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

Physical Review A

Stability of states in a squeezed environment

Kanwarpreet S. Grewal

Published Feb 13, 2003• 11 citations
Publisher

Abstract

Several recent studies on the subject of environment induced decoherence have suggested that the predictability sieve selects coherent states over squeezed states. Most of such studies have considered a system consisting of an oscillator linearly coupled to a bath of harmonic oscillators. In this paper, we consider an environment consisting of squeezed oscillators. We derive the master equation for an oscillator coupled to such an environment. We solve this master equation for the case of the oscillator being in a coherent state and for the oscillator in a squeezed state. We then compare the stability of coherent states and squeezed states in the general squeezed environment. Our aim is to find if coherent states are more stable than squeezed states in a squeezed environment as well or is this fact true only in an environment of coherent oscillator states? We argue that unless we show that coherent states are preferred in a nonclassical environment as well, we cannot assume that coherent states form most environments and therefore the study of the stability of states only in an environment of coherent oscillator states is not a general case.

DOI
10.1103/physreva.67.022107

Related papers

Selection of Squeezed States via Decoherence

Gheorghe Sorin Paraoanu

In the framework of Lindblad theory for open quantum systems, we calculate the entropy of a damped quantum harmonic oscillator which is initially in a quasi-free state. The maximally predictable states are identified as those states producing the minimum entropy increase after a long enough time. In general, the states with a squeezing parameter depending on the environment's diffusion coefficients and friction constant are singled out, but if the friction constant is much smaller than the oscillator's frequency, coherent states (or thermalized coherent states) are obtained as the preferred classical states.

•Jan 1, 1999•3 citations

Selection of squeezed states via decoherence

Gh.-S Paraoanu

In the framework of Lindblad theory for open quantum systems, we calculate the entropy of a damped quantum harmonic oscillator which is initially in a quasi-free state. The maximally predictable states are identified as those states producing the minimum entropy increase after a long enough time. In general, the states with a squeezing parameter depending on the environment's diffusion coefficients and friction constant are singled out, but if the friction constant is much smaller than the oscillator's frequency, coherent states (or thermalized coherent states) are obtained as the preferred classical states.

arXiv:quant-ph/0205127•Europhysics Letters (EPL)•Aug 1, 1999•4 citations

Dynamics of decoherence without dissipation in a squeezed thermal bath

Subhashish Banerjee, Rupamanjari Ghosh

We study a generic open quantum system where the coupling between the system and its environment is of an energy-preserving quantum nondemolition (QND) type. We obtain the general master equation for the evolution of such a system under the influence of a squeezed thermal bath of harmonic oscillators. From the master equation it can be seen explicitly that the process involves decoherence or dephasing without any dissipation of energy. We work out the decoherence-causing term in the high- and zero-temperature limits and check that they match with known results for the case of a thermal bath. The decay of the coherence is quantified as well by the dynamics of the linear entropy of the system under various environmental conditions. We make a comparison of the quantum statistical properties between QND and dissipative types of evolution using a two-level atomic system and a harmonic oscillator.

arXiv:quant-ph/0703054•Journal of Physics A Mathematical and Theoretical•Oct 23, 2007•57 citations

Purity and decoherence in the theory of a damped harmonic oscillator

Аурелиан Исар, A. Sãndulescu, W. Scheid

For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude, and weak coupling cases, and the Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with variances that are constant in time. For pure states, generalized nonlinear Schrödinger-type equations corresponding to these master equations are also obtained. Then the condition for purity of states of a damped harmonic oscillator is considered in the framework of Lindblad theory for open quantum systems. For a special choice of the environment coefficients, correlated coherent states with constant variances and covariance are shown to be the only states which remain pure all the time during the evolution of the considered system. In Karrlein-Grabert and Lindblad models, as well as in the particular models considered, expressions for the rate of entropy production are written, and it is shown that state which preserve their purity in time are also states which minimize entropy production and, therefore, are the most stable state under evolution in the presence of the environment, and play an important role in the description of decoherence phenomenon.

arXiv:quant-ph/0606134•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Dec 1, 1999•44 citations

Appearance of classical coherent oscillator states under environment-induced decoherence

Kanwarpreet S. Grewal

The existence of well-defined quasiprobabilities has long been known to be the signature of a classical state. Recent studies on environment induced decoherence have suggested the use of the Wigner function to illustrate the destruction of coherence on interaction with the environment. Due to the overcompleteness of coherent states, any state can be represented as a mixture of coherent states with a relative weight $P(v).$ This is known as the P representation of the state. In this paper we use the P representation of a state to see how its classical form emerges on interaction with the environment. We also use the concept of ``depth of classicality'' introduced recently to see how classicality is increased on interaction with the environment. We use the example of superposition of Gaussian wave packets for all the calculations. We also attempt to implement the predictability sieve using the P representation of a state. We use this definition of the predictability sieve to show that coherent states are more robust to environment-induced decoherence than squeezed states.

