Laser-cooled arrays or crystals of $^{171}\mathrm{Yb}$ ${}^{+}$ ions containing a single impurity, $^{172}\mathrm{Yb}$ ${}^{+}$ isotope, are confined in a linear radio-frequency Paul trap. Site-to-site hopping of the impurity ion, distinguished by a lack of fluorescence, is studied as a function of the $^{171}\mathrm{Yb}$ ${}^{+}$ laser-cooling parameters and as a function of the anisotropy of the trapping potential. Imaging of the independently resolved crystal sites permits the extraction of the impurity's hopping trajectory, from which the dwell times at a given site can be obtained as well as the spatial distribution of hopping rate and hopping destination. The onset of rapid hopping is found to occur at average thermal energies approaching a significant fraction of the Coulomb potential energy. Furthermore, the hopping rate is enhanced at trap anisotropies near the critical value for the structural phase transition to a two-dimensional zigzag phase. Finally, the hopping mobility of the impurity ion is observed to be highest near the center of the crystal, which may have an intrinsic cause related to the crystal structure and dynamics near the zigzag transition.Laser-cooled arrays or crystals of $^{171}\mathrm{Yb}$${}^{+}$ ions containing a single impurity, $^{172}\mathrm{Yb}$${}^{+}$ isotope, are confined in a linear radio-frequency Paul trap. Site-to-site hopping of the impurity ion, distinguished by a lack of fluorescence, is studied as a function of the $^{171}\mathrm{Yb}$${}^{+}$ laser-cooling parameters and as a function of the anisotropy of the trapping potential. Imaging of the independently resolved crystal sites permits the extraction of the impurity's hopping trajectory, from which the dwell times at a given site can be obtained as well as the spatial distribution of hopping rate and hopping destination. The onset of rapid hopping is found to occur at average thermal energies approaching a significant fraction of the Coulomb potential energy. Furthermore, the hopping rate is enhanced at trap anisotropies near the critical value for the structural phase transition to a two-dimensional zigzag phase. Finally, the hopping mobility of the impurity ion is observed to be highest near the center of the crystal, which may have an intrinsic cause related to the crystal structure and dynamics near the zigzag transition.

Physical Review AJun 6, 20116 citations

Dynamics of Trapped Ions Near the Linear-Zigzag Structural Phase Transition

Sara Ejtemaee

Laser-cooled ions held in a linear Paul trap with strong transverse confinement organize into a one-dimensional (1-D) linear crystal. If the transverse confinement is relaxed, the linear ion crystal undergoes a continuous, structural phase transition to a 2-D zigzag configuration. We study the dynamics near the critical point of the linear-zigzag transition. In the first part of this thesis, we study the spontaneous nucleation and dynamics of topological kink defects, formed as a result of a rapid quench across the linear-zigzag transition. The experimental results are compared to the Kibble-Zurek mechanism, which provides an intuitive model of defect formation and predicts a power-law scaling for the number of defectsformed as a function of transition quench rate. The second part of this thesis is focused on one of the key requirements for investigations of the near-transition dynamics in the quantum regime. To achieve an efficient ground state cooling of the zigzag vibrational mode, we demonstrate 3-D polarization-gradient cooling of strings of 1-4 trapped ions as an intermediate step between Doppler and sideband cooling, and study the polarization-gradient cooling rate and cooling limit as a function of the cooling beam intensity in and near the Lamb-Dicke regime. The results of this thesis pave the way towards our future experiments aimed at assessing the coherence time of a zigzag superposition state through measurements of tunneling oscillations.Laser-cooled ions held in a linear Paul trap with strong transverse confinement organize into a one-dimensional (1-D) linear crystal. If the transverse confinement is relaxed, the linear ion crystal undergoes a continuous, structural phase transition to a 2-D zigzag configuration. We study the dynamics near the critical point of the linear-zigzag transition. In the first part of this thesis, we study the spontaneous nucleation and dynamics of topological kink defects, formed as a result of a rapid quench across the linear-zigzag transition. The experimental results are compared to the Kibble-Zurek mechanism, which provides an intuitive model of defect formation and predicts a power-law scaling for the number of defectsformed as a function of transition quench rate. The second part of this thesis is focused on one of the key requirements for investigations of the near-transition dynamics in the quantum regime. To achieve an efficient ground state cooling of the zigzag vibrational mode, we demonstrate 3-D polarization-gradient cooling of strings of 1-4 trapped ions as an intermediate step between Doppler and sideband cooling, and study the polarization-gradient cooling rate and cooling limit as a function of the cooling beam intensity in and near the Lamb-Dicke regime. The results of this thesis pave the way towards our future experiments aimed at assessing the coherence time of a zigzag superposition state through measurements of tunneling oscillations.

Dec 14, 20150 citations

Thermodynamics and Quantum Correlations in Trapped Ion Crystals

Thaned Pruttivarasin, Michael T. Ramm, Manuel Gessner +1 more

Bulletin of the American Physical SocietyJun 6, 20130 citations

Multiple structural phase transitions in trapped ion Coulomb crystals

Dawei Liu, Ying Jiang, M. T. Song +2 more

Abstract We investigate the structural transitions of ion Coulomb crystals (ICCs) using molecular dynamics simulations, focusing on the effects of ion number and the anisotropy of the confining potential. Our simulations reveal transitions from linear to zigzag to shell formation and dissolution to a two-dimensional plane finally. We characterized the phase transition points, the number of phase transitions. This study provides a more detailed analysis than previous works and establishes a power-law relationship between the critical anisotropy parameter and ion number. Our results offer valuable insights for the precise determination of ICC structure, trapped ion counting, and trapping potential parameters in experimental settings.Abstract We investigate the structural transitions of ion Coulomb crystals (ICCs) using molecular dynamics simulations, focusing on the effects of ion number and the anisotropy of the confining potential. Our simulations reveal transitions from linear to zigzag to shell formation and dissolution to a two-dimensional plane finally. We characterized the phase transition points, the number of phase transitions. This study provides a more detailed analysis than previous works and establishes a power-law relationship between the critical anisotropy parameter and ion number. Our results offer valuable insights for the precise determination of ICC structure, trapped ion counting, and trapping potential parameters in experimental settings.

Journal of Physics B Atomic Molecular and Optical PhysicsSep 2, 20250 citations

Quantum phase transitions in an ion trap

Milburn

Quantum Electronics and Laser Science ConferenceJan 1, 20000 citations

Laser-cooled arrays or crystals of

^{171}\mathrm{Yb}

{}^{+}

ions containing a single impurity,

^{172}\mathrm{Yb}

{}^{+}

isotope, are confined in a linear radio-frequency Paul trap. Site-to-site hopping of the impurity ion, distinguished by a lack of fluorescence, is studied as a function of the

^{171}\mathrm{Yb}

{}^{+}

laser-cooling parameters and as a function of the anisotropy of the trapping potential. Imaging of the independently resolved crystal sites permits the extraction of the impurity's hopping trajectory, from which the dwell times at a given site can be obtained as well as the spatial distribution of hopping rate and hopping destination. The onset of rapid hopping is found to occur at average thermal energies approaching a significant fraction of the Coulomb potential energy. Furthermore, the hopping rate is enhanced at trap anisotropies near the critical value for the structural phase transition to a two-dimensional zigzag phase. Finally, the hopping mobility of the impurity ion is observed to be highest near the center of the crystal, which may have an intrinsic cause related to the crystal structure and dynamics near the zigzag transition.