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AIP conference proceedings

Optimal driving of Bose-Einstein condensates in optical cavities

Tommaso Caneva, Tommaso Calarco, Simone Montangero

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We apply quantum optimal control to enhance the performance of the experimental setup of Ref. [1], speeding up the system dynamics at time scales of the order of the quantum speed limit. We perform a fast crossing of the quantum phase transition the system undergoes under realistic experimental conditions, and we present a new scaling-based strategy to compute optimal pulses for systems at the thermodynamical limit.

DOI
10.1063/1.4903105

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We apply quantum optimal control to enhance the performance of the experimental setup of Ref. [1], speeding up the system dynamics at time scales of the order of the quantum speed limit. We perform a fast crossing of the quantum phase transition the system undergoes under realistic experimental conditions, and we present a new scaling-based strategy to compute optimal pulses for systems at the thermodynamical limit.
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit - the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision.Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity.However, this control is still sub-optimal.In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects.Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications.Indeed, it can engineer protocols at the quantum speed limit -the fastest achievable timescale of the transformation.Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices.We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.
We present experimental evidence of the successful closed-loop optimization of the dynamics of cold atoms in an optical lattice. We optimize the loading of an ultracold atomic gas minimizing the excitations in an array of one-dimensional (1D) tubes (3D-1D crossover) and we perform an optimal crossing of the quantum phase-transition from a superfluid to a Mott insulator in a 3D lattice. In both cases we enhance the experiment performances with respect to those obtained via adiabatic dynamics, effectively speeding up the process by more than a factor three while improving the quality of the desired transformation.
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.
We apply the concept of quantum speed limit (QSL)---the minimal time needed to perform a driven evolution---to complex interacting many-body systems where the effects of interactions have to be taken into account. We introduce a general strategy to eliminate the detrimental effects of the interparticle repulsion and drive the system at the QSL by applying a compensating control pulse (CCP). To prove the principles we consider a prototypical many-body system, a bosonic Josephson junction, and investigate a transfer of atoms from the ground state of one well to the ground state of the neighboring well, at increasing levels of complexity---from a textbook two-level approximation to full many-body treatment. By tracing the efficiency of the CCP protocol we show that the driven dynamics does follow the geodetic pathway and, therefore, it is optimal. The CCP strategy, applicable for a general interacting quantum many-body system with strong driving, can be of a practical relevance for the experimental implementation of quantum technology protocols, as quantum simulations or matter-wave metrology.