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Review of Scientific Instruments

Noise cancellation system for shaking optical lattice by controlling optical path

Hoon Yu, Jung Bog Kim

Published Jun 1, 2020• 2 citations
Publisher

Abstract

We present a simple way to control the phase of an optical lattice by detecting the interference signal of two beams. The optical lattice is intentionally shaken by varying the relative phase of the beams. However, the lattice may also be shaken by unwanted variations of the relative optical path length, e.g., due to mirror vibrations. The purpose of the servo is to attenuate these unwanted variations while the intended shaking remains. We demonstrate that the servo changes the relative phase between beams and follows the intended shaking function with 99% accuracy. The bandwidth for the acceptable attenuation of unwanted shaking, -13 dB, is measured to 1.2 kHz to control the atomic Bloch state. The servo will be implemented to attenuate the unknown system vibrations for a shaken lattice and engineer the momentum state of atoms trapped in the lattice. This idea can also be applied to any time varying experiment.

DOI
10.1063/5.0006608

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We present a simple way to control the phase of an optical lattice by detecting the interference signal of two beams. The optical lattice is intentionally shaken by varying the relative phase of the beams. However, the lattice may also be shaken by unwanted variations of the relative optical path length, e.g., due to mirror vibrations. The purpose of the servo is to attenuate these unwanted variations while the intended shaking remains. We demonstrate that the servo changes the relative phase between beams and follows the intended shaking function with 99% accuracy. The bandwidth for the acceptable attenuation of unwanted shaking, -13 dB, is measured to 1.2 kHz to control the atomic Bloch state. The servo will be implemented to attenuate the unknown system vibrations for a shaken lattice and engineer the momentum state of atoms trapped in the lattice. This idea can also be applied to any time varying experiment.
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.
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.
An optical lattice is a periodic light crystal constructed from the standing-wave interference patterns of laser beams. It can be used to store and manipulate quantum degenerate atoms and is an ideal platform for the quantum simulation of many-body physics. A principal feature is that optical lattices are flexible and possess a variety of multidimensional geometries with modifiable band-structure. An even richer landscape emerges when control functions can be applied to the lattice by modulating the position or amplitude with Floquet driving. However, the desire for realizing high-modulation bandwidths while preserving extreme lattice stability has been difficult to achieve. In this paper, we demonstrate an effective solution that consists of overlapping two counterpropagating lattice beams and controlling the phase and intensity of each with independent acousto-optic modulators. Our phase controller mixes sampled light from both lattice beams with a common optical reference. This dual heterodyne locking method allows exquisite determination of the lattice position, while also removing parasitic phase noise accrued as the beams travel along separate paths. We report up to 50dB suppression in lattice phase noise in the 0.1Hz - 1Hz band along with significant suppression spanning more than four decades of frequency. When integrated, the absolute phase diffusion of the lattice position is only 10Å over 10 s. This method permits precise, high-bandwidth modulation (above 50kHz) of the optical lattice intensity and phase. We demonstrate the efficacy of this approach by executing intricate time-varying phase profiles for atom interferometry.
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.
Motivated by recent results using shaken optical lattices to perform atom interferometry, we explore the splitting of an atom cloud trapped in a phase-modulated (‘shaken’) optical lattice. Using a simple analytic model we are able to show that we can obtain the simplest case of ±2ℏ k L splitting via single-frequency shaking. This is confirmed both via simulation and experiment. Furthermore, we are able to split with a relative phase θ between the two split arms of 0 or π depending on our shaking frequency. Addressing higher-order splitting, we determine that ±6ℏ k L splitting is sufficient to be able to accelerate the atoms in counterpropagating lattices. Finally, we show that we can use a genetic algorithm to optimize ±4ℏ k L and ±6ℏ k L splitting to within ≈0.1% by restricting our optimization to the resonance frequencies corresponding to single- and two-photon transitions between Bloch bands. As a proof-of-principle, an experimental demonstration of simplified optimization of 4ℏ k L splitting is presented.
We propose a method to create higher orbital states of ultracold atoms in the Mott regime of an optical lattice. This is done by periodically modulating the position of the trap minima (known as shaking) and controlling the interference term of the lasers creating the lattice. These methods are combined with techniques of shortcuts to adiabaticity. As an example of this, we show specifically how to create an anti-ferromagnetic type ordering of angular momentum states of atoms. The specific pulse sequences are designed using Lewis–Riesenfeld invariants and a four-level model for each well. The results are compared with numerical simulations of the full Schrödinger equation.