Abstract:
We propose a mechanism for perfect entanglement transport in anti-ferromagnetic (AFM) quantum spin chain systems with modulated exchange coupling and also for the modulation of on-site magnetic field. We use the principle of adiabatic quantum pumping process for entanglement transfer in the spin chain systems. We achieve the perfect entanglement transfer over an arbitrarily long distance and a better entanglement transport for longer AFM spin chain system than for the ferromagnetic one. We explain analytically and physically—why the entanglement hops in alternate sites. We find the condition for blocking of entanglement transport even in the perfect pumping situation. Our analytical solution interconnects quantum many body physics and quantum information science.

Abstract:
We propose a mechanism for perfect entanglement transport in anti-ferromagnetic (AFM) quantum spin chain systems with modulated exchange coupling along the xy plane and in the z direction. We use the principle of adiabatic quantum pumping process for entanglement transfer in the spin chain systems. In our proposed mechanism, perfect entanglement transfer can be achieved over an arbitraly long distance. We explain analytically and physically why the entanglement hops in alternate sites. We solve this problem by using the Berry phase analysis and Abelian bosonization methods. We find the condition for blocking of entanglement transport even in the perfect pumping condition. We also explain physically why entanglement transfer in AFM chain out performs the ferromagnetic chain. Our analytical solution interconnects quantum many body physics and quantum information science.

Abstract:
We present a study of adiabatic Cooper pair pumping in one dimensional array of Cooper pair boxes. We do a detailed theoretical analysis of an experimentally realizable stabilized charge pumping scheme in a linear array of Cooper pair boxes. Our system is subjected to synchronized flux and voltage fields and travel along a loop which encloses their critical ground state of the system in the flux-voltage plane. The locking potential in the sine-Gordon model slides and changes its minimum which yields the Cooper pair pumping. Our analytical methods are the Berry phase analysis and Abelian bosonization studies.

Abstract:
We study the dissipation physics of one dimensional mesoscopic superconducting quantum interference device array by using the field-theoretical renormalization group method. We observe length scale dependent superconductor-insulator quantum phase transition at very low temperature and also observe the dual behaviour of the system for the higher and lower values of magnetic field. At a critical magnetic field, we also observe a critical behaviour where the resistance is independent of length.

Abstract:
We present the study of Kondo effect in an interacting quantum wire. We mainly emphasis the effect of strong electronic correlations in the study of renormalization group flow diagram and the stability analysis of fixed points for both magnetic and nonmagnetic impurities. We observe that the behavior of the system is either in the single channel or in the two channel Kondo effect depending on the initial values of coupling constants and strong correlations.

Abstract:
We present the renormalization group (RG) flow diagram of a spin-half antiferromagnetic chain with magnetic impurity and one altered link. In this two parameters (competing interactions) model, one can find the complex phase diagram with many interesting fixed points. There is no evidence of intermediate stable fixed point in weak coupling phase. It may arise at the strong coupling phase. Depending on the strength of couplings the phases correspond either to a decoupled spin with Curie law behavior or a logarithmically diverging impurity susceptibility as in the two channel Kondo problem.

Abstract:
We present the quantum phase transition in two capacitively coupled arrays of superconducting quantum dots (SQD). We consider the presence of gate voltage in each superconducting island. We show explicitly that the co-tunneling process involves with two coupled SQD arrays, near the maximum charge frustration line is not sufficient to explain the correct quantum phases with physically consistent phase boundaries. We consider another extra co-tunneling process along each chain to explain the correct quantum phases with physically consistent phase boundaries. There is no evidence of supersolid phase in our study. We use Bethe-ansatz and Abelian bosonization method to solve the problem

Abstract:
We calculate the tunnelling resistance at the quantum critical point of a mesoscopic SQUIDs array in the presence of magnetic flux. We find the analytical relation between the magnetic flux induced dissipation strength and the Luttinger liquid parameter of the system. While the experimental finding for the system is around 40-50 mK, we find the behavior of the system even at lower temperatures through the analysis of renormalization group. Apart from the length scale dependent superconductor-insulator transition, we also predict the evidence of length scale independent metallic state. This study also emphasizes the importance of Co-tunelling effect.

Abstract:
We study clean superconducting quantum dots (SQD) and also site dependent Josephson couplings, on site charging energies and the intersite interactions in presence of gate voltage. We predict the existence of different fractionally quantized Cooper pair stair case with many interesting physical properties. The appearance of stair case is not only due to the Coulomb blocked phenomena but also for the site dependent Josephson couplings. We also explain physically the absence of other fractionally quantized Cooper pair stair case. The physics of fractionally quantized Cooper pair stair case has close resemblance with the fractionally quantized magnetization plateau of a spin chain system under a magnetic field.

Abstract:
We study the entanglement of a two-qubit system in a superconducting quantum dot (SQD) lattice in the presence of magnetic flux and gate voltage inhomogeneity. We observe a universal feature for the half-integer magnetic flux quantum which completely washes out the entanglement of the system both at zero and finite temperature. We observe that the ground state is always in a maximally entangled Bell state when there is no inhomogeneity in gate voltage in the superconducting quantum dot lattice. We find an important constraint in magnetic flux for ground state entanglement. We also observe few behavior of entanglement at finite temperature is in contrast with the zero temperature behavior.