Quantum Mechanics: Fundamentals and Applications to Technology

Singh, Jasprit; Murphy, R. D.

doi:10.1119/1.18771

Cited by 24 publications

(34 citation statements)

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“…Then, starting with the reduced Hamiltonian H = H 0 + H r + H I , use is made of first-order timedependent perturbation theory to calculate SE transitions probabilities between states of H 0 + H r while regarding H I ͑t͒ϳA r · ͓p + p c ͑t͔͒ as a perturbation. 10 The solution to ͉⌿ n 0 ͑t͒͘ of Eq. ͑2͒ can be represented in terms of eigenstates of basis states ͉ n 0 k͑t͒ , ͕n q,j ͖͘ = ͉ n 0 k͑t͒ ͉͕͘n q,j ͖͘ of the unperturbed Hamiltonian H 0 + H r as…”

Section: Quantum Dynamics and Theoretical Approachmentioning

confidence: 99%

Microcavity enhancement of spontaneous emission for Bloch oscillations

2007

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A theory for the spontaneous emission of a Bloch electron traversing a single energy miniband of a superlattice while accelerating under the influence of a constant external electric field and radiating into a microcavity is presented. In the analysis, the quantum electromagnetic radiation field is described by the dominant microcavity TE 10 rectangular waveguide mode in the Coulomb gauge, and the instantaneous eigenstates of the Bloch Hamiltonian are utilized as the basis states in describing the Bloch electron dynamics to all orders in the constant external electric field. The results show that the spontaneous emission amplitude, when analyzed over many integral multiple values of the Bloch period, gives rise to selection rules for photon emission in both frequency and wave number with preferred transitions at the Wannier-Stark ladder levels. From these selection rules, the total spontaneous emission probability is derived to first-order perturbation theory in the quantized radiation field. It is shown that the power radiated into the dominant TE 10 waveguide mode can be enhanced by an order of magnitude over the free-space value by tuning the Bloch frequency to align with the waveguide spectral density peak. A general expression for the total spontaneous emission probability is obtained in terms of arbitrary superlattice single band parameters, showing multiharmonic behavior and cavity tuning properties. For GaAs-based superlattices, described in the nearest-neighbor tight-binding approximation, the power radiated into the waveguide from spontaneous emission due to Bloch oscillations in the terahertz frequency range is estimated to be several microwatts.

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Section: Quantum Dynamics and Theoretical Approachmentioning

confidence: 99%

Microcavity enhancement of spontaneous emission for Bloch oscillations

2007

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“…Consider the one-dimensional time-independent Schrodinger equation [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] −h 2 2m d 2 dx 2 ψ(x) + V (x) ψ(x) = E ψ(x).…”

Section: General Analysis a Shabat-zakharov Systemsmentioning

confidence: 99%

Some general bounds for one-dimensional scattering

1999

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One-dimensional scattering problems are of wide physical interest and are encountered in many diverse applications. In this article I establish some very general bounds for reflection and transmission coefficients for one-dimensional potential scattering. Equivalently, these results may be phrased as general bounds on the Bogolubov coefficients, or statements about the transfer matrix. A similar analysis can be provided for the parametric change of frequency of a harmonic oscillator. A number of specific examples are discussed-in particular I provide a general proof that sharp step function potentials always scatter more effectively than the corresponding smoothed potentials. The analysis also serves to collect together and unify what would otherwise appear to be quite unrelated results. Physical Review A59 (1999) 427-438.

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“…It is one of the most important models in quantum mechanics [3,6], because an arbitrary potential can be approximated by a harmonic potential at the vicinity of a stable equilibrium point. Transmutation of the quantum harmonic oscillator may be described by the (time-dependent) Schrödinger equation, as…”

Section: Quantum Harmonic Oscillatormentioning

confidence: 99%

“…However, according to Heisenberg's uncertainty principle, such trajectories cannot be measured. So, during the last few decades, a great deal of attention and interest was directed, in both physics and philosophy, to the measurement problem in quantum mechanics [1][2][3][4][5][6]. For example, Berry [1] pointed out the existence of linear quantum chaos.…”

Section: Introduction and Basic Definitionsmentioning

confidence: 98%

On the invariance of maximal distributional chaos under an annihilation operator

Chen

2013

Applied Mathematics Letters

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a b s t r a c tIt is known that certain physical systems, which do not generate deterministic chaos under conventional frameworks, may generate such complex behavior in a quantum mechanical setting. In this paper, it is proved that the annihilation operator of an unforced quantum harmonic oscillator admits an invariant distributionally ϵ-scrambled set for any 0 < ϵ < 2, showing that this operator can exhibit maximal distributional chaos on an uncountable invariant subset.

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Quantum Mechanics: Fundamentals and Applications to Technology

Cited by 24 publications

References 0 publications

Microcavity enhancement of spontaneous emission for Bloch oscillations

Microcavity enhancement of spontaneous emission for Bloch oscillations

Some general bounds for one-dimensional scattering

On the invariance of maximal distributional chaos under an annihilation operator

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