Abstract
We propose a method for the fast generation of a quantum register of addressable qubits consisting of ultracold atoms stored in an optical lattice. Starting with a half filled lattice we remove every second lattice barrier by adiabatically switching on a superlattice potential which leads to a long wavelength lattice in the Mott insulator state with unit filling. The larger periodicity of the resulting lattice could make individual addressing of the atoms via an external laser feasible. We develop a Bose-Hubbard-like model for describing the dynamics of cold atoms in a lattice when doubling the lattice periodicity via the addition of a superlattice potential. The dynamics of the transition from a half filled to a commensurately filled lattice is analysed numerically with the help of the time evolving block decimation algorithm and analytically using the Kibble–Zurek theory. We show that the timescale for the whole process, i.e. creating the half filled lattice and subsequent doubling of the lattice periodicity, is significantly faster than adiabatic direct quantum-freezing of a superfluid into a Mott insulator for large lattice periods. Our method therefore provides a high-fidelity quantum register of addressable qubits on a fast timescale.
Highlights
1 2 x|a x| a x|a a short initialization time—and filling factor n = 1/2 we remove every second potential barrier by adiabatically turning on a superlattice
Since the tunnelling time in the large lattice limit is two orders of magnitude larger than in the small lattice limit, the total time required to initialize a MI state using our procedure is an order of magnitude faster than the direct quantum-freezing method
We have shown that the dynamics of an optical lattice whose periodicity is doubled via superlattice potentials is very well described by a two-mode Hubbard-like Hamiltonian
Summary
Inserting the approximate field operator equation (4) into the first term of equation (3) yields the single-particle part of the Hamiltonian in terms of ai† and bi†. Note that hopping between modes a and b within one site is not allowed by the symmetry properties of the GWFs. the inclusion of nonzero hopping matrix elements Jab and Jba is essential to accurately reproduce the single particle behaviour of the full Hamiltonian (3). By combining the mode functions shown in (b), we can construct two new mode functions corresponding to particles localized in either the left (c) or the right (d) well of a given site. The numerical values of Vα and Jα,β for V0 = 30ER are shown in figure 4(a) Using these parameters, we find that H 0(s) very accurately reproduces the band structure of the exact Hamiltonian for all values of s, justifying the utilization of the TB approximation and the corresponding GWFs
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