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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

Quantum control beyond the uncertainty limit of position and momentum using a Sagnac interferometer

Tatsuya Honda, Holger Friedrich Hofmann, M. Iinuma

Published Jan 1, 2020• 0 citations
Publisher

Abstract

To realize optimal simultaneous control of transverse position and momentum, we have constructed a Sagnac interferometer and evaluated the interference between spatial modes with extremely different profiles. The results are consistent with theoretical expectations.
DOI
10.1364/cleopr.2020.p5_6

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Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines in free space can then be tested by deriving a lower limit for the probability of finding the particle in a corresponding spatial interval at any intermediate time ttt. Here, it is shown that this lower limit can be violated by quantum superpositions of states confined within the respective position and momentum intervals. These violations of the particle propagation inequality show that quantum mechanics changes the laws of motion at a fundamental level, providing a different perspective on causality relations and time evolution in quantum mechanics.
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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.