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Journal of Experimental and Theoretical Physics Letters

Hybrid Atomic–Optical Quantum Gyrometry

V. A. Tomilin, L. V. Il’ichev

Published Feb 1, 2021• 3 citations
Publisher

Abstract

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.

DOI
10.1134/s0021364021030103

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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.
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.
The ability to make ultra-precise measurements is fundamentally important to science as it allows theories to be tested and refined. Interferometers offer unrivalled measurement precision and therefore form the basis of many metrology schemes. Research has shown that by using quantum states as inputs to interferometers, precisions better than anything possible classically can be achieved. Nevertheless, these states are difficult to produce and fragile to particle losses. Consequently, classical inputs, which are extremely robust, are used in experiments. Here, however, we propose experimentally accessible schemes to make quantum-limited measurements, in particular rotation measurements using Bose-Einstein condensates, that are robust to losses. We begin by describing how, by loading a Bose-Einstein condensate into an optical ring lattice, multiport beam splitters are created through a simple raising and lowering of potential barriers between sites. We then use these ‘splitters’ to create an atomic gyroscope. We demonstrate how to create several quantum states in the gyroscope, all capable of making rotation measurements. Whilst NOON states afford best precision in idealised set-ups, we find they are outperformed by ‘bat’ states for modest loss rates. However, bat states are not ideal as they are outperformed by classical states for large losses. A second gyroscope scheme is therefore developed. Using multiple momentum modes, rather than just two, we show quantum-limited precisions can be reached using states that have similar robustness to classical states. The final section focuses on the precision of linear interferometers. Recent work[1, 2] has calculated the theoretical optimum initial states for two-mode lossy interferometers. Here we present an experimental way to produce initial states that afford similar precisions to this optimum. We also consider lossy multimode interferometry and demonstrate a potential advantage over two-mode systems. It is thought with further investigation other advantages will be found.
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.
We construct a Mach-Zehnder interferometer using Bose-Einstein condensed rubidium atoms and optical Bragg diffraction. In contrast to interferometers based on normal diffraction, where only a small percentage of the atoms contribute to the signal, our Bragg diffraction interferometer uses all the condensate atoms. The condensate coherence properties and high phase-space density result in an interference pattern of nearly 100% contrast. The two arms of the interferometer may be completely separated in space, making it an ideal tool that can be used to detect vortices or other topological condensate phases.
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.