Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Open Systems & Information Dynamics

Anomalies in Strongly Coupled Harmonic Quantum Brownian Motion

Filippo Giraldi, Francesco Petruccione

Published Mar 1, 2013• 2 citations
Publisher

Abstract

The exact dynamics of a quantum damped harmonic oscillator coupled to a reservoir of boson modes has been formally described in terms of the coupling function, both in weak and strong coupling regime. In this scenario, we provide a further description of the exact dynamics through integral transforms. We focus on a special class of spectral densities, sub-ohmic at low frequencies, and including integrable divergencies referred to as photonic band gaps. The Drude form of the spectral densities is recovered as upper limit. Starting from special distributions of coherent states as external reservoir, the exact time evolution, described through Fox H-functions, shows long time inverse power law decays, departing from the exponential-like relaxations obtained for the Drude model. Different from the weak coupling regime, in the sub-ohmic condition, undamped oscillations plus inverse power law relaxations appear in the long time evolution of the observables position and momentum. Under the same condition, the number of excitations shows trapping of the population of the excited levels and oscillations enveloped in inverse power law relaxations. Similarly to the weak coupling regime, critical configurations give arbitrarily slow relaxations useful for the control of the dynamics. If compared to the value obtained in weak coupling condition, for strong couplings the critical frequency is enhanced by a factor 4.

DOI
10.1142/s1230161213500029

Related papers

Anomalies in Strongly Coupled Harmonic Quantum Brownian Motion II

Filippo Giraldi, Francesco Petruccione

The analysis of a strongly coupled harmonic quantum Brownian motion has been performed in [1] for a special class of spectral densities obtained as a generalization of the Drude model. In the present scenario, we extend the study of the strongly coupled harmonic quantum Brownian motion to regular spectral densities that are structured as sub-Ohmic at low frequencies and arbitrarily shaped at high frequencies. The bosonic environment is initially in the vacuum state unentangled from the coherent state of the main oscillator. As a generalization of the previous results, we obtain that the long time dynamics is determined uniquely by the initial condition and the low frequency structure of the spectral density. Also in the present framework, inverse power law regressions to the asymptotics appear. The position and the momentum tend to undamped oscillations. The number of excitations relaxes to its initial value with damped oscillations enveloped in inverse power law relaxations. For the momentum and the number of excitations the inverse power law decays become arbitrarily slow in critical configurations by approaching the upper bound of the sub-Ohmic regime. The critical frequencies of the main oscillator are determined by the first negative moment of the spectral densities. Differences with respect to the weak coupling regime arise.

Open Systems & Information Dynamics•Nov 25, 2013•0 citations

Critical frequency control in harmonic quantum Brownian motion

Filippo Giraldi, Francesco Petruccione

The dissipative effects of a quantum harmonic oscillator, initially set in a coherent state and linearly coupled to a continuous distribution of frequency modes, are analyzed over long time scales in relation to the behavior of the spectral density near an arbitrary band gap, arbitrarily shaped at the higher frequencies. The reservoir is initially set either in the vacuum state or in continuous distributions of coherent states. These distributions are arbitrarily shaped at high frequencies and structured in sub- or super-ohmic configurations near an arbitrary band gap frequency. Similarly to certain decoherence processes of a qubit, critical conditions emerge, such that arbitrarily slow inverse power law relaxations of the expectation values of the observables, are obtained by approaching the boundary between the sub- and the super-ohmic regimes. Also, in such critical conditions, a trapping of the number of excitations appears in the super-ohmic regime. The technique of critical frequency control, emerging in the scenario of the environment-induced decoherence of a qubit via the reservoir engineering approach, is extended to the harmonic quantum Brownian motion.

Journal of Physics A Mathematical and Theoretical•Dec 3, 2012•5 citations

Discontinuities in a damped quantum harmonic oscillator

Filippo Giraldi, Francesco Petruccione

The quantum model for a damped harmonic oscillator linearly coupled to a reservoir of continuous frequency modes has been exactly diagonalized either with or without the rotating wave approximation. The exact dynamics, formally described in terms of the coupling function, is analyzed for the Drude model. In this scenario, we focus on a class of couplings recovering the Drude form as a limiting case. The exact time evolution of the expectation values of the position, momentum and number operators are described through Fox H -functions, as well as the correlation function of the reservoir. In correspondence with the critical values of the frequency, discontinuities appear in the long time scale dynamics, arbitrarily slowing down the relaxations of the above observables. This effect allows one to enhance arbitrarily the lifetime of the excitations, giving relevant applications in the study of the quantum domain of opto-mechanical and nano-mechanical resonators. The critical frequency approach constitutes a further method of control in the scenario of environment-induced decoherence via reservoir engineering.

