Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Transient internal dynamics of a multilevel ion

Michael Schubert, Ingo Siemers, R. Blatt, Werner Neuhauser, P. E. Toschek

Published Oct 1, 1995• 46 citations
Publisher

Abstract

The autocorrelation ${\mathit{g}}^{(2)}$(\ensuremath{\tau}) of the photon-counting signal from laser-induced light scattering off a single trapped and laser-cooled ${\mathrm{Ba}}^{+}$ ion shows dramatic nonclassical effects: ${\mathit{g}}^{(2)}$(\ensuremath{\tau}) increasing upon delay \ensuremath{\tau} close to zero (``antibunching'') is accompanied (i) by its extreme peak values, (ii) by long transients and long appearance of subunity values (``sub-Poissonian light''), both extending much beyond the lifetime of the ion's resonance level, and (iii) by modulation from magnetic precession, as is common with quantum beats. These phenomena highlight the internal multilevel structure of the ion, hint at optical pumping, and prove the coherent evolution of the ion's internal state. The preparation of the ion in a coherent superposition by spontaneous decay is demonstrated. The counting variance of the scattered light, measured in terms of Mandel's Q parameter, deviates from that of classical light by up to \ensuremath{\Delta}Q=-7\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$.

DOI
10.1103/physreva.52.2994

Related papers

Photon antibunching and non-Poissonian fluorescence of a single three-level ion

Michael Schubert, Ingo Siemers, R. Blatt +2 more

The photon pair correlation in the laser-excited fluorescence of a single trapped and cooled ${\mathrm{Ba}}^{+}$ ion shows antibunching and, in addition, novel nonclassical phenomena absent in the fluorescence of two-level atoms. They include excessive transient values of the correlation caused by optical pumping, and temporally extended sub-Poissonian photon emission probability which arises from the transient excitation of nonabsorbing Raman coherence. The fluorescence also displays sub-Poissonian photon statistics.

Physical Review Letters•May 18, 1992•74 citations

Quantum optics of a single trapped ion

Bernd Appasamy, Jürgen Eschner, Yves Stalgies +2 more

A single trapped and cooled ion interacting with light is the realization of a fundamental system of quantum optics. Relevant viewpoints include the light scattering and its relation to the preparation of the ion, the dynamics of the ion's internal motion, and the dynamics of its vibrational motion. As cases in point, recent results are reviewed that illustrate those viewpoints: (i) The preparation of the ion, by spontaneous emission, in a superposition of energy eigenstates of quasi-permanent lifetime. (ii) The dispersive effect of quantum jumps of the ion, to and from a metastable state, that gives rise to internally self-locking the ion in either the light-scattering bright or the non-scattering dark state. (iii) The stochastic cooling of the ion by repeated null detection of its resonance scattering. These counter-intuitive phenomena characterize a physical system, where quantum mechanics models ensembles of observations.

Physica Scripta•Jan 1, 1995•5 citations

Quantum measurement and nonclassical vibration of an ion in a trap

R. Huesmann, Ch. Balzer, Bernd Appasamy +2 more

The microwave-induced dynamics of the nuclear spin and the laser-induced dynamics of the centre-of-mass motion of individual ions have been studied: (i) The phase shift of the hyperfine Larmor precession of a ground-state 171Yb+ ion upon pulsed variation of the ambient magnetic field has been measured by microwave-optical double resonance interpreted in terms of Mach-Zehnder interferometry and quantum ergodicity. Even a single measurement yields (partial) phase information. At the extremes of the fringes, the results of measurements are deterministic where ion probing is compatible with ion preparation, as demonstrated by laser-exciting an ion on an E2 line. (ii) Excitation and de-excitation spectra of the E2 line S1/2−D5/2 of an individual trapped 138Ba+ ion show different first-order sidebands of radial and axial ion vibration in the trap, since the vibrational distribution in the excited D5/2 level is modified by the ion being reduced to this level in null observations of resonance light. Delayed sideband deexcitation eventually leaves the ion in the Fock state |n=1〉 (“stochastic cooling”). Sideband modulation is identified as stroboscopic detection of the light-induced nutation.

