T. Dutta

Precision atomic spectroscopy is presently the work horse in quantum information technology, metrology, trace analysis and even for fundamental tests in physics. Stable lasers are inherent part of precision spectroscopy which in turn requires absolute wavelength markers suitably placed corresponding to the atomic species being probed. Here we present, new lines of tellurium (Te$_2$) which allows locking of external cavity diode laser (ECDL) for precision spectroscopy of singly charged barium ions. In addition, we have developed an ECDL with over 100 GHz mod-hop-free tuning range using commercially available diode from $\textit{Nichia}$. These two developments allow nearly drift-free operation of a barium ion trap set-up with one single reference cell thereby reducing the complexity of the experiment.

We develop a theory to address the non-equilibrium dynamics of phonons in a one-dimensional trapped ion system. We elaborate our earlier results obtained in Phys. Rev. Lett. {\bf 111}, 170406 (2013) to chart out the mechanism of dynamics-induced cooling and entanglement generation between phonons in these systems when subjected to a linear ramp protocol inducing site-specific tuning of on-site interactions between the phonons. We further extend these studies to non-linear ramps and periodic drive protocols and identify the optimal ramp protocol for minimal cooling and entanglement generation time. We qualitatively address the effect of noise arising out of fluctuation of the intensity of the laser used to generate entanglement and provide a detailed discussion of a realistic experimental setup which may serve as a test bed for our theory.

The branching fractions from the excited state $6P_{1/2}$ of singly charged barium ion has been measured with a precision $0.05%$ in an ion trap experiment. This measurement along with the known value of the upper state life-time allowed the determination of the dipole matrix elements for the transitions $P-S$ and $P-D$ to below one percent level. Therefore, for the first time it is now possible to compare the many body calculations of these matrix elements at level which is of significance to any parity non-conservation experiment on barium ion. Moreover, these dipole matrix elements are the most significant contributors to the parity violating matrix element between the $S-D$ transition, contributing upto $90%$ to the total. Our results on the dipole matrix elements are $3.306\pm0.014$ and $3.036\pm0.016$ for the $S-P$ and $P-D$ transitions respectively.

The presence of charged particles in an ion trap modifies the harmonic trapping potential in which they are trapped, leading to observed shifts in secular frequency as well as appearance of collective oscillation. In a linear trap geometry, both of these effects have been observed under different trapping conditions using narrow non-linear resonance and external excitation. The observations have been modeled with minimal fitting parameter showing good agreement with results obtained. The space charge in our experiment plays an important role in terms of criticality of the onset of collective oscillation.

We show that the ramp dynamics of phonons in an one-dimensional ion trap can be used for both generating multi-particle entangled states and motional state cooling of a string of trapped ions. We study such ramp dynamics using an effective Bose-Hubbard model which describes these phonons at low energies and show that specific protocols, involving site-specific dynamical tuning of the on-site potential of the model, can be used to generate entangled states and to achieve motional state cooling without involving electronic states of the ions. We compare and contrast our schemes for these to the earlier suggested ones and discuss specific experiments to realize the suggested protocols.

We propose a concrete experiment to probe the non-equilibrium local dynamics of the one-dimensional Bose-Hubbard model using a trapped ion system consisting of a linear chain of few Ba^+ ions prepared in a state of transverse motional mode which corresponds to a fixed number of phonons per ion. These phonons are well-known to be described by an effective Bose-Hubbard model. We propose a protocol which leads to a sudden local sign reversal of the on-site interaction strength of this Hubbard model at one of the sites and demonstrate that the subsequent non-equilibrium dynamics of the model can be experimentally probed by measuring the time-dependent phonon number in a specific motional state of the Ba+ ions. We back our experimental proposal with exact numerical calculation of the dynamics of a Bose-Hubbard model subsequent to a local quench.