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Physical Review A

Fast quantum driving in two-level systems with interaction and nonlinear sweep

Fu-Quan Dou, Jie Liu, Libin Fu

Published Aug 1, 2018• 15 citations
Publisher

Abstract

We investigate high-fidelity fast quantum driving in a generalized nonlinear two-level system with both interparticle interaction and nonlinear energy sweep. We find that fast quantum dynamics depend on the interaction, energy sweep parameter, and energy sweep strength. We show that the driving protocol for a large energy sweep parameter reaches a given final high fidelity in a shorter time. The interparticle interaction can influence the quantum driving dynamics and can even break the quantum speed limit of the linear model. For the attractive interaction, the minimal time decreases monotonically as energy sweep strength increases, while it increases for the repulsive interaction. We also study a critical behavior and obtain analytical expressions of a critical interaction or a critical sweep strength, beyond which the target state cannot be achieved with high fidelity.

DOI
10.1103/physreva.98.022102

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A fundamental requirement in quantum information processing and in many other areas of science is the capability of precisely controlling a quantum system by preparing a quantum state with the highest fidelity and/or in the fastest possible way. Here we present an experimental investigation of a two level system, characterized by a time-dependent Landau-Zener Hamiltonian, aiming to test general and optimal high-fidelity control protocols. The experiment is based on a Bose-Einstein condensate (BEC) loaded into an optical lattice, then accelerated, which provides a high degree of control over the experimental parameters. We implement generalized Landau-Zener sweeps, comparing them with the well-known linear Landau-Zener sweep. We drive the system from an initial state to a final state with fidelity close to unity in the shortest possible time (quantum brachistochrone), thus reaching the ultimate speed limit imposed by quantum mechanics. On the opposite extreme of the quantum control spectrum, the aim is not to minimize the total transition time but to maximize the adiabaticity during the time-evolution, the system being constrained to the adiabatic ground state at any time. We implement such transitionless superadiabatic protocols by an appropriate transformation of the Hamiltonian parameters. This transformation is general and independent of the physical system.
A remarkably simple result is derived for the minimal time Tmin required to drive a general initial state to a final target state by a Landau-Zener-type Hamiltonian or, equivalently, by time-dependent laser driving. The associated protocol is also derived. A surprise arises for some states when the interaction strength is bounded by a constant c. Then, for large c, the optimal driving is of type bang-off-bang and for increasing c one recovers the unconstrained result. However, for smaller c the optimal driving can suddenly switch to bang-bang type. We discuss the notion of quantum speed limit time.
We present experimental results on the preparation of a desired quantum state in a two-level system with the maximum possible fidelity using driving protocols ranging from generalizations of the linear Landau-Zener protocol to transitionless driving protocols that ensure perfect following of the instantaneous adiabatic ground state. We also study the minimum time needed to achieve a target fidelity and explore and compare the robustness of some of the protocols against parameter variations simulating a possible experimental uncertainty. In our experiments, we realize a two-level model system using Bose-Einstein condensates inside optical lattices, but the results of our investigation should hold for any quantum system that can be approximated by a two-level system.
We present experimental results on the preparation of a desired quantum state in a two-level system with the maximum possible fidelity using driving protocols ranging from generalizations of the linear Landau-Zener protocol to transitionless driving protocols that ensure perfect following of the instantaneous adiabatic ground state. We also study the minimum time needed to achieve a target fidelity and explore and compare the robustness of some of the protocols against parameter variations simulating a possible experimental uncertainty. In our experiments, we realize a two-level model system using Bose-Einstein condensates inside optical lattices, but the results of our investigation should hold for any quantum system that can be approximated by a two-level system.
We investigate the composite adiabatic passage (CAP) reported by B. T. Torosov et al. [Phys. Rev. Lett. 106, 233001 (2011)] in a nonlinear two-level system in which the level energies depend on the occupation of the levels, representing a mean-field type of interaction between the particles. A high-fidelity, fast, and robust quantum manipulation is achieved in the system. We consider the effect of interparticle interaction and find that it tends to increase the number of the pulse sequences. The CAP technique can suppress the nonadiabatic oscillations below the quantum-information benchmark ${10}^{\ensuremath{-}4}$, as long as there exist sufficiently long composite sequences. We analyze the robustness against the variations in the field parameters. The difference between the nonlinear and linear systems on the CAP technique is also discussed.