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arXiv:quant-ph/0512028 · Yuanzihe wuli pinglun

Non-Integer Quantum Transitions

Qiren Zhang

Published Dec 4, 2005• 0 citations
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Abstract

We show that in the quantum transition of a system induced by the interaction with an intense laser of circular frequency $ω$, the energy difference between the initial and the final states of the system is not necessarily being an integer multiple of the quantum energy $\hbarω$.

DOI
10.48550/arxiv.quant-ph/0512028

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We show that in the quantum transition of a system induced by the interaction with an intense laser of circular frequency ωωω, the energy difference between the initial and the final states of the system is not necessarily being an integer multiple of the quantum energy ℏω\hbarωℏω.
A small parameter is used to identify the orders of perturbation. The unperturbed Hamiltonian is assumed time-independent and can be diagonalized. The interaction of an electron with an applied electromagnetic field is governed by the gauge-invariant Hamiltonian. If both the initial and final energy levels are discretized, the delta function indicates that the transition happens only when the energy difference between the two levels matches the frequency of the perturbation. The delta function suggests that the absorption or stimulated emission happens only when the energy difference between the final and initial states matches precisely the frequency of the applied electromagnetic wave. The quantum transition induced by a monochromatic perturbation is determined by the matrix element between the initial and final states.
The goal of this experiment was to measure the hyperfine energy splittings of the ground to first excited state transitions in rubidium using saturated absorption spectroscopy. Using this technique, we measured these transition energy spectra by taking the difference of two photodiode outputs due to multiple beams of a single laser scanned over a range of frequencies and shone through a cell of Rb vapor. When the laser frequency was resonant with an atomic transition, photons of those frequencies were absorbed, leaving a dip in intensity of the beam measured at the photodiode. One of the two laser beams had its excitations saturated by a more intense, counter-propagating pump beam from the same laser. The pump beam saturated the absorption of the velocity equal zero atoms that the counter-propagating probe beam could have also interacted with due to no Doppler shift. At these frequencies the probe beam experienced less absorption that was measured by a photodiode. The photodiode output was calibrated to the change in frequency of the scanned laser using a Fabry-Pérot interferometer. The output of this interferometer served as a reference for how the laser frequency changed. Final results for the 87Rb F=1 spectrum accounted for the largest error with a maximum of 12.2% deviation from accepted energy spacing values due in part to systematic error. Other spectra measurements were in better agreement, possessing error ranging from 2.1% to 10.1% and some agreeing with accepted values to within our uncertainty.
We theoretically predict a nonequilibrium phase transition in quantum spin systems induced by a laser, which provides a purely quantum-mechanical way of coherently controlling magnetization. Namely, when a circularly polarized laser is applied to a spin system, the magnetic component of a laser is shown to induce a magnetization normal to the plane of polarization, leading to an ultrafast phase transition. We first demonstrate this phenomenon numerically for an S=1S=1S=1 antiferromagnetic Heisenberg spin chain, where a new state emerges with magnetization perpendicular to the polarization plane of the laser in place of the topologically ordered Haldane state. We then elucidate its physical mechanism by mapping the system to an effective static model. The theory also indicates that the phenomenon should occur in general quantum spin systems with a magnetic anisotropy. The required laser frequency is in the terahertz range, with the required intensity being within a prospective experimental feasibility.