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arXiv:1303.5615 · Physical Review A

Fast closed-loop optimal control of ultracold atoms in an optical lattice

S. Rosi, Alain Bernard, Nicole Fabbri, L. Fallani, C. Fort, M. Inguscio, Tommaso Calarco, Simone Montangero

Published Aug 1, 2013• 66 citations
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Abstract

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.

DOI
10.1103/physreva.88.021601

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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 large-scale dynamical simulation of the superfluid--Mott-insulator transition in a gas of ultracold atoms placed in an optical lattice is performed using the time-dependent Gutzwiller mean-field approach. This approximate treatment allows us to take into account most of the details of the recent experiment [Greiner et al., Nature (London) 415, 39 (2002)] where by changing the depth of the lattice potential an adiabatic transition from a superfluid to a Mott insulator state has been reported. Our simulations reveal a significant excitation of the system with a transition to insulator in restricted regions of the trap only.
We study the quantum phase transition from a superfluid to a Mott insulator of ultracold atoms in a three-dimensional optical lattice with adjustable filling factors. Based on the density-adjustable Bose–Einstein condensate we prepared, the excitation spectrum in the superfluid and the Mott insulator regime is measured with different ensemble-averaged filling factors. We show that for the superfluid phase, the center of the excitation spectrum is positively correlated with the ensemble-averaged filling factor, indicating a higher sound speed of the system. For the Mott insulator phase, the discrete feature of the excitation spectrum becomes less pronounced as the ensemble-averaged filling factor increases, implying that it is harder for the system to enter the Mott insulator regime with higher filling factors. The ability to manipulate the filling factor affords further potential in performing quantum simulation with cold atoms trapped in optical lattices.
We calculate the superfluid transition temperature for a two-component 3D Fermi gas in a 1D tight optical lattice and discuss a dimensional crossover from the 3D to quasi-2D regime. For the geometry of finite size discs in the 1D lattice, we find that even for a large number of atoms per disc the critical effective tunneling rate for a quantum transition to the Mott insulator state can be large compared to the loss rate caused by three-body recombination. This allows the observation of the Mott transition, in contrast to the case of Bose-condensed gases in the same geometry.
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.
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.