AIP conference proceedings•Jan 1, 1999•0 citations

Laser cooling and quantum jumps of a single indium ion

E. Peik, Guenter Hollemann, HERBERT WALTHER

We performed laser spectroscopy of ${\mathrm{In}}^{+}$ ions stored in a radio-frequency trap. The 5${\mathit{s}}^{2}$ $^{1}$${\mathit{S}}_{0}$\ensuremath{\rightarrow}5s5p $^{3}$${\mathit{P}}_{1}$ transition at 230.6 nm was excited and its hyperfine splitting and isotope shift have been measured. The lifetime of the $^{3}$${\mathit{P}}_{1}$ state was measured using intensity modulated laser excitation: \ensuremath{\tau}${(}^{3}$${\mathit{P}}_{1}$)=0.44(4) \ensuremath{\mu}s. A single indium ion was laser cooled using this intercombination line and dark periods in the fluorescence were observed when the metastable $^{3}$${\mathit{P}}_{0}$ state was populated by a magnetic dipole decay from $^{3}$${\mathit{P}}_{1}$. The radiative lifetime of the forbidden transition $^{3}$${\mathit{P}}_{0}$${\ensuremath{\rightarrow}}^{1}$${\mathit{S}}_{0}$ was determined from the duration of the dark periods: \ensuremath{\tau}${(}^{3}$${\mathit{P}}_{0}$)=0.14(2) s. This value is compared to calculations based on perturbation theory. Prospects for an optical frequency standard using the narrow 5${\mathit{s}}^{2}$ $^{1}$${\mathit{S}}_{0}$\ensuremath{\rightarrow}5s5p $^{3}$${\mathit{P}}_{0}$ resonance at 236.5 nm of a single laser-cooled indium ion are discussed.

Physical Review A•Jan 1, 1994•104 citations

Laser cooling and quantum jumps of a single indium ion

E. Peik, Guenter Hollemann, HERBERT WALTHER

We performed laser spectroscopy of ${\mathrm{In}}^{+}$ ions stored in a radio-frequency trap. The 5${\mathit{s}}^{2}$ $^{1}$${\mathit{S}}_{0}$\ensuremath{\rightarrow}5s5p $^{3}$${\mathit{P}}_{1}$ transition at 230.6 nm was excited and its hyperfine splitting and isotope shift have been measured. The lifetime of the $^{3}$${\mathit{P}}_{1}$ state was measured using intensity modulated laser excitation: \ensuremath{\tau}${(}^{3}$${\mathit{P}}_{1}$)=0.44(4) \ensuremath{\mu}s. A single indium ion was laser cooled using this intercombination line and dark periods in the fluorescence were observed when the metastable $^{3}$${\mathit{P}}_{0}$ state was populated by a magnetic dipole decay from $^{3}$${\mathit{P}}_{1}$. The radiative lifetime of the forbidden transition $^{3}$${\mathit{P}}_{0}$${\ensuremath{\rightarrow}}^{1}$${\mathit{S}}_{0}$ was determined from the duration of the dark periods: \ensuremath{\tau}${(}^{3}$${\mathit{P}}_{0}$)=0.14(2) s. This value is compared to calculations based on perturbation theory. Prospects for an optical frequency standard using the narrow 5${\mathit{s}}^{2}$ $^{1}$${\mathit{S}}_{0}$\ensuremath{\rightarrow}5s5p $^{3}$${\mathit{P}}_{0}$ resonance at 236.5 nm of a single laser-cooled indium ion are discussed.

