Yosuke Kayanuma

Wannier exciton in microcrystals

Abstract A simple variational calculation is presented of the ground state properties of the electron-hole system confined in three-dimensional quantum wells with spherical shape. As the radius of the wall is reduced to a few times the effective Bohr radius of the bulk exciton, the character of the ground state changes abruptly but continuously from that of a Wannier exciton confined as a quasiparticle to that of the electron and the hole confined as individual particles. The optical experiments on CuCl microcrystals in alkali halides and in silicate glasses are briefly discussed.

Nonadiabatic Transitions in Level Crossing with Energy Fluctuation. I. Analytical Investigations

A simple stochastic model is proposed describing the nonadiabatic transitions in level crossing with energy fluctuation. The model is an extension of Zeners model having a diagonal energy term fluctuating as a Markoffian Gaussian process. The transition rate P ∞ defined in terms of the diabatic basis is calculated exactly by the formal perturbation expansion with respect to the off-diagonal coupling in the two limiting cases: In the slow fluctuation limit, P ∞ coincides with the Landau-Zener formula, \(P_{\infty}=P_{\text{LZ}} \equiv 1 - \exp (-2 \pi J^{2}/\hbar |v|)\), where J is the off-diagonal coupling constant and v is the velocity of the change of the mean energy difference. In the strong damping limit, which is a limiting case of large fluctuation amplitude in the rapid fluctuation limit, P ∞ is given by the formula, \(P_{\infty}=P_{\text{SD}} \equiv \{1 - \exp (-4 \pi J^{2}/\hbar |v|)\}/2\).

Gauging a quantum heat bath with dissipative Landau-Zener transitions.

We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.

Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior

We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula that is applicable to models with a nondegenerate ground state is derived. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard Landau-Zener probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure off-diagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.

Resonant Secondary Radiation in Strongly Coupled Localized Electron-Phonon System

Numerical calculations of the resonant secondary radiation spectrum of the strongly coupled localized electron-phonon system are presented both for the stationary and transient responses. The time evolution of the transient response makes it clear how the line shape of the stationary radiation spectrum is formed in accordance with the three characteristic time-scale, namely, the phase relaxation time, the energy relaxation time and the population decay time.

Recoil Effect of Photoelectrons in the Fermi Edge of Simple Metals

High energy resolution photoelectron spectroscopy of conduction electrons in the vicinity of the Fermi edge in Al and Au at excitation energies of 880 and 7940 eV was carried out using synchrotron radiation. For the excitation energy of 7940 eV, the observed Fermi energy of Al shows a remarkable shift to higher binding energy as compared with that of Au, with accompanying broadening. This is due to the recoil effect of the emitted photoelectrons. The observed spectra are well reproduced by a simple model of Bloch electrons based on the isotropic Debye model.

Vibronic Problem for the Relaxed Excited State of the F -center in Alkali Halides. I. Vibronic Energy Schemes

The relaxed excited state of the F -center in alkali halides is studied theoretically as a vibronic system consisting of 2 s and 2 p electronic states interacting with local mode phonons. The model Hamiltonian is introduced which contains the s -, p - and d -like interaction modes. The vibronic problem for the s - and p -modes is solved numerically in the case of intermediate coupling strength and the energy schemes thus obtained are presented.

Coherent destruction of tunneling, dynamic localization, and the Landau-Zener formula

We clarify the internal relationship between the coherent destruction of tunneling (CDT) for a two-state model and the dynamic localization (DL) for a one-dimensional tight-binding model, under the periodical driving field. The time evolution of the tight-binding model is reproduced from that of the two-state model by a mapping of equation of motion onto a set of SU(2) operators. It is shown that DL is effectively an infinitely large dimensional representation of the CDT in the SU(2) operators. We also show that both of the CDT and the DL can be interpreted as a result of destructive interference in repeated Landau-Zener level crossings.

Stochastic Theory for Nonadiabatic Level Crossing with Fluctuating Off-Diagonal Coupling

A simple stochastic model is presented describing the nonadiabatic transitions in the level crossing with fluctuating off-diagonal coupling, in which the fluctuation is assumed to obey the Markoffian Gaussian process. The probability P that the transition occurs from one diabatic state to another is calculated exactly in the two limiting situations: In the slow fluctuation limit, P is given by \(P{=}1-\{1+(4{\pi}J^{2}/\hbar|v|)\}^{-1/2}\), where J is the averaged amplitude of the off-diagonal term and v is the velocity of the change of the energy difference between the crossing levels. In the rapid fluctuation limit, P is given by \(P{=}\{1-{\exp}(-4{\pi}J^{2}/\hbar|v|)\}/2\). The intermediate case is studied numerically by the Wiener-Hermite expansion method. Generally, P approaches not 1 but 1/2 in the limit of slow passage, namely, v →0.

Landau-Zener transitions in qubits controlled by electromagnetic fields

We investigate the influence of a dipole interaction with a classical radiation field on a qubit during a continuous change of a control parameter. In particular, we explore the non-adiabatic transitions that occur when the qubit is swept with linear speed through resonances with the time-dependent interaction. Two classic problems come together in this model: the Landau- Zener (LZ) and the Rabi problem. The probability of LZ transitions now depends sensitively on the amplitude, the frequency and the phase of the Rabi interaction. The influence of the static phase turns out to be particularly strong, since this parameter controls the time-reversal symmetry of the Hamiltonian. In the limits of large and small frequencies, analytical results obtained within a rotating- wave approximation compare favourably with a numerically exact solution. We discuss physical realizations in microwave optics, quantum dots and molecular nanomagnets.