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

arXiv:1109.1818

Time Evolution of Harmonic Oscillator Thermal Momentum Superposition States

Ole Steuernagel

Published Sep 9, 2011• 0 citations
arXivHTMLPDF

Abstract

The time evolution of thermal states of a mirror released from a tight harmonic trap is studied. After the release no dissipation is assumed to be present and the mirror is, after a time delay, kicked into a momentum superposition state. The thermal character of the initial state washes out the telltale interference patterns of the superposition but no loss of coherence is found. This investigation resolves a controversy about decoherence--without--dissipation and shows that entrained measurements can be surprisingly insensitive to temperature effects.

DOI
10.48550/arxiv.1109.1818

Related papers

Decoherence and thermalization dynamics of a quantum oscillator

V. V. Dodonov, Salomon Sylvain Mizrahi, A L de Souza Silva +1 more

We introduce the quantitative measures characterizing the rates of decoherence and thermalization of quantum systems. We study the time evolution of these measures in the case of a quantum harmonic oscillator whose relaxation is described in the framework of the standard master equation, for various initial states (coherent, `cat', squeezed and number). We establish the conditions under which the true decoherence measure can be approximated by the linear entropy 1-Tr 2 . We show that at low temperatures and for highly excited initial states the decoherence process consists of three distinct stages with quite different time scales. In particular, the `cat' states preserve 50% of the initial coherence for a long time interval which increases logarithmically with the increase of the initial energy.

arXiv:quant-ph/0004075•Journal of Optics B Quantum and Semiclassical Optics•May 24, 2000•37 citations

Can thermal quantum Gibbs states approve as quantum equilibrium states?

Ali Soltanmanesh

In this study, we investigate a quantum harmonic oscillator interacting with a thermal bath of oscillatory fields in a quantum circuit. By solving the Lindblad master equation, we calculate the resulting interference pattern from measuring the system in the momentum space. Interestingly, we show that even if one considers the decoherence effect, the system will keep some of its quantum properties. Indeed, the equilibration does not completely leave the system in a Gibbs state, and the system remains coherent. Moreover we discuss the requirements of a process that can be called a thermalization. We show that in our system, the quantum thermodynamic equilibration process cannot be considered a thermalization. Also, we discussed that a Lindblad system-bath interaction cannot be explained by a thermalization process. Such an effect strongly can be detected when the frequency of the central system is high and the temperature is low. Then, by introducing an entropy measure, we show that although the system is in maximum entropy, the equilibrium state is far from the Gibbs state.

arXiv:1802.07468•Feb 21, 2018•1 citation

Decoherence of multicomponent symmetrical superpositions of displaced quantum states

V. V. Dodonov, L A de Souza

We study the decoherence of superpositions of displaced quantum states of the form (where | g ⟩ is an arbitrary 'fiducial' state and is the usual displacement operator) within the framework of the standard master equation for a quantum damped or amplified harmonic oscillator interacting with a phase-insensitive (thermal) reservoir. We compare two simple measures of the degree of decoherence: the quantum purity and the height of the central interference peak of the Wigner function. We show that for N > 2 'mesoscopic' components of the superposition, the decoherence process cannot be characterized by a single decoherence time. Therefore, we distinguish the 'initial decoherence time' and 'final decoherence time' and study their dependence on the parameters α k and N . We obtain approximate formulae for an arbitrary state | g ⟩ and explicit exact expressions in the special case of | g ⟩ = | m ⟩, i.e., for (symmetrical) superpositions of displaced Fock states of occupation number m . We show that the superposition with a large number of components N and rich 'internal structure' ( m ∼ |α| 2 ) can be more robust against decoherence than simple superpositions of two coherent states (with m = 0), even if the initial decoherence times coincide. Also, we show how initial pure quantum superpositions are transformed into highly mixed and totally classical superpositions in the case of a phase-insensitive amplifier.

Journal of Physics A Mathematical and Theoretical•Oct 31, 2007•4 citations

Decoherence of wave packets in an anharmonic oscillator

Péter Földi, M. G. Benedict, Attila Czirják +1 more

The time evolution of wave packets in the Morse potential is investigated under the influence of the environment consisting of harmonic oscillators. These oscillators represent photon or phonon modes and are assumed to be in thermal equilibrium. Our model explicitly incorporates the fact that in the case of a nonequidistant spectrum the rates of the environment induced transitions are different for each transition. The nonunitary time evolution is visualized by the aid of the corresponding Wigner function. The time scale of decoherence is much shorter than that of dissipation, and gives rise to states that are mixtures of localized states along the phase-space orbit of the corresponding classical particle. This behavior is to a large extent independent of the coupling strength, the temperature of the environment, and also the initial state.

arXiv:quant-ph/0208141•Physical Review A•Mar 13, 2003•18 citations

Effect of initial correlations on short-time decoherence

Eric Lutz

We study the effect of initial correlations on the short-time decoherence of a particle linearly coupled to a bath of harmonic oscillators. We analytically evaluate the attenuation coefficient of the superposition of two wave packets both for a free and a harmonically bound particle, with and without initial thermal correlations between the particle and the bath. While short-time decoherence appears to be independent of the system in the absence of initial correlations, we find on the contrary that, for initial thermal correlations, decoherence becomes system dependent even for times much shorter than the characteristic time of the system. The temperature behavior of this system dependence is discussed.

arXiv:cond-mat/0208503•Physical Review A•Feb 25, 2003•18 citations

Superposition states at finite temperature

G. Huyet, Sonja Franke‐Arnold, Stephen Mark Barnett

We describe a method to create superposition states from a mixed state of a harmonic oscillator. If the initial state is described by a thermal state, then the resulting superposition state will be a ``hot'' superposition state. Such a state can be distinguished from a statistical mixture by its coherence properties. Here we suggest how to demonstrate the coherence of the superposition state by observing interference fringes when the two parts of the wave packet are overlapped. In the case of the mixed superposition state, a partial overlap may not be sufficient to observe the presence of fringes. We introduce therefore the idea of a coherence length for the wave packet and demonstrate its relevance for interferometry of mixed states. We illustrate our ideas with the example of superposition states for the motion of a single trapped ion.

