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arXiv:1407.3212 · Physical Review Letters

High-Fidelity Rapid Ground-State Loading of an Ultracold Gas into an Optical Lattice

Shumpei Masuda, Katsuhiro Nakamura, Adolfo del Campo

Published Aug 7, 2014• 77 citations
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Abstract

A protocol is proposed for the rapid coherent loading of a Bose-Einstein condensate into the ground state of an optical lattice, without residual excitation associated with the breakdown of adiabaticity. The driving potential required to assist the rapid loading is derived using the fast-forward technique, and generates the ground state in any desired short time. We propose an experimentally feasible loading scheme using a bichromatic lattice potential, which approximates the fast-forward driving potential with high fidelity.

DOI
10.1103/physrevlett.113.063003

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A protocol is proposed for the rapid coherent loading of a Bose-Einstein condensate into the ground state of an optical lattice, without residual excitation associated with the breakdown of adiabaticity. The driving potential required to assist the rapid loading is derived using the fast-forward technique, and generates the ground state in any desired short time. We propose an experimentally feasible loading scheme using a bichromatic lattice potential, which approximates the fast-forward driving potential with high fidelity.
We derive the driving potential that accelerates adiabatic population transfer from an initial state to a target state in a lattice system without unwanted excitation of other states by extending to discrete systems the fast-forward theory of adiabatic transfer. As an example, we apply the theory to a model that describes a Bose-Einstein condensate in a quasi-one-dimensional optical lattice, and show that modulation of the tilting of the lattice potential can transfer the population of the Bose-Einstein condensate from site to site with high fidelity and without unwanted excitations.
We present a scheme for nonadiabatically loading a Bose-Einstein condensate into the ground state of a one-dimensional optical lattice within a few tens of microseconds, i.e., typically in less than half the Talbot period. This technique of coherent control is based on sequences of pulsed perturbations, and the experimental results demonstrate its feasibility and effectiveness. As the loading process is much shorter than the traditional adiabatic loading time scale, this method may find many applications.
We present a shortcuts-to-adiabaticity protocol to load a spin-polarized ultracold Fermi gas from the ground ( s ) band into the first excited ( p ) band of a one-dimensional optical lattice. In contrast to a Bose-Einstein condensate in a shallow lattice—whose narrow quasimomentum distribution admits uniform lattice modulation—a noninteracting Fermi gas occupies the entire first Brillouin zone, rendering high-efficiency transfer across all momentum classes exceptionally challenging. To address this, we cast the loading process as a global, multiparameter optimization problem: We jointly optimize the timing of lattice-depth pulses and the corresponding phase shifts to maximize the ensemble-averaged transfer fidelity over all quasimomentum states. We demonstrate that fine phase tuning dramatically enhances loading efficiency, though the mean fidelity systematically decreases as more quasimomentum modes are occupied. Finally, we benchmark our shortcuts-to-adiabaticity protocol against established high-band-loading methods, underscoring its minimal hardware requirements and submillisecond timescales. Our work provides a practical path for rapid, high-fidelity preparation of Fermi gases in excited lattice orbitals, opening avenues for exploring orbital dynamics, anisotropic interactions, and many-body phenomena.
We optimize the turning on of a one-dimensional optical potential, VL(x,t)=S(t)V0cos2(kx){V}_{L}(x,t)=S(t){V}_{0}\phantom{\rule{0.2em}{0ex}}{\mathrm{cos}}^{2}(kx)VL​(x,t)=S(t)V0​cos2(kx) to obtain the optimal turn-on function S(t)S(t)S(t) so as to load a Bose-Einstein condensate into the ground state of the optical lattice of depth V0{V}_{0}V0​. Specifically, we minimize interband excitations at the end of the turn-on of the optical potential at the final ramp time tr{t}_{r}tr​, where S(tr)=1S({t}_{r})=1S(tr​)=1, given that S(0)=0S(0)=0S(0)=0. Detailed numerical calculations confirm that a simple unit cell model is an excellent approximation when the turn-on time tr{t}_{r}tr​ is long compared with the inverse of the band excitation frequency and short in comparison with nonlinear time $\ensuremath{\hbar}∕\ensuremath{\mu}$ where $\ensuremath{\mu}$ is the chemical potential of the condensate. We demonstrate using the Gross-Pitaevskii equation with an optimal turn-on function S(t)S(t)S(t) that the ground state of the optical lattice can be loaded with no significant excitation even for times tr{t}_{r}tr​ on the order of the inverse band excitation frequency.
We present a scheme for rapidly loading a Bose-Einstein condensate into a single Bloch state of a weak optical lattice at a quasimomentum of $q=\ensuremath{\Elzxh}k.$ Rabi cycling of the Bose-Einstein condensate between momentum states is modified by a phase shift applied to the lattice. By appropriately choosing the magnitude and timing of the phase shift, we demonstrate nearly perfect loading of the lattice ground state, the signature of which is an abrupt halt to the Rabi cycling.
We present an effective and fast (few microseconds) procedure for transferring a Bose–Einstein condensate from the ground state in a harmonic trap into the desired bands of an optical lattice. Our shortcut method is a designed pulse sequence where the time duration and the interval in each step are fully optimized in order to maximize robustness and fidelity of the final state with respect to the target state. The atoms can be prepared in a single band with even or odd parity, and superposition states of different bands can be prepared and manipulated. Furthermore, we extend this idea to the case of two-dimensional or three-dimensional optical lattices where the energies of excited states are degenerate. We experimentally demonstrate various examples and show very good agreement with the theoretical model. Efficient shortcut methods will find applications in the preparation of quantum systems, in quantum information processing, in precise measurement and as a starting point to investigate dynamics in excited bands.