Restoration of oscillations from an oscillation suppressed state in coupled oscillators is an important topic of research and has been studied widely in recent years. However, the same in the quantum regime has not been explored yet. Recent works established that under certain coupling conditions, coupled quantum oscillators are susceptible to suppression of oscillations, such as amplitude death and oscillation death. In this paper, for the first time, we demonstrate that quantum oscillation suppression states can be revoked and rhythmogenesis can be established in coupled quantum oscillators by controlling a feedback parameter in the coupling path. However, in sharp contrast to the classical system, we show that in the deep quantum regime, the feedback parameter fails to revive oscillations, and rather results in a transition from a quantum amplitude death state to the recently discovered quantum oscillation death state. We use the formalism of an open quantum system and a phase space representation of quantum mechanics to establish our results. Therefore, our study establishes that the revival scheme proposed for classical systems does not always result in restoration of oscillations in quantum systems, but in the deep quantum regime, it may give counterintuitive behaviors that are of a pure quantum mechanical origin.Restoration of oscillations from an oscillation suppressed state in coupled oscillators is an important topic of research and has been studied widely in recent years. However, the same in the quantum regime has not been explored yet. Recent works established that under certain coupling conditions, coupled quantum oscillators are susceptible to suppression of oscillations, such as amplitude death and oscillation death. In this paper, for the first time, we demonstrate that quantum oscillation suppression states can be revoked and rhythmogenesis can be established in coupled quantum oscillators by controlling a feedback parameter in the coupling path. However, in sharp contrast to the classical system, we show that in the deep quantum regime, the feedback parameter fails to revive oscillations, and rather results in a transition from a quantum amplitude death state to the recently discovered quantum oscillation death state. We use the formalism of an open quantum system and a phase space representation of quantum mechanics to establish our results. Therefore, our study establishes that the revival scheme proposed for classical systems does not always result in restoration of oscillations in quantum systems, but in the deep quantum regime, it may give counterintuitive behaviors that are of a pure quantum mechanical origin.

arXiv:2105.10640Chaos An Interdisciplinary Journal of Nonlinear ScienceJun 1, 202118 citations

Quantum Oscillators

Olivier Henri‐Rousseau, Paul Blaise

Wiley eBooksApr 22, 201119 citations

Equivalence of quantum harmonic oscillators and classical oscillators subject to random forces

Can Gokler

We show that the Schrödinger equation for the quantum harmonic oscillator can be derived as an approximation to the Newtonian mechanics of a classical harmonic oscillator subject to a random force for time intervals $O( m / \hbar)$ , when $\hbar / m \ll 1$ . Conversely, every solution to the Schrödinger equation, including all the superposition states, arises this way. In other words, the quantum harmonic oscillator is approximately nothing but the classical harmonic oscillator, with the same mass and frequency as the quantum harmonic oscillator, subject to a random force. We generalize the result to multiple non-interacting oscillators. We show that the Schrödinger equation for $n$ non-interacting quantum harmonic oscillators with masses $m_1, ..., m_n$ and frequencies $ω_1, ..., ω_n$ can be derived as an approximation to the Newtonian mechanics of $n$ non-interacting classical harmonic oscillators, with the same set of masses and frequencies as the quantum oscillators, subject to random forces. This is valid for time intervals $O( \tilde{m} / \hbar)$ , where $\tilde{m}$ is the mass of the minimum mass oscillator, when $\hbar/\tilde{m} \ll 1$ . Conversely, every solution, including all the entangled states, to the Schrödinger equation arises this way. In other words, $n$ non-interacting quantum harmonic oscillators are approximately nothing but $n$ non-interacting classical harmonic oscillators, with the same set of masses and frequencies as the quantum oscillators, subject to random forces. This provides a local Newtonian model of entanglement of non-interacting quantum oscillators. The correlations required by entangled states are embedded in the phase space probability density of the classical oscillators.We show that the Schrödinger equation for the quantum harmonic oscillator can be derived as an approximation to the Newtonian mechanics of a classical harmonic oscillator subject to a random force for time intervals $O( m / \hbar)$, when $\hbar / m \ll 1$. Conversely, every solution to the Schrödinger equation, including all the superposition states, arises this way. In other words, the quantum harmonic oscillator is approximately nothing but the classical harmonic oscillator, with the same mass and frequency as the quantum harmonic oscillator, subject to a random force. We generalize the result to multiple non-interacting oscillators. We show that the Schrödinger equation for $n$ non-interacting quantum harmonic oscillators with masses $m_1, ..., m_n$ and frequencies $ω_1, ..., ω_n$ can be derived as an approximation to the Newtonian mechanics of $n$ non-interacting classical harmonic oscillators, with the same set of masses and frequencies as the quantum oscillators, subject to random forces. This is valid for time intervals $O( \tilde{m} / \hbar)$, where $\tilde{m}$ is the mass of the minimum mass oscillator, when $\hbar/\tilde{m} \ll 1$. Conversely, every solution, including all the entangled states, to the Schrödinger equation arises this way. In other words, $n$ non-interacting quantum harmonic oscillators are approximately nothing but $n$ non-interacting classical harmonic oscillators, with the same set of masses and frequencies as the quantum oscillators, subject to random forces. This provides a local Newtonian model of entanglement of non-interacting quantum oscillators. The correlations required by entangled states are embedded in the phase space probability density of the classical oscillators.