Journal of Physics A Mathematical and Theoretical•Jun 27, 2012•5 citations

Reservoir for inverse-power-law decoherence of a qubit

Filippo Giraldi, Francesco Petruccione

The exact dynamics of a Jaynes-Cummings model for a qubit interacting with a continuous distribution of bosons, characterized by a special form of the spectral density, is evaluated analytically. The special reservoir is designed to induce anomalous decoherence, resulting in an inverse power-law relaxation, of power $3/2$, over an evaluated long time scale. If compared to the exponential-like relaxation obtained from the original Jaynes-Cummings model for Lorentzian-type spectral density functions, decoherence is strongly suppressed. The special reservoir exhibits a band-edge frequency coinciding with the qubit transition frequency. Known theoretical models of photonic band-gap media suitable for the realization of the designed reservoir are proposed.

arXiv:1011.0059•Physical Review A•Jan 18, 2011•10 citations

Entanglement dynamics for two harmonic oscillators coupled to independent environments

Ruggero Vasile

We study the entanglement evolution between two harmonic oscillators having different free frequencies each leaking into an independent bath. We use an exact solution valid in the weak coupling limit and in the short time non-Markovian regime. The reservoirs are identical and characterized by an Ohmic spectral distribution with Lorents-Drude cut-off. This work is an extension of the case reported in [Phys. Rev. A 80, 062324 (2009)] where the oscillators have the same free frequency.

arXiv:1002.0973•Physica Scripta•Sep 1, 2010•1 citation

Damped Oscillations of the Energy of a Bosonic Bath due to Spectral Gaps and Special Initial Correlations

Filippo Giraldi

The energy of the bosonic bath and the flow of quantum information in local dephasing channels are studied over short and long times in case the distribution of frequency modes of the bosonic bath exhibits a low-frequency gap. The initial conditions consist in special correlations between the qubit and the bosonic bath or are factorized, and involve thermal states of the whole system or of the bath. The low-frequency gap generates damped oscillations of the bath energy around the asymptotic value, for the correlated initial conditions, and induces the open system to alternately loose and gain information, for the factorized initial configurations. The long-time oscillations of the bath energy become regular and the frequency of the oscillations coincides with the upper cut-off frequency of the spectral gap. Regular long-time sequences of intervals are found over which the bath energy increases (decreases), for the correlated initial conditions, and information is lost (gained) by the open system, for the factorized initial configurations, even at different temperatures. This relation is reversed, if compared to the one obtained without the low-frequency gap, and can fail if the spectral density is tailored near the spectral gap according to power laws with odd natural powers.

