Conditions for formation and trapping of the two-ion Coulomb cluster in the dissipative optical superlattice

Abstract

Conditions have been studied under which a polychromatic optical superlattice can form and trap the Coulomb cluster of two strongly interacting ions. In our previous work (Krasnov I V and Kamenshchikov L P 2014 Opt. Comm. 312 192) this new all-optical method of obtaining and confining the Coulomb clusters was demonstrated by numerical simulations for special values of the optical superlattice parameters and in the case of Yb ions. In the present paper the conditions are explicitly formulated, under which the long-lived two-ion cluster in the superlattice cell is formed. The peculiarity of these conditions is the renormalization of the ion-ion Coulomb interaction. Notably, the renormalized Coulomb force is determined by the effective charge which depends on the light field parameters and can strongly differ from the "bare" ion charge. This result can be accounted for by the combined manifestation of the quantum fluctuations of optical forces, nonlinear dependence of these forces on the velocity, and non-Maxwellian (Tsallis type) velocity distribution of the ions in the optical superlattice. Explicit analytical formulas are also obtained for the parameters of the optical two-ion cluster.

The internal energy expression of a long-range interaction complex system and its statistical physical properties

“…Du [22] found that the q-exponential of a sum can be applied as the product of the q-exponential based on the probabilistically independent postulate employed in nonextensive statistical mechanics. Krasnov [23] also found q-exponential type velocity distribution of the ions in the optical superlattice. Chen et al [24] presented a new method based on the q-exponential distribution to suppress the noise and increase the accuracy of feature extraction for ultrasonic Lamb wave signals.…”

Ion Coulomb crystal in a polychromatic optical superlattice

“…The detailed discussion of equations ( 2) and ( 3) and physical sense of different terms of this equation is included into [14][15][16]. Here, we only note some key factors important for understanding the results of our simulations.…”

“…The parameter ζ = s 0 /ω R L (the analogue of the Knudsen number of problem [16]) is small, therefore, the particle motion is overdamped [14,15].…”

“…In our previous papers [13][14][15] another method for alloptical ion trapping, the confinement of ions in a three-dimensional (3D) dissipative polychromatic optical superlattice (OSL) of deep potential wells [16,17], was proposed and investigated. We proved that such an OSL is able to form twoand three-ion clusters (consisting of strongly coupled ions of ytterbium, 171 Yb + ) and to confine them for the time varying from several seconds to several tens of seconds, depending on the period of OSL (1.5-3 mm).…”

“…We proved that such an OSL is able to form twoand three-ion clusters (consisting of strongly coupled ions of ytterbium, 171 Yb + ) and to confine them for the time varying from several seconds to several tens of seconds, depending on the period of OSL (1.5-3 mm). It is also shown that the formation of long-lived two-ion Coulomb clusters is only possible if the depth of the potential wells of OSL is sufficiently large as compared with the cluster Coulomb energy [15]. However, beforehand it is not obvious that this method is applicable for the creation and rather long confinement of the many-ion Coulomb cluster since the total Coulomb energy U c of such a cluster increases considerably with the increasing ion number N 1 (e.g.…”