It is well known that ions stored in a Paul trap, one of the most versatile tools in atomic, molecular, and optical (AMO) physics, may undergo a transition from a disordered cloud state to a geometrically well-ordered crystalline state, the Wigner crystal. In this paper we predict that close to the transition, the average lifetime ${\overline{\ensuremath{\tau}}}_{m}$ of the metastable cloud follows a power law, ${\overline{\ensuremath{\tau}}}_{m}\ensuremath{\sim}{(\ensuremath{\gamma}\ensuremath{-}{\ensuremath{\gamma}}_{c})}^{\ensuremath{-}\ensuremath{\beta}}$, where ${\ensuremath{\gamma}}_{c}$ is the value of the damping constant at which the transition occurs. The exponent $\ensuremath{\beta}$ depends on the trap control parameter $q$ , but is independent of both the number of particles $N$ stored in the trap and the trap control parameter $a$ , which determines the shape (oblate, prolate, or spherical) of the ion cloud. In addition, we find that for given $a$ and $q, {\ensuremath{\gamma}}_{c}$ scales approximately like ${\ensuremath{\gamma}}_{c}=Cln[ln(N)]+D$ as a function of $N$ , where $C$ and $D$ are constants. Our predictions may be tested experimentally with equipment already available at many AMO laboratories. In addition to their importance in AMO trap physics, we also discuss possible applications of our results to other periodically driven many-particle systems, such as, e.g., particle accelerator beams, and, based on our trap results, conjecture that power laws characterize the phase transition to the Wigner crystal in all such systems.It is well known that ions stored in a Paul trap, one of the most versatile tools in atomic, molecular, and optical (AMO) physics, may undergo a transition from a disordered cloud state to a geometrically well-ordered crystalline state, the Wigner crystal. In this paper we predict that close to the transition, the average lifetime ${\overline{\ensuremath{\tau}}}_{m}$ of the metastable cloud follows a power law, ${\overline{\ensuremath{\tau}}}_{m}\ensuremath{\sim}{(\ensuremath{\gamma}\ensuremath{-}{\ensuremath{\gamma}}_{c})}^{\ensuremath{-}\ensuremath{\beta}}$, where ${\ensuremath{\gamma}}_{c}$ is the value of the damping constant at which the transition occurs. The exponent $\ensuremath{\beta}$ depends on the trap control parameter $q$, but is independent of both the number of particles $N$ stored in the trap and the trap control parameter $a$, which determines the shape (oblate, prolate, or spherical) of the ion cloud. In addition, we find that for given $a$ and $q, {\ensuremath{\gamma}}_{c}$ scales approximately like ${\ensuremath{\gamma}}_{c}=Cln[ln(N)]+D$ as a function of $N$, where $C$ and $D$ are constants. Our predictions may be tested experimentally with equipment already available at many AMO laboratories. In addition to their importance in AMO trap physics, we also discuss possible applications of our results to other periodically driven many-particle systems, such as, e.g., particle accelerator beams, and, based on our trap results, conjecture that power laws characterize the phase transition to the Wigner crystal in all such systems.

arXiv:1512.02534Physical Review AApr 27, 20165 citations

Critical Phenomena and Phase Transitions

John F. Nagle

Springer eBooksJan 1, 197528 citations

Universal heating curve of damped Coulomb plasmas in a Paul trap

J. D. Tarnas, Yunseong Nam, R. Blümel

A charged-particle cloud in a Paul trap is a nonlinear system that exhibits deterministic heating, i.e., conversion of energy provided by the radio-frequency (rf) drive of the trap into the disordered, gaslike motions of the trapped particles. In the presence of weak damping clouds reach an equilibrium state in which heating and cooling balance. For large damping, a cloud may collapse into a crystal. While the rf heating power of a given cloud depends sensitively on its particle number, its equilibrium size, the damping, and the control parameters of the trap, we find that scaling the heating power of the cloud with respect to its associated Coulomb-decoupled, non-interacting-gas state, and its equilibrium size with respect to its crystal size, results in a single, universal heating curve, independent of particle number and trap control parameters.A charged-particle cloud in a Paul trap is a nonlinear system that exhibits deterministic heating, i.e., conversion of energy provided by the radio-frequency (rf) drive of the trap into the disordered, gaslike motions of the trapped particles. In the presence of weak damping clouds reach an equilibrium state in which heating and cooling balance. For large damping, a cloud may collapse into a crystal. While the rf heating power of a given cloud depends sensitively on its particle number, its equilibrium size, the damping, and the control parameters of the trap, we find that scaling the heating power of the cloud with respect to its associated Coulomb-decoupled, non-interacting-gas state, and its equilibrium size with respect to its crystal size, results in a single, universal heating curve, independent of particle number and trap control parameters.

Physical Review AOct 4, 201312 citations

Elements of Phase Transitions and Critical Phenomena

秀稔西森, Hidetoshi Nishimori, Gerardo Ortíz

Jan 1, 20110 citations

Universal critical phenomena of the cloud

\rightarrow

crystal phase transition in the Paul trap: Powerlaws

q

, but is independent of both the number of particles

N

stored in the trap and the trap control parameter

a

, which determines the shape (oblate, prolate, or spherical) of the ion cloud. In addition, we find that for given

a

and $q, {\ensuremath{\gamma}}_{c}$ scales approximately like ${\ensuremath{\gamma}}_{c}=Cln[ln(N)]+D$ as a function of

N

, where

C

and

D

are constants. Our predictions may be tested experimentally with equipment already available at many AMO laboratories. In addition to their importance in AMO trap physics, we also discuss possible applications of our results to other periodically driven many-particle systems, such as, e.g., particle accelerator beams, and, based on our trap results, conjecture that power laws characterize the phase transition to the Wigner crystal in all such systems.