arXiv:1707.00604•Open Systems & Information Dynamics•Sep 1, 2018•1 citation
The exact dynamics of a quantum damped harmonic oscillator coupled to a reservoir of boson modes has been formally described in terms of the coupling function, both in weak and strong coupling regime. In this scenario, we provide a further description of the exact dynamics through integral transforms. We focus on a special class of spectral densities, sub-ohmic at low frequencies, and including integrable divergencies referred to as photonic band gaps. The Drude form of the spectral densities is recovered as upper limit. Starting from special distributions of coherent states as external reservoir, the exact time evolution, described through Fox H-functions, shows long time inverse power law decays, departing from the exponential-like relaxations obtained for the Drude model. Different from the weak coupling regime, in the sub-ohmic condition, undamped oscillations plus inverse power law relaxations appear in the long time evolution of the observables position and momentum. Under the same condition, the number of excitations shows trapping of the population of the excited levels and oscillations enveloped in inverse power law relaxations. Similarly to the weak coupling regime, critical configurations give arbitrarily slow relaxations useful for the control of the dynamics. If compared to the value obtained in weak coupling condition, for strong couplings the critical frequency is enhanced by a factor 4.
The analysis of a strongly coupled harmonic quantum Brownian motion has been performed in [1] for a special class of spectral densities obtained as a generalization of the Drude model. In the present scenario, we extend the study of the strongly coupled harmonic quantum Brownian motion to regular spectral densities that are structured as sub-Ohmic at low frequencies and arbitrarily shaped at high frequencies. The bosonic environment is initially in the vacuum state unentangled from the coherent state of the main oscillator. As a generalization of the previous results, we obtain that the long time dynamics is determined uniquely by the initial condition and the low frequency structure of the spectral density. Also in the present framework, inverse power law regressions to the asymptotics appear. The position and the momentum tend to undamped oscillations. The number of excitations relaxes to its initial value with damped oscillations enveloped in inverse power law relaxations. For the momentum and the number of excitations the inverse power law decays become arbitrarily slow in critical configurations by approaching the upper bound of the sub-Ohmic regime. The critical frequencies of the main oscillator are determined by the first negative moment of the spectral densities. Differences with respect to the weak coupling regime arise.
The dissipative effects of a quantum harmonic oscillator, initially set in a coherent state and linearly coupled to a continuous distribution of frequency modes, are analyzed over long time scales in relation to the behavior of the spectral density near an arbitrary band gap, arbitrarily shaped at the higher frequencies. The reservoir is initially set either in the vacuum state or in continuous distributions of coherent states. These distributions are arbitrarily shaped at high frequencies and structured in sub- or super-ohmic configurations near an arbitrary band gap frequency. Similarly to certain decoherence processes of a qubit, critical conditions emerge, such that arbitrarily slow inverse power law relaxations of the expectation values of the observables, are obtained by approaching the boundary between the sub- and the super-ohmic regimes. Also, in such critical conditions, a trapping of the number of excitations appears in the super-ohmic regime. The technique of critical frequency control, emerging in the scenario of the environment-induced decoherence of a qubit via the reservoir engineering approach, is extended to the harmonic quantum Brownian motion.
The quantum model for a damped harmonic oscillator linearly coupled to a reservoir of continuous frequency modes has been exactly diagonalized either with or without the rotating wave approximation. The exact dynamics, formally described in terms of the coupling function, is analyzed for the Drude model. In this scenario, we focus on a class of couplings recovering the Drude form as a limiting case. The exact time evolution of the expectation values of the position, momentum and number operators are described through Fox H -functions, as well as the correlation function of the reservoir. In correspondence with the critical values of the frequency, discontinuities appear in the long time scale dynamics, arbitrarily slowing down the relaxations of the above observables. This effect allows one to enhance arbitrarily the lifetime of the excitations, giving relevant applications in the study of the quantum domain of opto-mechanical and nano-mechanical resonators. The critical frequency approach constitutes a further method of control in the scenario of environment-induced decoherence via reservoir engineering.
The exact dynamics of a Jaynes-Cummings model for a qubit interacting with a continuous distribution of bosons, characterized by a special form of the spectral density, is evaluated analytically. The special reservoir is designed to induce anomalous decoherence, resulting in an inverse power-law relaxation, of power 3/23/23/2, over an evaluated long time scale. If compared to the exponential-like relaxation obtained from the original Jaynes-Cummings model for Lorentzian-type spectral density functions, decoherence is strongly suppressed. The special reservoir exhibits a band-edge frequency coinciding with the qubit transition frequency. Known theoretical models of photonic band-gap media suitable for the realization of the designed reservoir are proposed.
The energy of the bosonic bath and the flow of quantum information in local dephasing channels are studied over short and long times in case the distribution of frequency modes of the bosonic bath exhibits a low-frequency gap. The initial conditions consist in special correlations between the qubit and the bosonic bath or are factorized, and involve thermal states of the whole system or of the bath. The low-frequency gap generates damped oscillations of the bath energy around the asymptotic value, for the correlated initial conditions, and induces the open system to alternately loose and gain information, for the factorized initial configurations. The long-time oscillations of the bath energy become regular and the frequency of the oscillations coincides with the upper cut-off frequency of the spectral gap. Regular long-time sequences of intervals are found over which the bath energy increases (decreases), for the correlated initial conditions, and information is lost (gained) by the open system, for the factorized initial configurations, even at different temperatures. This relation is reversed, if compared to the one obtained without the low-frequency gap, and can fail if the spectral density is tailored near the spectral gap according to power laws with odd natural powers.