Fast Coherent Control Of Cold Atoms And Its Applications

Adiabatic processes in quantum mechanics are very useful to prepare and ma-nipulated quantum states but have the drawback of requiring long operation times."Shortcuts to Adiabaticity"(STA)provides a toolbox of methods to improve on adia-batic processes on atom cooling,population transfer,and spin control,et al.Using these methods one can derive alternative processes which work for much shorter times with perfect fidelity.We mainly focus on the fast and robust transport of atom,fric-tionless dynamics of cold atoms and study the applications of quantum interference,quantum thermaldynamics,and quantum information processing.During the three years’ working,I obtained these results which listed as follows,(1)We propose trigonometric protocols for fast and robust atomic transport,tak-ing into account cubic or quartic anharmonicities of the trapping potential.Numeri-cal analysis demonstrates that this choice of the trajectory minimizes the final residual energy efficiently,and shows extraordinary robustness against anharmonic parameters.These results might be of interest for the state-of-the-art experiments on ultracold atoms and ions.(2)We present a novel method for fast transport of Bose-Einstein condensates(BECs)in anharmonic traps and in the presence of atom-atom interactions.By com-bining variational approximation and inverse engineering methods,we derive a set of Ermakov-like equations including the coupling between the center of mass motion and the breathing mode.By an appropriate inverse engineering strategy of those equations,we then design the trap trajectory for the desired boundary conditions.Numerical exam-ples for cubic or quartic anharmonicities are provided for fast and high-fidelity transport of BEC.Such an approach shall have potential applications in atom interferometer and quantum information processing.(3)We propose a method for shortcut to adiabatic control of soliton matter waves in harmonic traps.The tunable interaction controlled by Feshbach resonance is in-versely designed to achieve fast and highfdelity compression of soliton matter waves as compared to the conventional adiabatic compression.These results pave the way to control the nonlinear dynamics for matter waves and optical solitons by using shortcuts to adiabaticity。(4)Motivated by shortcuts to adiabatic expansion/compression of cold atoms in trapping potentials,we investigate the maximum power output of quantum Carnot en-gine in a time-dependent box potential.In addition,a thermodynamic cycle using a Bose-Einstein condensate with nonlinear interactions as the working medium has been investigated.Exploiting Feshbach resonances to change the interaction strength of the BEC allows us to do work by expanding and compressing the gas.To combat this we design a shortcut to adiabaticity which can achieve an effective adiabatic evolution in a finite time,therefore significantly reducing the out-of-equilibrium excitations in the BEC.We investigate the effect of the shortcut to adiabaticity on the efficiency and pow-er output of the engine and show that the strength of the nonlinearity serves a useful tool to enhance the system’s performance.