This paper demonstrates how quantum optimal control can be used to perform shaken lattice interferometry. The first objective is to translate the five fundamental stages of interferometry (splitting, propagation, reflection, counter propagation and recombination) into quantum optimal control problems parametrized by the time horizon of each stage. The timing of each stage is then studied in relationship to its overall influence on the interferometer performance. This is done by comparing the population distributions obtained for a range of different accelerations and using Fisher information to estimate the sensitivity of the resulting accelerometer. These encouraging results highlight the effectiveness of quantum optimal control for the the design of next-generation atom-based interferometers.
This paper demonstrates how quantum optimal control can be used to perform shaken lattice interferometry. The first objective is to translate the five fundamental stages of interferometry (splitting, propagation, reflection, counter propagation and recombination) into quantum optimal control problems parametrized by the time horizon of each stage. The timing of each stage is then studied in relationship to its overall influence on the interferometer performance. This is done by comparing the population distributions obtained for a range of different accelerations and using Fisher information to estimate the sensitivity of the resulting accelerometer. These encouraging results highlight the effectiveness of quantum optimal control for the the design of next-generation atom-based interferometers.
We introduce shaken lattice interferometry with atoms trapped in a one-dimensional optical lattice. By phase modulating (shaking) the lattice, we control the momentum state of the atoms. Through a sequence of shaking functions, the atoms undergo an interferometer sequence of splitting, propagation, reflection, reverse propagation, and recombination. Each shaking function in the sequence is optimized with a genetic algorithm to achieve the desired momentum state transitions. As with conventional atom interferometers, the sensitivity of the shaken lattice interferometer increases with interrogation time. The shaken lattice interferometer may also be optimized to sense signals of interest while rejecting others, such as the measurement of an ac inertial signal in the presence of an unwanted dc signal.
Since the first demonstrations in 1991, atom interferometry has been a burgeoning field of research. The work done in this field is motivated by the potential sensitivity improvements that atom-based devices can have over the current state-of-the-art light- and MEMS-based devices. This dissertation presents a new and unique approach to atom interferometry in that we perform the basic interferometric sequence of splitting, propagation, reflection, reverse-propagation, and recombination with atoms trapped in a phase-modulated (shaken) optical lattice. In both simulation and experiment we demonstrate a one-dimensional shaken lattice interferometer configured as an accelerometer. The interferometry sequence is developed through the use of learning and optimal control algorithms that allow us to implement the desired state-to-state transformations and perform the desired operations, e.g. splitting and recombination of the atoms trapped in the lattice. This device has a sensitivity that scales as the square of the interrogation time and an ability to distinguish both the magnitude and sign of an applied acceleration signal. Furthermore we show that we can tailor the transfer function of the interferometer to be sensitive to a signal of interest, e.g. an AC signal of a given frequency. Finally, we explore the analytics of shaken lattice interferometry and offer some suggestions as to the future of this new technology.
Quantum optimal control is an important technology that enables fast state preparationand gate design. In the absence of an analytic solution, most quantum optimal control methods rely on an iterative scheme to update the solution estimate. At present, the convergence rate of existing solvers is, at most, superlinear. In this thesis, we develop a new general purpose solver for quantum optimal control, Quantum PRojection Operator-based Newton method for Trajectory Optimization (Q-PRONTO). Specifically, the proposed approach uses a projection operator to incorporate the Schr¨odinger equation directly into the cost function, which is then minimized using a Newton descent method. The resulting method guarantees monotonic convergence at every iteration and quadratic convergence in proximity of the solution. We then implement the method to different quantum applications: the first application is shaken lattice interferometry, which is a novel atom-based interferometry for quantum sensing; the second application is fluxonium qubit, which is a novel superconducting qubit for quantum computing. The potential of Q-PRONTO is showcased by computing an interferometry sequence for shaken lattice interferometry and designing a quantum gate for fluxonium qubit. The encouraging simulation results represent a first step in the development of a new paradigm for both quantum sensing and quantum computing.
We experimentally demonstrate a shaken-lattice interferometer. Atoms are trapped in the ground Bloch state of a red-detuned optical lattice. Using a closed-loop optimization protocol based on the dcrab algorithm, we phase-modulate (shake) the lattice to transform the atom momentum state. In this way, we implement an atom beam splitter and build five interferometers of varying interrogation times T_{I}. The sensitivity of shaken-lattice interferometry is shown to scale as T_{I}^{2}, consistent with simulation (2C. A. Weidner, H. Yu, R. Kosloff, and D. Z. Anderson, Phys. Rev. A 95, 043624 (2017).PLRAAN2469-992610.1103/PhysRevA.95.043624). Finally, we show that we can measure the sign of an applied signal and optimize the interferometer in the presence of a bias signal.
The creation of a 1D matter-wave interferometer can be achieved by utilizing ultracold atoms loaded into an optical lattice. By shaking the lattice via either phase or frequency modulation, the traditional steps of interferometry- effectively splitting, propagating, reflecting, again propagating and then recombining the atomic wavefunction- can be implemented, allowing for the sensing of inertial signals. This approach is interesting, since the atoms can be supported against external forces and perturbations, and the system can be completely reconfigurable on-the-fly for a new design goal. We report on experimental results in which atoms are cooled into a dipole trap and subsequently loaded into an optical lattice. Shaking protocols for obtaining interferometry steps are derived via machine learning and quantum optimal control methods. We report experimental progress in realizing a shaken lattice interferometer and its sensitivity to an applied acceleration signal along with the possibility of tailoring the signal to specific scenarios. Additionally, closed loop learning from the experiment to improve signal sensitivity is explored and demonstrated.
The creation of a matter-wave interferometer can be achieved by loading Bose-Einstein condensed atoms into an optical lattice. By shaking the lattice via either phase or frequency modulation, the traditional steps of interferometry; splitting, propagating, reflecting, again propagating and then recombining the atomic wavefunction, can be implemented, allowing for the sensing of broad range of inertial signals. This approach is interesting, since the atoms can be supported against external forces and perturbations, and the system can be completely reconfigurable on-the-fly for a new design goal. We report on theoretical and experimental results in which atoms are cooled to degeneracy in a dipole trap and subsequently loaded into a multidimensional optical lattice. Shaking protocols for obtaining interferometry steps are derived via machine-design approaches consisting of machine learning and quantum optimal control. Experimental confirmation of the designed operation of a two-dimensional vector accelerometer is shown and its performance to applied accelerations measured. Both the direction and magnitude of the applied signal is varied and validation of both scenarios presented.