Free field realization of the BMS Ising model

In this work, we study the inhomogeneous BMS free fermion theory, and show that it gives a free field realization of the BMS Ising model. We find that besides the BMS symmetry there exists an anisotropic scaling symmetry in BMS free fermion theory. As a result, the symmetry of the theory gets enhanced to an infinite dimensional symmetry generated by a BMS-Kac-Moody algebra, similar to the one in the BMS free scalar model. Different from the BMS free scalar case, the Kac-Moody level in the algebra is nonvanishing now such that the corresponding modules are further enlarged to BMS-Kac-Moody staggered modules. We show that there exists an underlying $W(2,2,1)$ structure in the operator product expansion of the currents, and the BMS-Kac-Moody staggered modules can be viewed as highest-weight modules of this $W$-algebra. Moreover we obtain the BMS Ising model by a fermion-boson duality. This BMS Ising model is not a minimal model with respect to BMS$_3$, since the minimal model construction based on BMS Kac determinant always leads to chiral Virasoro minimal models. Instead, the underlying algebra of the BMS Ising model is the $W(2,2,1)$-algebra, which can be understood as a quantum conformal BMS$_3$ algebra.Comment: 49 pages; v2: references added, typos corrected, statement modified; v3: references added, typos corrected, more explanations adde

Spatial damping of propagating sausage waves in coronal cylinders

Sausage modes are important in coronal seismology. Spatially damped propagating sausage waves were recently observed in the solar atmosphere. We examine how wave leakage influences the spatial damping of sausage waves propagating along coronal structures modeled by a cylindrical density enhancement embedded in a uniform magnetic field. Working in the framework of cold magnetohydrodynamics, we solve the dispersion relation (DR) governing sausage waves for complex-valued longitudinal wavenumber $k$ at given real angular frequencies $\omega$. For validation purposes, we also provide analytical approximations to the DR in the low-frequency limit and in the vicinity of $\omega_{\rm c}$, the critical angular frequency separating trapped from leaky waves. In contrast to the standing case, propagating sausage waves are allowed for $\omega$ much lower than $\omega_{\rm c}$. However, while able to direct their energy upwards, these low-frequency waves are subject to substantial spatial attenuation. The spatial damping length shows little dependence on the density contrast between the cylinder and its surroundings, and depends only weakly on frequency. This spatial damping length is of the order of the cylinder radius for $\omega \lesssim 1.5 v_{\rm Ai}/a$, where $a$ and $v_{\rm Ai}$ are the cylinder radius and the Alfv\'en speed in the cylinder, respectively. We conclude that if a coronal cylinder is perturbed by symmetric boundary drivers (e.g., granular motions) with a broadband spectrum, wave leakage efficiently filters out the low-frequency components.Comment: 6 pages, 2 figures, to appear in Astronomy & Astrophysic

Quantum non-demolition measurement of photon number with atom-light interferometers

When atoms are illuminated by an off-resonant field, the AC Stark effect will lead to phase shifts in atomic states. The phase shifts are proportional to the photon number of the off-resonant illuminating field. By measuring the atomic phase with newly developed atom-light hybrid interferometers, we can achieve quantum non-demolition measurement of the photon number of the optical field. In this paper, we analyze theoretically the performance of this QND measurement scheme by using the QND measurement criteria established by Holland et al [Phys. Rev. A 42, 2995 (1990)]. We find the quality of the QND measurement depends on the phase resolution of the atom-light hybrid interferometers. We apply this QND measurement scheme to a twin-photon state from parametric amplifier to verify the photon correlation in the twin beams. Furthermore, a sequential QND measurement procedure is analyzed for verifying the projection property of quantum measurement and for the quantum information tapping. Finally, we discuss the possibility for single-photon-number-resolving detection via QND measurement