [Formula: see text] of this model as [Formula: see text], in which the sequence converges to a probability measure [Formula: see text] on the associated classical phase space [Formula: see text]. This measure is a symmetric convex sum of two Dirac measures related by the underlying [Formula: see text]-symmetry of the model, and as such the classical limit exhibits spontaneous symmetry breaking, too. Our proof of convergence is heavily based on Perelomov-style coherent spin states and at some stage it relies on (quite strong) numerical evidence. Hence the proof is not completely analytic, but somewhat hybrid.

Three-tangle of a general three-qubit state in the representation of Majorana stars

Majorana stars, the $2j$ spin coherent states that are orthogonal to a spin-$j$ state, offer a visualization of general quantum states and may disclose deep structures in quantum states and their evolutions. In particular, the genuine tripartite entanglement - the three-tangle of a symmetric three-qubit state, which can be mapped to a spin-3/2 state, is measured by the normalized product of the distance between the Majorana stars. However, the Majorana representation cannot applied to general non-symmetric $n$-qubit states. We show that after a series of SL$(2,\mathbb{C})$ transformations, non-symmetric three-qubit states can be transformed to symmetric three-qubit states, while at the same time the three-tangle is unchanged. Thus the genuine tripartite entanglement of general three-qubit states has the geometric representation of the associated Majorana stars. The symmetrization and hence the Majorana star representation of certain genuine high-order entanglement for more qubits are possible for some special states. In general cases, however, the constraints on the symmetrization may prevent the Majorana star representation of the genuine entanglement.

Spin cat-state family for Heisenberg-limit metrology

We identify a class of superposition spin coherent states that enable measurements with a Heisenberg-limit (HL) precision. We demonstrate that a superposition of any two antipodal points on the Bloch sphere (two antipodal spin coherent states) can provide the HL precision. This finding suggests a universal strategy for the generation of quantum states for HL metrology and offers a physically clear perspective on the relation between the HL precision and two-mode cat states. We show that antipodal cat states suitable for HL metrology can be generated using cavity quantum electrodynamics structures.