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arXiv:2007.02150 · Chinese Journal of Physics

Effects of quenching protocols based on parametric oscillators

Mariagiovanna Gianfreda, Giulio Landolfi

Published Aug 8, 2021• 0 citations
arXivHTMLPDF
DOI
10.1016/j.cjph.2021.07.017

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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.
We study the squeezing as well as the statistical properties of the output radiation from a degenerate parametric oscillator coupled to a squeezed vacuum reservoir employing the stochastic differential equations associated with the normal ordering. It is found that the degree of squeezing of the output radiation is less than the corresponding cavity radiation. However, for output radiation the correlation of the quadrature operators evaluated at different times also exhibits squeezing, which is the reason for quenching of the overall noise in one of the quadrature components of the squeezing spectrum even when the oscillator is coupled to a vacuum reservoir. Moreover, coupling the oscillator to the squeezed vacuum reservoir enhances the squeezing exponentially and it also increases the mean photon number.
We introduce a finite-time protocol that thermalizes a quantum harmonic oscillator, initially in its ground state, without requiring a macroscopic bath. The method uses a second oscillator as an effective environment and implements sudden quenches of the oscillator frequencies and coupling. Owing to the Gaussian nature of the dynamics, the thermalization condition reduces to three solvable equations, yielding exact analytic solutions for a dense discrete set of temperatures and numerical solutions in all other cases. Any target temperature can be approximated with arbitrary precision, with a trade-off between speed and accuracy. The simplicity of the protocol makes it a promising tool for rapid, controlled thermalization in quantum thermodynamics experiments and state preparation.