European Quantum Electronics Conference (EQEC)•Aug 24, 2005•2 citations

Optical coherent transients: Generalized two-level solutions

Axel Schenzle, Richard G. Brewer

Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole (${T}_{2}$) and population (${T}_{1}$) decay times appear. A similar description has been carried over recently into the microwave and infrared regions as well. At visible-ultraviolet wavelengths, however, a more general solution is required because the transition levels do not constitute an isolated system and also spontaneous emission can no longer be disregarded. As a consequence, the lower (1) and upper (2) transition levels are characterized by vastly different decay rates (${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$) and the lifetime ${T}_{1}$ is no longer a defined quantity. In view of laser-induced coherent transient phenomena now being observed, we present general solutions of the density-matrix equations of motion for an optically resonant two-level system in contact with a multilevel reservoir where ${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.

Physical Review A•Nov 1, 1976•83 citations
The autocorrelation g(2){\mathit{g}}^{(2)}g(2)(\ensuremath{\tau}) of the photon-counting signal from laser-induced light scattering off a single trapped and laser-cooled Ba+{\mathrm{Ba}}^{+}Ba+ ion shows dramatic nonclassical effects: g(2){\mathit{g}}^{(2)}g(2)(\ensuremath{\tau}) increasing upon delay \ensuremath{\tau} close to zero (antibunching'') is accompanied (i) by its extreme peak values, (ii) by long transients and long appearance of subunity values (sub-Poissonian light''), both extending much beyond the lifetime of the ion's resonance level, and (iii) by modulation from magnetic precession, as is common with quantum beats. These phenomena highlight the internal multilevel structure of the ion, hint at optical pumping, and prove the coherent evolution of the ion's internal state. The preparation of the ion in a coherent superposition by spontaneous decay is demonstrated. The counting variance of the scattered light, measured in terms of Mandel's Q parameter, deviates from that of classical light by up to \ensuremath{\Delta}Q=-7\ifmmode\times\else\texttimes\fi{}10\ensuremath−4{10}^{\mathrm{\ensuremath{-}}4}10\ensuremath−4.
The photon pair correlation in the laser-excited fluorescence of a single trapped and cooled Ba+{\mathrm{Ba}}^{+}Ba+ ion shows antibunching and, in addition, novel nonclassical phenomena absent in the fluorescence of two-level atoms. They include excessive transient values of the correlation caused by optical pumping, and temporally extended sub-Poissonian photon emission probability which arises from the transient excitation of nonabsorbing Raman coherence. The fluorescence also displays sub-Poissonian photon statistics.
A single trapped and cooled ion interacting with light is the realization of a fundamental system of quantum optics. Relevant viewpoints include the light scattering and its relation to the preparation of the ion, the dynamics of the ion's internal motion, and the dynamics of its vibrational motion. As cases in point, recent results are reviewed that illustrate those viewpoints: (i) The preparation of the ion, by spontaneous emission, in a superposition of energy eigenstates of quasi-permanent lifetime. (ii) The dispersive effect of quantum jumps of the ion, to and from a metastable state, that gives rise to internally self-locking the ion in either the light-scattering bright or the non-scattering dark state. (iii) The stochastic cooling of the ion by repeated null detection of its resonance scattering. These counter-intuitive phenomena characterize a physical system, where quantum mechanics models ensembles of observations.
