Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators

Abstract

In this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering π periodically pumped parameters (oscillator frequencies and coupling) and using suitable transformations, we show that the quantum dynamics can be determined by two classical Meissner oscillators. We then study analytically the stability of these differential equations and the dynamics of photon excitations and entanglement in the quantum system numerically. Our analysis shows two interesting results, which can be summarized as follows: (i) Classical instability of classical analog of quantum oscillators and photon excitation numbers (expectations Nj) are strongly correlated, and (ii) photon excitations and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts and provide a nice complement to the existing works studying the dynamics of coupled quantum oscillators.

Virtual Excitations and Entanglement Dynamics and Polygamy in Three Ultra‐Strongly Coupled Systems

“…This finding can be used to consider virtual excitations as a kind of quantum correlation. [ 11,12,52 ] Furthermore, the virtual excitations can be used to quantify quantum resources beyond entanglement. Here, to show the interplay between excitations, we plot in Figure 6 , the dynamics of the trade‐off quantities $$$$\begin{eqnarray} \delta ^{i}_{jk}&=& N_{i|j}+N_{i|k}-N_{i|jk}, \quad k,l,m=a,b,c \end{eqnarray}$$$$…”

“…Motivated by the results of refs. [11,12], which demonstrate the interaction between entanglement and virtual excitations, we ask a fundamental question: whether virtual excitations are distributed in the same way that entanglement is.…”

“…\end{align}$$Since the coupling becomes ultra‐strong, the ground state becomes populated with virtual excitations. This is due to the counter‐rotating terms, [ 11,12 ] which simultaneously create the excitations in two modes. Then we will consider the ground state $$ \rho (0)=|000\rangle \langle 000|$$.…”

“…[1][2][3][4][5][6][7] The importance of the USC lies in its potential effects on several physical phenomena, including photon blockade, [8] Purcell effect, [9] Zeno effect, [10] and maintaining entanglement by virtual excitations of a vacuum state. [11,12] The fluctuations of the vacuum are one of the most striking phenomena of modern physics and have colossal applications in quantum technologies. [13,14] The vacuum in USC systems becomes populated by short-lived particles called virtual (not being absorbed by detectors) excitations.…”