A classically chaotic system consisting of a Paul trapped ion and a sequences of standing laser pulses is treated quantum-mechanically. Under the circumstance of time-dependence, we derive the transition probability from the ion's motional state to ', and find, in the first-order approximation, the classically chaotic character disappears. Theoretical analysis and numerical calculations show that by regulating the phase parameter we can control the transition probability. When reaches some specific values, the transition from the state to ' is forbidden and, for some laser periods, resonance occurs, which leads to the corresponding transitions between different motional states. The time-evolution of an initial motional state just over one period is also studied in detail.A classically chaotic system consisting of a Paul trapped ion and a sequences of standing laser pulses is treated quantum-mechanically. Under the circumstance of time-dependence, we derive the transition probability from the ion's motional state to ', and find, in the first-order approximation, the classically chaotic character disappears. Theoretical analysis and numerical calculations show that by regulating the phase parameter we can control the transition probability. When reaches some specific values, the transition from the state to ' is forbidden and, for some laser periods, resonance occurs, which leads to the corresponding transitions between different motional states. The time-evolution of an initial motional state just over one period is also studied in detail.

Communications in Theoretical PhysicsOct 15, 20046 citations

Quantum optics with a single trapped ion

Randall G. Hulet, Jonas Bergquist, David J. Wineland

Journal of the Optical Society of America BFeb 1, 19870 citations

Observation of a midinfrared fine-structure transition for the single trapped barium ion

Alan A. Madej, J. D. Sankey, G. R. Hanes +2 more

We report observation of laser excitation of a narrow, magnetic-dipole-allowed, infrared transition in a single trapped ion. Quantum jumps of a ${\mathrm{Ba}}^{+}$ atom were observed using a diode laser tuned in resonance with the excited-state 5d $^{2}$ ${\mathit{D}}_{3/2}$ --5d $^{2}$ ${\mathit{D}}_{5/2}$ transition at 12.48 \ensuremath{\mu}m. Single-ion resonance line shapes were obtained and a transition frequency of \ensuremath{\nu}=24 012 033\ifmmode\pm\else\textpm\fi{}11 MHz was determined. Calculated quantum jump rates of the D-D transition for the applied laser spectral brightness yield agreement with experimentally observed values.We report observation of laser excitation of a narrow, magnetic-dipole-allowed, infrared transition in a single trapped ion. Quantum jumps of a ${\mathrm{Ba}}^{+}$ atom were observed using a diode laser tuned in resonance with the excited-state 5d $^{2}$${\mathit{D}}_{3/2}$--5d $^{2}$${\mathit{D}}_{5/2}$ transition at 12.48 \ensuremath{\mu}m. Single-ion resonance line shapes were obtained and a transition frequency of \ensuremath{\nu}=24 012 033\ifmmode\pm\else\textpm\fi{}11 MHz was determined. Calculated quantum jump rates of the D-D transition for the applied laser spectral brightness yield agreement with experimentally observed values.

Physical Review AFeb 1, 199215 citations

Quantum Optics of Single, Trapped Ions

Wayne M. Itano, Jonas Bergquist, F. Diedrich +1 more

Springer eBooksJan 1, 19903 citations

Spectroscopy with single-trapped ions

HERBERT WALTHER

In this paper experiments with single trapped ions are reviewed. They are performed with the aim of developing a new frequency standard and to perform cavity quantum electrodynamics experiments with single ions. For a new optical frequency standard we are investigating the 5s21S0 implied by 5s5p3P0 transition of a single trapped laser-cooled 115In(superscript + ion. This line with a natural linewidth of only 0.8 Hz is highly immune to systematic frequency shifts. For sideband laser cooling and fluorescence detection of the indium ion the 5s21S0 implied by 5s5p3P1 transition at 230.6 nm is used. Temperatures below 100 (mu) K and a mean vibrational quantum number <n><1 of the ion in the trap have been reached. For the clock transition a resolution of 1.3 multiplied by 10-13 (linewidth 170 Hz) has been obtained so far, limited by the short term frequency fluctuations of the clock laser. The absolute frequency of the 1S0 implied by 3P0 transition was measured by making a link to the reference frequency of the methane-stabilized HeNe laser using a frequency chain. In the second part of the paper the present status of the experiments on the ion trap laser are briefly described.In this paper experiments with single trapped ions are reviewed. They are performed with the aim of developing a new frequency standard and to perform cavity quantum electrodynamics experiments with single ions. For a new optical frequency standard we are investigating the 5s21S0 implied by 5s5p3P0 transition of a single trapped laser-cooled 115In(superscript + ion. This line with a natural linewidth of only 0.8 Hz is highly immune to systematic frequency shifts. For sideband laser cooling and fluorescence detection of the indium ion the 5s21S0 implied by 5s5p3P1 transition at 230.6 nm is used. Temperatures below 100 (mu) K and a mean vibrational quantum number <n><1 of the ion in the trap have been reached. For the clock transition a resolution of 1.3 multiplied by 10-13 (linewidth 170 Hz) has been obtained so far, limited by the short term frequency fluctuations of the clock laser. The absolute frequency of the 1S0 implied by 3P0 transition was measured by making a link to the reference frequency of the methane-stabilized HeNe laser using a frequency chain. In the second part of the paper the present status of the experiments on the ion trap laser are briefly described.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEJun 29, 20010 citations

We report observation of laser excitation of a narrow, magnetic-dipole-allowed, infrared transition in a single trapped ion. Quantum jumps of a

{\mathrm{Ba}}^{+}

atom were observed using a diode laser tuned in resonance with the excited-state 5d

^{2}

{\mathit{D}}_{3/2}

--5d

^{2}

{\mathit{D}}_{5/2}

transition at 12.48 \ensuremath{\mu}m. Single-ion resonance line shapes were obtained and a transition frequency of \ensuremath{\nu}=24 012 033\ifmmode\pm\else\textpm\fi{}11 MHz was determined. Calculated quantum jump rates of the D-D transition for the applied laser spectral brightness yield agreement with experimentally observed values.