Controlling soliton excitations in Heisenberg spin chains through the magic angle

Lu, Jianghua; Zhou, Lan; Kuang, Le‐Man; Sun, C. P.

doi:10.1103/physreve.79.016606

Cited by 10 publications

(7 citation statements)

References 32 publications

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“…Importantly, the complex interactions between atomic and photonic components produce a variety of effects. Solitonic behavior has been predicted in the 1D coupled cavity wave guide realizations of the Dicke model [20] and the XXZ model in the presence of a tilted magnetic field [21]. If one is considering, for example, the type of localized/delocalized behavior typically found in strongly interacting systems, it is of vital importance not to be distracted by the background effects which come from the delocalized behaviour of photons themselves.…”

Section: Introductionmentioning

confidence: 99%

Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian

et al. 2009

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The Jaynes-Cummings-Hubbard (JCH) system describes a network of single-mode photonic cavities connected via evanescent coupling. Each cavity contains a single two level system which can be tuned in resonance with the cavity. Here we explore the behavior of single excitations (where an excitation can be either photonic or atomic) in the linear JCH system, which describes a coupled cavity waveguide. We use direct, analytic diagonalization of the Hamiltonian to study cases where inter-cavity coupling is either uniform or varies parabolically along the chain. Both excitations located in a single cavity, as well as one excitation as a Gaussian pulse spread over many cavities, are investigated as initial states. We predict unusual behavior of this system in the time domain, including slower than expected propagation of the excitation, and also splitting of the excitation into two distinct pulses, which travel at distinct speeds. In certain limits, we show that the JCH system mimics two Heisenberg spin chains.

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Section: Introductionmentioning

confidence: 99%

Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian

et al. 2009

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“…As mentioned in Ref. , in the larger external field limit, the Hamiltonian can be reduced to

H = - (1 + \frac{γ}{2} si {normaln}^{2} θ) J \sum_{j = 1}^{f} L_{j} \cdot L_{j + 1} - \frac{γ}{2} J (3 co {normals}^{2} θ - 1) \sum_{j = 1}^{f} L_{j}^{z} \cdot L_{j + 1}^{z} + B \sum_{j = 1}^{f} L_{j}^{z},

where γ = Δ − 1. Now, we introduce the Holstein–Primakoff transformation for the spin operators

L_{j}^{+} = b_{j}^{†} \sqrt{2 S - b_{j}^{†} b_{j}},

L_{j}^{-} = (\sqrt{2 S - b_{j}^{†} b_{j}}) b_{j},

L_{j}^{z} = b_{j}^{†} b_{j} - S,

where the annihilation operators b j and the creation operators

b_{j}^{†}

obey the bosonic commutation relations

[b_{j}, b_{j^{'}}^{†}] = δ_{j j^{'}}

and

[b_{j}^{†}, b_{j^{'}}^{†}] = [b_{j}, b_{j^{'}}] = 0

.…”

Section: Spin Chain Model Hamiltonianmentioning

confidence: 94%

Controlling quantum breathers in Heisenberg ferromagnetic spin chains via an oblique magnetic field

Tang

2014

Physica Status Solidi (b)

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An analytical study on controlling quantum breathers in one-dimensional ferromagnetic XXZ spin chains through an oblique magnetic field is presented in this paper. Based on the time-dependent Hartree approximation and the semidiscrete multiple-scale method, we prove the existence of quantum breathers, analyze conditions for their appearance, and discuss their properties. Our results show that the appearance and features of quantum breathers can be controlled by varying the value of the oblique angle u.

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“…As pointed out in the beginning, the extended BH model Hamiltonian for HCB can be mapped to the classical XXZ ferromagnetic Heisenberg spin- 1 2 Hamiltonian, on taking spin coherent state average of the Hamiltonian (15). The topic of magnetic solitons in Heisenberg chains that has been studied for over two decades [20,21] continues to attract attention in recent times [22] as well. While the order parameter for BEC is the condensate density ρ s (z) = ρ(z)(1−ρ(z)), the relevant order parameter for the spin Hamiltonian is S z (z), which can found from the HCB boson density ρ(z) by using the identity S z = [(1/2) − ρ(z)].…”

Section: Hcb Solitons Mapped To Magnetic Solitons In Heisenberg mentioning

confidence: 99%

“…For a spin system, ω is just the precession frequency due to a corresponding "magnetic field" along the z-axis. Thus the gauge-transformed evolution equation (22) which led to solitons (44), also describes those for the continuum dynamics of the following dimensionless anisotropic Heisenberg spin Hamiltonian:…”

Section: Hcb Solitons Mapped To Magnetic Solitons In Heisenberg mentioning

confidence: 99%

Solitons in a hard-core bosonic system: Gross–Pitaevskii type and beyond

Balakrishnan

Satija

2015

Pramana - J Phys

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A unified formulation that obtains solitary waves for various background densities in the Bose-Einstein condensate of a system of hard-core bosons with nearest neighbor attractive interactions is presented. In general, two species of solitons appear: A nonpersistent (NP) type that fully delocalizes at its maximum speed, and a persistent (P) type that survives even at its maximum speed, and transforms into a periodic train of solitons above this speed. When the background condensate density is nonzero, both species coexist, the soliton is associated with a constant intrinsic frequency, and its maximum speed is the speed of sound. In contrast, when the background condensate density is zero, the system has neither a fixed frequency, nor a speed of sound. Here, the maximum soliton speed depends on the frequency, which can be tuned to lead to a cross-over between the NP-type and the P-type at a certain critical frequency, determined by the energy parameters of the system. We provide a single functional form for the soliton profile, from which diverse characteristics for various background densities can be obtained. Using the mapping to spin systems enables us to characterize the corresponding class of magnetic solitons in Heisenberg spin chains with different types of anisotropy, in a unified fashion.

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Controlling soliton excitations in Heisenberg spin chains through the magic angle

Cited by 10 publications

References 32 publications

Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian

Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian

Controlling quantum breathers in Heisenberg ferromagnetic spin chains via an oblique magnetic field

Solitons in a hard-core bosonic system: Gross–Pitaevskii type and beyond

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