Search results for "harmonic oscillator"
showing 10 items of 109 documents
Direct Evaluation of Path Integrals
2001
Every time τ n is assigned a point y n . We now connect the individual points with a classical path y(τ). y(τ) is not necessarily the (on-shell trajectory) extremum of the classical action. It can be any path between τ n and τn−1 specified by the classical Lagrangian \(L(y,\dot{y},t).\)
Quasi-Two-Dimensional Superfluid Fermionic Gases
2005
We study a quasi two-dimensional superfluid Fermi gas where the confinement in the third direction is due to a strong harmonic trapping. We investigate the behavior of such a system when the chemical potential is varied and find strong modifications of the superfluid properties due to the discrete harmonic oscillator states. We show that such quasi two-dimensional behavior can be created and observed with current experimental capabilities.
Nanoscale Heat Engine Beyond the Carnot Limit
2013
We consider a quantum Otto cycle for a time-dependent harmonic oscillator coupled to a squeezed thermal reservoir. We show that the efficiency at maximum power increases with the degree of squeezing, surpassing the standard Carnot limit and approaching unity exponentially for large squeezing parameters. We further propose an experimental scheme to implement such a model system by using a single trapped ion in a linear Paul trap with special geometry. Our analytical investigations are supported by Monte Carlo simulations that demonstrate the feasibility of our proposal. For realistic trap parameters, an increase of the efficiency at maximum power of up to a factor of 4 is reached, largely ex…
Coherent and squeezed vibrations for discrete variable harmonic oscillators
2009
In this work we study different types of coherent and squeezed states for the Charlier, Kravchuk and Meixner oscillators. We calculate the average values of different observables corresponding to the coherent states. We found that the coherent and squeezed states of the Kravchuk oscillator are unstable. There are also coherent and squeezed states that are similar to the coherent and squeezed states of the harmonic oscillator. We have introduced a discrete variable model for the biophoton coherent radiation, and the coherent thermal and squeezed thermal states. © 2009 Taylor & Francis.
Three-mode two-boson Jaynes–Cummings model in trapped ions
2006
In this paper, we analyse a two-boson three-mode Jaynes–Cummings model which can be implemented in the context of trapped ions. The symmetries of the Hamiltonian are brought to light and analysed in detail in order to solve the eigenvalue problem. The calculation of the time evolution operator shows the possibility of realizing interesting applications, such as the generation of nonclassical states.
Strong-coupling expansion for the anharomonic oscillators −d2/dx 2+x 2+λx 2N
1992
A perturbation expansion based on a modified and scaled harmonic oscillator combined with Pade extrapolation techniques has been used to determine the expansion of the ground-state energy in fractional and negative powers of the coupling constant, valid for large values of λ.
Remarks on mapping properties for the Bargmann transform on modulation spaces
2011
We investigate the mapping properties for the Bargmann transform and prove that this transform is isometricand bijective from modulation spaces to convenient Banach spaces of analytic functions.
Exactly solvable model of two three-dimensional harmonic oscillators interacting with the quantum electromagnetic field: The far-zone Casimir-Polder …
2005
We consider two three-dimensional isotropic harmonic oscillators interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-like transformation, we can obtain transformed operators such that the Hamiltonian of the system, when expressed in terms of these operators, assumes a diagonal form. We are also able to obtain an expression for the energy shift of the ground state, which is valid at all orders in the coupling constant. From this energy shift the nonperturbative Casimir-Polder potential energy between the two oscillators can be obtained. When approximated to the fourth order in the electric charge, the well-known expressi…
Loss of coherence and dressing in QED
2006
The dynamics of a free charged particle, initially described by a coherent wave packet, interacting with an environment, i.e. the electromagnetic field characterized by a temperature $T$, is studied. Using the dipole approximation the exact expressions for the evolution of the reduced density matrix both in momentum and configuration space and the vacuum and the thermal contribution to decoherence, are obtained. The time behaviour of the coherence lengths in the two representations are given. Through the analysis of the dynamic of the field structure associated to the particle the vacuum contribution is shown to be linked to the birth of correlations between the single momentum components o…
An application of the arithmetic euler function to the construction of nonclassical states of a quantum harmonic oscillator
2001
Abstract All quantum superpositions of two equal intensity coherent states exhibiting infinitely many zeros in their Fock distributions are explicitly constructed and studied. Our approach is based on results from number theory and, in particular, on the properties of arithmetic Euler function. The nonclassical nature of these states is briefly pointed out. Some interesting properties are brought to light.