Physical Review A•Mar 15, 2001•11 citations
The time evolution of thermal states of a mirror released from a tight harmonic trap is studied. After the release no dissipation is assumed to be present and the mirror is, after a time delay, kicked into a momentum superposition state. The thermal character of the initial state washes out the telltale interference patterns of the superposition but no loss of coherence is found. This investigation resolves a controversy about decoherence--without--dissipation and shows that entrained measurements can be surprisingly insensitive to temperature effects.
We introduce the quantitative measures characterizing the rates of decoherence and thermalization of quantum systems. We study the time evolution of these measures in the case of a quantum harmonic oscillator whose relaxation is described in the framework of the standard master equation, for various initial states (coherent, `cat', squeezed and number). We establish the conditions under which the true decoherence measure can be approximated by the linear entropy 1-Tr 2 . We show that at low temperatures and for highly excited initial states the decoherence process consists of three distinct stages with quite different time scales. In particular, the `cat' states preserve 50% of the initial coherence for a long time interval which increases logarithmically with the increase of the initial energy.
In this study, we investigate a quantum harmonic oscillator interacting with a thermal bath of oscillatory fields in a quantum circuit. By solving the Lindblad master equation, we calculate the resulting interference pattern from measuring the system in the momentum space. Interestingly, we show that even if one considers the decoherence effect, the system will keep some of its quantum properties. Indeed, the equilibration does not completely leave the system in a Gibbs state, and the system remains coherent. Moreover we discuss the requirements of a process that can be called a thermalization. We show that in our system, the quantum thermodynamic equilibration process cannot be considered a thermalization. Also, we discussed that a Lindblad system-bath interaction cannot be explained by a thermalization process. Such an effect strongly can be detected when the frequency of the central system is high and the temperature is low. Then, by introducing an entropy measure, we show that although the system is in maximum entropy, the equilibrium state is far from the Gibbs state.
We study the decoherence of superpositions of displaced quantum states of the form (where | g ⟩ is an arbitrary 'fiducial' state and is the usual displacement operator) within the framework of the standard master equation for a quantum damped or amplified harmonic oscillator interacting with a phase-insensitive (thermal) reservoir. We compare two simple measures of the degree of decoherence: the quantum purity and the height of the central interference peak of the Wigner function. We show that for N > 2 'mesoscopic' components of the superposition, the decoherence process cannot be characterized by a single decoherence time. Therefore, we distinguish the 'initial decoherence time' and 'final decoherence time' and study their dependence on the parameters α k and N . We obtain approximate formulae for an arbitrary state | g ⟩ and explicit exact expressions in the special case of | g ⟩ = | m ⟩, i.e., for (symmetrical) superpositions of displaced Fock states of occupation number m . We show that the superposition with a large number of components N and rich 'internal structure' ( m ∼ |α| 2 ) can be more robust against decoherence than simple superpositions of two coherent states (with m = 0), even if the initial decoherence times coincide. Also, we show how initial pure quantum superpositions are transformed into highly mixed and totally classical superpositions in the case of a phase-insensitive amplifier.
The time evolution of wave packets in the Morse potential is investigated under the influence of the environment consisting of harmonic oscillators. These oscillators represent photon or phonon modes and are assumed to be in thermal equilibrium. Our model explicitly incorporates the fact that in the case of a nonequidistant spectrum the rates of the environment induced transitions are different for each transition. The nonunitary time evolution is visualized by the aid of the corresponding Wigner function. The time scale of decoherence is much shorter than that of dissipation, and gives rise to states that are mixtures of localized states along the phase-space orbit of the corresponding classical particle. This behavior is to a large extent independent of the coupling strength, the temperature of the environment, and also the initial state.
We study the effect of initial correlations on the short-time decoherence of a particle linearly coupled to a bath of harmonic oscillators. We analytically evaluate the attenuation coefficient of the superposition of two wave packets both for a free and a harmonically bound particle, with and without initial thermal correlations between the particle and the bath. While short-time decoherence appears to be independent of the system in the absence of initial correlations, we find on the contrary that, for initial thermal correlations, decoherence becomes system dependent even for times much shorter than the characteristic time of the system. The temperature behavior of this system dependence is discussed.
We describe a method to create superposition states from a mixed state of a harmonic oscillator. If the initial state is described by a thermal state, then the resulting superposition state will be a ``hot'' superposition state. Such a state can be distinguished from a statistical mixture by its coherence properties. Here we suggest how to demonstrate the coherence of the superposition state by observing interference fringes when the two parts of the wave packet are overlapped. In the case of the mixed superposition state, a partial overlap may not be sufficient to observe the presence of fringes. We introduce therefore the idea of a coherence length for the wave packet and demonstrate its relevance for interferometry of mixed states. We illustrate our ideas with the example of superposition states for the motion of a single trapped ion.