We consider a harmonic oscillator (HO) with a time-dependent frequency which undergoes two successive abrupt changes. By assumption, the HO starts in its fundamental state with frequency ω 0 , then, at t = 0, its frequency suddenly increases to ω 1 and, after a finite time interval τ , it comes back to its original value ω 0. Contrary to what one could naively think, this problem is quite a non-trivial one. Using algebraic methods, we obtain its exact analytical solution and show that at any time t > 0 the HO is in a vacuum squeezed state. We compute explicitly the corresponding squeezing parameter (SP) relative to the initial state at an arbitrary instant and show that, surprisingly, it exhibits oscillations after the first frequency jump (from ω 0 to ω 1), remaining constant after the second jump (from ω 1 back to ω 0). We also compute the time evolution of the variance of a quadrature. Last, but not least, we calculate the vacuum (fundamental state) persistence probability amplitude of the HO, as well as its transition probability amplitude for any excited state.
We found new signatures of the dynamical Casimir effect (DCE) in the context of superconducting circuits. We show that if the recent experiment made by Wilson et al, which brought the DCE into reality for the first time, is repeated with slight modifications (for instance, different values for the capacitance of the SQUID), three remarkable results will show up, namely: (i) a quite different spectral distribution for the created particles, deviating from the typical parabolic shape; (ii) an enhancement by a factor of approximately 5 × 10 3 in the number of created particles with half driven frequency of the effective moving mirror and (iii) an enhancement by a factor of 3 × 10 2 in the particle creation rate. These results may guide the experimentalists in their search for alternative routes to observe the DCE in future experiments.
Using operator ordering techniques based on Baker-Campbell-Hausdorff (BCH) relations of the su(1,1) Lie algebra and a time-splitting approach, we present an alternative method of solving the dynamics of a time-dependent quantum harmonic oscillator for any initial state. We find an iterative analytical solution given by simple recurrence relations that are very well suited for numerical calculations. We use our solution to reproduce and analyse some results from the literature to prove the usefulness of our method. We also discuss the efficiency in squeezing by comparing the parametric resonance modulation with the so-called Janszky-Adam scheme.
Motivated by experiments in which moving boundaries are simulated by timedependent properties of static systems, we discuss the model of a massless scalar field submitted to a time-dependent Robin boundary condition (BC) at a static mirror in 1 + 1 dimensions. Using a perturbative approach, we compute the spectral distribution of the created particles and the total particle creation rate, considering a thermal state as the initial field state.
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