Physical Review A•Apr 15, 2002•4 citations

Non-classicality of squeezed non-Markovian processes

Mehdi Abdi, Moslem Zarei

We study nonclassical effects in the dynamics of an open quantum system. The model involves a harmonic oscillator coupled to a reservoir of non-interacting harmonic oscillators. Different system-bath interaction schemes as well as reservoir states are considered. Particularly, the squeezed reservoirs coupled to the system through single and two quanta exchange processes are put in the spotlight. We investigate the quantumness conveyed to the system through the bath by computing a nonclassicality measure for different bath properties and when the memory effects are appreciable. The measure of nonclassicality is calculated for projective measurements both in the number state basis and a basis formed by a set of coherent states. Our results show that in both bases the measure exhibits characteristic features for each bath state and the form of its interaction with the system. Some of those features are independent from the measurement scheme (number or coherent), and thus, emergent from the bath and its interaction with the probe system. This allows for fingerprinting and identifying the environmental effects by tracking a given probe with appropriate measurements. Hence, may prove useful for distinguishing different sources of decoherence.

arXiv:2305.09323•May 16, 2023•0 citations
Several recent studies on the subject of environment induced decoherence have suggested that the predictability sieve selects coherent states over squeezed states. Most of such studies have considered a system consisting of an oscillator linearly coupled to a bath of harmonic oscillators. In this paper, we consider an environment consisting of squeezed oscillators. We derive the master equation for an oscillator coupled to such an environment. We solve this master equation for the case of the oscillator being in a coherent state and for the oscillator in a squeezed state. We then compare the stability of coherent states and squeezed states in the general squeezed environment. Our aim is to find if coherent states are more stable than squeezed states in a squeezed environment as well or is this fact true only in an environment of coherent oscillator states? We argue that unless we show that coherent states are preferred in a nonclassical environment as well, we cannot assume that coherent states form most environments and therefore the study of the stability of states only in an environment of coherent oscillator states is not a general case.
In the framework of Lindblad theory for open quantum systems, we calculate the entropy of a damped quantum harmonic oscillator which is initially in a quasi-free state. The maximally predictable states are identified as those states producing the minimum entropy increase after a long enough time. In general, the states with a squeezing parameter depending on the environment's diffusion coefficients and friction constant are singled out, but if the friction constant is much smaller than the oscillator's frequency, coherent states (or thermalized coherent states) are obtained as the preferred classical states.
In the framework of Lindblad theory for open quantum systems, we calculate the entropy of a damped quantum harmonic oscillator which is initially in a quasi-free state. The maximally predictable states are identified as those states producing the minimum entropy increase after a long enough time. In general, the states with a squeezing parameter depending on the environment's diffusion coefficients and friction constant are singled out, but if the friction constant is much smaller than the oscillator's frequency, coherent states (or thermalized coherent states) are obtained as the preferred classical states.
We study a generic open quantum system where the coupling between the system and its environment is of an energy-preserving quantum nondemolition (QND) type. We obtain the general master equation for the evolution of such a system under the influence of a squeezed thermal bath of harmonic oscillators. From the master equation it can be seen explicitly that the process involves decoherence or dephasing without any dissipation of energy. We work out the decoherence-causing term in the high- and zero-temperature limits and check that they match with known results for the case of a thermal bath. The decay of the coherence is quantified as well by the dynamics of the linear entropy of the system under various environmental conditions. We make a comparison of the quantum statistical properties between QND and dissipative types of evolution using a two-level atomic system and a harmonic oscillator.
For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude, and weak coupling cases, and the Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with variances that are constant in time. For pure states, generalized nonlinear Schrödinger-type equations corresponding to these master equations are also obtained. Then the condition for purity of states of a damped harmonic oscillator is considered in the framework of Lindblad theory for open quantum systems. For a special choice of the environment coefficients, correlated coherent states with constant variances and covariance are shown to be the only states which remain pure all the time during the evolution of the considered system. In Karrlein-Grabert and Lindblad models, as well as in the particular models considered, expressions for the rate of entropy production are written, and it is shown that state which preserve their purity in time are also states which minimize entropy production and, therefore, are the most stable state under evolution in the presence of the environment, and play an important role in the description of decoherence phenomenon.
The existence of well-defined quasiprobabilities has long been known to be the signature of a classical state. Recent studies on environment induced decoherence have suggested the use of the Wigner function to illustrate the destruction of coherence on interaction with the environment. Due to the overcompleteness of coherent states, any state can be represented as a mixture of coherent states with a relative weight P(v).P(v).P(v). This is known as the P representation of the state. In this paper we use the P representation of a state to see how its classical form emerges on interaction with the environment. We also use the concept of ``depth of classicality'' introduced recently to see how classicality is increased on interaction with the environment. We use the example of superposition of Gaussian wave packets for all the calculations. We also attempt to implement the predictability sieve using the P representation of a state. We use this definition of the predictability sieve to show that coherent states are more robust to environment-induced decoherence than squeezed states.
We study nonclassical effects in the dynamics of an open quantum system. The model involves a harmonic oscillator coupled to a reservoir of non-interacting harmonic oscillators. Different system-bath interaction schemes as well as reservoir states are considered. Particularly, the squeezed reservoirs coupled to the system through single and two quanta exchange processes are put in the spotlight. We investigate the quantumness conveyed to the system through the bath by computing a nonclassicality measure for different bath properties and when the memory effects are appreciable. The measure of nonclassicality is calculated for projective measurements both in the number state basis and a basis formed by a set of coherent states. Our results show that in both bases the measure exhibits characteristic features for each bath state and the form of its interaction with the system. Some of those features are independent from the measurement scheme (number or coherent), and thus, emergent from the bath and its interaction with the probe system. This allows for fingerprinting and identifying the environmental effects by tracking a given probe with appropriate measurements. Hence, may prove useful for distinguishing different sources of decoherence.