We investigate a new type of quantum ratchet which may be realised by cold atoms in a double-well optical lattice which is pulsed with unequal periods.
The classical dynamics is chaotic and we find the classical diffusion rate $D$ is asymmetric in momentum up to a finite time $t_r$.
The quantum behaviour produces a corresponding asymmetry in the momentum distribution which is 'frozen-in' by Dynamical Localisation provided the break-time $t^* > t_r$. We conclude that the cold atom ratchets require $Db/ \hbar \sim 1$ where b is a small deviation from period-one pulses.
We report on a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. Each step of the walk consists of a coin toss (a microwave pulse) followed by a unitary shift operator (a resonant ratchet pulse). We carry out a comprehensive experimental study on the effects of various parameters, including the strength of the shift operation, coin parameters, noise, and initialization of the system on the behavior of the walk. The walk dynamics can be well controlled in our experiment; potential app…
We consider classical dynamics of a 1D system of $N$ particles bouncing on an oscillating mirror in the presence of gravitational field. The particles behave like hard balls and they are resonantly driven by the mirror. We identify the manifolds the particles move on and derive the effective secular Hamiltonian for resonant motion of the particles. Proper choice of time periodic oscillations of the mirror allows for engineering of the effective behaviour of the particles. In particular, the system can behave like a $N$-dimensional fictitious particle moving in an $N$-dimensional crystalline st…
Cold atoms in an optical lattice provide an ideal platform for studying Bloch oscillations. Here, we extend Bloch oscillations to two superposed optical lattices that are accelerated away from one another, and for the first time show that these symmetric Bloch oscillations can split, reflect and recombine matter waves coherently. Using the momentum parity-symmetry of the Hamiltonian, we map out the energy band structure of the process and show that superpositions of momentum states are created by adiabatically following the ground state of the Hamiltonian. The relative phase and velocity of th…
We use quantum and classical adiabatic capture theories to study the chemical reaction Li + CaH -> LiH + Ca. Using a recently developed ab initio potential energy surface, which provides an accurate representation of long-range interactions in the entrance reaction channel, we calculate the adiabatic channel potentials by diagonalizing the atom-molecule Hamiltonian as a function of the atom-molecule separation. The resulting adiabatic channel potentials are used to calculate both the classical and quantum capture probabilities as a function of collision energy, as well as the temperature depen…
We propose an analog quantum simulator for simulating real time dynamics of $(1+1)$-d non-Abelian gauge theory well within the existing capacity of ultracold atom experiments. The scheme calls for the realization of a two-state ultracold fermionic system in a 1-dimensional bipartite lattice, and the observation of subsequent tunneling dynamics. Being based on novel loop string hadron formalism of SU(2) lattice gauge theory, this simulation technique is completely SU(2) invariant and simulates accurate dynamics of physical phenomena such as string breaking and/or pair production. The scheme is …
We show that the integral cross sections for state-to-state quantum scattering of cold molecules in a magnetic field can be efficiently computed using the total angular momentum representation despite the presence of unphysical Zeeman states in the eigenspectrum of the asymptotic Hamiltonian. We demonstrate that the unphysical states arise due to the incompleteness of the space-fixed total angular momentum basis caused by using a fixed cutoff value $J_\text{max}$ for the total angular momentum of the collision complex $J$. As a result, certain orbital angular momentum ($l$) basis states lack t…
