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:quant-ph/0309003 · Journal of Physics A Mathematical and General

Squeezed states of the generalized minimum uncertainty state for the Caldirola–Kanai Hamiltonian

Sang Pyo Kim

Published Nov 18, 2003• 14 citations
arXivHTMLPDF

Abstract

We show that the ground state of the well-known pseudo-stationary states for the Caldirola–Kanai Hamiltonian is a generalized minimum uncertainty state, which has the minimum allowed uncertainty Δ q Δ p = ℏσ 0 /2, where σ 0 (⩾1) is a constant depending on the damping factor and natural frequency. The most general symmetric Gaussian states are obtained as the one-parameter squeezed states of the pseudo-stationary ground state. It is further shown that the coherent states of the pseudo-stationary ground state constitute another class of the generalized minimum uncertainty states.

DOI
10.1088/0305-4470/36/48/011

Related papers

Thermodynamics of squeezed states for the Kanai-Caldirola Hamiltonian

J. Aliaga, G. Crespo, Araceli N. Proto

Using the maximum-entropy approach, we analyze the appearance of coherent and squeezed states for the Kanai-Caldirola Hamiltonian, making it possible to extend the analysis easily to the so-called generalized harmonic oscillator and a sort of two-photon Hamiltonian, for both the zero and nonzero temperature cases. A connection between the possibility of obtaining squeezing and the relevant operators included in the density matrix is shown. Finally, a comparison with pertinent previous results in the literature is also presented.

Physical Review A•Oct 1, 1990•17 citations

Dynamics of squeezed states of a generalized quantum parametric oscillator

Şirin A. Büyükaşık, Zehra Çayiç

Time-evolution of squeezed coherent states of a generalized Caldirola-Kanai type quantum parametric oscillator is found explicitly using the exact evolution operator obtained by the Wei-Norman algebraic approach. Properties of these states are investigated according to the parameters of the unitary squeeze operator and the time-variable parameters of the generalized quadratic Hamiltonian. As an application, we consider exactly solvable quantum models with specific frequency modification for which the corresponding classical oscillator is in underdamping case and driving forces are of sinusoidal type. For each model we explicitly provide the evolution of the squeezed coherent states and discuss their behavior.

Journal of Physics Conference Series•Apr 1, 2019•0 citations

Squeezing and resonance in a generalized Caldirola-Kanai type quantum parametric oscillator

Şirin A. Büyükaşık

The evolution operator of a Caldirola-Kanai type quantum parametric oscillator with a generalized quadratic Hamiltonian is obtained using the Wei-Norman Lie algebraic approach, and time evolution of the eigenstates of a harmonic oscillator and Glauber coherent states is found explicitly. Behavior of this oscillator is investigated under the influence of the external mixed term B(t)(q^p^+p^q^)/2, which affects the squeezing properties of the wave packets, and linear terms D0(t)q^, E0(t)p^ responsible for their displacement in time. According to this, we construct all exact quantum models with different parameters B(t), for which the structure of the Caldirola-Kanai oscillator in position space is preserved. Then, for each model, we obtain explicit solutions and analyze the squeezing and displacement properties of the wave packets according to the frequency modification by B(t) and periodic forces in the corresponding classical equation of motion.

Journal of Mathematical Physics•Aug 1, 2018•12 citations

Quasi-coherent states for damped and forced harmonic oscillator

Mustafa Dernek, Nuri Ünal

In this study, first we construct the quasi-coherent states for a damped and forced harmonic oscillator and discuss the transition of the system from the damped oscillations to forced steady state oscillations. Second, we generalize the Caldirola-Kanai Hamiltonian into the new systems such as the frequency and the mass parameters are time dependent and discuss three examples of them.

Journal of Mathematical Physics•Sep 1, 2013•3 citations

The Minimum-Uncertainty Squeezed States for the Simple Harmonic Oscillator

Sergey Kryuchkov, Sergeĭ K. Suslov, José M. Vega-Guzmán

We describe a six-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions. The corresponding photons statistics are discussed and some applications to quantum optics, cavity quantum electrodynamics, and superfocusing in channeling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.

•Jan 4, 2012•2 citations

The minimum-uncertainty squeezed states for atoms and photons in a cavity

Sergey Kryuchkov, Sergeĭ K. Suslov, José M. Vega-Guzmán

We describe a multi-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of the corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions and the corresponding photon statistics are discussed. Some applications to quantum optics, cavity quantum electrodynamics and superfocusing in channelling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.

arXiv:1201.0841•Journal of Physics B Atomic Molecular and Optical Physics•May 9, 2013•32 citations
We show that the ground state of the well-known pseudo-stationary states for the Caldirola–Kanai Hamiltonian is a generalized minimum uncertainty state, which has the minimum allowed uncertainty Δ q Δ p = ℏσ 0 /2, where σ 0 (⩾1) is a constant depending on the damping factor and natural frequency. The most general symmetric Gaussian states are obtained as the one-parameter squeezed states of the pseudo-stationary ground state. It is further shown that the coherent states of the pseudo-stationary ground state constitute another class of the generalized minimum uncertainty states.
Using the maximum-entropy approach, we analyze the appearance of coherent and squeezed states for the Kanai-Caldirola Hamiltonian, making it possible to extend the analysis easily to the so-called generalized harmonic oscillator and a sort of two-photon Hamiltonian, for both the zero and nonzero temperature cases. A connection between the possibility of obtaining squeezing and the relevant operators included in the density matrix is shown. Finally, a comparison with pertinent previous results in the literature is also presented.
Time-evolution of squeezed coherent states of a generalized Caldirola-Kanai type quantum parametric oscillator is found explicitly using the exact evolution operator obtained by the Wei-Norman algebraic approach. Properties of these states are investigated according to the parameters of the unitary squeeze operator and the time-variable parameters of the generalized quadratic Hamiltonian. As an application, we consider exactly solvable quantum models with specific frequency modification for which the corresponding classical oscillator is in underdamping case and driving forces are of sinusoidal type. For each model we explicitly provide the evolution of the squeezed coherent states and discuss their behavior.
The evolution operator of a Caldirola-Kanai type quantum parametric oscillator with a generalized quadratic Hamiltonian is obtained using the Wei-Norman Lie algebraic approach, and time evolution of the eigenstates of a harmonic oscillator and Glauber coherent states is found explicitly. Behavior of this oscillator is investigated under the influence of the external mixed term B(t)(q^p^+p^q^)/2, which affects the squeezing properties of the wave packets, and linear terms D0(t)q^, E0(t)p^ responsible for their displacement in time. According to this, we construct all exact quantum models with different parameters B(t), for which the structure of the Caldirola-Kanai oscillator in position space is preserved. Then, for each model, we obtain explicit solutions and analyze the squeezing and displacement properties of the wave packets according to the frequency modification by B(t) and periodic forces in the corresponding classical equation of motion.
We describe a six-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions. The corresponding photons statistics are discussed and some applications to quantum optics, cavity quantum electrodynamics, and superfocusing in channeling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.
We describe a multi-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of the corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions and the corresponding photon statistics are discussed. Some applications to quantum optics, cavity quantum electrodynamics and superfocusing in channelling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.