The microwave-induced dynamics of the nuclear spin and the laser-induced dynamics of the centre-of-mass motion of individual ions have been studied: (i) The phase shift of the hyperfine Larmor precession of a ground-state 171Yb+ ion upon pulsed variation of the ambient magnetic field has been measured by microwave-optical double resonance interpreted in terms of Mach-Zehnder interferometry and quantum ergodicity. Even a single measurement yields (partial) phase information. At the extremes of the fringes, the results of measurements are deterministic where ion probing is compatible with ion preparation, as demonstrated by laser-exciting an ion on an E2 line. (ii) Excitation and de-excitation spectra of the E2 line S1/2−D5/2 of an individual trapped 138Ba+ ion show different first-order sidebands of radial and axial ion vibration in the trap, since the vibrational distribution in the excited D5/2 level is modified by the ion being reduced to this level in null observations of resonance light. Delayed sideband deexcitation eventually leaves the ion in the Fock state |n=1〉 (“stochastic cooling”). Sideband modulation is identified as stroboscopic detection of the light-induced nutation.
We performed laser spectroscopy of In+{\mathrm{In}}^{+}In+ ions stored in a radio-frequency trap. The 5s2{\mathit{s}}^{2}s2 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}5s5p 3^{3}3P1{\mathit{P}}_{1}P1​ transition at 230.6 nm was excited and its hyperfine splitting and isotope shift have been measured. The lifetime of the 3^{3}3P1{\mathit{P}}_{1}P1​ state was measured using intensity modulated laser excitation: \ensuremath{\tau}(3{(}^{3}(3P1{\mathit{P}}_{1}P1​)=0.44(4) \ensuremath{\mu}s. A single indium ion was laser cooled using this intercombination line and dark periods in the fluorescence were observed when the metastable 3^{3}3P0{\mathit{P}}_{0}P0​ state was populated by a magnetic dipole decay from 3^{3}3P1{\mathit{P}}_{1}P1​. The radiative lifetime of the forbidden transition 3^{3}3P0{\mathit{P}}_{0}P0​${\ensuremath{\rightarrow}}^{1}$S0{\mathit{S}}_{0}S0​ was determined from the duration of the dark periods: \ensuremath{\tau}(3{(}^{3}(3P0{\mathit{P}}_{0}P0​)=0.14(2) s. This value is compared to calculations based on perturbation theory. Prospects for an optical frequency standard using the narrow 5s2{\mathit{s}}^{2}s2 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}5s5p 3^{3}3P0{\mathit{P}}_{0}P0​ resonance at 236.5 nm of a single laser-cooled indium ion are discussed.
We performed laser spectroscopy of In+{\mathrm{In}}^{+}In+ ions stored in a radio-frequency trap. The 5s2{\mathit{s}}^{2}s2 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}5s5p 3^{3}3P1{\mathit{P}}_{1}P1​ transition at 230.6 nm was excited and its hyperfine splitting and isotope shift have been measured. The lifetime of the 3^{3}3P1{\mathit{P}}_{1}P1​ state was measured using intensity modulated laser excitation: \ensuremath{\tau}(3{(}^{3}(3P1{\mathit{P}}_{1}P1​)=0.44(4) \ensuremath{\mu}s. A single indium ion was laser cooled using this intercombination line and dark periods in the fluorescence were observed when the metastable 3^{3}3P0{\mathit{P}}_{0}P0​ state was populated by a magnetic dipole decay from 3^{3}3P1{\mathit{P}}_{1}P1​. The radiative lifetime of the forbidden transition 3^{3}3P0{\mathit{P}}_{0}P0​${\ensuremath{\rightarrow}}^{1}$S0{\mathit{S}}_{0}S0​ was determined from the duration of the dark periods: \ensuremath{\tau}(3{(}^{3}(3P0{\mathit{P}}_{0}P0​)=0.14(2) s. This value is compared to calculations based on perturbation theory. Prospects for an optical frequency standard using the narrow 5s2{\mathit{s}}^{2}s2 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}5s5p 3^{3}3P0{\mathit{P}}_{0}P0​ resonance at 236.5 nm of a single laser-cooled indium ion are discussed.
Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole (T2{T}_{2}T2​) and population (T1{T}_{1}T1​) decay times appear. A similar description has been carried over recently into the microwave and infrared regions as well. At visible-ultraviolet wavelengths, however, a more general solution is required because the transition levels do not constitute an isolated system and also spontaneous emission can no longer be disregarded. As a consequence, the lower (1) and upper (2) transition levels are characterized by vastly different decay rates (${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$) and the lifetime T1{T}_{1}T1​ is no longer a defined quantity. In view of laser-induced coherent transient phenomena now being observed, we present general solutions of the density-matrix equations of motion for an optically resonant two-level system in contact with a multilevel reservoir where ${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.