The eigenmodes of a spatially inhomogeneous laser

K. Kaufmann, Wolfgang Weidlich

Philippe Grangier, J.-Ph. Poizat

Chang Wang, Kody J. H. Law, P. G. Kevrekidis +1 more

We study the structure, stability, and dynamics of dark solitary waves in parabolically trapped, collisionally inhomogeneous Bose-Einstein condensates (BECs) with spatially periodic variations of the scattering length. This collisional inhomogeneity yields a nonlinear lattice, which we tune from a small-amplitude, approximately sinusoidal structure to a periodic sequence of densely spaced spikes. We start by investigating time-independent inhomogeneities, and we subsequently examine the dynamical response when one starts with a collisionally homogeneous BEC and then switches on an inhomogeneity either adiabatically or nonadiabatically. Using Bogoliubov-de Gennes linearization as well as direct numerical simulations of the Gross-Pitaevskii equation, we observe dark solitary waves, which can become unstable through oscillatory or exponential instabilities. We find a critical wavelength of the nonlinear lattice that is comparable to the healing length. Near this value, the fundamental eigenmode responsible for the stability of the dark solitary wave changes its direction of movement as a function of the strength of the nonlinearity. When it increases, it collides with other eigenmodes, leading to oscillatory instabilities; when it decreases, it collides with the origin and becomes imaginary, illustrating that the instability mechanism is fundamentally different in wide-well versus narrow-well lattices. When starting from a collisionally homogeneous setup and switching on inhomogeneities, we find that dark solitary waves are preserved generically for aligned lattices. We briefly examine the time scales for the onset of solitary-wave oscillations in this scenario.

W. J. Firth

Yuh‐Jen Cheng, Anthony E.. Siegman

We propose a generalized radiation-field quantization formalism, where quantization does not have to be referenced to a set of power-orthogonal eigenmodes as conventionally required. This formalism can be used to directly quantize the true system eigenmodes, which can be non-power-orthogonal due to the open nature of the system or the gain/loss medium involved in the system. We apply this generalized field quantization to the laser linewidth problem, in particular, lasers with non-power-orthogonal oscillation modes, and derive the excess-noise factor in a fully quantum-mechanical framework. We also show that, despite the excess-noise factor for oscillating modes, the total spatially averaged decay rate for the laser atoms remains unchanged.

Zhi Jiao Deng, Xing Yao Mi, Ruo Kun Cai +2 more

In this paper, we investigate the non-Hermitian skin effect in a semi-infinite Fock-state lattice, where the inherent coupling scales as \sqrt{n}. By analytically solving a non-uniform, non-reciprocal SSH model, we demonstrate that the intrinsic inhomogeneous coupling, in combination with nonreciprocity, fundamentally modifies the conventional skin effect. Instead of accumulating at the physical boundary, all eigenmodes become compressed and skewed within a finite spatial range determined by the inhomogeneous profile-a phenomenon we term the confined non-Hermitian skin effect. Consequently, the evolution of the probability distribution on the lattice starting from a single site is doubly confined: it is spatially bounded to a finite range by the inhomogeneous coupling, and further restricted to a one-sided trajectory at the edge of this range by the non-reciprocity. Moreover, a feasible experimental scheme based on a single trapped ion is also proposed. This work reveals how engineered coupling profiles in synthetic dimensions can reshape non-Hermitian properties and enable new protocols for quantum state manipulation.