Classical periodic motion of atomic-electron wave packets

Yeazell, John A.; Mallalieu, Mark; Parker, James; Stroud, C. R.

doi:10.1103/physreva.40.5040

Cited by 110 publications

(57 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Alber and co-workers proposed a scheme for generating electron wave packets with laser pulses [9]. Ten Wolde et al [10,11] and Yeazell et al [12,13] independently demonstrated radially as well as angularly localized electron wave packets, observed via the revival of the electron density on a (sub-)picosecond time scale.The experiment involves a tunable extreme ultraviolet (XUV) nanosecond laser source, based on third harmonic generation in a pulsed gas jet; this system and the method of separating the XUV from the fundamental UV, obtained from a frequency-doubled pulsed dye laser, as well as other technicalities were described before [14]. The XUV source, operated at 92.3 nm, is tuned on resonance with P͑1͒, R͑0͒, and R͑1͒ B 2 X(17,0) Lyman band transitions of H 2 .…”

mentioning

confidence: 99%

See 1 more Smart Citation

Observation of Coherent Wave Packets in a Heavy Rydberg System

Reinhold

Ubachs

2001

Phys. Rev. Lett.

View full text Add to dashboard Cite

Coherent dynamical behavior is observed in the heavy Rydberg system H 1 H 2 . Because of the large mass, time scales of the wave-packet evolution are orders of magnitude slower than for a Rydberg electron. In the presence of a weak electric field, wave packets made up of about 1000 Stark states are excited by near-Fourier transform limited nanosecond laser pulses. Pulsed-field dissociation reveals coherent time evolution on a microsecond time scale, observed as oscillations with frequencies explained by a linear Stark model applied to the H 1 H 2 system. DOI: 10.1103/PhysRevLett.88.013001 PACS numbers: 33.80.Rv, 33.55.Be, 03.65.Ge Studies of the quantum behavior of the infinite series of states associated with a 1͞r potential usually focus on the prototypical Rydberg atom [1], which consists of a heavy positively charged ionic particle and a light negatively charged particle, the Rydberg electron, attracting each other via the Coulomb potential ͑V c ϳ 1͞r͒. The quantized energy levels of such a system are represented by the Rydberg formula:where R is the Rydberg constant, n is the principal quantum number, and d is the quantum defect. The value of the Rydberg constant for an atomand hence the level density is nearly equal for all atoms, because m͞m e m A 1 ͑͞m A 1 1 m e ͒ ഠ 1 for all atoms; the same holds for electronic Rydberg states of molecules in which case the core is a molecular cation.This Letter deals with molecular Rydberg states of a different kind, which may be called "Rydberg states of nuclear motion," which are associated with the Coulomb potential between separated charges of heavy mass, referred to as ion-pair potentials. The large reduced mass m of such a system leads to a value of R ion-pair ͑m͞m e ͒R`orders of magnitude larger than the atomic Rydberg constant; in the case of an H 1 H 2 ion-pair system, m ͑1͞2͒M H results in an increase of the Rydberg constant by 3 orders of magnitude. Notice that in accordance with Eq. (1) binding energies and also level separations for a given quantum number become larger, while separations at a given energy become smaller, therewith opening a range for investigations on the behavior in the 1͞r potential and the transition from quantum to classical behavior.Coulomb potentials of ion-pair systems can also be viewed as a class of molecular potentials describing an ionic bond. A remarkable difference from other potentials is the infinite number of bound states of nuclear motion (rovibrational states) supported close to the dissociation threshold; potentials associated with a covalent bond typically show an asymptotic shape of V n ϳ 1͞r n with n 3 6 and consequently support a finite number of bound states. A connection between the standard treatment of molecules on the one hand, using potentials of electronic states and quantized nuclear motion described by vibrational and rotational quantum numbers y and J, and an ion-pair Rydberg model on the other was established by identifying the effective principal quantum number n with y 1 J 1 1 while the angular moment...

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Observation of Coherent Wave Packets in a Heavy Rydberg System

Reinhold

Ubachs

2001

Phys. Rev. Lett.

View full text Add to dashboard Cite

show abstract

“…(5)- (8), it is easy to verify that T n n (0) = 1 for n = n and 0 for n = n. We shall present all results of this work by making use of (5) rather than (2). In close analogy with the result for the single kicked atoms [10], the autocorrelation function for the twice kicked atoms can be written as…”

Section: Wave Packet and Autocorrelation Functionmentioning

confidence: 94%

“…The Rydberg wave packets in atoms were first created by photoexcitation using ultrashort pulses [1,2]. But since the pioneering experiment of Jones et al [3], unipolar electric field pulses of tetrahertz spectrum, often called half-cycle pulses (HCPs), have been found to provide a very convenient tool to produce such packets.…”

Section: Introductionmentioning

confidence: 99%

Fractional Revival of Rydberg Wave Packets in Twice-Kicked One-Dimensional Atoms

Chatterjee¹,

Saha

Talukdar

2011

Acta Phys. Pol. A

View full text Add to dashboard Cite

We study revival and fractional revival phenomena of wave packets in a one-dimensional Rydberg atom irradiated by two time-delayed half-cycle pulses using an autocorrelation function characterized by electronic transition probabilities as weighting factors rather than modeling them by a Gaussian or Lorentzian distribution. If the momentum (q2) delivered to the atom by the second kick is much smaller than that (q1) imparted by the first one, the times of revival and fractional revival coincide with those of the single kicked atom. For q2 ≥ q 1 4 appearance of revival and fractional revival depends on both the values of q2 and time delay t1 between the pulses but more sensitively on t1. The number of fractional revivals tends to become numerous as the value of t1 increases.

show abstract

“…While the question of achieving the classical limit of quantum dynamics of simple systems via appropriately constructed coherent states [11,12,13,14] has been a longstanding one, interesting experiments have been carried out recently to demonstrate such a classical limit in quantum systems [15]. More recently the classical limit of the commensurate anisotropic oscillator has been investigated experimentally [16] in a laser resonator by exploiting the analogy between the Schrödinger equation for the two-dimensional harmonic oscillator and the paraxial wave equation for the spherical resonators [17,18].…”

Section: Introductionmentioning

confidence: 99%

Commensurate anisotropic oscillator,SU(2) coherent states and the classical limit

Kumar¹,

Dutta-Roy²

2008

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Abstract. We demonstrate a formally exact quantum-classical correspondence between the stationary coherent states associated with the commensurate anisotropic two-dimensional harmonic oscillator and the classical Lissajous orbits. Our derivation draws upon earlier work of Louck et al [1973 J. Math. Phys. 14 692] wherein they have provided a non-bijective canonical transformation that maps, within a degenerate eigenspace, the commensurate anisotropic oscillator on to the isotropic oscillator. This mapping leads, in a natural manner, to a Schwinger realization of SU (2) in terms of the canonically transformed creation and annihilation operators. Through the corresponding coherent states built over a degenerate eigenspace, we directly effect the classical limit via the expectation values of the underlying generators. Our work completely accounts for the fact that the SU(2) coherent state in general corresponds to an ensemble of Lissajous orbits.

show abstract

Classical periodic motion of atomic-electron wave packets

Cited by 110 publications

References 9 publications

Observation of Coherent Wave Packets in a Heavy Rydberg System

Observation of Coherent Wave Packets in a Heavy Rydberg System

Fractional Revival of Rydberg Wave Packets in Twice-Kicked One-Dimensional Atoms

Commensurate anisotropic oscillator,SU(2) coherent states and the classical limit

Contact Info

Product

Resources

About