M. Mukherjee

Interfacing ion qubits in separate traps is among the challenges towards scaling up ion quantum computing. This theoretical study focuses on using a conducting wire to couple the motional quantum states of ions in separate planar traps. This approach of interfacing ion traps provides an alternative to coupling distant qubits with lasers. We include the effects of $1/f^{\tildeα}$ (Anomalous) surface heating noise, using aggregate and recent experimental findings as the basis for an analytical model of the motional state decoherence time $t_{\mathrm{deco.}}$. Our optimized design for the coupling system can be used to exchange quantum information with a time $t_{\mathrm{ex.}}$ less than one tenth of the information decay time $t_{\mathrm{deco.}}$. We derive a coefficient $ζ$ which relates the capacitances of each part of the coupling system and corrects an oversight common to several previous works. Where possible, we calculate the classical signal strength and classical noise strength, and use the criterion (classical) signal-to-noise-ratio $\ge 10$ to further constrain design parameters. Ranges for all parameters are discussed, and the ratio $t_{\mathrm{deco.}} /t_{\mathrm{ex.}}$ and the signal-to-noise ratio for thermal noise are plotted to assess specific parameter ranges for which transfer of quantum information is possible. Although $1/f^{\tildeα}$ surface noise significantly constrains parameter ranges, we find no barriers to exchanging quantum information between ion qubits in separate surface traps using a conducting wire. Moreover, this should be possible using existing technologies and materials, and singly-charged ions.

In a Radio-Frequency linear ion trap, 1D ion chains are routinely generated in laboratories around the world. They present a non-homogenous ion density along the chain. The possibility of generating uniformly distributed ion chain, where the distance between any adjacent ions is a constant, would open up new type of experiments in the context of Quantum Information and in the study of the Homogeneous Kibble-Zurek mechanism.

An equally spaced linear chain of ions provides a test-bed for studying the defect formation in a finite size 1D system. In particular, defect formation related to topological phase transition from a linear configuration to a zig-zag one is of interest here. A semi-empirical expression provides an excellent agreement to the numerical results. The non-adiabatic transition between the chain and zig-zag topologies for a finite size system of 30 ions shows clear distinction from non-uniformly distributed ion chain. Thus the underlying Homogeneous Kibble-Zurek model can be tested in presently accessible ion trap experiments. Furthermore, our study indicates collective defect behaviour appearing through the correlation length measurements.

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.

A linear ion trap setup has been developed for studying the dynamics of trapped ion cloud and thereby realizing possible systematics of a high precision measurement on a single ion within it. The dynamics of molecular nitrogen ion cloud has been investigated to extract the characteristics of the trap setup. The stability of trap operation has been studied with observation of narrow nonlinear resonances pointing out the region of instabilities within the broad stability region. The secular frequency has been measured and the motional spectra of trapped ion oscillation have been obtained by using electric dipole excitation. It is applied to study the space charge effect and the axial coupling in the radial plane.

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.

In this work, we propose a new design of an ion trap which can enable us to generate state specific Berry phase in a single trapped ion. Such a design will enable us to study the physics at the boundary of abelian and non-abelian symmetries and can also have significant impact in quantum computation.

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.

We have estimated the size of the light-shifts due to parity nonconservation (PNC) interactions in different isotopes of Ba+ and Ra+ ions based on the work of Fortson [Phys. Rev. Lett. 70, 2383 (1993)]. We have used the nuclear spin independent (NSI) amplitudes calculated earlier by us [Phys. Rev. Lett. 96, 163003 (2006); Phys. Rev. A 78, 050501(R) (2008)] and we have employed the third order many-body perturbation theory (MBPT(3)) in this work to estimate the nuclear spin dependent (NSD) amplitudes in these ions. Ra+ is found to be more favourable than Ba+ for measuring both the NSI and NSD PNC observables.

In many applications of the simple three-element einzel lens, such as injecting a low energy ion beam into a high-field Penning trap, there is a need for small-angle steering as well as focusing of the beam. We have analyzed a diagonalslit cylinder serving as the middle electrode of such a lens and have shown that such an electrode configuration significantly diminishes the aberration associated with such a deflection.

Single trapped and laser cooled Radium ion as a possible candidate for measuring the parity violation induced frequency shift has been discussed here. Even though the technique to be used is similar to that proposed by Fortson [1], Radium has its own advantages and disadvantages. The most attractive part of Radium ion as compared to that of Barium ion is its mass which comes along with added complexity of instability as well as other issues which are discussed here