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Open Physics

Optimal control for generating excited state expansion in ring potential

Hoon Yu, Seung Jin Kim, Jung Bog Kim

Published Jul 28, 2020• 1 citation
Publisher

Abstract

Abstract We applied an optimal control algorithm to an ultra-cold atomic system for constructing an atomic Sagnac interferometer in a ring trap. We constructed a ring potential on an atom chip by using an RF-dressed potential. A field gradient along the radial direction in a ring trap known as the dimple-ring trap is generated by using an additional RF field. The position of the dimple is moved by changing the phase of the RF field [1]. For Sagnac interferometers, we suggest transferring Bose–Einstein condensates to a dimple-ring trap and shaking the dimple potential to excite atoms to the vibrational-excited state of the dimple-ring potential. The optimal control theory is used to find a way to shake the dimple-ring trap for an excitation. After excitation, atoms are released from the dimple-ring trap to a ring trap by adiabatically turning off the additional RF field, and this constructs a Sagnac interferometer when opposite momentum components are overlapped. We also describe the simulation to construct the interferometer.

DOI
10.1515/phys-2020-0171

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Abstract We applied an optimal control algorithm to an ultra-cold atomic system for constructing an atomic Sagnac interferometer in a ring trap. We constructed a ring potential on an atom chip by using an RF-dressed potential. A field gradient along the radial direction in a ring trap known as the dimple-ring trap is generated by using an additional RF field. The position of the dimple is moved by changing the phase of the RF field [1]. For Sagnac interferometers, we suggest transferring Bose–Einstein condensates to a dimple-ring trap and shaking the dimple potential to excite atoms to the vibrational-excited state of the dimple-ring potential. The optimal control theory is used to find a way to shake the dimple-ring trap for an excitation. After excitation, atoms are released from the dimple-ring trap to a ring trap by adiabatically turning off the additional RF field, and this constructs a Sagnac interferometer when opposite momentum components are overlapped. We also describe the simulation to construct the interferometer.
The manipulation of ultracold atoms in radio-frequency (RF)-dressed potentials offers unique advantages over static magnetic traps, such as the ability to create more complex potential landscapes, better control of atomic states, and increased robustness to environmental noise. Among the accessible geometries, ring traps are particularly promising for atomic Sagnac interferometers, which can be used to measure rotational motion with high sensitivity. Here, the authors demonstrate the state-dependent transport of atoms in an RF-dressed ring trap on an atom chip. By exploiting the polarization-dependent coupling of RF fields to different atomic hyperfine states, the authors achieve controlled transport of atoms in opposite directions. This approach targets the development of compact, high-precision devices for applications in inertial navigation and rotation sensing.
This thesis describes the experimental realisation of state-dependent traps employing RF-dressed adiabatic potentials. Rb-87 atoms have been successfully confined to chip-based atom traps that can independently address atomic ground states defined by the total angular momentum, F. The ring-shaped trap can be used as a Sagnac interferometer to measure rotation with respect to the inertial frame of reference. The results of spatially dependent radio frequency field polarisation control in this trap resulted in counterpropagating motion of the atoms in the F = 1 and F = 2 states.
Sagnac interferometers with massive particles promise unique advantages in achieving high-precision measurements of rotation rates over their optical counterparts. Recent proposals and experiments are exploring nonballistic Sagnac interferometers where trapped atoms are transported along a closed path. This is achieved by using superpositions of internal quantum states and their control with state-dependent potentials. We address emergent questions regarding the dynamical behavior of Bose-Einstein condensates in such an interferometer and its impact on rotation sensitivity. We investigate complex dependencies on atomic interactions as well as trap geometries, rotation rates, and speed of operation. We find that temporal transport profiles obtained from a simple optimization strategy for noninteracting particles remain surprisingly robust also in the presence of interactions over a large range of realistic parameters. High sensitivities can be achieved for short interrogation times far from the adiabatic regime. This highlights a route to building fast and robust guided-ring Sagnac interferometers with fully trapped atoms.
We have constructed an asymmetric matter-wave beam splitter and a ring potential on an atom chip with Bose-Einstein condensates using radio-frequency dressing. By applying rf field parallel to the quantization axis in the vicinity of the static trap minima added to perpendicular rf fields, versatile controllability on the asymmetry of rf-dressed potentials is realized. Asymmetry of the rf-induced double well is controlled over a wide range without discernible displacement of each well. Formation of an isotropic ring potential on an atom chip is achieved by compensating the gradient due to gravity and inhomogeneous coupling strength. In addition, position and rotation velocity of a BEC along the ring geometry are controlled by the relative phase and the frequency difference between the rf fields, respectively.
We present a method for the creation of closed-loop lattices for ultra-cold atoms using dressed potentials. We analytically describe the generation of trap lattices that are state-dependent with dynamically controlled lattice depths and positioning. In a design akin to a synchronous motor, the potentials arise from the combination of a static, ring-shaped quadrupole field and multipole radio-frequency fields. Our technique relies solely on static and radio-frequency (rf) magnetic fields, enabling the creation of robust atom traps with simple control via rf amplitudes and phases. Potential applications of our scheme span the range from quantum many-body simulations to guided Sagnac interferometers.
This thesis presents the experimental scheme for a guided cold atom Sagnac interferometer. Although atom interferometers have become an established method for precision measurements, a feasible clock-scheme based on fully guided atoms has yet to be realised. Radio frequency potentials, generated by a chip, provide a means to create a compact, fully controllable guided atom interferometer. The experimental infrastructure for a rubidium cold atom system is built and characterised. A chip-based atomic clock scheme is presented, utilising state-dependent guiding around a ring shaped trap. The chip design to form the trap and operate the interferometer is presented, and a vacuum compatible PCB has been designed and commercially manufactured to provide atomic transport and compression towards an atom chip. This project is part of the larger MatterWave project. In collaboration with Birmingham and Crete, the Matterwave project aims to develop ultra-sensitive matter-wave interferometry for compact devices.