Spin Coherent States Research Articles

Larmor Precession and Tunnelling Time of a Non-RelativisticNeutral Spin-1/2 Particle Through an Arbitrary Potential Barrier

We investigate the Larmor precession of a non-relativistic neutralspin-1/2 particle in a uniform constant magnetic field confined tothe region of a one-dimensional arbitrary potential barrier. With thehelp of a general spin coherent state it is explicitly shown that thespin precession time is equal to the dwell time. For the special caseof a symmetric rectangular potential barrier, the precession time isalso in agreement with the transmission time. We present a numericalestimation of the precession time showing an apparent superluminaltunnelling.

Method of collective degrees of freedom in spin-coherent-state path integral

We present a detailed field theoretic description of those collective degrees of freedom (CDF) which are relevant to study macroscopic quantum dynamics of a quasi-one-dimensional ferromagnetic domain wall. We apply spin coherent state path integral (SCSPI) in the proper discrete time formalism (a) to extract the relevant CDF's, namely, the center position and the chirality of the domain wall, which originate from the translation and the rotation invariances of the system in question, and (b) to derive effective action for the CDF's by elimination of environmental zero-modes with the help of the {\it Faddeev-Popov technique}. The resulting effective action turns out to be such that both the center position and the chirality can be formally described by boson coherent state path integral. However, this is only formal; there is a subtle departure from the latter.

Rényi-Wehrl entropies as measures of localization in phase space

We generalize the concept of the Wehrl entropy of quantum states which gives a basis-independent measure of their localization in phase space. We discuss the minimal values and the typical values of these R{enyi-Wehrl entropies for pure states for spin systems. According to Lieb's conjecture the minimal values are provided by the spin coherent states. Though Lieb's conjecture remains unproven, we give new proofs of partial results that may be generalized for other systems. We also investigate random pure states and calculate the mean Renyi-Wehrl entropies averaged over the natural measure in the space of pure quantum states.

QUANTUM-CLASSICAL CROSSOVER OF THE ESCAPE RATE IN THE NANO-FERROMAGNET WITH COMPLEX CRYSTAL SYMMETRY

We investigate the quantum-classical crossover of the escape rate in the nanoscale ferromagnetic particle with complex crystal symmetries placed in an external field along the hard anisotropy axis. We use the periodic instanton technique based on the spin coherent state representation and the condition of the first-order crossover to determine the type of crossover. In the high field limit of ∊(=1-Hc/H)→0 the crossover is found to be second-order. We also calculate the crossover temperature with leading order behavior of T0~∊1/2.

Coherence and squeezing in superpositions of spin coherent states

We consider the superpositions of spin coherent states and study the coherence properties and spin squeezing in these states. The spin squeezing is examined using a new version of spectroscopic squeezing criteria. The results show that the antibuching effect can be enhanced and spin squeezing can be generated in the superpositions of two spin coherent states.

SEMICLASSICAL EXPRESSION OF THE SPIN PROPAGATOR

We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay attention to the extra phase. This extra correction of phase is related to an anomaly in the fluctuation determinant. We show that if this extra factor is included, the semiclassical propagator has the correct short time behaviour to O(T2), and demonstrate its consistency under dissection of the path.

Larmor precession and barrier tunneling time of a neutral spinning particle

The Larmor precession of a neutral spinning particle in a magnetic field confined to the region of a one-dimensional rectangular barrier is investigated for both a nonrelativistic and a relativistic incoming particle. The spin precession serves as a clock to measure the time spent by a quantum particle traversing a potential barrier. With the help of a general spin coherent state it is explicitly shown that the precession time is equal to the dwell time in both the nonrelativistic and relativistic cases. We also present a numerical estimation of the precession time showing an apparent superluminal tunneling.

Observation of radical pair zero quantum coherence effects in the FT-EPR spectra of SO 3− and e aq− generated by photoionization of sulfite ions

The time evolution of the intensities of FT-EPR signals from the hydrated electron (e aq −) and SO 3 − radical formed by photoionization of SO 3 2− in aqueous solution shows an oscillatory pattern. The effect is attributed to the coherent S–T 0 spin state evolution in the [e aq −⋯SO 3 −] radical pair producing spin polarization in the free radicals. The damping of these oscillations is not as strong as that predicted by the radical pair mechanism (RPM) chemically induced dynamic electron polarization (CIDEP) theory formulated by Adrian [Chem. Phys. Lett. 272 (1997) 120]. The experimental data can serve to test alternative theoretical descriptions of RPM CIDEP in terms of coherent radical pair spin state evolution combined with diffusive motion of the radicals.

Spin squeezing in nonlinear spin-coherent states

We introduce the nonlinear spin coherent state via its ladder operator formalism and propose a type of nonlinear spin coherent state by the nonlinear time evolution of spin coherent states. By a new version of spectroscopic squeezing criteria we study the spin squeezing in both the spin coherent state and nonlinear spin coherent state. The results show that the spin coherent state is not squeezed in the x, y, and z directions, and the nonlinear spin coherent state may be squeezed in the x and y directions.

