Motivated by recent studies of circuit complexity in weakly interacting scalar field theory, we explore the computation of circuit complexity in Z2 Even Effective Field Theories (Z2 EEFTs). We consider a massive free field theory with higher-order Wilsonian operators such as ϕ4, ϕ6, and ϕ8. To facilitate our computation, we regularize the theory by putting it on a lattice. First, we consider a simple case of two oscillators and later generalize the results to N oscillators. This study was carried out for nearly Gaussian states. In our computation, the reference state is an approximately Gaussian unentangled state, and the corresponding target state, calculated from our theory, is an approximately Gaussian entangled state. We compute the complexity using the geometric approach developed by Nielsen, parameterizing the path-ordered unitary transformation and minimizing the geodesic in the space of unitaries. The contribution of higher-order operators to the circuit complexity in our theory is discussed. We also explore the dependency of complexity on other parameters in our theory for various cases.

In this article, we investigate the physical implications of the causality constraint via effective sound speed cs(≤ 1) on Quantum Circuit Complexity(QCC) in the framework of Cosmological Effective Field Theory (COSMOEFT) using the two-mode squeezed quantum states. This COS-MOEFT setup is constructed using the Stückelberg trick with the help of the lowest dimensional operators, which are broken under time diffeomorphism. In this setup, we consider only the contribution from two derivative terms in the background quasi de Sitter metric. Next, we compute the relevant measures of circuit complexity and their cosmological evolution for different cs by following two different approaches, Nielsen's and Covariance matrix method. Using this setup, we also compute the Von-Neumann and Rényi entropy, which finally establishes an underlying connecting relationship between the entanglement entropy and circuit complexity. Essentially, we study the behaviour of the circuit complexity measures and entanglement entropy with respect to the scale factor and cs and find various interesting unexplored features within the window, 0.024 ≤ cs ≤ 1, which is supported by both causality and cosmological observation. Finally, we also comment on the connection between the circuit complexity, entanglement entropy and equilibrium temperature for different cs lying within the mentioned window.

In this work, we explore the effects of quantum quenching on the circuit complexity of quenched quantum field theory with weakly coupled quartic interactions. We use the invariant operator method under a perturbative framework to compute the ground state of this system. We give the analytical expressions for specific reference and target states using the ground state of the system. Using a particular cost functional, we show the analytical computation of circuit complexity for the quenched and interacting field theory. Furthermore, we give a numerical estimate of circuit complexity with respect to the quench rate, δt, for two coupled oscillators. The parametric variation in the unambiguous contribution of the circuit complexity for an arbitrary number of oscillators has been studied with respect to the dimensionless parameter (t/δt). We comment on the variation in the circuit complexity for different values of coupling strength, different numbers of oscillators and even in different dimensions.

In this paper we study the application of four-mode squeezed states in the cosmological context, studying two weakly coupled scalar fields in the planar patch of the de Sitter space. We construct the four-mode squeezed state formalism and connect this concept with the Hamiltonian of the two coupled inverted harmonic oscillators having a time-dependent effective frequency in the planar patch of the de Sitter space. Further, the corresponding evolution operator for the quantum Euclidean vacuum state has been constructed, which captures its dynamics. Using the Heisenberg picture coupled differential equations describing the time evolution for all squeezing parameters (amplitude, phase and angle) have been obtained, for the weakly coupled two scalar field model. With the help of these evolutions for the coupled system, we simulate the dynamics of the squeezing parameters in terms of conformal time. From our analysis, we observe interesting dynamics, which helps us to explore various underlying physical implications of the weakly coupled two scalar field system in the planar patch of the de Sitter cosmological background.

In the past few years, photonic crystal fibre (PCF) in the Terahertz spectrum is drawing significant attention because of its multifaceted applications in high-speed data communication, spectroscopy, sensing, etc. The proposed PCF structure is based on a Teflon solid core surrounded by porous cladding. Teflon has been used as a background material because of its high flexibility and the possibility of making longer PCFs, which is capable of guiding waves in the THz region. The porous cladding consists of circular air-holes positioned hexagonally whose diameters increase with each subsequent layer keeping the pitch constant thus providing a graded-index profile. The diameters of air holes in each hexagonal layer are 1 mm, 1.2 mm and 1.5 mm respectively, maintaining a constant pitch of 2mm and a perfectly matched layer (PML) thickness of 3mm. We have examined the transmission characteristics of the proposed profile in the frequency range of 0.8 THz to 2.5 THz. The modal solution of the profile is solved using the Finite Element Method based on COMSOL Multiphysics version 5.5. Using the graded-index profile, we have obtained a large effective modal area of around 5.6 mm2 at 1 THz and a low confinement loss of 2.25 × 10−4 dB/km at the same frequency. Due to this large effective modal area, we get higher damage threshold and weaker non-linear effects, making it suitable for high power applications.