Thermoelectricity of cold ions in optical lattices

Abstract

We study analytically and numerically the thermoelectric properties of cold ions placed in an optical lattice. Our results show that the transition from sliding to pinned phase takes place at a certain critical amplitude of lattice potential being similar to the Aubry transition for the Frenkel-Kontorova model. We show that this critical amplitude is proportional to the cube of ion density that allows to perform experimental realization of this system at moderate lattice amplitudes. We show that the Aubry phase is characterized by the dimensionless Seebeck coefficient about 50 and the figure of merit being around 8. We propose possible experimental investigations of such system with cold ions and argue that the experiments with electrons on liquid helium surface can also help to understand its unusual properties. The obtained results represent also a challenge for modern methods of quantum chemistry and material science. arXiv:1901.09588v1 [cond-mat.quant-gas]

Properties of phonon modes of an ion-trap quantum computer in the Aubry phase

“…where the effective momentum p i = 1/(x i −x i−1 ) 2 is conjugated to x i and the kick function is g(x) = − sin x − (ω 2 /K)x. In [19,27], it is shown that this map (2) describes well the actual equilibrium ion positions even when all interactions between ions are taken into account. Let us define the average ion density ν = N/L where L is the number of spatial periods of the optical lattice.…”

“…Examples of ion positions for KAM and Aubry phases are given in Appendix Figs. A1, A2 (see also [19,27]). The phase space of the map (2) and the equilibrium ion positions are shown in Appendix tions near the equilibrium positions and then the phonon spectrum and eigenmodes are obtained by matrix diagonalization.…”

“…. , N [19,24,27]. In the nearest neighbor approximation for interacting ions, these conditions lead to the symplectic map giving the recurrence relation of equilibrium ion positions x i…”

“…The equilibrium ion positions are obtained numerically by the gradient method [24] and/or by the Metropolis algorithm described and already used in [19,26,27]. The main minimization procedure starts from the ground state configuration at K = 0 with subsequent step by step increase of K followed by energy minimization at each K (see also discussion below).…”

“…However, when the optical lattice amplitude K exceeds a certain critical value K c , the chain enters in the Aubry pinned phase with the appearance of an excitation gap ω g which is independent of the chain length and of the number of ions. The main properties of this charge system are described in [18,19,26,27]. However, these studies mainly addressed the transport properties of charges, while for the analysis of the robustness of the quantum gates it is necessary to understand the properties of phonon excitations of the ion chain and its response to the recoil momentum transfer from the laser pulses acting on internal ion states.…”