Tuning heat transport in trapped-ion chains across a structural phase transition

Abstract

We explore heat transport across an ion Coulomb crystal beyond the harmonic regime by tuning it across the structural phase transition between the linear and zigzag configurations. This demonstrates that the control of the spatial ion distribution by varying the trapping frequencies renders ion Coulomb crystals an ideal test-bed to study heat transport properties in finite open system of tunable non-linearities. 64.60.Ht, 05.70.Fh, 37.10.Ty Ultracold ion Coulomb crystals represent one of the most promising platforms for the simulation of many-body physics thanks to the high degree of spatial and temporal control of mesoscopic ion crystals they afford us with [1][2][3]. Recent years have seen a shift away from the study of ground and thermal state properties, towards the exploration of the potential role of ion traps as a test-bed for models of nonequilibrium statistical mechanics.In this context it is important to recognize that in addition to the electronic spin degrees of freedom trapped ions also possess motional degrees of freedom that can exhibit highly non-trivial static and dynamical properties including classical and quantum phase transitions. Indeed, ion Coulomb crystals confined in ion traps may support a wide variety of phases including a linear chain and a doubly-degenerate zigzag phase, extending further to increasingly complex configurations in two and three spatial dimensions [4][5][6]. The associated structural phase transitions between those configurations are generally of first order, with the exception of the linear-to-zigzag phase transition which is known to be of second order [7][8][9]. As a symmetry breaking scenario, it provides a natural testing ground for universal dynamics of phase transitions and topological defect formation [9][10][11][12], recently explored in the laboratory [13][14][15][16].Another fundamental setting in non-equilibrium statistical mechanics considers the thermal transport in low-dimensional systems, which exhibits a rich variety of anomalous features, including the breakdown of Fourier's law of heat conduction, instances in which sub-diffusive and super-diffusive behavior can be observed [17][18][19], as well as the divergence of the thermal conductivity with the system size [20,21]. Most rigorous theoretical results have been obtained for exactly solvable quasi-free models while systems with non-linearities are typically exceedingly difficult to treat. Equally, the controlled generation of non-linear physics in mesoscopic ion crystals is non-trivial and much recent progress has concerned harmonic models of complex networks and trapped-ion chains [22][23][24]. The richest phenomenology however can be expected in nonintegrable models [25] which mandates the development of both theoretical and experimental methods for their examination.In this Letter, we advance further the case for trapped ions as a model system for the examination of challenging problems in mesoscopic physics by considering continuously driven ion chains between two thermal reservoirs as a plat...

Crossover between different universality classes: Scaling for thermal transport in one dimension

“…For example, in virtue of the DW systems, one may be able to vary the phonons spectrum by tuning system temperatures, and finally manipulate heat. Such an idea would be realized by variation of the trapping frequencies in the recent focused ion chains [55], where a structural phase transition very similar to the DW systems has been found [56].…”

Formation of helical ion chains

“…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].…”

Asymmetric heat transport in ion crystals

“…The γ n are friction coefficients and ξ n (t) are uncorrelated Gaussian noise forces satisfying ξ n (t) = 0 and ξ n (t)ξ m (t ′ ) = 2D n δ nm δ(t − t ′ ), D n being the diffusion coefficients. These Gaussian forces are formally the time derivatives of independent Wiener processes (Brownian motions) ξ n (t) = √ 2D n dWn dt [32,40] and Eq. (3) is a stochastic differential equation (SDE) in the Stratonovich sense [40].…”

“…[ [31][32][33][34] and interesting phenomena like phase transitions have been investigated [31][32][33]. The idea of using locallycontrolled traps is already mentioned in [31] to implement disorder and study its effects.…”