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Journal of Experimental and Theoretical Physics Letters

Barrier–Well Potential Configuration for Quantum Gyroscope Based on Atomic BEC Geometric Phase

V. A. Tomilin, A. M. Rostom, Leonid V. Il'ichov

Published Feb 26, 2024• 1 citation
Publisher

Abstract

A perspective scheme of quantum gyroscope based on measurement of geometric phase emerging in atomic Bose–Einstein condensate (BEC) was developed. The main elements of the device are two ring-shaped BEC configurations intercepted by a pair of localized potentials—a barrier and a well. Their placement in each ring defines their orientation with respect to the angular velocity of rotation of the device’s frame. Proper variation of the parameters of the barriers and wells induces opposite-sign geometric phases in the BEC modes. Difference of these phases can be measured in interference experiment. We present results of geometric phase calculations for BEC of 87Rb atoms in ring potentials of 0.5 cm diameter and angular velocities comparable to that of the Earth’s rotation.

DOI
10.1134/s0021364024600320

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A perspective scheme of quantum gyroscope based on measurement of geometric phase emerging in atomic Bose–Einstein condensate (BEC) was developed. The main elements of the device are two ring-shaped BEC configurations intercepted by a pair of localized potentials—a barrier and a well. Their placement in each ring defines their orientation with respect to the angular velocity of rotation of the device’s frame. Proper variation of the parameters of the barriers and wells induces opposite-sign geometric phases in the BEC modes. Difference of these phases can be measured in interference experiment. We present results of geometric phase calculations for BEC of 87Rb atoms in ring potentials of 0.5 cm diameter and angular velocities comparable to that of the Earth’s rotation.
Abstract Perspective methods of quantum metrology are highly suitable for designing new types of gyroscopes. Matter waves-based gyroscopic schemes have already been implemented in optical setups. In the nearing future, it might be possible to implement them with macroscopic coherent structures of atomic Bose-Einstein condensates (BECs). This work considers a ring-shaped BEC configuration interrupted by a localized potential “defect.” It is shown that variation of the shape of this “defect” generates atomic geometric phase. In a pair of such configurations opposite geometric phases may be obtained, with their difference equal to zero in absence of rotation. This difference can be revealed by observing interference of the atoms from different configurations. Calculation of resulting geometric phases is carried out for a model “defect” in a ring of 0.5 cm diameter detecting Earth’s diurnal rotation.
Abstract A concept of hybrid atom-optical quantum gyroscope based on ring-shaped Bose–Einstein condensate (BEC) of atoms is developed. Optical probe field grants the systems sensitivity to rotation and detects the condensate response to rotation via optical interferometry. Measurement of rotation angular velocity may ideally be fulfilled without loss of atoms, but inevitably leads to degradation of BEC spatial coherence. We construct a mathematical model of this crucial phenomenon. A quantum master equation for BEC state is derived and solved analytically in the slow decoherence limit.
A conceptual model of a promising quantum accelerometer based on a two-mode atomic Bose–Einstein condensate has been proposed. Acceleration generates a specific difference in geometric phases between the condensate modes, which shifts the interference pattern of matter waves. The modes have ring configurations, in the plane of which the measured acceleration vector lies. The homogeneity of the potentials of the ring configurations is interrupted by additional localized potentials generated by defects. Under the variation of the parameters of appropriately located defects with a certain structure, the wavefunctions of the condensate modes acquire geometric phases that differ in the presence of acceleration. Calculations performed for ring configurations of the condensate of 87Rb atoms with a radius of 0.25 mm has showed that the proposed scheme can detect a microgravity of ~10–6–10–7g.
A “hybrid” atomic–optical scheme of an interferometer–gyroscope has been proposed and investigated. It is based on the ring configuration of a Bose–Einstein condensate that is intercepted by an additional potential barrier or well. This ring configuration defect is created by a nonresonant radiation beam that interacts dispersively with the atoms located in its region. The beam propagates along one of the arms of a Mach–Zehnder interferometer. The rotation of the gyrometer reference system modifies the state of the condensate due to the mentioned potential defect and it, in turn, changes the conditions of interference of radiation interacting with atoms. In contrast to the well-known ideas of using the Bose–Einstein condensate in gyrometry, which imply the destruction of the condensate in order to directly observe its interference, the proposed scheme ideally operates without the loss of atoms by the condensate. The efficiency of the scheme has been estimated for realistic conditions.
We consider a problem of geometric phase generation in a system of two interacting bosons confined in a narrow ring potential with a localized defect. Geometric phase emerges from variation of parameters of the defect. Particle interaction is taken into account within a framework of the Lieb-Liniger model. The energy spectrum is evaluated and its dependence on the parameters of the problem is described. It is shown that the interaction leads to increase of the geometric phase for a given contour of variations. The work is motivated by earlier proposed ideas of quantum gyroscope and quantum accelerometer based on atomic Bose-Einstein condensates.
Vortex nucleation is the key technology to realize quantum gyroscope in Bose-Einstein Condensates (BEC). Through mass investigation and research, the recent research status of vortex nucleation in Bose-Einstein Condensates is presented, the theory and experimentation about imprinting phase, rotating the potential trap and transferring the orbital angular momentum of a photon to generate BEC vortex are analyzed and compared in detail, furthermore, an improved method of rotating the potential trap to generate vortex is proposed. Quantum gyroscope based on BEC vortex has the potential advantages of realizing the ultra high sensitivity and small volume of quantum gyroscope. This paper aims to promote the development of quantum vortex gyroscope, which attracts extensive attention of domestic scholars.