We consider an optomechanical system composed of a trapped ion dispersively coupled to a single mode of a pumped optical cavity. We focus on a parameter range for which the semiclassical description predicts two clearly distinct equilibrium configurations in the limits of small and large photon pumping, while a bistable regime is found for intermediate pumping. This semiclassical description, however, is not valid in close proximity to the system transitions or when the mean photon number is low. Here, we provide a numerical analysis of the fully quantum state in the few-photon regime, exploring the features of the asymptotic state across the transition and analyzing possible markers of semiclassical bistability. We find an increase in the entropy of the system and of the entanglement in the transition region but no clear signatures of metastability in the spectrum of the evolution.We consider an optomechanical system composed of a trapped ion dispersively coupled to a single mode of a pumped optical cavity. We focus on a parameter range for which the semiclassical description predicts two clearly distinct equilibrium configurations in the limits of small and large photon pumping, while a bistable regime is found for intermediate pumping. This semiclassical description, however, is not valid in close proximity to the system transitions or when the mean photon number is low. Here, we provide a numerical analysis of the fully quantum state in the few-photon regime, exploring the features of the asymptotic state across the transition and analyzing possible markers of semiclassical bistability. We find an increase in the entropy of the system and of the entanglement in the transition region but no clear signatures of metastability in the spectrum of the evolution.

arXiv:2110.13843Physical Review AOct 19, 20215 citations

Optical Transitions

Springer eBooksMay 9, 20060 citations

Optical transitions

Jérôme Faist

Oxford University Press eBooksMar 14, 20131 citation

Quantum mechanical interaction of light with atoms

Peter Blood

Abstract The quantum mechanical description of the interaction of light with atoms treats absorption, gain, and recombination as upward and downward induced transitions of electrons between two states by perturbation due to the optical electric field. This provides the basis for a quantitative theory of diode lasers. The chapter begins with Einstein’s description of absorption, stimulated emission, and spontaneous emission, setting the scene for calculation of the transition probability by solving the time-dependent Schrödinger equation for a coherent superposition of the wavefunctions of two states. The resulting absorption spectrum has a Lorentzian lineshape due to dephasing of these wavefunctions. Expressions for the optical absorption cross section and Einstein coefficients are derived in terms of the dipole matrix element, and the dipole is illustrated using a hypothetical one-dimensional atom. Fermi’s Golden Rule for transitions to a continuum of states (as in quantum wells) is introduced in terms of the momentum matrix element.Abstract The quantum mechanical description of the interaction of light with atoms treats absorption, gain, and recombination as upward and downward induced transitions of electrons between two states by perturbation due to the optical electric field. This provides the basis for a quantitative theory of diode lasers. The chapter begins with Einstein’s description of absorption, stimulated emission, and spontaneous emission, setting the scene for calculation of the transition probability by solving the time-dependent Schrödinger equation for a coherent superposition of the wavefunctions of two states. The resulting absorption spectrum has a Lorentzian lineshape due to dephasing of these wavefunctions. Expressions for the optical absorption cross section and Einstein coefficients are derived in terms of the dipole matrix element, and the dipole is illustrated using a hypothetical one-dimensional atom. Fermi’s Golden Rule for transitions to a continuum of states (as in quantum wells) is introduced in terms of the momentum matrix element.

Oct 1, 20150 citations

Collisional frequency shift of a trapped-ion optical clock

Amar C. Vutha, Tom Kirchner, P. Dubé

Collisions with background gas can perturb the transition frequency of trapped ions in an optical atomic clock. We develop a nonperturbative framework based on a quantum channel description of the scattering process and use it to derive a master equation which leads to a simple analytic expression for the collisional frequency shift. As a demonstration of our method, we calculate the frequency shift of the ${\mathrm{Sr}}^{+}$ optical atomic clock transition due to elastic collisions with helium.Collisions with background gas can perturb the transition frequency of trapped ions in an optical atomic clock. We develop a nonperturbative framework based on a quantum channel description of the scattering process and use it to derive a master equation which leads to a simple analytic expression for the collisional frequency shift. As a demonstration of our method, we calculate the frequency shift of the ${\mathrm{Sr}}^{+}$ optical atomic clock transition due to elastic collisions with helium.

arXiv:1705.10019Physical Review AAug 11, 201725 citations

The General Optical Transition

John N. Dodd

Springer eBooksJan 1, 19910 citations

{\mathrm{Sr}}^{+}

optical atomic clock transition due to elastic collisions with helium.