Optically induced structural phase transitions in ion Coulomb crystals

We investigate numerically the structural dynamics of ion Coulomb crystals confined in a three-dimensional harmonic trap when influenced by an additional one-dimensional optically induced periodical potential. We demonstrate that transitions between thermally excited crystal structures, such as body-centered cubic and face-centered cubic, can be suppressed by a proper choice of the potential depth and periodicity. Furthermore, by varying the harmonic trap parameters and/or the optical potential in time, controlled transitions between crystal structures can be obtained with close to unit efficiency.

Figure 1

(a) Projection image of an ion Coulomb crystal composed of $N=1000$ ions in a trap with ${\nu }_r=200$ kHz and ${\nu }_z=100$ kHz with a fcc crystalline core of 125 ions (larger red dots). (b) Time evolution of the fits with fcc (solid line) and bcc (dashed line) crystal structures for initialization with a fcc core and the fit with bcc (dash-dotted line) and fcc (dotted line) structures for a bcc initial core, without an optical potential. The average is taken over 32 simulations. (c) Evolution of a single sample realization with an initial fcc core.

Figure 2

Average number of fcc ions (out of 64 core ions) after 10 ms of propagation versus dipole potential depths. The initial state has an ideal fcc core. The solid line and circles show the trap as in Fig. 1, with the crystal aligned with the [011] axis along $z$, and $\Lambda =13.0\mu$m; the dashed line and triangles show the spherical trap with ${\nu }_r={\nu }_z=150$ kHz, the [001] axis along $z$, and $\Lambda =20.1\mu$m; the dash-dotted line and stars show the spherical trap, the [111] axis along $z$, and $\Lambda =23.2\mu$m. The inset shows the corresponding average rms fit deviation. In all cases the stationary temperature is 0.5 mK (dotted line).

Figure 3

Schematic of crystal structure transformation from fcc to bcc along the Bain path using a fixed optical potential. (a) Two fcc unit cells (center face ions removed at front and at back for clarity). Shaded planes indicate standing-wave potential minima. (b) After a uniform expansion in the transverse directions (density reduced by a factor of 2) a bcc unit cell is obtained (red solid lines).

Figure 4

Continuous switching of ion Coulomb structures by varying the trap frequencies ${\nu }_r$ and ${\nu }_z$ with a fixed optical potential ($V_0=10$ mK). (a) Time dependence of ${\nu }_r$ (solid) and ${\nu }_z$ (dashed) for switching of fcc to bcc (bottom curves) and bcc to fcc (top curves). (b) Corresponding fraction of core ions (out of 64) in a fcc configuration.