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arXiv:2308.13397 · Entropy

Adiabatic Shortcuts Completion in Quantum Field Theory: Annihilation of Created Particles

Nicolás F. Del Grosso, Fernando C. Lombardo, Francisco Diego Mazzitelli, Paula I. Villar

Published Aug 23, 2023• 4 citations
arXivHTMLPDF

Abstract

Shortcuts to adiabaticity (STA) are relevant in the context of quantum systems, particularly regarding their control when they are subjected to time-dependent external conditions. In this paper, we investigate the completion of a nonadiabatic evolution into a shortcut to adiabaticity for a quantum field confined within a one-dimensional cavity containing two movable mirrors. Expanding upon our prior research, we characterize the field's state using two Moore functions that enables us to apply reverse engineering techniques in constructing the STA. Regardless of the initial evolution, we achieve a smooth extension of the Moore functions that implements the STA. This extension facilitates the computation of the mirrors' trajectories based on the aforementioned functions. Additionally, we draw attention to the existence of a comparable problem within nonrelativistic quantum mechanics.

DOI
10.3390/e25091249

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Shortcuts to adiabaticity (STA) are relevant in the context of quantum systems, particularly regarding their control when they are subjected to time-dependent external conditions. In this paper, we investigate the completion of a nonadiabatic evolution into a shortcut to adiabaticity for a quantum field confined within a one-dimensional cavity containing two movable mirrors. Expanding upon our prior research, we characterize the field's state using two Moore functions that enables us to apply reverse engineering techniques in constructing the STA. Regardless of the initial evolution, we achieve a smooth extension of the Moore functions that implements the STA. This extension facilitates the computation of the mirrors' trajectories based on the aforementioned functions. Additionally, we draw attention to the existence of a comparable problem within nonrelativistic quantum mechanics.
The development of quantum technologies present important challenges such as the need for fast and precise protocols for implementing quantum operations. Shortcuts to adiabaticity (STAs) are a powerful tool for achieving these goals, as they enable us to perform an exactly adiabatic evolution in finite time. In this paper, we present a shortcut to adiabaticity for the control of an optomechanical cavity with two moving mirrors. Given reference trajectories for the mirrors, we find analytical expressions that give us effective trajectories which implement an STA for the quantum field inside the cavity. We then solve these equations numerically for different reference protocols, such as expansions, contractions and rigid motions, thus confirming the successful implementation of the STA and finding some general features of these effective trajectories.
We analyze shortcuts to adiabaticity (STA) and their completions for the quantum harmonic oscillator (QHO) with time-dependent frequency, as well as for quantum field theory (QFT) in non-stationary backgrounds. We exploit the analogy with one-dimensional quantum mechanics, and the well known correspondence between Bogoliubov coefficients in the QHO and transmission/reflection amplitudes in scattering theory. Within this framework, STA protocols for the QHO are equivalent to transmission resonances, while STA in QFT with homogeneous backgrounds correspond to reflectionless potentials. Moreover, using the connection between particle creation and squeezed states, we show how STA completions can be understood in terms of the anti-squeezing operator.
The adiabatic theorem and shortcuts to adiabaticity for time-dependent open quantum systems are explored in this paper. Starting from the definition of dynamical stable decoherence-free subspace, we show that, under a compact adiabatic condition, the quantum state remains in the time-dependent decoherence-free subspace with an extremely high purity, even though the dynamics of the open quantum system may not be adiabatic. The adiabatic condition mentioned here in the adiabatic theorem for open systems is very similar to that for closed quantum systems, except that the operators required to change slowly are the Lindblad operators. We also show that the adiabatic evolution of decoherence-free subspaces depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems be engineered according to the incoherent control protocol. In addition, shortcuts to adiabaticity for adiabatic decoherence-free subspaces are also presented based on the transitionless quantum driving method. Finally, we provide an example that consists of a two-level system coupled to a broadband squeezed vacuum field to show our theory. Our approach employs Markovian master equations and the theory can apply to finite-dimensional quantum open systems.
Adiabatic quantum computing (AQC) is an approach for solving optimization problems and has advantages against environmental decoherence and certain kinds of random unitary perturbations; however, long coherence time of quantum systems is required to meet the adiabatic criteria for the implementation of AQC. To break the dilemma of evolution time in AQC, the method of shortcuts to adiabaticity (STA) is employed to speed up the evolution process and suppress the nonadiabatic transitions. In this work we demonstrate the application of STA in AQC by implementing a fast two-bit Grover's algorithm with STA in an ion trap system, and the method here is also applicable for realizing Grover's algorithm with more entries.
This research examines the fast forwad and shortcut to adiabaticity (STA) method in accelerating adiabatic dynamics applied to two level systems. The fast forwad and shortcut to adiabaticity (STA) method is a strategy developed to accelerate the evolution of quantum systems from the initial state to the final state in a short time. In this method, the acceleration scheme is built by modifying the Hamiltonian through the addition of additional terms to the initial Hamiltonian as regularization terms so that the time-dependent Schrodinger equation is still fulfilled. The formulation of the problem in this study is how to find the regularization term and additional Hamiltonian of the fast forwad and STA methods. The methodology used to obtain regularization terms with adiabatic magnetic field and analysis of wave function solutions and additional Hamiltonians. The results of the study are regularization terms and additional Hamiltonians to shorten the dynamics of the system adiabatically. In the fast forwad method to obtain the regularization term, one energy information of the system is required, while in the STA method all energy information of the system is required