arXiv:2010.14930Oct 26, 20202 citations

Quantum Oscillators

A. M. Perelomov

Springer eBooksJan 1, 19860 citations

Quantum correlations and measurements in tri-partite quantum systems.

Bahari Idrus

Correlations and entanglement in a chain of three oscillators A,B,C with \nnearest neighbour coupling is studied. Oscillators A,B and B,C are coupled \nbut there is no direct coupling between oscillators A,C. Examples with initial \nfactorizable states are considered, and the time evolution is calculated. It \nis shown that the dynamics of the tri-partite system creates correlations and \nentanglement among the three oscillators and in particular, between oscillators \nA,C which are not coupled directly. We have performed photon number \nselective and non-selective measurements on oscillator A and we investigated \ntheir effects on the correlations and entanglement. It is shown that, before \nthe measurement, the correlations between oscillators A,C can be stronger \nthan the correlations of oscillators A,B. Moreover, some entanglement witness \nshows that oscillators A,C are entangled but the oscillators A,B might \nor might not be entangled. By using quantum discord, which measures the \nquantumness of correlations, it is shown that there are quantum correlations \nbetween oscillators A,B and after the measurements in both cases of selective \nand non-selective measurements, oscillators A,B and A,C become classically \ncorrelated.Correlations and entanglement in a chain of three oscillators A,B,C with \nnearest neighbour coupling is studied. Oscillators A,B and B,C are coupled \nbut there is no direct coupling between oscillators A,C. Examples with initial \nfactorizable states are considered, and the time evolution is calculated. It \nis shown that the dynamics of the tri-partite system creates correlations and \nentanglement among the three oscillators and in particular, between oscillators \nA,C which are not coupled directly. We have performed photon number \nselective and non-selective measurements on oscillator A and we investigated \ntheir effects on the correlations and entanglement. It is shown that, before \nthe measurement, the correlations between oscillators A,C can be stronger \nthan the correlations of oscillators A,B. Moreover, some entanglement witness \nshows that oscillators A,C are entangled but the oscillators A,B might \nor might not be entangled. By using quantum discord, which measures the \nquantumness of correlations, it is shown that there are quantum correlations \nbetween oscillators A,B and after the measurements in both cases of selective \nand non-selective measurements, oscillators A,B and A,C become classically \ncorrelated.

Jan 1, 20110 citations

Quantum Oscillations

F. Suekane

Lecture notes in physicsJan 1, 20215 citations

O( m / \hbar)

, when

\hbar / m \ll 1

. Conversely, every solution to the Schrödinger equation, including all the superposition states, arises this way. In other words, the quantum harmonic oscillator is approximately nothing but the classical harmonic oscillator, with the same mass and frequency as the quantum harmonic oscillator, subject to a random force. We generalize the result to multiple non-interacting oscillators. We show that the Schrödinger equation for

n

non-interacting quantum harmonic oscillators with masses

m_1, ..., m_n

and frequencies

ω_1, ..., ω_n

can be derived as an approximation to the Newtonian mechanics of

n

non-interacting classical harmonic oscillators, with the same set of masses and frequencies as the quantum oscillators, subject to random forces. This is valid for time intervals

O( \tilde{m} / \hbar)

, where

\tilde{m}

is the mass of the minimum mass oscillator, when

\hbar/\tilde{m} \ll 1

. Conversely, every solution, including all the entangled states, to the Schrödinger equation arises this way. In other words,

n

non-interacting quantum harmonic oscillators are approximately nothing but

n

non-interacting classical harmonic oscillators, with the same set of masses and frequencies as the quantum oscillators, subject to random forces. This provides a local Newtonian model of entanglement of non-interacting quantum oscillators. The correlations required by entangled states are embedded in the phase space probability density of the classical oscillators.