Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.

arXiv:1206.4772Physical Review LettersOct 15, 2012181 citations

Quantum state manipulation with trapped ions

Q. A. Turchette, B. E. King, Christopher J. Myatt +6 more

APSApr 1, 19980 citations

Energy-level structure of ion cloud and crystal in a linear Paul trap

Wei Wen, Wei Dong Wu, Yan‐Li Zhou +2 more

Ion cloud and crystal are recognized as two distinct states in ion traps, but there is no theory that can describe the energy-level structures of these two states from the perspective of quantum theory. In this paper, we construct a model describing ions in a linear Paul trap to investigate the energy-level structure with the linear response function, which is often used in the field of condensed matter to compute the energy-level of electrons or plasmas. We support a method to calculate the energy-level of both the crystal and cloudy states of trapped ions in a linear Paul trap. Furthermore, we present the energy-level diagram of two trapped ions and give a quantum interpretation for the fluorescence hysteresis loops that were observed in our laboratory. This is a fundamental theory that will help us to understand the crystallization and cooling processes of ions in a linear Paul trap.Ion cloud and crystal are recognized as two distinct states in ion traps, but there is no theory that can describe the energy-level structures of these two states from the perspective of quantum theory. In this paper, we construct a model describing ions in a linear Paul trap to investigate the energy-level structure with the linear response function, which is often used in the field of condensed matter to compute the energy-level of electrons or plasmas. We support a method to calculate the energy-level of both the crystal and cloudy states of trapped ions in a linear Paul trap. Furthermore, we present the energy-level diagram of two trapped ions and give a quantum interpretation for the fluorescence hysteresis loops that were observed in our laboratory. This is a fundamental theory that will help us to understand the crystallization and cooling processes of ions in a linear Paul trap.

New Journal of PhysicsAug 26, 20140 citations

Crystallization of Ca+ ions in a linear rf octupole ion trap

K. Okada, Kazuhiro Yasuda, Toshinobu Takayanagi +3 more

A laser-cooling experiment with ${\mathrm{Ca}}^{+}$ ions trapped in a linear rf octupole ion trap is presented. The phase transition of the laser-cooled ${\mathrm{Ca}}^{+}$ ions from the cloud to the crystal state is observed by an abrupt dip of the laser-induced fluorescence spectrum and indicates that mK temperatures are obtained. We have also performed molecular dynamics simulations under various conditions to confirm this property by deducing axially symmetric structures of Coulomb crystals and by evaluating the translational temperatures of the laser-cooled ions. The simulation results show that for small numbers of ions novel ring-shaped crystals are produced. As the number of ions is increased, cylindrical layers in the ring crystal are sequentially formed. For more than 100 ions, also hexagonal and spiral structures emerge in parts of the large-size ion crystal, which has a length on the order of millimeters for the present geometrical arrangement and voltages. An advantage of the linear rf octupole trap is its large almost-field-free region in the middle of the trap, where the micromotion amplitude is small for trapped ions. These results demonstrate that such a multipole trap has attractive features for quantum computing and ultracold ion-atom collision studies.A laser-cooling experiment with ${\mathrm{Ca}}^{+}$ ions trapped in a linear rf octupole ion trap is presented. The phase transition of the laser-cooled ${\mathrm{Ca}}^{+}$ ions from the cloud to the crystal state is observed by an abrupt dip of the laser-induced fluorescence spectrum and indicates that mK temperatures are obtained. We have also performed molecular dynamics simulations under various conditions to confirm this property by deducing axially symmetric structures of Coulomb crystals and by evaluating the translational temperatures of the laser-cooled ions. The simulation results show that for small numbers of ions novel ring-shaped crystals are produced. As the number of ions is increased, cylindrical layers in the ring crystal are sequentially formed. For more than 100 ions, also hexagonal and spiral structures emerge in parts of the large-size ion crystal, which has a length on the order of millimeters for the present geometrical arrangement and voltages. An advantage of the linear rf octupole trap is its large almost-field-free region in the middle of the trap, where the micromotion amplitude is small for trapped ions. These results demonstrate that such a multipole trap has attractive features for quantum computing and ultracold ion-atom collision studies.

Physical Review AMar 22, 200752 citations

Quantum Engineering with Trapped Ions

J. F. Poyatos, S. A. Gardiner, R. Walser +3 more

Springer eBooksJan 1, 19971 citation

A laser-cooling experiment with

{\mathrm{Ca}}^{+}

ions trapped in a linear rf octupole ion trap is presented. The phase transition of the laser-cooled

{\mathrm{Ca}}^{+}

ions from the cloud to the crystal state is observed by an abrupt dip of the laser-induced fluorescence spectrum and indicates that mK temperatures are obtained. We have also performed molecular dynamics simulations under various conditions to confirm this property by deducing axially symmetric structures of Coulomb crystals and by evaluating the translational temperatures of the laser-cooled ions. The simulation results show that for small numbers of ions novel ring-shaped crystals are produced. As the number of ions is increased, cylindrical layers in the ring crystal are sequentially formed. For more than 100 ions, also hexagonal and spiral structures emerge in parts of the large-size ion crystal, which has a length on the order of millimeters for the present geometrical arrangement and voltages. An advantage of the linear rf octupole trap is its large almost-field-free region in the middle of the trap, where the micromotion amplitude is small for trapped ions. These results demonstrate that such a multipole trap has attractive features for quantum computing and ultracold ion-atom collision studies.