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Journal of Experimental and Theoretical Physics

Geometric Phase-Mediated Quantum Gyroscope

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

Published Sep 1, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776122090096

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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.
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.
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.
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 “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.
A promising practical application of entanglement is metrology, where quantum states can be used to make measurements beyond the shot noise limit. Here we consider how metrology schemes could be realised using atomic Bose-Einstein condensates (BECs) trapped in different potentials. In particular, we show that if a trapped BEC is rotated at just the right frequency, it can undergo a quantum phase transition characterised by large-scale entanglement spreading across the system. This simple process of stirring can generate interesting quantum states such as macroscopic superpositions of all the atoms flowing in opposite directions around a ring-shaped potential. We consider different trapping potentials and show how this leads to different entangled states. In particular, we find that by reducing the dimensionality of the system to one or two dimensions, it is possible to generate entangled states that are remarkably robust to the loss of atoms and so are ideally suited to precision measurement schemes.