Multiphoton dissociation of a diatomic molecule including the effects of the continuum

Graham, R.; Höhnerbach, M.

doi:10.1103/physreva.45.5078

Cited by 15 publications

(15 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Plots for this case also appear in Ref. 13. Interestingly, the agreement between the approximate solution and the numerical solution is still quite good, especially at larger coupling strengths.…”

Section: ͑9͒mentioning

confidence: 59%

“…Graham and Höhnerbach refer to this regime as the "quasidegenerate limit" and give the same lowest-order expressions as we derive. [12][13][14] Schweber utilized the Bargmann Hilbertspace representation, 15 and Crisp solved recurrence relations; 16 both of these authors found higher-order corrections beyond what we present. We take yet a different approach.…”

Section: Adiabatic Approximation In the Displaced Oscillator Basismentioning

confidence: 82%

See 1 more Smart Citation

Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator

et al. 2005

View full text Add to dashboard Cite

Recent experiments on quantum behavior in microfabricated solid-state systems suggest tantalizing connections to quantum optics. Several of these experiments address the prototypical problem of cavity quantum electrodynamics: a two-level system coupled to a quantum harmonic oscillator. Such devices may allow the exploration of parameter regimes outside the near-resonance and weak-coupling assumptions of the ubiquitous rotating-wave approximation ͑RWA͒, necessitating other theoretical approaches. One such approach is an adiabatic approximation in the limit that the oscillator frequency is much larger than the characteristic frequency of the two-level system. A derivation of the approximation is presented, together with a discussion of its applicability in a system consisting of a Cooper-pair box coupled to a nanomechanical resonator. Within this approximation the time evolution of the two-level-system occupation probability is calculated using both thermal-and coherent-state initial conditions for the oscillator, focusing particularly on collapse and revival phenomena. For thermal-state initial conditions parameter regimes are found in which collapse and revival regions may be clearly distinguished, unlike the erratic evolution of the thermal-state RWA model. Coherentstate initial conditions lead to complex behavior, which exhibits sensitive dependence on the coupling strength and the initial amplitude of the oscillator state. One feature of the regime considered here is that closed-form evaluation of the time evolution may be carried out in the weak-coupling limit, which provides insight into the differences between the thermal-and coherent-state models. Finally, potential experimental observations in solid-state systems, particularly the Cooper-pair box-nanomechanical resonator system, are discussed and found to be promising.

show abstract

Section: ͑9͒mentioning

confidence: 59%

Section: Adiabatic Approximation In the Displaced Oscillator Basismentioning

confidence: 82%

Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator

et al. 2005

View full text Add to dashboard Cite

show abstract

“…where x = r/r 0 − 1, r 0 is the equilibrium value of the inter-nuclear distance r and β is a range parameter. D is the dissociation energy, which has been extensively studied in a wider context of this model [37,38]. Defining λ = 2µDr 2 0 β 2 2 and s = −…”

Section: Review Of the Morse Model Of A Vibrating Moleculementioning

confidence: 99%

Sub-Planck-scale structures in a vibrating molecule in the presence of decoherence

et al. 2009

View full text Add to dashboard Cite

We study the effect of decoherence on the sub-Planck scale structures of the vibrational wave packet of a molecule. The time evolution of these wave packets is investigated under the influence of a photonic or phononic environment. We determine the master equation describing the reduced dynamics of the wave-packet and analyze the sensitivity of the sub-Planck structures against decoherence in the case of a hydrogen iodide (HI) molecule.

show abstract

“…Swain [21,22] has expressed the eigenvalues of Eq. (20) in terms of infinitely continued fractions. While this gives a formally exact solution of the problem, the final analysis has to be done numerically by truncating the infinite fractions.…”

Section: The Atom-field Statesmentioning

confidence: 99%

Application of the displaced oscillator basis in quantum optics

Crisp

1992

Phys. Rev. A

View full text Add to dashboard Cite

Fock states and coherent states have been widely applied in analyses of quantum-optics experiments. In this paper, the application of a set of basis functions that consist of a product of displaced harmonicoscillator states for the electromagnetic field and atomic states that are eigenfunctions of the momentum operator will be explored. For the case of a single mode, these states are the exact eigenfunctions in the limiting case where the electromagnetic-field mode frequency is much larger than the atomic transition frequency. This choice of basis functions will be used to analyze the interaction of a nonrelativistic, "two-level" atom with a single-frequency, quantized electromagnetic-field mode. Since in this basis the sign of the displacement of the electromagnetic-field state depends on the state of the atom, these new basis wave functions exhibit explicitly some aspects of atom-field correlations that are intrinsically quantum mechanical in nature. The analysis will be performed in the electric-dipole approximation for an atomic system that obeys the 6m=0 selection rule. The rotating-wave-approximation (RWA) terms cannot be made negligible through judicious choice of the field polarization for this system. The diamagnetic term, e A /2mc, which is of the same order of magnitude as the RWA terms, is taken into account exactly by slightly modifying the traditional approach to quantizing the electromagnetic field. In this way the physical effects of the diamagnetic term are absorbed into a new electromagnetic cavity mode frequency. An approximate expression for the combined system's energy eigenvalues is found up to third order in the ratio of one-half the atomic transition frequency to the mode frequency. This expression indicates that inclusion of the RWA terms adds a small "ripple" on top of the smoothly varying energy eigenvalues when they are plotted as a function of the atom-field coupling constant. The ripple is interpreted as "interference" between two displaced oscillator-field states that represents the unperturbed state. When the Fock states are used as the basis for expanding the wave function of this system, a formidable five-term recurrence relation results. However, expanding the wave function in terms of the displaced harmonic-oscillator basis results in a less formidable three-term recurrence relation for the quantum coefficients.PACS number(s): 42.50.Lc, 03.65.Ge

show abstract

Multiphoton dissociation of a diatomic molecule including the effects of the continuum

Cited by 15 publications

References 19 publications

Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator

Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator

Sub-Planck-scale structures in a vibrating molecule in the presence of decoherence

Application of the displaced oscillator basis in quantum optics

Contact Info

Product

Resources

About