Trapped ions in optical lattices for probing oscillator chain models

Abstract

We show that a chain of trapped ions embedded in microtraps generated by an optical lattice can be used to study oscillator models related to dry friction and energy transport. Numerical calculations with realistic experimental parameters demonstrate that both static and dynamic properties of the ion chain change significantly as the optical lattice power is varied. Finally, we lay out an experimental scheme to use the spin degree of freedom to probe the phase space structure and quantum critical behavior of the ion chain.

Formation of helical ion chains

“…The results shown in figure 3a) are in good agreement with the predicted scaling of W 2 ∝ v 1/3 . For an accurate quantification of the scaling behaviour we plot W 2 N 2 v 2/3 versus N 3 v to collapse the three curve as suggested by equation (18). This plot is shown in figure 3b) where indeed the collapse of the curves is clearly visible.…”

“…Apart from the equilibrium studies of the rich structural phase diagram, there is an increasing interest in investigating the nonlinear and nonequilibrium dynamical phenomena by exploiting the various ion crystal structural transitions in a precisely controlled experimental setting. Some examples of the studies of the nonlinear dynamics of ion crystals include the simulation of linear and nonlinear Klein-Gordon fields on a lattice [11], the study of nucleation of topological defects [12][13][14], dynamics of discrete solitons [15,16], dry friction [17][18][19][20], as as well as proposals to realize models related to energy transport [18,21] and synchronization [22]. Even though all of the above experiments and proposals are classical, the high degree of isolation of the ion crystals from the surrounding environment implies also the possibility to enter the regime where quantum mechanical effects must be accounted for to describe critical phenomena [11,[23][24][25] and where the quantum motion can be utilized for quantum information processing using trapped ions [26,27].…”

Sub-micron positioning of trapped ions with respect to the absolute center of a standing-wave cavity field

“…Second, superposing a steep and short-scale periodic optical potential to a shallow rf trap allows studies of structural [20][21][22] and dynamical phase transitions (e.g. Coulomb-Frenkel-Kontorova model [23][24][25][26]40]). As demonstrated in [17], localizing an ion in a standing wave cavity field also allows for a better control of the ion-cavity coupling strength, which can be of interest for quantum information processing applications, such as single-photon generation [41,42], quantum memory [27,28], photon counters [29], single ion-photon interfaces [43,44], or for cavity-mediated cooling [45].…”

Multislip Friction with a Single Ion

“…This has been demonstrated in AFM simulations [19][20][21][22] and experiments [23][24][25] where single-slip and multislip events have been clearly differentiated. However, in the absence of control over dissipation rates and the microscopic energy landscape, it is difficult to tie the observations to ab initio friction models.Following theoretical proposals [26][27][28][29], we have recently demonstrated a trapped-ion friction emulator with extensive control over all microscopic interface parameters [30][31][32]. In analogy to AFM, the emulator features a small probe (one or several trapped ions) transported over a In this Letter, we study multislip friction in deep substrate potentials.…”

“…Following theoretical proposals [26][27][28][29], we have recently demonstrated a trapped-ion friction emulator with extensive control over all microscopic interface parameters [30][31][32]. In analogy to AFM, the emulator features a small probe (one or several trapped ions) transported over a periodic substrate potential created by an optical standing wave [Figs.…”