Thecoherent-state wave function for solid 3He

A new class of variational wave functions describing many-bodysystems with spin-dependent correlations is used to study solid3He. The idea of spin coherent states is used to construct avariational coherent-state wave function for solid 3He as anantisymmetrized Jastrow-Nosanow wave function that also containsspin-dependent correlations. We investigate this wave function by avariational Monte Carlo method. The addition of triplet(three-body) correlations produces a ground-state energy perparticle that is a considerable improvement upon other variationalresults, but still appreciable discrepancies with the experimentremain. We speculate that such discrepancies point to anon-negligible effect of more-than-three-body correlations for bothliquid and solid 3He.

Spin tunneling and topological selection rules for integer spins

We present topological interference effects for the tunneling of a single large spin, which are caused by the symmetry of a general class of magnetic anisotropies. The interference originates from spin Berry phases associated with different tunneling paths exposed to the same dynamics. Introducing a generalized path integral for coherent spin states, we evaluate transition amplitudes between ground as well as low-lying excited states. We show that these interference effects lead to topological selection rules and spin-parity effects for integer spins that agree with quantum selection rules and which thus provide a generalization of the Kramers degeneracy to integer spins. Our results apply to the molecular magnets Mn12 and Fe8.

The semiclassical propagator for spin coherent states

We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay particular attention to the “extra phase” discovered by Solari and Kochetov, and show that this correction is related to an anomaly in the fluctuation determinant. We show that, once this extra factor is included, the semiclassical propagator has the correct short time behavior to O(T2), and demonstrate its consistency under dissection of the path.

Invariant spin coherent states and the theory of the quantum antiferromagnet in a paramagnetic phase

The consistent theory of the Heisenberg quantum antiferromagnet in the disordered phase with short range antiferromagnetic order was developed on the basis of the path integral for the spin coherent states. We have presented the Lagrangian of the theory in a form which is explicitly invariant under rotations and have found natural variables in the term of which one can construct a natural perturbation theory. The short wave spin fluctuations are similar to the spin wave theory ones, and the long wave spin fluctuations are governed by the nonlinear sigma model. We have also demonstrated that the short wave spin fluctuations have to be considered accurately in the framework of the discrete version in time of the path integral. In the framework of our approach we have obtained the response function for the spin fluctuations for the whole region of the frequency $\omega$ and the wave vector ${\bf k}$ and have calculated the free energy of the system.

Generation of spin squeezing via continuous quantum nondemolition measurement

Continuous quantum nondemolition monitoring of a collective atomic spin with an off-resonant laser beam has been performed. Squeezed atomic spin states have thereby been produced with spin noise reduction to 70% below the standard quantum limit expected for a coherent spin state.

Quantum dynamics of a generalized Coleman-Hepp model

Studies on a generalized Coleman-Hepp model are done on the basis of a spin coherent state representation and a transformation property of the model Hamiltonian. Namely, transforming the original model Hamiltonian into a simpler form, we can determine time evolution of the whole system by successive applications of rotation operators in a spinor space. Dynamics of detector spins as well as that of an incident particle are fully discussed. Explicit numerical evaluations are also performed. Relevance of our solution to a generalized Cini model is also briefly mentioned.

Crossover between first- and second-order transitions of a spin tunneling in a magnetic field

Based on the spin-coherent state path integral, we have considered the quasiclassical escape rate transition for the nano-spin system. Expanding the period of the classical motion in the imaginary time around the top of the potential barrier, we have presented the boundary between the first- and the second-order transition, and the corresponding crossover temperature for the uniaxial and the biaxial spin system.

Overlap integral for quantum skyrmions

Making use of the method of spin coherent states, we obtained an analytical form of the overlap integral for quantum skyrmions.

DiscreteQ- andP-symbols for spins

Non-orthogonal bases of projectors on coherent states are introduced to expand hermitean operators acting on the Hilbert space of a spin s. It is shown that the expectation values of a hermitean operator A in a family of (2s+1)(2s+1) spin-coherent states determine the operator unambiguously. In other words, knowing the Q-symbol of A at (2s+1)(2s+1) points on the unit sphere is already sufficient in order to recover the operator. This provides a straightforward method to reconstruct the mixed state of a spin since its density matrix is explicitly parametrized in terms of expectation values. Furthermore, a discrete P-symbol emerges naturally which is related to a basis dual to the original one.

On the completeness of coherent states generated by binomial distribution

We demonstrate the completeness of boson- and spin-coherent states generated by binomial distribution by furnishing the exact analytical form of their respective positive weight functions in resolution of unity. These weight functions are solutions of the associated truncated Stieltjes power-moment problem. We elaborate on the non-unique character of these solutions.

Solitons in the system of interacting Frenkel excitons

The possible formation of solitons in a Frenkel exciton system, with exciton-exciton interaction only, is studied taking into account the Pauli character of exciton operators. This is realized by choosing the trial function of the system in the form which is the particular representation of the spin coherent state for spin 1/2. Possible solutions include both `bright' and `dark' solitons. Strict conditions for the existence and stability of particular types of soliton are formulated by imposing limitations on the values of the system parameters and soliton velocity. The energy-momentum relation for both types of solution is obtained. It is concluded that neither kind of soliton can exist if the effective dynamical interaction is a repulsive one. Recent references concerning `bright' and `dark' solitons are critically assessed.